Influence of the electric polarization on carrier transport and ... - Qucosa

Influence of the electric polarization on carrier transport and recombination dynamics in ZnO-based heterostructures

Von der Fakultät für Physik und Geowissenschaften der Universität Leipzig genehmigte DISSERTATION zur Erlangung des akademischen Grades Doctor rerum naturalium Dr. rer. nat. vorgelegt von Diplom-Physiker Matthias Brandt geboren am 10. Mai 1981 in Hohenmölsen

Gutachter:

Prof. Dr. Marius Grundmann, Universität Leipzig Prof. Dr. David C. Look, Wright State University

Datum der Einreichung: 2. Dezember 2009 Datum der Beschlussfassung: 16. August 2010

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Bibliographische Beschreibung Brandt, Matthias ‘Influence of the electric polarization on carrier transport and recombination dynamics in ZnO-based heterostructures’ Universität Leipzig, Dissertation 201 S.∗ , 269 Lit.∗ , 78 Abb., 3 Anlagen Referat: Die vorliegende Arbeit befasst sich mit dem Einfluss der elektrischen Polarisation auf Eigenschaften freier Träger in ZnO basierten Halbleiterheterostrukturen. Dabei werden insbesondere Transporteigenschaften freier Träger sowie deren Rekombinationsdynamik untersucht. Die Arbeit behandelt vier inhaltliche Schwerpunkte. Der erste Schwerpunkt liegt auf den physikalischen Eigenschaften der verwendeten Materialen, hier wird der Zusammenhang der Bandlücke und der Gitterkonstanten von Mgx Zn1−x O Dünnfilmen und deren Magnesiumgehalt beschrieben. Weiterhin wird die Morphologie solcher Filme diskutiert. Auf unterschiedliche Substrate und Abscheidebedingungen wird dabei detailliert eingegangen. Der zweite Schwerpunkt behandelt die Eigenschaften undotierter und phosphordotierter ZnO und Mgx Zn1−x O Dünnfilme. Die strukturellen, Transport- und Lumineszenzeigenschaften werden hier verglichen und Rückschlüsse auf die Züchtungsbedingungen gezogen. Im dritten Schwerpunkt werden Quanteneffekte an ZnO/Mgx Zn1−x O Grenzflaechen behandelt. Hierbei wird insbesondere auf den Einfluss der elektrischen Polarisation eingegangen. Die Präsenz eines zweidimensionalen Elektronengases wird nachgewiesen, und die notwendigen Bedingungen zur Entstehung des sogenannten qunatum confined Stark-effects werden dargelegt. Insbesondere wird hier auf züchtungsrelevante Parameter eingegangen. Den vierten Schwerpunkt stellen Kopplungsphänomene in ZnO/BaTiO3 Heterostrukturen dar. Dabei werden zuerst die experimentell beobachten Eigenschaften verschiedener Heterostrukturen die auf unterschiedlichen Substraten gezüchtet wurden aufgezeigt. Hier stehen strukturelle und Transporteigenschaften im Vordergrund. Ein Modell zur Beschreibung der Ausbildung von Raumladungszonen in derartigen Heterostrukturen wird eingeführt und zur Beschreibung der experimentellen Ergebnisse angewandt. Die Nutzbarkeit der ferroelektrischen Eigenschaften des Materials BaTiO3 in Kombination mit halbleitendem ZnO wurden untersucht. Hierzu wurden ferroelektrische Feldeffekttransistoren unter Verwendung beider Materialien hergestellt. Die prinzipielle Eignung der Bauelemente als nichtflüchtige Speicherelemente wurde nachgewiesen.

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... S. (Seitenzahl insgesamt) ... Lit. (Anzahl der im Literaturverzeichnis ausgewiesenen Literaturangaben

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Summary of the scientific results of the dissertation

“Influence of the electrical polarization on carrier transport and recombination dynamics in ZnO–based heterostructures” submitted by

Matthias Brandt prepared at Fakultät für Physik und Geowissenschaften der Universität Leipzig Institut für Experimentelle Physik II, Abteilung Halbleiterphysik November 2009

1

Introduction

ZnO is a transparent oxide semiconductor with a bandgap energy of Eg ≈ 3.37 eV at room temperature. The wide gap and the strong exciton binding energy of about 60 meV make it an interesting material for optoelectronic applications in the blue and near UV range of the electromagnetic spectrum. These interesting material properties triggered a wave of scientific investigation in the past decade, although reports of the materials properties date back as late as the 1920s [1] . A first report on transport measurements in ZnO single crystals and thin films emerged in 1935 [2] . Intrinsic n– type conductivity was confirmed in these primary studies. It was found, that a highly doped layer can exist on the surface of the single crystals, and that its presence depended on the surface polarity of the single crystal [3] . It has been argued, that the internal polarization is responsible for the formation of accumulation and depletion layers at the Zn– and O–faces, respectively [3] . The properties of such accumulation layers were investigated in the present study in ZnO and Mgx Zn1−x O thin films. As the wurtzite crystal system lacks inversion symmetry, and the ZnO crystal is partially ionic, a spontaneous polarization must arise in parallel to the [0001] direction. In contrast to GaN and its ternary alloys, where detailed experimental data on the spontaneous and piezoelectric polarization and their dependence on the composition of the ternary materials are available, only a few experimental reports are given for ZnO and its related compounds [4–8] . In a heterostructure the electric polarization in adjacent materials can be different due to the different layer composition, and in the case of pseudomorph layers due to the strain of the layers. A sheet charge at the heterointerface will result from that difference. Accumulation of free carriers is possible at the heterointerfaces and can lead to the formation of two dimensional carrier gases. In this study n–type ZnO was investigated. Therefore only the formation of a two–dimensional electron gas (2DEG) is expected in equilibrium. The transport properties inside this 2DEG differ from that of a three dimensional electron gas in the bulk, for example an increased mobility is expected. This can be employed for the development of highly efficient devices, such as high electron mobility transistors. The properties of a 2DEG forming in the ZnO/Mgx Zn1−x O system were studied in this work. In contrast, the discontinuities in the electric polarization can also induce effects which are detrimental to device performance. One of the effects investigated in detail in the recent past is the quantum confined Stark–effect (QCSE). The difference in polarization between the barrier Mgx Zn1−x O and the well material of a quantum well (QW) structure ZnO leads to different sheet charges on both sides of the well, resulting in an electric field within. The square well potential is changed into a trapezoid potential. The transition energy between electrons and holes is reduced, but more importantly, the maxima of the electron and hole occupation probability become spatially separated. This results in a decrease of the overlap of the electron and holes wave–functions, a decrease in the oscillator strength and the radiative recombination efficiency. Lately extensive efforts are undertaken to avoid this effect and the corresponding reduction of the radiative recombination efficiency in light emitting devices. Therefore, growth studies of GaN related devices in non polar orientav

tion are frequent in the recent past. Despite these considerations from the device design point of view, the observation of the QCSE is interesting, as basic properties, such as the dependence of the polarization on the alloy composition and the motion of carriers in the plane of the QW become accessible to experimental observation. It was shown [9] that the QCSE can be diminished by a controlled damage of the crystal, resulting in a smear out of the heterointerfaces. In the converse argument the presence of the effect is an indicator for atomically abrupt interfaces. The conditions necessary for the occurence of the QCSE were therefore investigated, both in experiment and by calculations. All these considerations apply to a static electric polarization. It is however possible to change the electric polarization externally, for example by mechanical stress and electric and magnetic fields. In the present study, the material ZnO was coupled with the ferroelectric BaTiO3 in order to reveal the effects arising from the presence of a fixed and a switchable polarization component in a heterostructure. The combination of these materials is of special interest, as both materials represent model materials for their individual material classes, and a combination does not face chemical incompatibilities, as both materials are oxides. The influence of the ZnO polarization on the ferroelectric hysteresis and the possibility of an application of such heterostructures as non volatile memory elements were studied.

2

Epitaxy of ZnO and Mgx Zn1−x O on ZnO substrates

In any material system investigated, the homoepitaxial growth of the respective material has significant advantages over the growth on heterogenous materials. Among them are the perfect lattice match, leading to a significant reduction of the density of dislocations upon growth as well as the equal lattice expansion coefficient. This avoids the risk of the formation of cracks and dislocations upon cooling from elevated temperatures, at which the growth process takes place. Further, the substrate material equals that of the film, reducing in–diffusion of impurities from the substrate. The state of the art ZnO substrate material available was investigated and compared with respect to the applicability in the present study. Important issues are the substrate quality, the conductivity of the substrate, which should be as low as possible in order to observe the transport processes in the thin films only, and the substrate price. Only hydrothermally grown material proved applicable in the light of transport investigations. A thermal pretreatment of the substrates necessary to produce surfaces suitable for epitaxy is discussed [10] . The mechanisms involved in the homoepitaxial growth of ZnO were investigated. Within the temperature range available layer by layer growth was observed rather than step flow growth [11] . A significant reduction of the density of dislocations was seen in comparison to ZnO grown on sapphire substrates [12] . The density of donors in undoped homoepitaxial ZnO thin films was investigated and a net doping concentration of 6 × 1014 cm−3 was found [10] . The very pure material is ideally suited for doping experiments. Rutherford–backscattering channeling studies confirmed that the crystalline quality of the thin films is close to that of single crystals [13] The properties of nominally undoped ZnO and Mgx Zn1−x O thin films grown on ZnO are strongly influenced by the oxygen partial pressure during growth. The II–VI ratio in the films is controlled by the partial pressure of oxygen radicals in the growth chamber. For films grown at low oxygen partial pressures an increased c–axis lattice constant is observed for both the ZnO and Mgx Zn1−x O thin films, most likely due to an increasing density of charged intrinsic defects. This thesis is supported by an increase in the zinc interstitial related luminescence and the free electron concentration upon decrease of the oxygen partial pressure [14] . Very similar results were seen in phosphorous doped ZnO and Mgx Zn1−x O thin films grown in ZnO. This indicates that intrinsic defects (and therein mainly zinc on interstitial site) are responsible for the apparent n–type conductivity and the free electron concentration in these samples. Transport measurements on phosphorous doped homoepitaxial ZnO thin films showed high electron mobilities of up to 800 cm2 /Vs around 70 K and 170 cm2 /Vs at room temperature. Exact modeling vi

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of the transport properties using a numerical solution of the Boltzmann–transport–equation indicated, that the scattering processes involved equal that of ZnO single crystals [13] . Vicinal growth was observed for one of the ZnO:P films with a phosphorous content of 0.01 wt.% P2 O5 in the target grown at 0.1 mbar oxygen partial pressure [15] . The growth of Mgx Zn1−x O thin films on ZnO substrates was investigated. It was shown, that the temperature required for step flow growth was lower than for pure ZnO. This was explained by the presence of compressive strain in the films, in accordance with the argumentation given in Refs. [16] . Perfect vicinal surfaces were prepared, depending on the miscut of the substrate [17] . Such layers represent an ideal starting point for the fabrication of heterostructures with atomically flat interfaces and are therefore of great value both to fundamental studies and for device applications. The lattice constants a and c of Mgx Zn1−x O systematically change with the Mg content x in relaxed Mgx Zn1−x O layers, where a increases with x and c decreases with x. It was shown that Mgx Zn1−x O can be grown pseudomorphically on ZnO [18] (see Fig. 1 (a)). The c axis lattice constant changes systematically with x. The linear relationship cps = c0 + kc,ps ∗ x with kc,ps = −0.064 Å was found from data obtained in the present study and in accordance with the experimental data given in Ref. [19] , and are explained by classical theory of elasticity. Also for the Mgx Zn1−x O thin films grown on ZnO, the influence of the growth conditions was studied. The composition of the group II constituents depends on the background pressure in the chamber. The concentration of the lighter Mg atoms compared to Zn atoms is reduced by almost a factor of three within the range of oxygen partial pressures available in the present growth setup. Interestingly the concentration of P in doped thin films does change accordingly. It is concluded, that the atomic mass (which differs between Mg and P by only 20%) of the individual element influences the kinetic scattering processes with the background gas and therefore the composition of the plasma at the substrate position. The similarities of the incorporation of Mg and P indicate that P is like Mg mainly introduced into the ZnO host lattice on Zn site, in accordance with theoretical calculations [20] . This contradicts the assumption that phosphorous would form a PO acceptor. Instead, the defect PZn is a donor, which could in principle emit three electrons. Nevertheless, the formation of phosphorous related acceptors is predicted [20] , by the formation of a defect complex involving two zinc vacancies. A transport study revealed that the mobility in the phosphorous doped Mgx Zn1−x O thin films grown on ZnO is comparable to that of the homoepitaxial ZnO:P films. Also the donor concentration, and the dependence on the oxygen partial pressure were found very similar. The critical donor concentration and activation energy in the dilute limit of the dominant donor in phosphovii

rous doped ZnO and Mgx Zn1−x O layers grown on ZnO was for the first time determined to be of NC = 8.3 × 1018 cm−3 and ED0 = 56 meV, respectively [21] (see Fig. 1 (b)). The thermal activation of phosphorous related acceptor was studied in ZnO and Mgx Zn1−x O thin films grown on ZnO. A transition to p–type conduction was never observed. However an increase of the resistivity by more than 6 orders of magnitude was observed in the Mgx Zn1−x O layers deposited at the highest oxygen partial pressures. This provides evidence of the activation of the phosphorous related acceptors in Mgx Zn1−x O . The contribution of a degenerate layer to the sample conduction was often found in homoepitaxial samples and was removed by annealing in oxygen, indicating that the origin of the degenerate layer are intrinsic defects, likely to be formed at the surface. The separation of the conduction of the degenerate layer and the bulk of the film was partially possible employing a correction scheme as proposed in Ref. [22] . A determination of the properties of the individual layers however is not possible without further assumptions, as the incorporation of the defects, responsible for the formation of the degenerate layer is not homogeneous. A more sophisticated approach was employed in this study, which allowed an unambiguous evaluation of the transport properties of the individual layers. The separation of the conductivity of individual conductive paths is possible from magnetic field dependent measurements by the maximum entropy mobility spectrum approach. The individual properties of bulk conduction of a Mgx Zn1−x O thin film grown on ZnO and the conduction of the degenerate layer were revealed over a wide range of temperatures. Indications of two dimensional transport were found. Such a detailed study of the parallel conduction processes in ZnO and related heterostructures has not been reported so far.

3

Quantum effects in ZnO/Mgx Zn1−x O heterostructures

2D growth in the Burton–Cabrera–Frank mode is observed for the ZnO/Mgx Zn1−x O single heterostructures and ZnO/Mgx Zn1−x O quantum wells grown on a–sapphire. The effective surface roughness however in these samples is of the order of the thickness of the quantum–wells present in the structures. However, polarization induced electron accumulation layers were observed both for single heterostructures and quantum wells capacitance–voltage spectroscopy and temperature dependent Hall effect measurements [23] . Indications for the presence of a 2DEG in ZnO/Mgx Zn1−x O QWs grown on ZnO were also found by temperature dependent Hall effect measurements [17] . Quantum confinement effects were confirmed previously by photoluminescence (PL) measurements [24] . A narrowing of the PL peak width is observed in quantum–wells grown on ZnO, especially for low well widths, due to the higher influence of the interface roughness on thinner quantum wells [17] . Careful control of the laser fluence applied to the PLD target resulted in a significant improvement of the quality of the heterointerface in ZnO/Mgx Zn1−x O heterostructures. The use of a slanted QW allowed the observation of quantum confinement effects in QW of different thicknesses in one sample with a well defined barrier composition. A pronounced QCSE was observed in PLD grown samples for the first time, indicating that atomically abrupt interfaces exist in the samples. Comparison with data obtained on MBE grown samples given in the literature [25] revealed, that the samples discussed here equal the MBE grown samples both in interface quality and in density of non–radiative recombination centers (see Fig. 2).

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Effects of the polarization in ZnO/BTO heterostructures

ZnO/BTO heterojunctions were successful synthesized on both Si and STO substrates. A substrate preparation routine following Ref. [26] was applied to commercially available STO substrates and produced perfect vicinal substrates with step edges of unit cell height. The structural and electrical properties of the structures grown on the lattice matched STO substrates are by far superior to these of the samples grown on Si [27] . Vicinal BTO thin films with step edges of unit cell step height were grown on STO up to a critical thickness of roughly 45 nm in concordance with viii

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Ref. [28] . A leakage current density as low as jl < 10−9 A/cm2 was found from I–V measurements on ZnO/BTO heterostructures grown on STO. From the curves obtained the polarization of the ZnO layer PZnO = 0.2 ± 0.05 µC and the coercive field of the BTO EC = 12.5 ± 1 kV/cm were estimated. A detailed model was developed to understand the coupling of the ZnO and BTO polarization and the formation of depletion layers in the ZnO introduced by the sheet charge related to the change of the polarization at a ZnO/BTO heterointerface [29] . Employing the aforementioned model the Sawyer–Tower loops of single BTO layers, ZnO/BTO single heterojunctions and ZnO/BTO double heterojunctions could be accurately described, and the material parameters of the individual layer were extracted. Qualitative description of the C–V loops of ZnO/BTO double heterostructures was also possible from this model [30] . Ferroelectric thin film field effect transistors were demonstrated on the basis of ZnO/BTO heterostructures. The transistors were normally–on and showed output currents of up to 10 µA, which can be controlled over more than 6 orders of magnitude by the gate voltage. A reproducible nonvolatile memory effect was observed due to the ferroelectric polarization in the BTO [31] (see Fig. 2 (b)).

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

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Contents 1 Introduction

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2 Experimental Techniques 2.1 Pulsed laser deposition . . . . . . . . . . 2.2 Atomic force microscopy (AFM) . . . . . 2.3 X-ray diffraction (XRD) . . . . . . . . . 2.4 Hall-effect . . . . . . . . . . . . . . . . . 2.5 Luminescence measurements . . . . . . . 2.6 Rectifying contancts . . . . . . . . . . . 2.7 Current–voltage measurements (I–V) . . 2.8 Capacitance–Voltage spectroscopy (C–V) 2.9 Sawyer–Tower measurements (ST) . . . . 2.10 Other techniques . . . . . . . . . . . . .

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3 Physical properties of materials employed 3.1 Binary ZnO and ternary Mgx Zn1−x O . . . . . . . . . . . . . 3.1.1 Change of the bangap energy . . . . . . . . . . . . . 3.1.2 Influence of the Mg content x on the lattice constants 3.2 Growth of ZnO and Mgx Zn1−x O thin films . . . . . . . . . . 3.2.1 Growth of ZnO on sapphire substrates . . . . . . . . 3.2.2 Growth of Mgx Zn1−x O on sapphire substrates . . . . 3.2.3 ZnO substrate material . . . . . . . . . . . . . . . . . 3.2.4 ZnO substrate preparation . . . . . . . . . . . . . . . 3.2.5 Growth of ZnO on ZnO substrates . . . . . . . . . . 3.2.6 Growth of Mgx Zn1−x O on ZnO substrates . . . . . . 3.3 The perovskites BaTiO3 and SrRuO3 . . . . . . . . . . . . . 3.4 Summary and conclusion . . . . . . . . . . . . . . . . . . . .

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4 Properties of ZnO and Mgx Zn1−x O single layers 4.1 Properties of homoepitaxial ZnO thin films . . . . . . . . . . . . 4.1.1 Properties of nominally undoped homoepitaxial ZnO thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Properties of phosphorous doped homoepitaxial ZnO thin films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Evaluation of the transport properties by mobility spectrum analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

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Contents 4.3 4.4

Properties of phosphorous doped Mgx Zn1−x O thin films grown on ZnO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . 90

5 Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures 93 5.1 Principle considerations . . . . . . . . . . . . . . . . . . . . . . 93 5.2 Carrier confinement in ZnO/Mgx Zn1−x O single heterostructures 96 5.3 Electron accumulation in ZnO/Mgx Zn1−x O quantum wells . . . 98 5.3.1 Single quantum wells grown on a-plane sapphire . . . . . 98 5.3.2 Single quantum wells grown on ZnO substrates . . . . . 99 5.4 The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.4.1 Literature data on the QCSE in ZnO/Mgx Zn1−x O Quantum wells . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.4.2 Luminescence phenomena related to presence of the QCSE106 5.4.3 Observation of the QCSE in ZnO/Mgx Zn1−x O quantum wells grown by PLD . . . . . . . . . . . . . . . . . . . . 108 5.5 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . 118 6 Polarization related effects in ZnO/BaTiO3 heterostructures 121 6.1 Effects observed in ZnO/BTO heterostructures . . . . . . . . . . 122 6.1.1 ZnO/BTO samples grown on Si . . . . . . . . . . . . . . 122 6.1.2 ZnO/BTO samples grown on lattice matched substrates 124 6.2 Theory of coupling phenomena in ZnO/BTO heterostructures . 131 6.2.1 Derivation of a model describing the coupling phenomena 131 6.2.2 Application of the model to experimental data . . . . . . 137 6.3 ZnO/BTO based ferroelectric thin film transistors . . . . . . . . 143 6.4 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . 147 7 Summary and outlook 149 7.1 Summary and conclusion . . . . . . . . . . . . . . . . . . . . . . 149 7.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Acknowledgement

187

Curriculum Vitae Address . . . . . Personal Details . Education . . . . Language Skills .

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Chapter 1 Introduction ZnO is a transparent oxide semiconductor with a bandgap energy of Eg = 3.37 eV at room temperature [1] . The wide gap and the strong exciton binding energy of 60 meV [1] make it an interesting material for optoelectronic applications in the blue and near UV range of the electromagnetic spectrum. Its outstanding material properties triggered a wave of scientific investigations in the past decade. However, numerous reports of the materials properties date back as late as the 1920’s [2] . First experiments revealing the conductivity of polycrystalline ZnO were already reported in that time [3,4] . A first report on transport measurements in ZnO single crystals and thin films emerged in 1935 [5] . An intrinsic n-type conductivity was discovered in these first studies. Detailed information on the thermal activation of the conductivity was given in the 1950’s [6,7] , and first tentative assignments of the defects involved to their chemical nature were given. Further the mechanisms limiting the mobility were investigated and theoretically modeled. Fundamental material parameters like the effective electron mass and Debye temperature were estimated in this process [8] . At the same time first indications were found, that a highly doped layer exists near the surface of the single crystals, and that its presence can be controlled by the atmosphere the crystal is exposed to [9] . More detailed investigations showed, that the formation of these accumulation layers depends on the polarity of the surface where the treatment is applied to [10] . As the wurtzite crystal system lacks inversion symmetry, and the ZnO crystal is partially ionic, a spontaneous polarization must arise parallel to the [0001] direction [11] . It was argued, that this internal polarization is responsible for the formation of accumulation and depletion layers at the Zn- and O-faces, respectively [10] and that quantization effects will play a role in the case of accumulation [12] . The properties of such accumulation layers will be investigated in the present study in ZnO and Mgx Zn1−x O thin films. Theoreticians have calculated the charge per atom, and the lattice parameters of the material, resulting in values for the spontaneous polarization of PZnO = −0.032 C/m2 [13] , PZnO = −0.05 C/m2 [11] and PZnO = −0.057 C/m2 [14] . The spread of the values obtained in this way is larger in other studies, which partially rely on experimental values for the lattice constants [15,16] . First experimental studies employing second harmonic generation yielded a value of 1

1. Introduction PZnO = −0.07 ± 0.015 C/m2 [17] . The influence of the ZnO polarization on the electronic structure and the formation of defects was studied by photoluminescence spectroscopy, current– voltage, capacitance–voltage, and Hall-effect investigations [18–23] . The relative intensity of luminescence features differs reproducibly, which was explained by phenomenological models involving the different positions of the Fermi-level [20] . Different free carrier concentrations are apparent [19,21–23] , chemical differences are reported [18] and a remarkable difference in the work function was observed between the O- and the Zn-face [19] . Recently more elaborate calculations of surface reconstruction mechanisms were carried out, which showed, that both polar ZnO and nonpolar surfaces show different surface reconstructions [24] which contribute to the compensation of the internal polarization creating an externally neutral crystal. The polarity of ZnO single crystals can be easily determined by etching the polar surface [25] . Nondestructive methods involve more complexity, especially if applied to thin films. Rather complex techniques like anomalous dispersion X-ray diffraction [26–28] , scanning nonlinear dielectric microscopy [29] , angular resolved X-ray photoelectron diffraction [30,31] and coaxial impact collision ion scattering spectroscopy [32–34] were successfully employed in order to determine the polar orientation of ZnO thin films. However, non of these investigations was able to reveal the magnitude of the spontaneous polarization. A different approach can, however, be adapted from ongoing research into other wurtzite type material systems. Detailed investigations were carried out in the GaN/AlGaN system [39,40] . Therein, the dependence of both spontaneous polarization and piezoelectric polarization on the Al concentration was determined from the carrier density in two-dimensional electron gases forming at hetereointerfaces. Similar investigations were carried out in the ZnO/Mgx Zn1−x O system [35–37] . Further experimental values have been obtained by numerical evaluation of the photoluminescence shift in ZnO/Mgx Zn1−x O quantum well structures due to the internal electric fields arising from the different electric polarization of the well and the barrier material [38] . The values of the effective polarization, the sum of piezoelectric and spontaneous polarization, extracted from these different considerations differ by up to 30% among themselves and from theoretical values as given in [13] . The dependence of the spontaneous polarization derived in these studies on the Mg content x is given in Fig. 1.1. The decomposition of the effective polarization into the spontaneous and piezoelectric polarization introduces further uncertainties, as the lattice constants and piezoelectric coefficients have to be known, which are both subject to experimental error. Therefore it seems beneficial to think of alternative routes for the determination of the spontaneous polarization in ZnO and its compounds. The difference in the electric polarization in ZnO/Mgx Zn1−x O heterostructures gives rise to unique effects. Carrier accumulation is possible at the heterointerfaces and can lead to the formation of two-dimensional carrier gases (2DEG) [41] . The transport properties inside this 2DEG differ from that of a three-dimensional electron gas (3DEG) in the bulk, which can be exploited for the development of highly efficient devices, such as high electron mobil2

0.04 0.03

P (C/m2 )

0.02 0.01 0 −0.01 −0.02 0

0.05

0.1

0.15 0.2 0.25 Mg content x

0.3

0.35

0.4

Figure 1.1: Change in the spontaneous polarization Psp (dotted lines), piezoelectric polarization Ppe (dashed lines) and resultant polarization (solid lines) at a ZnO/Mgx Zn1−x O heterointerface as a function of the x. Red lines after Ref. [35] , blue lines after Ref. [36] , green line after Ref. [37] and black line after Ref. [38] .

ity transistors. The mechanisms involved in the formation of a 2DEG in the ZnO/Mgx Zn1−x O system will be studied in this work. In contrast, the discontinuities in the electric polarization can also induce effects which are detrimental to device performance. One of the effects investigated in detail in the recent past is the quantum confined Stark-effect (QCSE). The change in polarization between the barrier and the well material of a quantum well (QW) structure in a wurtzite material such as ZnO or GaN and their compounds leads to an electric field inside the quantum well. The square well potential is changed into a triangular potential. The transition energy between electron and hole states is reduced, but more importantly, the maxima of the electron and hole occupation probability become spatially separated. This results in a decrease of the overlap of the electron and hole wave-functions, a decrease in the oscillator strength and the radiative recombination efficiency. Lately extensive efforts are undertaken to avoid this effect in light emitting devices. Therefore, growth studies of GaN-related materials in non polar orientation are frequent in the recent past [42,43] . First attempts of the realization of non-polar material are also reported from the ZnO system [44,45] . Despite these considerations from the device design point of view, the observation of the QCSE is interesting, as basic properties, such as the dependence of the polarization on the alloy composition and the motion of carriers in the QW 3

1. Introduction become accessible to experimental observation. The observable phenomena related to the QCSE and the conditions necessary to its observation will be investigated. All the above mentioned considerations apply to a static electric polarization. It is however possible to change the electric polarization externally, for example by mechanical stress and by electric and magnetic fields. In the present study, the material ZnO will be coupled with the ferroelectric BaTiO3 in order to reveal the physical mechanisms arising from the presence of a fixed and a switchable polarization component in a heterostructure. The combination of these materials is of special interest, as both materials represent model materials for their individual material classes, and a combination does not face chemical incompatibilities, as both materials are oxides. The influence of the ZnO polarization on the ferroelectric hysteresis will be studied, and the possibility of an application of such heterostructures as non volatile memory elements will be investigated. This thesis is organized as follows: In Chap. 2 experimental techniques and equipment involved will be briefly discussed. Chapter 3 gives an overview over the physical parameters of the material systems involved and growth conditions and morphology of the samples investigated. The structural, electric and luminescence properties of undoped and phosphorous doped ZnO and Mgx Zn1−x O thin films grown on ZnO are discussed in Chap. 4. Chapter 5 is devoted to quantum effects in ZnO/Mgx Zn1−x O films, the focus here is on the formation of 2DEGS and the presence or absence of the QCSE. The unique coupling effects discovered in ZnO/BTO heterostructures are disscussed in Chap. 6, a quantitative model is introduced and nonvolatile memory device demonstrated. Chapter 7 summarizes the thesis and gives an outlook on further work planned or recommended by the author.

4

Chapter 2 Experimental Techniques Within this chapter experimental techniques involved in the present study will be briefly described. Herein an illustration of these techniques will be emphasized which have been personally employed by the author. Other techniques will only be mentioned with reference to literature giving the full experimental details and the persons performing the experiments.

2.1

Pulsed laser deposition

Pulsed laser deposition (PLD) was used for the fabrication of all samples regarded in the following. A detailed description of the method, its development and the material system deposited in the semiconductor physics group of the Universität Leipzig can be found in Ref. [46] . In the PLD processes a target of the respective material is hit by a focused laser beam. The wavelength of the laser beam is 248 nm, which is emitted from a LPX305 KrF excimer laser bought from Coherent Lambda Physik. The laser is pulsed, with a pulse length of 5 ns, and a repetition frequency of 1–30 Hz. The energy per pulse can be set between 500 and 1,000 mJ. Around 20% of this intensity is lost by reflection and absortion at the optical elements within the light path (mirrors, the lense, and the entrance window of the chamber). The laser fluence, meaning the power density of the inbound laser beam on the target can be selected by moving the lense off focus. The target consists of a sintered ceramic pelled. The poweder is homogenized before in an agate mill, and pressed into the pelled. The substrate is mounted onto a circular rotating substrate holder, which is radiatively heated from the back side. The heater itself consists of Kantal wire, which is periodially folded and anclosed by alumina tubes. behind the heater several metal reflection screens are mounted, to ensure a highly efficient heat transport to the substrate holder. The laser beam excites the electron system of the target, which is partially relaxed to the phonon system of the target material. Multiple processes take place in parallel which are summarized in Ref. [47] . It is important to note that the energy introduced by the laser beam both results in evaporation of the target and thermal heating, which will eventually result in a liquid phase on 5

2. Experimental Techniques the target surface. The evaporated components will be further heated by the laser pulse, and partially ionized. The plasma in the vicinity of the target surface can also contribute to the sputtering of the target and will speed up the creation of atomic and ionic species. In contrast, the molten target material is typically not emitted from the target. It is however possible, that due to the rapid expansion of the heated material parts of the liquid material will form a drop moving into the direction of the target. Such a large portion of target material will not redistribute on the substrate surface as the single atoms, which results in the formation of micrometer sized hillocks, named droplets. Detailed investigations were carried out on the kinetic of the individual constituent of the plasma [48–50] . Nevertheless, the exact interactions are not yet completely understood. This study does not aim to contribute to the understanding of the processes in the laser plasma. Nevertheless, as the plasma kinetic influences the composition of the film it will be regarded in the presenty study. Among the parameters varied during the growth of the thin films, the substrate temperature, the chamber background pressure and the laser fluence will be varied.

2.2

Atomic force microscopy (AFM)

In the present study three different AFM setups were used. The reason is the temporal availability of the individual setups. Initial studies were carried out on a Veeco Metrology Dimension 3100 with a nanoscope IVa controller in the semiconductor physics group. Additionally a Veeco Metrology Dimension 3000 with a nanoscope III controller in the group of Prof. Dr. Friedrich Kremer at the Universität Leipzig was used. Further a Park system XE-150 microscope as employed in the study. All measurements were performed using standard silicon non contact cantilevers, and the images were obtained in the non-contact mode. In the case of the Veeco Metrology instruments, a special non-contact mode named ‘tapping’ was used. The measurements were performed by the author, Helena Hilmer, Stefan Schöche, and Gregor Zimmermann.

2.3

X-ray diffraction (XRD)

For all XRD investigations presented in this study a Philips Analytical Materials Research X’Pert Diffractometer was used. The instrument possesses two different goniometers, one for wide angle measurements and one for high resolution (HR-XRD). Cu Kα radiation is used in both cases, however for the HR-XRD measurements a Bartels monochromator is introduced into the light path. Herein a pointshaped Cu Kα1 beam is selected by four Ge (220) reflection. The detector was either kept open (for rocking curve measurements) or a Bonse–Hart analyzer crystal with acceptance angle of 12 arcsec (triple axis configuration, for reciprocal space maps) was used. The measurements were performed by Dr. habil. Michael Lorenz, Christof Dietrich, Stefan Schöche, and Jan Zippel. 6

2.4. Hall-effect

2.4

Hall-effect

For the magnetotransport measurements conducted in this study two different setup were employed. The setup available at the semiconductor physics group features a Keithley 220 current source, with a current range between 1 nA and 1 A. All measurements were performed in the van-der-Pauw geometry. Different contact configurations are scanned by a Keithley 7065 Hall-measurement card. The signal is detected with a Keithley 2000 multimeter. A temperature range between ≈ 20 K and 800 K is accessible. A magnetic field of up to 0.43 T can be applied. For the magnetic field dependent measurements a setup at the Forschungszentrum Dresden Rossendorf is used. The measurement device is a Lakeshore 9700A cryostat, herein magnetic field of up to 9 T can be applied. The measurements were performed by Danilo Buerger. For the evaluation of the measured data a exact solution of the Boltzmanntransport-equation (BTE) is used, as outlined in Refs. [51,52] . Herein the relationship between the Hall- and drift mobility one is calculated via the perturbations of the electron distribution function caused by a external electrical field F and magnetic field B respectively. In this case the BTE can be written as:      e ~kx ∂f df ~ky ∂f −B , (2.1) F +B = ~ me ∂kx me ∂ky dt coll where e is the elementary charge, ~ is Plancks constant, me the electron effective mass, f the electron distribution function, kx and ky are the components of the
electron wavevector in the plane perpendicular to the magnetic field and df denotes the change in f due to collisions of the carriers. This equation dt coll can be solved by the Ansatz of two coupled perturbation terms Φx and Φy : f = f0 −

∂f0 e~F (kx Φx + ωc ky Φy ) me ∂E

where ωc =

eB , me

(2.2)

which are linked by Lc Φx = 1 + ωc2 Φy

(2.3)

Lc Φy = −Φx .

(2.4)

and Herein E demarks the carrier energy and Lc the so called collision-operator Lc Φ(E) = So Φ(E) + νel Φ(E) − Si (Φ(E)) ,

(2.5)

where So and Si denote the inelastic rates of scattering in and out respectively and νel the combined rates of all elastic scattering processes, which can be calculated assuming a relaxation time τi for each scattering process by X X1 νi = νel = . (2.6) τ i i i 7

2. Experimental Techniques The scattering processes included are: scattering at ionized impurities, scattering at the acoustic deformation potential, piezoelectric scattering and polaroptical scattering. All relaxation rates were calculated following the assumption of isotropic and parabolic bands and the absence of screening apart form ionized impurity scattering, which is given in the Brooks–Herring approximation [53,54] . The scattering rate of ionized impurity scattering is  2 2 2 2 2 NI e ln(1 + βBH ) − βBH (1 + βBH ) √ νionizedimpurity = 3/2 , (2.7) E εε0 16π 2me where βBH

2m = ~



6kT me

1/2

LD .

(2.8)

LD is the Debye length, β = 1/(kB T ) with kB the Boltzmann constant and T the absolute temperature, ε the relative dielectric constant of ZnO, ε0 the dielectric constant of free space and NI is related to the density of ionized impurities and can be expressed as NI = 2NA + n by assuming singly ionized donors and acceptors. For piezoelectric scattering [53] 1/2

νpiezoelectric

me e 2 P 2 1 = 3/2 2 2 π~ εε0 β E 1/2

(2.9)

e2 /c

pz l is used, where P = εε0 +e 2 /c is the electromechanical coupling coefficient conpz l taining the isotropic piezoelectric coefficient epz and the longitudinal elastic constant cl . The acoustic deformation potential scattering is modeled by [53] √ 3/2 2 2me XC 1/2 E , (2.10) νacousticdeformationpotential = π~4 βcl

where XC stands for the hydrostatic deformation potential of the conduction band. For a non degenerate semiconductor the scattering in and out rates of polar optical phonon scattering can be written as: ~βωo − Θ/T − So = Npo (λ+ λo ) = Npo (λ+ λo ) o + e o + e

(2.11)

and − ~βωo + + − Θ/T + + Si = Npo (λ− λi Φ ) = Npo (λ− λi Φ ) , i Φ + e i Φ + e

(2.12)

where Npo designates the phonon occupation number given by the Bose–Einstein ± distribution, and λ± o and λi are the scattering in and out rates respectively, independent of the phonon occupation number. The indices + and − give reference to the fact that the terms are evaluated at the Energies E + kB Θ and E − kB Θ respectively, where Θ is the Debye temperature and ωo the optical phonon frequency. For these rates the following equations hold:     ± √ a + 1 e2 kB me 1 1 Θ ± , √ λo = √ − ln ± (2.13) a − 1 4 2π~2 ε0 ε∞ ε E 8

2.5. Luminescence measurements   √ e2 kB me 1 Θ 1 ± √ λi = √ − 4 2π~2 ε0 ε∞ ε E where

! ± a + 1 2E + kB Θ − 1 , (2.14) p ln 2 E(E + kB Θ) a± − 1 r

~ωo . (2.15) E The perturbation terms were evaluated in a seven step iteration process for any temperature recorded in the experiment. From the perturbation terms the components σxx and σxy of the conductivity tensor can be computed by numerical integration over energy space, and the Hall-mobility can be calculated as well as the Hall-factor, which in turn allows to calculate the drift mobility. R ∂f 2 ne2 dE Φx E 3/2 ∂E σxx = − , (2.16) R √ 3 me dE Ef (E, T ) a± =

σxy

1±

R ∂f dE Φy E 3/2 ∂E 2 ne2 . =− ωc R √ 3 me dE Ef (E, T )

(2.17)

An iterative technique has to be applied for a complete modeling of a data set, as the free electron concentration enters the term for ionized impurity scattering. This is altered by the Hall-factor in the experiment and must be corrected after a calculation the drift mobility. This corrected value of the free electron concentration enters a succeeding calculation of the mobility, and so on. A self consistent solution can be obtained within two or three iterations.

2.5

Luminescence measurements

Within this study photoluminescence (PL) and cathodoluminescence (CL) measurements were perfomed. The PL measurements were conducted at 2 K and room temperature, while the CL measurements take place at roughly 10 K. In the PL measurements the samples were excited, depending on the Mg content in the barrier, by the 325 nm line of a cw HeCd laser (KIMMON IK3552RG) or a frequency multiplied tuneable 200 fs pulse titanium doped sapphire laser (Coherent Mira 900F, pumped by an Nd:YAG-Laser Verdi V 10). The luminescence was dispersed by either a 320 mm or a 1,000 mm monocromator using different gratings. For time resolved measurements a Hamamatsu R3809U-52 microchannel photomultipliertube was used. The experimental conditions are in great detail described in Refs. [55,56] . The PL measurements were performed by Gabriele Benndorf, Christof Dietrich, Susanne Heitsch, Johannes Kupper, Martin Lange, Alexander Müller, and Marko Stölzel. The CL was measured by Jörg Lenzner and Jan Zippel.

2.6

Rectifying contancts

In order to perform capacitance spectroscopic measurements rectifying contacts have to be prepared. Great expertise exist in the semiconductor physics group 9

2. Experimental Techniques regarding this topic. Two types of contacts are used, thermally evaporated Pd Shottky-contacts and reactively sputtered metal contacts. A comprehensive review on the properties of Pd contacts is given in Ref. [47,57] . Details on sputtered contacts can be found in Refs. [58,59] .

2.7

Current–voltage measurements (I–V)

The current transport trough a space charge region is limited a potential barrier accompanied by the bending of the bands in the semiconductor. The current voltage dependence can be modeled as 

I(V ) = I0 exp



e(V − IRs ηkB T





−1 +

V − IRs , Rp

(2.18)

where I and V are the current and voltage respectively, Rs and Rp denote the sample series and parallel resistance η is the ideality factor and I0 describes the saturation current. A detailed derivation of the model equation can be found in Ref. [60] . In this work the current flowing through a diode is modeled using a least squares fit. Therein the characteristic is calculated numerically following Eqn. 2.18.

2.8

Capacitance–Voltage spectroscopy (C–V)

The capacitance of a Schottky diode can be written as C(V ) = A

s

εε0 eNt , 2(Φb − V )

(2.19)

where C and V are capacitance and voltage, respectively, εr and ε0 denote the relative permittivity of the sample and the permittivity of free space, A is the sample cross sectional area and Φb is the barrier height. The net dopant concentration Nt can be calculated from the inversion of the C–V dependence. Further the density of accumulated carriers in potential minima such as QWs can be determined, as outlined in Ref. [61] . Additionally a time dependence of the emission of carriers from their parent defects exist, which depends on their activation energy. Thermal admission spectroscopy (TAS) measures the frequency and temperature dependence of the conductance and capacitance of a sample. The activation energy of the defects in the probed sample volume can be derived from the resonance frequency found in the conductance versus frequency and capacitance versus frequency dependence and the temperature. A detailed derivation can be found in Ref. [47,62] . The C–V and TAS measurements discussed in the present thesis were performed by Dr. Holger von Wenckstern and Alexander Lajn. 10

2.9. Sawyer–Tower measurements (ST)

V Vin Cst

Vo

Figure 2.1: Schematics of the Sawyer Tower measurement circuit. (Courtesy of Venkata M. Voora)

2.9

Sawyer–Tower measurements (ST)

In order to determine the electric polarization of a ferroelectric, the Sawyer– Tower measurement method is frequently employed [63] . Herein a sinusoidal voltage is applied to a series of a known standard capacitor and the ferroelectric sample. The total voltage and the voltage across the sample are monitored, classically on an two plate oscilloscope. The electric field versus voltage dependence can be derived from the measurement signal. In the simplest case the electric field in the sample is proportional to the voltage across the sample, and the polarization is proportional to the input voltage. However, this requires that the electric field is constant within the sample. The analysis fails, if this simplifying assumption is not fulfilled. A detailed model for the response of complex semiconductor–ferroelectric heterostructures will be discussed in the present thesis. The measurements presented in the present thesis were performed by the author, Nurdin Ashkenov and Venkata M. Voora.

2.10

Other techniques

In this work results obtained through other techniques are evaluated and discussed, which will not be explained in great detail. Dr. Rüdiger SchmidtGrund, Helena Hilmer, Philipp Kühne, Stefan Schöche, Chris Sturm and David Schumacher performed the spectroscopic ellipsometry measurements on the samples studied in this work. Christoph Meinecke performed the RBS and PIXE measurements discussed in this work. Dr. Gerald Wagner, Prof. Dr. Werner Mader, Dr. Herbert Schmid (both Universität Bonn) obtained the CBED and TEM images given in this work.

11

2. Experimental Techniques

12

Chapter 3 Physical properties of materials employed 3.1

Binary ZnO and ternary MgxZn1−xO

ZnO crystallizes in the wurtzite structure (Fig. 3.1). Among it’s remarkable properties are the direct bandgap at 3.37 eV [64] at room temperature and the high exciton binding energy of ≈ 60 meV [1] . The high bandgap energy results in transparency of ZnO in the visibe range, making it suitable as a material for visible-blind photodetectors [65] . The high exciton binding energy in principle allows the fabrication of highly efficient excitonic devices operating at room temperature, making ZnO an interesting candidate for UV light emitters. Indeed LED’s [66] and lasing from ZnO structures [67] was reported. The internal quantum efficiency of ZnO-based devices can be improved by the formation of heterostructures with it’s ternary alloys [68,69] . Both the group II and group VI constituent can be replaced. Oxygen was substituted successfully by sulphur [70] . The focus of this work will solely be on substituting Zn, as the PLD system employed in all the growth studies is, like most PLD systems available, excellently applicable for the deposition of oxides, but lacks capability for the deposition of sulfides, selenides or telurides. In the literature the materials MgZnO [71] , CdZnO [72] and BeZnO [68] were proposed, even quartanery BeMgZnO [73] and MgCdZnO [74] were considered. Both MgZnO and BeZnO show a higher electronic bandgap than pure ZnO, the bandgap of CdZnO is reduced in comparison to ZnO. The synthesis of CdZnO is problematic because of the low solubility of Cd in ZnO [74] . Finally, it is important to mention that Cd falls under the substances controlled by the EU’s RoHS directive, making it an unfavorable material in any application. In contrast to rocksalt MgO, BeO has the hexagonal wurtzite structure, making it an interesting option for bandgap engineering. However it is classified as highly toxic in the EU, excluding its use within the present study. We will therefore rely on the use of ZnO/Mgx Zn1−x O heterostructures in the following. The incorporation of Mg into the ZnO lattice changes it’s properties. Over a wide range of Mg contents a linear change of the properties can be assumed (Vegard’s rule) with respect to the Mg content. As MgO and ZnO cyrstallize in different crystal structures, an 13

3. Physical properties of materials employed

Figure 3.1: The two polar orientations of the wurtzite material ZnO: (a) O-face polarity and (b) Zn-face polarity.

abrupt phase transition is expected at a certain Mg content [75] . At this point the material properties change instantly. Therefore, the material properties are not directly a weighted average of these of MgO and ZnO. For a more exact description a parabolic ‘bowing’ behaviour of the individual material constant can be modeled in the continuous part of the individual dependence on the Mg content x.

3.1.1

Change of the bangap energy

First of all, with increasing Mg content x the bandgap of Mgx Zn1−x O increases. Therefore both the optical absorption and emission spectra are shifted towards higher energies. Numerous experimental data was reported, employing techniques as PL, spectroscopic ellipsometry and optical absorption measurements [76–78] . Whereas the absorption measurements yield the optical bandgap by an extrapolation or exact modeling of the data in the proximity of a steep increase in the absorption, PL measurements can give information about the energetical position of the excitonic recombination. Exemplarily, data on the luminescence peak position obtained by PL are given in Fig. 3.2. Whereas the PL technique is more accurate in terms of energetic position, it does not probe the bandgap directly. The values measured have to be corrected by the exciton binding energy, which is in principle a function of x, investigated in detail in [79] . It appears that for low Mg concentration an excitonic spectrum is observed which resembles that of pure ZnO. With increasing Mg content, the excitons become localized in minima of spatial potential fluctuations [80] . These 14

3.1. Binary ZnO and ternary Mgx Zn1−x O fluctuations originate from the inhomogenous distribution of Mg atoms in the lattice which can be purely stochastic or induced by a clustering, as outlined in Ref. [81] . However, the binding or localization energy of the exciton is a slowly varying function of x, allowing the interpolation of the PL peak position versus the Mg content x by a linear or quadratic approximation function. In order to correlate the PL peak position with the actual Mg content, the chemical composition has to be determined. The Mg content x was probed by RBS, as published in [55,82] . However, the error determining the Mg content in such a measurement is comparably large. From the experimental data an empirical relationship between the x content and the PL peak position was obtained and reported in previous studies [55,79,81] . In these three studies Mgx Zn1−x O was investigated, however, the focus was different. While [81] focuses on Mgx Zn1−x O thin films and especially QW structures incorporating these as a barrier material, the range of x values investigated is limited to 0.05 ≤ x ≤ 0.25. This range was extended in [55] up to values of x = 0.35, with a lower bound of x = 0.08. In Ref. [79] samples with comparatively low Mg content were investigated, including x values between 0.005 and 0.1. The relations obtained in these studies are plotted in Fig. 3.2. In the present thesis the empirical relationship given in [55] is used, as the Mgx Zn1−x O materials employed here typically show a Mg concentration of x ≥ 0.1. The determination of the PL peak energy is, especially at room temperature, much easier than the chemical analysis using RBS. The inversion of the derived empirical relationship allows a fast determination of the Mg content. As the measurement itself is very accurate, the main source of error remains that of the RBS measurement used for derivation of the empirical standard curve. The PL investigation therefore represents a valid substitute for the more complicated RBS measurement, once the empirical standard curve is known.

3.1.2

Influence of the Mg content x on the lattice constants

Lattice constants of relaxed Mgx Zn1−x O films An increase in the Mg concentration in the ternary alloy Mgx Zn1−x O leads to a change in the lattice constants. Various authors have evaluated this relationship for at least one decade. An enormous amount of data was gathered, however the values reported vary. Several reasons account for this. Most importantly the changes in the lattice constants are small compared to other material system as GaN/AlGaN and GaAs/AlGaAs. Much data was obtained by XRD investigations of Mgx Zn1−x O thin films. Having a comparatively small sample volume, the intensity of the X-ray diffraction peaks is low for such samples. Crystal imperfections are unavoidable in heteroepitaxial ZnO and Mgx Zn1−x O thin films and broaden the diffraction peaks. The broadening of the peak hinders investigations employing high-resolution X-ray scattering techniques as the wider angular distribution reduces the peak intensity per unit angle. As the growth is carried out at high temperatures on not lattice matched sub15

3. Physical properties of materials employed

PL peak energy [eV]

4.4 4.2 4.0 3.8 3.6 3.4 0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Mg content Figure 3.2: Peak position of photoluminescence of Mgx Zn1−x O thin films as taken from Ref. [55] (red dots) and Ref. [79] (blue triangles). The red line indicates a quadratic least squares fit taken from Ref. [55] .

strates which even have different thermal expansion coefficients, the films can be under mechanical stress at room temperature, even if they are relaxed at the growth temperature. Often, the thickness of the thin films is not sufficient for a complete relaxation of the film upon cooling. An excerpt of experimental data reported in literature is given in Tab. 3.1. The absolute change in the lattice constants per unit of Mg content ka , kc is given. The contraction of the c-axis constant with increasing Mg content x is apparent from all experiments. Due to some spread in the experimental values, the four closest results are averaged (Refs. [83–86] ), giving a value of kc = −0.1235 Å, which will be used in the following analysis. The situation is more complicated for the a-axis constant. ZnO and its ternary compounds show a preferential growth along the c-axis [87–90] . Therefore, the a-axis lattice constant can only be determinated from asymmetric reflexes, which are broadened compared to the symmetric reflexes, or sometimes are not resolved at all. Two possible values of the a-axis expansion will be regarded, ka = 0.036 Å as reported in Refs. [91–93] and ka = 0.05 Å as reported in Ref. [36] . The value reported in Refs. [84,94] is omitted, as a shrinking of the a-axis constant is reported, which might be caused by the different substrate material. From investigations carried out in the semiconductor physics group in Leipzig an expansion in the a-axis constant is observed [79,86] . Also, from both works it is evident, that the c-axis lattice constant is not only a function of the Mg content x, but also of the oxygen partial pressure during growth. Such an influence cannot be clearly resolved 16

3.1. Binary ZnO and ternary Mgx Zn1−x O Table 3.1: Change of lattice constants with increasing magnesium content for various growth methods: molecular beam epitaxy (MBE), radical source molecular beam epitaxy (rs-MBE), metal-organic vapor phase epitaxy (MOVPE), laser molecular beam epitaxy (LMBE) and combinatorial laser molecular beam epitaxy (C-LMBE).

Reference [95] [83] [91–93] [36] [84,94] [85] [86]

Growth

Substrate

Thickness

kc [Å]

rs-MBE a-sapphire MOVPE c-sapphire PLD c-sapphire MBE a-sapphire MBE Si (111) C-LMBE c-sapphire PLD a-sapphire

700 nm 300-700 nm 300 nm 500 nm 400 nm

-0.17 -0.126 -0.11

1000 nm

single p(O2 ) [96] [97]

this work

LMBE MBE PLD

ZnO ZnO ZnO

200–300 nm 800 nm 300 nm

-0.138 -0.12 -0.11 -0.16 -0.077 -0.063 -0.064

ka [Å]

0.036 0.05 -0.05 0.058 0.058

for the a-axis lattice constant. However, it was demonstrated in Ref. [79] that both lattice constants of pure ZnO thin films change with the oxygen partial pressure. With lower oxygen partial pressure during growth the c-axis constant expands while the a-axis constant shrinks. The actual shift of the lattice constant introduced by the oxygen partial pressure is of the order of the shift due to the Mg incorporation, which hinders the determination of the coefficients kc and ka .

Lattice constants of pseudomorphic Mgx Zn1−x O films In contrast to relaxed Mgx Zn1−x O films, where a sizeable amount of publications exist, only few reports are available on Mgx Zn1−x O thin films grown on ZnO substrates [96,97] . As these lattice-matched substrates have both a very similiar lattice constant and a nearly identical thermal expansion coefficient pseudomorphic growth of the Mgx Zn1−x O layers can be achieved. In that case, up to a critical thickness the a-axis constant coincides with that of the substrate, but the c-axis constant differs. As the a-axis lattice constant of Mgx Zn1−x O is larger than that of ZnO, the Mgx Zn1−x O will be under compressive strain, which results in an increase of the c-axis. However, the c-axis constant of relaxed Mgx Zn1−x O is smaller than that of ZnO, therefore the caxis lattice constant of Mgx Zn1−x O is not trivially predictable. In a wurtzite crystal the strain in an epilayer pseudomorphically grown along the c-axis can be calculated following Ref. [98] : 0001 ǫ⊥ = −2

17

C13 ǫk . C33

(3.1)

3. Physical properties of materials employed

MgxZn1-xO

cps a0

ZnO c0 Figure 3.3: Principle of pseudomorphic growth, unit cells are exemplarily shown to the right. A Mgx Zn1−x O film grown on top of a unstrained pure ZnO substrate adopts the a-axis lattice constant of the underlying substrate a0 . The film is compressively strained leading to expansion of the unlocked c-axis lattice constant to the value cps .

Where ǫ⊥ = (cstrained − crelaxed )/crelaxed and ǫk = (astrained − arelaxed )/arelaxed and C13 and C33 are elastic constants, taken to be C13 = 106.1GPa and C33 = 209.5GPa [99] . Assuming a linear change of the lattice constants with Mg content x cx = c0 + kc x and ax = a0 + ka x

(3.2)

where a0 and c0 are the lattice constants of an unstrained pure ZnO substrate. This assumption does not necessarily hold true for the hydrothermal substrates employed in this study due to their comparatively high Li content, resulting in a slight change of the substrate lattice constant. Therefore only the change of the film lattice constant with respect to the substrate is monitored. A Mgx Zn1−x O film grown on such a substrate adopts the a-axis constant of the substrate a0 (see Fig. 3.3), ǫk =

a0 − ax ka x = . ax a0 + ka x

(3.3)

As outlined in 3.1.2 the a-axis constant expands with increasing Mg content x, therefore the pseudomorphic Mgx Zn1−x O film is under compressive strain. From (3.3) the c lattice constants of a pseudomorphic Mgx Zn1−x O layer on ZnO can be calculated and a quantity kc,ps , the change of the c-axis constant per unit of Mg content x can be defined: kc,ps = kc + (c0 + kc x)2

C13 ka C13 ka ≈ kc + 2c0 , C33 a0 + ka x C33 a0

(3.4)

where the approximation in 3.4 is for small x, making kc,ps a constant. It has 18

3.1. Binary ZnO and ternary Mgx Zn1−x O

(a) (0 0 2) on O130

Log10(Intensity (counts)) 4

3.87

3.5 3

q⊥ (nm−1)

3.86

2.5

3.85

2 1.5

3.84

1

3.83

0.5

−0.014

−0.012

−0.01 −1

q|| (nm )

(b) (1 0 4) on O130

−0.008

Log10(Intensity (counts))

7.7

2.5

q⊥ (nm−1)

7.69

2

7.68

1.5 1

7.67

0.5 7.66

3.57

3.575

3.58

−1

q|| (nm )

3.585

Figure 3.4: Reciprocal space map (RSM) of the (a) (002) and (b) (104) reflection of a Mgx Zn1−x O thin film containing a ZnO QW grown on a ZnO substrate (O130) obtained from CrysTec. The color scale represents the log10 of the scattered X-ray intensity (counts). (Data measured by Dr. Michael Lorenz)

19

3. Physical properties of materials employed

(a) (0 0 2) on TD2

Log (Intensity (counts)) 10

3.87

3.5

q⊥ (nm−1)

3.86

3 2.5

3.85

2

3.84

1.5

3.83

1

3.82 2

0.5 3

4

−1

q|| (nm )

(b) (1 0 4) on TD2

5

6

−3

x 10

Log10(Intensity (counts)) 2.5

7.705

−1

q⊥ (nm )

7.7

2

7.695

1.5

7.69

1

7.685 0.5

7.68 3.542 3.543 3.544 3.545 3.546 3.547 −1

q (nm ) ||

Figure 3.5: RSM of the (a) (002) and (b) (104) reflection of a Mgx Zn1−x O thin film containing a ZnO QW grown on a ZnO (00010 substrate (TD2) obtained from Tokio Denpa. The color scale represents the log10 of the scattered X-ray intensity (counts). (Data measured by Dr. Michael Lorenz)

20

3.1. Binary ZnO and ternary Mgx Zn1−x O to be mentioned that even for x 7→ 1, kc x and ka x are small compared to c0 and a0 , and therefore the error introduced by the approximation are below 2% for the values of kc , ka , c0 and a0 obtained in the ZnO/Mgx Zn1−x O system. The coefficient kc,ps is determined from the values of the lattice constants given in Refs. [96,97] and tabulated in Tab. 3.1. The experimental values of the lattice constants are plotted in Fig. 3.6. Mgx Zn1−x O layers containing ZnO single quantum wells were deposited on the O-face of hydrothermally grown ZnO wafers obtained from CrysTec GmbH (CT) and Tokio Denpa (TD), respectively. The properties of the QW’s will be discussed in Chap. 5.4. As the QW’s are embedded into the Mgx Zn1−x O layers, it is reasonable to assume that their lattice constant equals that of the substrate, while the Mgx Zn1−x O is under biaxial strain. High resolution X-ray diffraction experiments (HR-XRD) were carried out and confirm pseudomorphic growth. Reciprocal space maps of the (002) and (104) reflections of a Mgx Zn1−x O thin film containing a QW grown on a substrate obtained from CrysTec (here O130) and Tokio Denpa (here TD2) are shown in Fig. 3.4 and Fig. 3.5, respectively. The total film thickness of the sample grown on the CT substrate is around 100 nm, resulting in comparatively weak film peaks, especially in the asymmetric reflex. Nevertheless, the a-axis constant can be resolved to equal that of the substrate, proving pseudomorphic growth. The c-axis constant of both substrate and film was obtained from the (002) reflex. Despite the total thickness of the film grown on the TD substrate being around 1200 nm and a Mg content of x = 0.175, the film is not relaxed. The critical thickness of a film of this Mg content was calculated to be 128 nm following the Matthew and Blakeslee model [100] . The results obtained from these experiments are compared with values obtained from Refs. [96,97] in Fig. 3.6. A linear fit to the data obtained in the present study is applied in order to determine the coefficient kc,ps from the experimental data yielding a value of kc,ps = −0.064 Å. This is in remarkable agreement with the value obtained in a fit to the data given in Ref. [97] (see Tab.3.1). Further the expected change in c-axis lattice constant versus Mg content x for a relaxed layer and a pseudomorphic film are shown assuming kc = −0.1235 Å and ka = 0.036 Å, again resulting in an excellent agreement with the experimental data in this work and that reported in Ref. [97] . A value of kc,ps = −0.065 Å is calculated following (3.4) for an ka = 0.036 Å. Using the value of ka = 0.05 Å would result in kc,ps = −0.042 Å, which deviates from the experimental value by about 30 percent. One might of course argue, that this can be compensated by a larger change in the c-axis lattice constant with Mg content. A kc = −0.145 Å would be necessary to give the same kc,ps = −0.065 Å for ka = 0.05 Å. In principle any pair of values solving (3.4) with kc,ps ≈ −0.064 Å can be regarded. Among these are the values obtained in Ref. [86] for individual p(O2 ), giving kc,ps = −0.066 Å, in very good agreement with the lattice constant of the pseudomorphic films. In the following the values for kc and ka will be limited to −0.16 Å ≤ kc ≤ −0.1235 Å and 0.036 Å ≤ ka ≤ 0.058 Å. This however gives an error bar of 20% of the mean value for both material constants, and shows the neccessity of more detailed 21

3. Physical properties of materials employed

0

Change in c-axis constant [˚ A]

−0.01

−0.02

−0.03

−0.04

−0.05

−0.06 0

relaxed pseudomorphic Nishimoto et al. Ref (96) Matsui et al. Ref (97) own data 0.1

0.2 Mg content x

0.3

0.4

Figure 3.6: Change in the c-axis lattice constant of Mgx Zn1−x O thin films vs. Mg content x. The solid blue line shows the contraction of the c-axis in a relaxed layer, while the red line shows the contraction in a pseudomorphic film. and △ show values for pseudomorphic layers as published in Ref. [97] and Ref. [96] respectively, + denotes data points obtained in this study. The solid black line shows the change in c-axis constant assuming a kc = −0.064 Å, as obtained from a linear fit to the own experimental data.

22

3.2. Growth of ZnO and Mgx Zn1−x O thin films investigations on the Mgx Zn1−x O lattice constant in relaxed films. Also the growth of single crystals of homogenous composition and variable Mg content would be desirable, increasing the sample volume and reducing the peak width significantly.

3.2

Growth of ZnO and MgxZn1−xO thin films

In any material system investigated, the epitaxial growth of the respective material has significant advantages over the growth on heterogenous materials. Among them are the perfect lattice match, leading to a significant reduction of the density of dislocations upon growth as well as the equal lattice expansion coefficient. This avoids the risk of the formation of cracks and dislocations upon cooling from elevated temperatures where the growth process takes place. Further, the substrate material equals that of the film, reducing contamination by diffusion from the substrate. Nevertheless, even under optimal conditions, the substrate material available is always contaminated by some kind of impurities. The density and nature of impurities mostly depends on the growth process of the substrate itself. While for many semiconductors (especially Si) purification methods like zone melting exist, the application of these methods to ZnO has not yet been published. In order to understand the advantages over the growth of ZnO on sapphire a summary of morphologic and structural properties of ZnO thin films grown on sapphire will be given in Chap. 3.2.1. The properties of available substrate materials will be reviewed in Chap. 3.2.5. The choice of substrate material used in the present work will be motivated from comparing these properties. As differences exist in the growth of ZnO and Mgx Zn1−x O, the growth of Mgx Zn1−x O on sapphire is documented in Chap. 3.2.2, while details on Mgx Zn1−x O films grown on ZnO are given in Chap. 3.2.6.

3.2.1

Growth of ZnO on sapphire substrates

Like for GaN sapphire is the most frequently used substrate in ZnO epitaxy. This is understandable, as both GaN and ZnO are transparent in the visible range, and the fabrication of transparent devices requires an equally transparent substrate. Sapphire delivers this property. Further the substrate is insulating, leaving the conductivity of the samples in principle uninfluenced. It has to be remarked, however, that sapphire contains Al, which is a donor in ZnO. The influence of interdiffusion between the ZnO film and the substrate is discussed in Ref. [101] . The crystal structure and the lattice constants of GaN and ZnO are very similar, (for GaN: c = 0.5185 nm, a = 0.3189 nm). Also the thermal expansion coefficients of both materials are very close (6.51 × 10−6 K−1 for ZnO and 5.59 × 10−6 K−1 for GaN [102] ) compared to that of sapphire with 7.0×10−6 K−1 [103] and silicon 2.59×10−6 K−1 . Considering these similarities, GaN has also been proposed as a buffer layer for ZnO growth on sapphire [102] . It is further easy to understand why sapphire is a favourable choice compared to the cheaper Si substrate. Within the present study the influence of GaN buffer layers will not be regarded, as the PLD system employed is solely de23

3. Physical properties of materials employed veloped for deposition of oxide materials. Only ZnO and Mgx Zn1−x O layers grown on sapphire and ZnO substrates will be regarded. The morphology of the ZnO thin films grown on sapphire will be compared with the morphological results of GaN films on the same substrate reported in the literature, due to the similarities outlined above. Growth experiments were carried out on thermally pretreated a-plane sapphire substrates. These are annealed in air at 1200◦ C. After annealing the surface is perfectly flat, and atomic steps of 4.8 nm height are visible. Then the samples are inserted into the growth chamber and heated to the growth temperature under the oxygen pressure present during growth. A laser power density of around 1.6 mJ/cm2 is applied to ablate the target. The substrates are rotated during growth for the fabrication of a film of homogeneous thickness. A number of 10,000 laser pulses was used for all of the samples discussed in the following. A final thickness ranging from 140 nm to 210 nm was measured. Thickness variations can however be observed, due to the following reasons. First kinetic processes in the PLD plasma are controlled by the chamber pressure and influence the plasma density at the substrate location. Second the adsortion, reorganization and desorption processes taking place on the film surface are influenced by both the partial pressure of the film constituents and the temperature of the film surface. Finally, the oxygen partial pressure controls the II/VI ratio during the deposition process. Within the experiments carried out, the oxygen partial pressure and the substrate temperature were varied. Figure 3.7 summarizes results obtained by AFM on films grown at 650◦ C and 700◦ C. Four samples are shown, which were grown at (a) 700◦ C and p(O2 ) = 0.1 mbar; (b) 700◦ C and p(O2 ) = 0.002 mbar; (c) 650◦ C and p(O2 ) = 0.1 and (d) 650◦ C and p(O2 ) = 0.002. All of the films deposited clearly reveal monolayer steps at the surface. However the density of surface defects is different. Especially for the films grown at 700◦ C large hexagonal pits are observed on the surface. The density of these pits is counted in the 2 µm×2 µm AFM images, and is compared in Fig. 3.7 (e). It can be seen that the pit density is always lower for samples grown at 650◦ C, and that for this temperature the density of pits increases with increasing oxygen partial pressure. Also, if pits are present they are always smaller in size compared to pits found in the samples grown at 700◦ C. Figure 3.7 (f) shows again the density of the pits along with the thickness of the thin films as determined by spectroscopic ellipsometry measurements. The film thickness increases by 15% within the range of oxygen partial pressures. The presence of pits is well known from heteroepitaxial growth of GaN, and ascribed to multiple origins. In general, all ascriptions rely on dislocations penetrating the film, and emerging at the pit position. Such defects have influence on the formation of heterostructures in the films and can lead to significant interface degradation. Pit-like defects originating from threading dislocations have been claimed to be responsible for the so called ‘V-defect’ in InGaN/GaN multiple quantum wells leading to a significant broadening of the luminescence observed [104] . Therefore surface defects have been investigated in the GaN system in great detail. 24

3.2. Growth of ZnO and Mgx Zn1−x O thin films

210

4.0 3.5

2.5 flach 700

2.0

flach 650

1.5 1.0 0.5

0.8 190 0.6 180 0.4 170

Pit density (µm-2)

Film thickness (nm)

3.0 Pit density (µm-2)

1.0

200

0.2 160

0.0 150 0.001

-0.5 0.001

0.010

0.100

0.0 0.010

0.100

p[O2] (mbar)

p[O2] (mbar)

Figure 3.7: 2 µm×2 µm AFM images of ZnO thin films grown on a-plane sapphire. The substrate temperature is 700◦ C for (a), (b) and 650◦ C for (c), (d). The oxygen partial pressure was 0.1 mbar for (a), (c) and 0.002 mbar for (b), (d). (e) Pit density vs. oxygen partial pressure as obtained from the AFM images. (f ) Pit density and film thickness as determined by spectroscopic ellipsometry vs. oxygen partial pressure for samples grown at 650◦ C.

25

3. Physical properties of materials employed

Figure 3.8: Example for double spirals and islands present on one ZnO thin film grown in sapphire. Black circles indicate the double spiral mounds containing a threading dislocation with a screw component parallel to [0001], white encircled mounds are islands without a dislocation. (Courtesy of Gregor Zimmermann)

Heying et al. [105] regarded the surface tension introduced by the dislocation line, following Burton, Cabrera and Frank [106] and Frank [107] . GaN films were grown by MBE on MOCVD grown GaN templates. Whereas the MOCVD templates show straight steps and two types of depressions, hexagonally shaped spiral hillock without depressions are observed in the MBE grown films. The depressions are assigned to two types of dislocations. Small depressions (diameter ≈ 36 nm, depths ≈ 0.6 nm) are assigned to pure edge type dislocations (Burgers vector b = 1/3[1120]) while larger depressions (diameter ≈ 62 nm, depths ≈ 1.8 nm) are assigned to mixed type dislocations (b = 1/3[1123]). This is supported by two steps being terminated by the larger depressions. It was argued that the presence of depressions is less likely in an non-equilibrium growth process like MBE (and even more PLD, which is of importance for the present work), and in such a process otherwise straight steps will wind around threading dislocations, leading to the formation of hexagonal hillocks. However, the critical radius is a function of the III/V ratio and depressions were also observed for a III/V ratio slightly larger then 1. The same authors pointed out in another paper (Ref. [108] ) that the size of depressions can increase with increasing film thickness, however no conclusions were drawn about the origins of 26

3.2. Growth of ZnO and Mgx Zn1−x O thin films this process. Scanning tunneling microscopy investigations revealed [109] , that the depressions terminating edge type dislocations with Burgers vector b = 1/3[1120] have a triangular shape. The base of the depression is an isosceles triangle of 7 × a-axis constant edge length with one side reduced to 6 × a-axis edge length, due to the dislocation. The base of the depression is surrounded by elevated plateaus of an equally triangular shape with it’s edge length being integer powers of two of the base edge length. It is interesting to note, that among these values ≈ 32 nm and ≈ 64 nm can be found, being close to the size of the small and larger depressions found in Ref. [105] . Liu et al. [110] have shown that among the dislocations with a screw component the distribution of Burgers vectors b = j[0001] is not uniform. Each value of j is represented by a different number of monolayer steps emerging from the dislocation at the surface. Values of j equaling 1/2 (one step emerging) and 1 (two steps emerging) are found frequently, but even up to j = 5 (10 steps emerging from the dislocation) are present in the samples in that study. According to Frank [107] screw dislocation in equilibrium can have an open core. The size of this void is given by µb2 (3.5) r= 2 , 8π γ based on the surface tension introduced by a dislocation in a fluid-like material [107] . Here µ is the rigidity modulus and γ is the surface energy. Thereas, the size of the open core is proportional to the square of the magnitude of the Burgers vector. However Northrup et al. [111] argued, that giving the material constants of GaN, the size of this open core dislocations should not exceed 3 Å for a Burgers vector with a screw component of [0001] while experiments revealed sizes of around 60 nm [112,113] . The authors therefore theoretically investigated a mechanism leading to a reduction of the GaN(1010) surface energy by hydrogen termination of dangling bonds stabilizing large core diameters. It is remarked, that the pits observed in our experiments can reach diameters of up to 100 nm. Cui and Li [114] discussed the possibility of merging of dislocations with a screw component, forming double spirals or closed loop spirals and thereby reducing the overall dislocation density with increasing film thickness. In their paper they further argue, that a double spiral should grow faster in height than a single spiral. Therefore, given a sufficiently large film thickness, only double spirals would be visible on the sample. Figure 3.8 shows a 2 µm×2 µm AFM image of a ZnO sample grown on a-plane sappire of roughly 1 µm thickness. The sample is grown at 700◦ C and p(O2 ) = 0.002 mbar. Double spirals, comparatively large pits and mounds without a spiral-like shape are visible on one sample. The growth speed of mounds without a threading dislocation almost equals that of spiral mounds, even after a film thickness of 1 µm no distinct height differences are seen for both types of mounds. This is somewhat unexpected, as other studies have shown that spiral mounds should, given sufficiently large adatom concentration, grow always faster than mounds without spirals [115] . It has to be mentioned however, that the authors investigated Pt thin film growth, a comparatively simple material system. In ZnO additional complications in a theoretical prediction occur from the inter27

3. Physical properties of materials employed play of its two constituents and the polar nature of the material. Further, the non equilibrium growth conditions introduced by the PLD process provides a certain kinetic energy for the adatoms, which gives them the ability to overcome energetic barriers forming at the step edges, at least to some extend, and therefore increases the speed of island growth. In order to further understand the formation of pits, and their comparatively large size seen in this study, a growth evolution study was carried out. Therefore films were grown at 700◦ C and p(O2 ) = 0.016 mbar, a condition resulting in a high density of large pits. A number of 100, 300, 1,000, 3,000 and 10,000 pulses was used for deposition. AFM measurements of the surface morphology were carried out and are shown in Fig. 3.9. For 100 pulses (Fig. 3.9 (a)) the steps of the sapphire substrate are still observable, and only a few point shaped hillocks are visible on the film. The density of these hillocks increases after the deposition of 300 pulses (Fig. 3.9 (b)), but the steps on the sapphire substrates are still observable. The hillocks are separated, a coherent film growth has not yet started. After depositing 1,000 pulses (Fig. 3.9 (c)) beginning coalescence of neighboring hillocks is observed. The surface contains a significant fraction of holes which most likely originate at the sapphire substrate. Note that the height scale of Fig. 3.9 (c) is 6.4 nm, the height determined by spectroscopic ellipsometry instead is 10.5 nm (see Fig. 3.9 (f)). It is known that AFM measurements underestimate the depth of narrow features due to the tip curvature. It is therefore well possible that the pits go down to the substrate. After 3,000 pulses (Fig. 3.9 (d)) coalescence of the growth seeds has progressed, and uniform terraces of width of several tens to hundreds of nm are visible. Still a comparatively high density of pits is observed. For the film thickness attained it is impossible to judge whether the pits penetrate the film down to the substrate surface or whether they are at least partially filled with material. For a number of 10,000 pulses deposited (Fig. 3.9 (e)) terraces are clearly observed on the film, and separated by steps of c/2 and c. The width of the terraces is of the order of tens to hundreds of nm, and depends largely on the miscut of the substrate chosen. The thickness of the films shown in Fig. 3.9 (a)–(e) was measured by spectroscopic ellipsometry and is depicted versus the number of laser pulses in Fig. 3.9 (f). Along with the experimental data a thickness extrapolation is given assuming a strictly linear dependence of film thickness on the number of laser pulses. It can be seen, that the film thickness remains smaller than the extrapolated value in the initial stage of the film growth, but then advances to the expected value with a steeper slope than in the extrapolation. Assuming that the growth after 10,000 pulses represents a steady state condition or being at least very close to this, the following conclusions can be drawn: • The growth of ZnO thin films starts in a nucleation process. The growth rate during nucleation is reduced compared to the steady state growth, resulting in an offset of the experimental thickness in the initial stages of the growth towards lower film thickness. This nucleation is observed in Fig. 3.9 (a) and (b). 28

3.2. Growth of ZnO and Mgx Zn1−x O thin films

Film thickness (nm)

100.0

10.0

1.0

0.1 100

1,000

10,000

Number of PLD pulses

Figure 3.9: 2 µm×2 µm AFM images of ZnO thin films after (a) 100, (b) 300, (c) 1,000, (d) 3,000 and (e) 10,000 pulses. The thickness of the films, as determined by spectroscopic ellipsometry, is depicted in (f ). The solid line shows the extrapolated thickness assuming a steady state growth after 10,000 pulses.

29

3. Physical properties of materials employed • Once the growth seeds are formed they start growing in a 3-dimensional growth mode. Seeds gather material from the surrounding area, and preferentially grow in the c direction. This is evident by the steeper increase of the film thickness in comparison to the steady state growth. The preferential growth of ZnO along this direction is known from investigations of single crystals, thin films and nanostructures [87–90] . It is possible to grow nanowires with high aspect ratios [116] under adequate growth conditions. During this process further nucleation might take place, depending on the diffusion length of the adatoms on the substrate. This might further be a reason why many experimenters show an improvement in ZnO growth if a low temperature buffer layer is introduced during the growth process. Regarding the growth evaluation presented in this study a low temperature will lead to low diffusion length of ZnO adatoms on the substrate, increasing the density of growth seeds. Further, the adatoms, as gathered from the substrate will arrive at a side facet of the growth seed. The surface energy is minimal on the c-plane, but has a local minimum on the m-plane [117] . Upon a lower temperature the probability decreases that an adatom arrives at the lowest point in energy space, but rather sticks to a local minimum. The preference of c-axis orientated growth of the seeds will therefore be not as pronounced as at higher temperatures. This will lead to an increased in-plane growth and speeds up the following growth step. • During 3-dimensional growth the seeds also expand in the in-plane direction, leading to the inevitable coalescence of the seeds. This process is fast in the beginning, but slows down as more and more of the surface is covered by ZnO. If further adatoms are adsorbed onto the ZnO, they will reorganize to the c-planes facing upwards, as these are the surfaces of minimal energy. However on this surfaces step edges represent even lower energy minima, due to the higher number of bonds they provide to the adatoms. In this step the growth mode changes from 3-dimensional to 2-dimensional. The actual nature of the 2-dimensional growth now depends on the density of dislocations, the availability of the ZnO constituents and the temperature. As for most applications a flat surface is advantegeous, step-flow growth mode is desired. This growth mode replaces layer by layer growth if the temperature is sufficient that the diffusion length of adatoms exceeds the average terrace width [118] . At this point a low growth temperature would be disadvantegeous, giving a limit to the usability of the ‘low temperature buffer’. It has to be remarked, that control of the 2-dimensional growth mode is not only possible by the temperature but also by the miscut of the substrate, which reduces the average step width. It has indeed been reported in the GaN system that growth on vicinal substrates improves the surface morphology [119] . • As outlined, the transition between 3-dimensional and 2-dimensional growth is not abrupt. Parts of the sample will be growing 3-dimensionally, thus in out-of-plane and in-plane direction simultaneously, while other 30

3.2. Growth of ZnO and Mgx Zn1−x O thin films parts show step mediated 2-dimensional growth. Therefore pits can be present on the sample up to comparatively large thicknesses and essentially represent voids which go down towards the substrate. It can of cause not be excluded that the pits are partially filled with material, but this seems rather unlikely, regarding the tendency of the adatoms to reach positions of minimal energy. Further the steeper increase in thickness with increasing number of laser pulses in the 3-dimensional growth regime compared to the steady state condition suggests that a part of the film has to be unfilled, as the steady state condition represents the growth rate at complete layer filling. The reduction of the lateral pit size is most likely induced by a form of lateral overgrowth slowly reducing the diameter. It can be stated, that most of the pits observed in this study are not of the same origin as the pits observed in the GaN system. It can of course not be concluded, that upon closure of a pit a dislocation remains due to different orientation of the growth seeds surrounding the pit, however the dislocation is not the main driving force for generating a hollow structure within the film.

3.2.2

Growth of Mgx Zn1−x O on sapphire substrates

As the aim of the present study is the investigation of the effects of the electric polarization on carrier transport and recombination properties, for example in ZnO/Mgx Zn1−x O heterostructures, the growth of Mgx Zn1−x O thin films is an important issue. The same argumentation for the choice of sapphire as substrate holds as it does for pure ZnO. The lattice constants vary only slightly (see Chap. 3.1.2), which should in principle result in very similar growth conditions. This assumption was extensively tested in Ref. [81] , and will therefore not be discussed in great detail here. However a short summary will be given, along with some extended explanations on the growth mechanism exceeding these in Ref. [81] . Fig. 3.10 shows AFM images obtained on four representative Mgx Zn1−x O thin films. A ZnO QW of variable thickness is included in all of the samples. A comparison between layers with and without a QW however does not show a qualitative difference in surface morphology. Two of them (depicted in Fig. 3.10 (a) and (b)) are directly deposited onto sapphire, while for the other two (depicted in Fig. 3.10 (c) and (d)) a roughly 100 nm thick ZnO buffer layer was introduced. The Mg content x is given in the caption. The thickness of the films is intentionally unhomogeneous, as described in Chap. 5.4. The thickness of the layers however, exceeds 100 nm even for the thinnest part of the film. Therefore it is reasonable to assume that a steady state growth is reached, as described in Chap. 3.2.1. For the sample with the lowest Mg content (x = 0.17) directly grown on sapphire (Fig. 3.10 (a)) steps of c/2 height are visible. The morphology however is clearly distinguished from that of pure ZnO thin films. Even as the film is completely closed rather steep hillocks are observed on the sample. The growth mode is clearly 2-dimensional, however a transition to island growth is observed. The width of steps is of the order of tens of nm, an exciton localized in a quantum well with a radius of 31

3. Physical properties of materials employed

Figure 3.10: 2 µm×2 µm AFM images of Mgx Zn1−x O thin films grown on sapphire substrates. The growth temperature was about 650◦ C, the oxygen partial pressure 0.004 mbar. The Mg content x was determined by RT PL to be (a) 0.17 (b) 0.28 (c) 0.3 and (d) 0.32 respectively. The samples shown in (a) and (b) are grown directly onto sapphire, while for (c) and (d) a ≈ 100 nm ZnO buffer layer was used.

roughly 2 nm will therefore not face a variation of the thickness more than a single step. It is however not clear, if the thickness of a QW is homogeneous over the whole sample, as parts of the hillocks might grow faster than for example valleys between them, resulting in an inhomogeneous distribution of the ZnO between the Mgx Zn1−x O layers. This might contribute to a broadening in the QW luminescence of the sample. Figure 3.10 (b) shows a sample with an Mg content x = 0.3. The surface of the sample is very rough and no atomic steps can be observed. The growth is clearly 3-dimensional, and no features corresponding to hexagonal structures can be observed. It can be speculated that the film is highly disordered due to the Mg concentration being significantly above the solution limit in equilibrium (2%) [120] . XRD measurements however revealed, that the sample crystallized in the wurtzite structure and is solely c-axis oriented. Figure 3.10 (c) shows a thin film of equal Mg content x deposited onto a approximately 100 nm thick ZnO buffer layer. The 32

3.2. Growth of ZnO and Mgx Zn1−x O thin films morphology resamples that of ZnO thin films grown on sapphire. Steps of c/2 height are visible. Two lines are marked in the AFM image, labeled as A and B edge, respectively. The labeling is adopted from Ref. [121] , where both kinds of step edges have been observed in the GaN system. The origin of this phenomenon is due to the fact that despite having a hexagonal symmetry in the arrangement of atoms, the tetrahedral coordination of ZnO or GaN results in an angular separation of the in-plane bonds by 120◦ . The {1010} family of directions therefore splits into two subfamilies, one of them being parallel to a bond (perpendicular to a B edge, from now on called B direction), the other one being centered between two bonds (perpendicular to an A edge, from now on called A direction). If a step propagates into the A direction two dangling bonds are available for adatoms, enhancing the growth speed. In contrast a step propagating into the B direction offers only one dangling bond to adatoms leading to a lower growth speed. As an A edge propagates, it tends to facet into B egdes, leaving a zigzag shape behind, as visible in Fig. 3.10 (c). As the wurtzite lattice has a binary stacking sequence, the arrangement of bonds is rotated by 180◦ in every successive layer. Necessarily A and B edges have to alternate. The B edge neighboring the A edge is marked likewise, a strait edge without remarkable facets. Double spirals are partially observed, however due to the vicinal substrate propagating steps dominate the surface. As no island formation takes place, and no hillocks are observed apart from that of spiral winding around dislocations with a screw component, it is concluded that the sample grows in the step flow mode. This is an improvement compared with the growth of pure ZnO and Mgx Zn1−x O directly on sapphire, which both tend to form islands in the layer by layer growth mode. As both temperature and miscut of the substrate are roughly equal, the origin of this behavior has to be clarified. A possible explanation is the reduction of the surface diffusion barrier by compressive strain, as has been experimentally [122] and theoretically [123,124] shown in the literature. As the a-axis constant of Mgx Zn1−x O is larger than that of ZnO the introduction of a ZnO buffer layer might give rise to the step flow growth of the Mgx Zn1−x O layer via the strain formed within. Figure 3.10 (d) shows an AFM image of a Mgx Zn1−x O thin film with x = 0.32 grown on a ZnO buffer layer. The film shows a number of pits, and additionally double spirals are visible. Also a closed loop spiral can be seen, indicative for partial annealing of dislocations with a screw component in this film.

3.2.3

ZnO substrate material

In order to choose ZnO substrates suitable for epitaxy, the properties of available substrate material will be reviewed in the following. Three major growth techniques are used nowadays for the production of ZnO single crystals: growth from the vapor phase, from the melt and from aqueous solution. All of these processes are carried out at elevated temperatures and pressures, each of them having its advantages and disadvantages. While the cleanest material can be grown from the vapor phase [125,126] , the throughput of this process is very limited, resulting in high prices of this substrate material. Recently, the availabil33

3. Physical properties of materials employed Table 3.2: Suppliers and growth methods of ZnO single crystals investigated. Some of these crystals were investigated by Holger von Wenckstern, which is denoted by the abbreviation HvW. SCVT stands for seeded chemical vapor transport, while IKZ denotes the ‘Institut für Kristallzüchtung’ in Berlin. Prices are given if applicable.

Label

Supplier

Method

VP1 VP2 MG1 MG2 MG3 HT1 HT2 HT3

Eagle-Picher Zn-Technologies Cermet Inc. IKZ, Berlin IKZ, Berlin Mateck GmbH CrysTec Tokyo Denpa

SCVT SCVT Skull melting Bridgeman Bridgeman Hydrothermal Hydrothermal Hydrothermal

Ref. [125] [126] [127,128] [129–131] [129–131] [132] [133] [134]

Price

Data

n.a. n.a. ≈ 300$ n.a n.a n.a ≈ 50 e ≈ 300 e

HvW HvW

HvW

ity of the material also became very limited, removing that kind of substrates virtually from the free market. The purity of melt grown substrates is not as high as that of vapor phase material [128] , and lattice imperfections are a big issue in this material [130,131] . For the crystals grown from aqueous solution it is important to note that solving agents, so called mineralizers have to be added to the material [88,135,136] . For ZnO these mineralizers are typical group I-hydroxides, especially KOH and LiOH are very popular [88,135,136] . While the crystalline quality of these materials can be very high [88] , a contamination of the substrate by the mineralizer is unavoidable. This has a significant influence on the properties of the crystals. The free carrier concentration and mobility of selected single crystals is displayed in Fig. 3.11 respectively. The labels in the graphs are given in Tab. 3.2 along with information on the supplier, growth technique and pricing, if available. The crystals labeled MG2 and MG3 were kindly provided by the ‘Institut für Kristallzüchtung’ in Berlin. Some of the crystals have been measured by Holger von Wenckstern, which is also denoted in Tab. 3.2. Reviewing the transport data, the mobility is the highest in the vapor-phase grown samples and the commercially available melt-grown sample. The free carrier concentration exceeds that of the hydrothermally grown samples, but is below that of the samples MG2 and MG3. The latter can be easily explained by the purity of the powder employed in the growth process, being 99.99% only [131] , and the incorporation of intrinsic donors due to oxygen deficiency during growth. Annealing experiments could therefore somewhat reduce the free carrier concentration and increase the room temperature mobility [129] . It has further been shown, that the crystals were suitable for epitaxy of pseudomorphic Mgx Zn1−x O thin films of high structural quality [137] . Nevertheless, these cyrstals are not suitable to serve as a substrate in the present study as the observation of 2-dimensional transport in the samples would be concealed by the high conductivity of the substrate. Similar arguments hold for the substrate MG1 and the substrates grown from the vapor phase. In all 34

3.2. Growth of ZnO and Mgx Zn1−x O thin films

1017

n (cm -3)

1015

1013

1011

VP1

HT1

VP2

HT2

MG1

HT3

MG2 MG3

109 0

5

10

15

20

25

30

35

40

45

50

1000/T (1/K)

µH (cm 2/Vs)

1.000 VP1

HT1

VP2

HT2

MG1

HT3

MG2 MG3

100 30

50

70

100

200

300

T (K)

Figure 3.11: Free electron concentration and mobility in various ZnO substrates versus temperature. Labels are explained in Tab. 3.2. Some of the crystals were measured by Holger von Wenckstern, as denoted in Tab. 3.2.

35

3. Physical properties of materials employed of these crystals the conductivity is greater than 103 Ω−1 m−1 , and therefore not suitable for the utilization in this study. The situation is different for the crystals grown from aqueous solution. The main impurities in these crystals are the group I elements Li and K [88,138] , as far as data is available. If these elements are incorporated on Zn site they act as acceptors and reduce the free electron concentration in the samples significantly [139] . It is however noteworthy, that these elements might also be introduced on interstitial site [140,141] . This fact has been mentioned as one possible explanation for the difficulties in obtaining p-type ZnO by the doping with group I elements, despite the high concentrations incorporated. Regarding the single crystals investigated in this study two different regimes are found. The crystals HT1 and HT2 show a very low free carrier concentration (1013 cm−3 and below) and are only accessible to Hall-effect investigation at temperature above 180 K. Below this value the conductivity of the substrates is virtually zero. Further, by an annealing step, which is required in the substrate preparation steps prior to epitaxy (see Chap. 3.2.4), the resistivity increases even further. These substrates are highly suitable for electrical investigations of the films thereon, as they do not contribute to the overall conductivity. However, care has to be taken regarding sample HT3. As the composition varies between individual samples (a detailed investigation is given in Ref. [88] , Fig. 13) the conductivity might be higher. Therefore prior to the growth the conductivity was measured and only substrates with very low conductivity are employed in the present study, so influence of the substrate conductivity can be neglected in all following considerations. For the experiments two types of substrates have been used: substrates provided by CrysTec GmbH, Germany, and substrates provided by Tokio Denpa Inc., Japan. The quality of the substrates obtained from both suppliers will be discussed in the following section.

3.2.4

ZnO substrate preparation

As outlined in the previous section, substrates grown by the hydrothermal method are the most promising candidates for the investigation of conductive ZnO thin films, as these substrates do not produce an additional conductive channel in parallel to the thin film in question. This is ideal for the determination of the carrier concentration and mobility in the thin films, for example in doping experiments. Despite these advantages, the number of reports regarding successful homoepitaxy are very limited (see Fig. 9.1 in Ref. [47] ). One particular reason for that is the state the substrates are delivered in. It was shown, that the surface of the crystals is covered by a damaged layer, which extends into the bulk material up to 1 µm [142,143] . It has further been argued, that this damage is introduced by the polishing process the vendors apply to the substrates. Indeed, significant scratches have been observed by AFM investigations on the substrate surfaces [47] . In an attempt to improve the substrate quality chemical cleaning, etching and thermal annealing experiments have been carried out [47,142,144,145] . It is shown, that the oxygen-face of the substrates recovers upon annealing above 1,000◦ C 36

3.2. Growth of ZnO and Mgx Zn1−x O thin films

1

3.83 −0.016 −1

q (nm )

4.025

−0.014

0.5 −8

−6

−4

−1

⊥

1.5

3.835

1

3.83 2

−1

10

2 4.04 1.5 4.035

4.025 −6

4 −3 x 10

1

−4

−2

0

3.835

1

3.83

0.5 −4

−1

q (nm ) ||

(g)

−2 −3 x 10

−1

⊥

1.5

q (nm )

3.84

⊥

−1

q (nm )

2

−6

10

2 1.5

7.68

1

7.675

4 6 −3 x 10

0.5 3.535

3.54

3.545

||

O65 O−face (1 0 4)

1.5 1

4.035 4.03

0.5 −8

−6

−4

−2

−1

q (nm ) ||

3.55

3.555

(h)

0 2 −3 x 10

Log10(Intensity (counts))

7.695

2

4.04

4.025 −10

−1

q (nm )

(f)

4.045

2.5

3.845

3.555

7.685

7.67

Log10(Intensity (counts))

4.05

3

−8

2

q (nm )

O65 O−face (1 0 1)

3.55

Log (Intensity (counts))

(e)

3.85

3.825

−1

−1

7.69

0.5

||

Log10(Intensity (counts))

3.855

3.545

q (nm )

O64 O−face (1 0 4)

2.5

(d) O65 O−face (0 0 2)

3.54

7.695

4.03

0.5

||

0.5

||

Log (Intensity (counts))

4.045

q (nm )

2

3.84

⊥

−1

2.5

0

1

(c)

4.05

3

q (nm )

2 −3 x 10

−1

3.85

q (nm )

O64 O−face (1 0 1)

3.5

−2

1.5

7.68

7.67 3.535

⊥

10

3.845

3.825

2

7.685

(b)

Log (Intensity (counts))

3.855

0

−1

||

(a) O64 O−face (0 0 2)

−2

q (nm )

2.5

7.675

q (nm )

||

1

2.5

7.69 −1

−0.018

1.5

4.035

10

7.69

⊥

−0.02

2

4.04

Log (Intensity (counts))

7.695

2.5

4.03

0.5

TD5 O−face (1 0 4)

3

−1

−1

⊥

1.5

3.835

q (nm )

2

3.84

⊥

−1

q (nm )

2.5

10

4.045

3

3.845

Log (Intensity (counts))

4.05

3.5

3.85

3.825

TD5 O−face (1 0 1)

⊥

10

q (nm )

Log (Intensity (counts))

3.855

q (nm )

TD5 O−face (0 0 2)

2

7.685

1.5

7.68

1

7.675 7.67

0.5 3.535

3.54

3.545

−1

q (nm ) ||

3.55

3.555

(i)

Figure 3.12: Comparison of reciprocal space maps of the (from left to right) (002), (101) and (104) reflexes obtained on 3 different substrates, namely (from top to bottom) a TD substrate and two selected CT substrates. The color scale represents the log10 of the scattered X-ray intensity (counts). (Data obtained by Dr. Michael Lorenz)

37

3. Physical properties of materials employed in an oxygen atmosphere [144–148] . Similar improvement was found for other surfaces [145,147,149] . The substrates employed in this study are typically of oxygenface polarity. HR-XRD measurements carried out on the substrates reveal that the structural quality of the substrates is varying. A comparison of reciprocal space maps obtained from the samples in the as delivered state is given in Fig. 3.12. Substrates obtained from TD show very narrow peaks. No splitting of the symmetric and the asymmetric reflexes is observed for these substrates, as shown in Fig. 3.12 (a)–(c). In contrast the structural quality of the CT substrates varies strongly. Substrates with structural properties similar to the TD substrates have been measured, however most of the material shows inferior quality in the as delivered state. Two examples are shown in Fig. 3.12 (d)–(f) and Fig. 3.12 (g)–(i). As reported in the literature [144] , the structural properties of annealed substrates improve significantly. Further the surface morphology of the substrates improved, as also reported in Refs. [144–148] . In order to illustrate this, AFM height images from substrates used in this study are shown in Fig. 3.13. The as-received state is shown in Fig. 3.13 (a). The substrate shows a very rough surface. After annealing for 2 hours in 700 mbar oxygen at a temperature of 1,000◦ C the surface of the substrates shows steps of c/2 height, as depicted in Fig. 3.13 (b)–(d). The morphology of the substrates can be different, due to the miscut of the substrates. A substrate with a very small miscut is shown in Fig. 3.13 (b). The few steps available due to the non zero miscut, however, tend to meander and form small islands and holes of c/2 height on the substrate. In contrast, the substrate shown in Fig. 3.13 (c) has a miscut of approximately 0.3◦ , resulting in a vicinal surface with parallel step edges. It is interesting to note, the signs of scratches from the polishing process have remained on the substrate, meaning that nearly no ZnO material has evaporated from the surface at the temperatures used in the annealing. Some of the substrate show surface defects (as depicted in Fig. 3.13 (d)), which might be connected to crystal defects extending into the bulk of the substrate. The different morphological and structural properties of the substrates influence the thin films grown on them, which will be extensively discussed in the following sections.

3.2.5

Growth of ZnO on ZnO substrates

Following the approach employed in the study of heteroepitaxial growth on sapphire, measurements of the morphology of homoepitaxially grown ZnO films were carried out. Therefore undoped ZnO layers were deposited onto the Oface of CT crystals. Figure 3.14 shows homoepitaxial ZnO thin films grown at different temperatures and oxygen partial pressures. Resulting AFM height images of size 2 µm×1 µm are summarized in Fig. 3.14. For low growth temperature (470 and 550 ◦ C, as shown in Fig. 3.14 (f) and Fig. 3.14 (e) respectively) a 3-dimensional growth is observed. For Tg = 470◦ C nanocrystallites with a size of ≈ 30 nm form. Increasing the growth temperature to 550◦ C leads to a coarsening of the crystallites due to the increased diffusion length of adatoms 38

3.2. Growth of ZnO and Mgx Zn1−x O thin films

Figure 3.13: 2 µm×2 µm AFM height images of ZnO substrates purchased from CrysTec GmbH. (a) without thermal annealing, (b)–(d) after thermal annealing. Different substrate miscut can be seen in (b) and (c). Extended crystal defects were observed on some of the substrates as depicted in (d).

39

3. Physical properties of materials employed

p(O2) = 0.1 mbar

Figure 3.14: 2 µm×1 µm AFM height images of homoepitaxial ZnO thin films. All films are grown on the O-face of CT crystals. The oxygen partial pressure was (a) 0.1 and (b)–(f ) 0.016 mbar. The substrate temperature was set to (a) and (c) 650◦ C; (b) 700◦ C; (d) 610◦ C; (e) 550◦ C and (f ) 470◦ C. (Measurements performed by Heidemarie Schmidt (now Forschungszentrum Rossendorf))

on the surface. The average size of the crystallites is about 400 nm. Beginning at a temperature of 610◦ C (visualized in Fig. 3.14 (d)) a transition into a 2-dimensional growth mode occurs. While the lateral dimension of surface features reduces slightly 250 nm compared to the film grown at 550◦ C the height of the features is dramatically reduced. Hexagonal symmetry is observed, and even c/2 steps can be seen. The surface is still somewhat roughened by island nucleation of the next layers to be formed, making the overall image seeming rough. This changes as the temperature is raised to 650◦ C (Fig. 3.14 (c)). Hexagonal hillocks with a average diameter of 400 nm are observed, defined by steps of c/2 height. The average width of terraces is 30 nm. Increasing the temperature further to 700◦ C (Fig. 3.14 (b)) results in both an increase of hillock diameter and terrace width, indicative for the increase in the surface diffusion length. Also the strictly hexagonal symmetry of surface features breaks down, as neighboring islands coalesce. Further increase of the temperature would increase the island size even more, and lead to a reproduction of the stepped terraces of the substrates by the thin films. Interestingly the island size also 40

3.2. Growth of ZnO and Mgx Zn1−x O thin films increases upon a change in oxygen partial pressure from p(O2 ) = 0.016 mbar to p(O2 ) = 0.1 mbar (compare Fig. 3.14 (a) and (c)). An average hillock diameter of 700 nm is reached, along with a terrace width of 80 nm. It has to be pointed out, that changing the oxygen partial pressure influences the film growth in more then one way. The motion of particles in the plasma plume is influenced by the pressure inside the growth chamber, as is the stoichiometry of the film. As oxygen atoms are much lighter then Zn atoms (16 amu/65.4 amu) the scattering probability for oxygen increases with respect to zinc atoms as the oxygen partial pressure increases. Therefore during the comparatively short travel time of the plasma, the surface of the growing film might be subject to excess zinc. As all of the films are grown in the oxygen polarity (as confirmed by convergent beam electron diffraction (CBED), compare Fig. 3.17), only a single oxygen bond points upwards from completely filled layer. Under slightly oxygen deficient conditions, arriving zinc atoms will therefore be only weakly bonded and have an increased surface diffusion length. Following the 5ns laser pulse and the traveling time of the plasma a large window is available for a complete oxidation of the forming layer. Such a behavior would lead to an improvement of the surface morphology. Despite being a possible scenario, this mechanism is rather speculative, as the processes involved are not yet completely understood. It is worthwhile to investigate the influence of the oxygen partial pressure on the thin films grown, therefore, for example in the doping experiments reported in Chap. 4 series of samples are grown under different oxygen partial pressures, leaving all other parameters constant. The structural properties of homoepitaxial ZnO thin films have been studied by HR-XRD, TEM and HR-TEM. Reciprocal space maps of a selected homoepitaxial ZnO thin film grown on the O-face of a CT substrate are shown in Fig. 3.15. No splitting between the film and the substrate peak is observed in the symmetrical (002) reflex (Fig. 3.15 (a)). The film peak is as least as narrow as the peak of the substrate (compare Fig. 3.12). A modulation in the out of plane reciprocal lattice vector q⊥ is observed due to Pendellösung oscillations. This points towards a discontinuity at the interface between film and substrate, and the film thickness can be determined from these oscillations. In this particular case the thickness was determined to be 980 ± 30 nm, being in perfect agreement with the aspired thickness of 1 µm, which was controlled by the number of laser pulses during the deposition process. An empirical growth rate for ZnO grown on sapphire determined like in Fig. 3.9 (f) was used. In the asymmetric (104) reflection a finite broadening is observed (as seen in Fig. 3.15 (b)), which could be interpreted as a mismatch between the a-axis lattice constants of film and substrate, or which can originate from the mosaicity of the substrate. A broadening of the (104) is observed for some of the CT substrates (refer to Fig. 3.12). TEM images were obtained under different imaging conditions. Fig. 3.16 shows a homoepitaxial thin film under (a) ~g = (0002) and (b) ~g = (1100) imaging condition. The interface between substrate and film is seen in both images by a dark horizontal line. In the image obtained under ~g = (0002) imaging conditions dislocations are visible (dark lines in Fig. 3.16 (a)) above the 41

3. Physical properties of materials employed

(a) ZnO (0 0 2)

Log10(Intensity (counts)) 3.5

3.855

3

−1

q⊥ (nm )

3.85

2.5

3.845 3.84

2

3.835

1.5

3.83

1

3.825 3.82 −4

0.5 −2

0

−1

2

q|| (nm )

(b) ZnO (1 0 4)

4 −3 x 10

Log10(Intensity (counts))

7.69

3

7.685

2

−1

q⊥ (nm )

2.5

1.5

7.68

1 0.5

7.675 3.545

3.55

−1

q|| (nm )

3.555

Figure 3.15: Reciprocal space maps of the (a) (002) and (b) (104) reflex of a homoepitaxial ZnO thin film determined by HR-XRD. The color scale represents the log10 of the scattered X-ray intensity (counts). (Data obtained by Dr. Michael Lorenz)

42

3.2. Growth of ZnO and Mgx Zn1−x O thin films

Figure 3.16: Cross section TEM bright field images of a homoepitaxial ZnO thin film under (a) (0002) and (b) (-1100) imaging condition. Beam direction parallel to [1120]. (Images obtained by Dr. Gerald Wagner (ZnO on ZnO) and Dr. Herbert Schmid (Universität Bonn) (ZnO on sapphire))

Figure 3.17: CBED diffraction patterns as obtained (a) from measurements on an O-polar homoepitaxial ZnO thin film (b) from simulations for an O-polar ZnO crystal. The beam direction is [0110]. (Courtesy of Dr. Gerald Wagner)

horizontal line. The contrast vanishes under ~g = (1100) imaging conditions, indicating that the burgers vectors of the dislocations have to be of c type. In the inset a bright field TEM image of a ZnO thin film grown on sapphire is shown under (nachgucken) imaging conditions. The density of dislocations is significantly reduced in the homoepitaxial thin film due to the perfect lattice match with the substrate. The nature of the interface layer however remains unresolved. In order to exclude that it corresponds to an inversion boundary, within the TEM study the polarity of the thin films was determined by convergent beam electron diffraction (CBED). The fine structure patterns of the (0002), (0000) and (0002) diffraction are shown in Fig. 3.17 as obtained from (a) measurement and (b) simulation for oxygen polar ZnO. The exact congruence of the patterns confirms the O-face polarity of the homoepitaxial ZnO thin film. HR-TEM images of the interface between the film and the substrate were 43

3. Physical properties of materials employed

Figure 3.18: Cross section HR-TEM image of the interface between a homoepitaxial thin film and the substrate. Beam direction is parallel [1120]. (Courtesy of Dr. Gerald Wagner)

recorded and are shown in Fig. 3.18. It can be seen that the interface layer has an extension of one to two unit cells. It is further observed that the interface is not related to a stacking fault or any other kind of extended lattice imperfection. The nature of the interface layer remains unclear, it might however be speculated, that, as it is not due to extended defects, an increased density of points defects might play a role. These could be of vacancy type, substitutional atoms which gather at the crystal surface [150] or hydrogen which was involved in surface reconstruction [151,152] of the substrate and is introduced on interstitial site. Also intrinsic interstitial defects might be a possible origin. Regardless of the actual nature of the defects, the density be must considerable, given the contrast in the TEM images. It is important to note, that any of the defects discussed will form electronic states in the bandgap and therefore change the local density of free carriers. Depending on the nature of the defects introduced, an accumulation of donor or acceptor defects is possible. While acceptor defects would lower the Fermi-level and lead to a depletion of free electrons, donor defects would rise the Fermi-level and increase the free electron density in the vicinity of the interface. Exceeding a critical density, which is experimentally determined in Chap. 4.3 this would introduce a degenerate layer. It was reported that especially the density of group III elements is increased at the surface of O-face ZnO single crystals [150,153] . A contribution from a degenerate layer was indeed reported for such crystals [153,154] . Also the influence of hydrogen on the conductivity of a surface layer on single crystals is discussed in the literature [155–157] . The contribution of these layers to the overall conduction of the single crystal is not negligible [153,154] . The interface layer may therefore have an equally important influence on the transport properties measured in the homoepitaxial thin films. In order to understand the mechanisms involved in the growth of the homoepitaxial thin films a growth evolution study was carried out, as already conducted for the growth of ZnO thin films on sapphire in Chap. 3.2.1. Figure 3.19 shows 44

3.2. Growth of ZnO and Mgx Zn1−x O thin films

d) Figure 3.19: 2 µm×0.5 µm AFM height images of homoepitaxial ZnO thin films of different thickness. All films were deposited at a temperature of 650◦ C and a oxygen partial pressure of 0.016 mbar. A substrate prior to growth is shown in (a), films with a thickness of (b) 8 nm, (c) 25 nm and (d) 1,000 nm. (Data acquired by Heidemarie Schmidt (now Forschungszentrum Rossendorf))

the surface morphology for homoepitaxial ZnO thin films of different thickness. The substrate surfaces show vicinal steps, from which the miscut can be determined. For the substrate in Fig. 3.19 (a) a miscut of 0.1◦ was determined from the AFM height image. Figure 3.19 (b) shows the morphology of a homoepitaxial ZnO thin film of approximately 8 nm thickness. It can be seen, that the film is not completely closed, indicating an inhomogeneous nucleation of the ZnO film on the substrate. Adatoms gather around these islands and become incorporated at upsteps. However the lateral size of the randomly distributed islands is more than a factor of 10 higher than the thickness of the film grown, indicating a 2-dimensional growth mode. Also the existence of circular shaped depressions indicates a coalescence of the growth seeds, which is dominated by diffusion of adatoms to the nearest upsteps. As the film thickness increases, the layers close completely , as can be seen for the film with a thickness of 25 nm (Fig. 3.19 (c)). Meandering steps and islands of the next overlayer are visible, as typical for layer by layer growth. The miscut of the substrate is resembled by the sequence of the meandering steps. However, a stable step flow growth cannot be achieved for the combination of growth temperature and substrate miscut, as the diffusion length of adatoms is below the average step distance of the vicinal substrate (in this case roughly 125 nm). Therefore upon increase of the layer thickness hexagonal hillocks form, the height and size of the hillocks increases with increasing film thickness (Fig. 3.19).

3.2.6

Growth of Mgx Zn1−x O on ZnO substrates

For the realization of single heterostructures and quantum wells, Mgx Zn1−x O thin films were grown onto ZnO substrates. It was anticipated that sample structure and morphology would improve in comparison to Mgx Zn1−x O thin films grown on sapphire as was observed for the ZnO thin films. Therefore morphological investigations were carried out on Mgx Zn1−x O thin films grown on the O-face of CT substrates. All films discussed in this section contain a ZnO quantum well, again following the assumption that the very thin quantum well 45

3. Physical properties of materials employed

Figure 3.20: AFM height images of Mgx Zn1−x O thin films grown on ZnO. (a) 2 µm×2 µm height image of a sample grown at p(O2 ) = 0.002 mbar and Tg = 680◦ C; (b) 10 µm×10 µm height image of a sample grown at p(O2 ) = 0.002 mbar and Tg = 660◦ C; (c) 2 µm×2 µm height image of a sample grown at p(O2 ) = 0.004 mbar and Tg = 630◦ C (d) temperature progress during the deposition of the films shown in (a)–(c)

layer does not influence the final morphology. Figure 3.20 shows AFM height images of three samples grown under different deposition conditions. HR-XRD measurements confirm pseudomorphic growth for all the thin films discussed in the section. Structural data is given in Chap. 3.1.2. The sample shown in Fig. 3.20 (a) was deposited at p(O2 ) = 0.002 mbar and an approximate growth temperature of 680◦ C. It has to be mentioned that the substrate heater in the deposition chamber is operated at constant power. The temperature is monitored, however depending on the oxygen partial pressure, the heating time prior to deposition and the temperature of the outer walls of the deposition chamber the actual substrate temperature is not trivialy predictable (see Fig. 3.20 (d)). The sample grown at 680◦ C shows a high density of pits on the surface. Further a mostly vicinal arrangement of the steps edges is visible. This results are somewhat unexpected, as for similar growth conditions hexagonal hillocks are formed for homoepitaxial ZnO thin films. A similar morphology is reported in literature [158] . In that study ZnO thin films are grown homoepitaxially onto the Zn- and the O-face of ZnO single crystals. At temperatures above 850◦ C hexagonal pits are formed on the O-polar films. The Zn-face shows a stepped 46

3.2. Growth of ZnO and Mgx Zn1−x O thin films surface without pit formation. The differences are explained in the framework of Ref. [159] by the number of dangling bonds emerging from the surface of the film to bind arriving adatoms. Reducing the growth temperature leads to a layer by layer growth mode with hexagonal hillocks similar to that reported in Chap. 3.2.5. A more complete explanation is given by Chen et al. [160] and Ko et al. [161] who observed in MBE grown O-polar ZnO thin films that pits only form under zinc rich conditions. Again considering the mobility of adatoms they concluded that excess zinc adatoms are able to overcome the Ehrlich– Schwoebel barrier [118] and migrate to an higher level terrace. This leaves a depression behind. Given the stoichiometric target applied in PLD, and the higher vapor pressure of oxygen, an increased growth temperature would also increase the Zn/O ratio, explaining the observations in Ref. [158] . Further, as the vapor pressure of Mg is lower than that of Zn [92] , an increased Mg content x would result in an even increased excess of the group II constituent. This could lower the temperature required for the process to take place, as indeed observed in our experiments. Fig. 3.20 (b) shows an 10 µm×10 µm AFM height image of a sample deposited at p(O2 ) = 0.002 mbar and an approximate growth temperature of 660◦ C. A vicinal surface is visible, and the formation of pits was completely suppressed. A limited meandering and the formation of islands of the next overlayer is visible indicating that the sample is at the transition between step flow growth and layer by layer growth. The diffusion length of adatoms on the surface must roughly equal the terrace width. Fig. 3.20 (c) shows a 2 µm×2 µm AFM height image of a sample deposited at p(O2 ) = 0.004 mbar and an average growth temperature of 630◦ C. The sample shows a perfectly vicinal surface with equally spaced and ideal parallel terrace edges. It is noteworthy, that the miscut of the substrate is with 0.32◦ much higher than for the sample shown in Fig. 3.20 (b), being 0.05◦ . At least one pit is visible on the film surface, however in this case the pit most likely originates from a threading dislocation. As no steps emerge from the pits, the dislocation can only be of pure edge type. Nevertheless, the perfection of the surface is unsurpassed by any other film grown in this study. In order to understand the influence of the substrate miscut and Mg content x in more detail, a series of Mgx Zn1−x O thin films with varying Mg content x was deposited on two batches of substrates, one with a high miscut (≈ 0.3◦ ) and one with a low miscut (< 0.1◦ ). 2 µm×2 µm AFM images obtained on these samples are shown in Fig. 3.21. All samples were grown under an oxygen partial pressure of 0.002 mbar and at 650 ◦ C in order to exclude any influence of the temperature and partial pressure on the sample morphology. The samples shown in Fig. 3.21 (a) and (b) are both deposited on substrates with a miscut around 0.3◦ . Both samples show vicinal steps, very similar to the sample shown in Fig. 3.20 (c). The sample shown in Fig. 3.21 (b) with x = 0.33 shows a relative high density of pits, which are not present in the sample shown in Fig. 3.21 (a) with x = 0.23. In comparison, the samples shown in Fig. 3.21 (c) and (d) were grown on substrates with smaller miscuts of 0.05◦ and 0.1◦ , respectively. The sample depicted in Fig. 3.21 (c) is grown at conditions which favour the beginning of island formation, very much like the sample shown in 47

3. Physical properties of materials employed

Figure 3.21: 2 µm×2 µm AFM height images of Mgx Zn1−x O samples with various Mg contents grown on substrates of different miscuts. (a) x = 0.23, substrate miscut 0.31◦ (b) x = 0.33, substrate miscut 0.3◦ (c) x = 0.18, substrate miscut 0.05◦ (d) x = 0.32, substrate miscut 0.1◦ .

Fig. 3.20 (b). Both samples are grown under conditions close to the transition between step flow growth and layer by layer growth. In contrast, Fig. 3.21 (d) displays a sample which is clearly grown in the layer by layer growth mode, despite the larger miscut of the substrate. Additionally small pits are visible, as in the sample given in Fig. 3.21 (b). Interestingly both Mgx Zn1−x O thin films have a high Mg content x above 0.3. Therefore the pits can be ascribed to the piercing points of misfit dislocations introduced by the high strain between film and substrate. It is therefore also understandable, why the sample shown in Fig. 3.21 (d) is grown in the layer by layer growth mode. Upon the introduction of misfit dislocations part of the compressive strain is relaxed. Therefore the reduction of the surface diffusion barrier decreases, and the conditions favouring the step flow growth mode are not present. In contrast, the sample shown in Fig. 3.21 (b) retains the step flow growth mode, despite the higher density of pits and therefore dislocations due to the higher miscut of the substrate. In summary the following conclusions can be drawn from the growth experiments. Three main parameters influence the surface morphology 48

3.3. The perovskites BaTiO3 and SrRuO3 of Mgx Zn1−x O thin films grown pseudomorphically on ZnO: The growth temperature A higher growth temperature increases the surface diffusion length of the adatoms. If the temperature exceeds a critical value, however, the formation of pits becomes likely. The actual mechanism involved remains unclear, as the c-plane represents the absolute minimum in surface energy. It has been lined out, that a change in composition towards Zn rich condition give rise to a motion of adatoms to higher terraces, leaving the depressions behind [160,161] . The miscut of the substrate Upon increase of the miscut the distance between vicinal steps decreases, increasing the probability for an adatom to arrive at an upstep during its diffusive motion on the underlying terrace. The Mg content An increase in the Mg content increases the compressive strain imposed on the film. As already argued for Mgx Zn1−x O films grown on sapphire the surface diffusion is enhanced via reduction of the surface diffusion barrier by the compressive strain [122–124] . Therefore an effective adatom diffusion length can be defined for different Mg contents. The strain of the Mgx Zn1−x O layer can, however, be partially relaxed by the introduction of misfit dislocations. The probability for this process increases with increasing Mg content x. Also, the density of misfit dislocations increases with increasing Mgx Zn1−x O film thickness, making the effective adatom diffusion length a function of sample thickness. Additionally, as the vapor pressures of Mg and Zn differ, an increased Mg content x leads to an excess of the group II constituent, which can further give rise to the formation of pits by a mechanism involving adatom migration across upsteps [160,161] .

3.3

The perovskites BaTiO3 and SrRuO3

In contrast to ZnO and Mgx Zn1−x O, where the electric polarization is fixed to the lattice, ferroelectric materials allow a control of the electric polarization by an external electric field. Within the class of oxide ferroelectrics numberous materials crystallize in the perovskite structure. Among these BaTiO3 (BTO) is one of the most popular materials, and is often chosen as a model material. The perovskite structure is displayed in Fig. 3.22. Like for ZnO, initial experiments regarding the growth of BTO thin films were carried out. Two basic systems are regarded, BTO grown on Si substrates and on lattice matched SrTiO3 (STO) substrates. While BTO substrates exist, the quality of these substrates is questionable (Ref. [162] ). Also, the substrates are with more the 600 e very pricey, while STO substrates are available from ≈ 30 e on. Further, due to the different lattice constants a strain induced enhancement of the ferroelectric polarization of very thin BTO layers was predicted [163–165] and experimentally observed in films deposited on STO [166] . Fig. 3.23 shows 2 µm×2 µm images of the surface of as delivered STO substrates from two suppliers (Fig. 3.23 (a) Crystal GmbH [167] and Fig. 3.23 (b) 49

3. Physical properties of materials employed

Figure 3.22: Perovskite unit cell (ABO3 ) with blue A, cyan B and red O atoms. In the case of BaTiO3 the smaller Ti atom in the center of the unit cell is able to move to off center position in the low symmetry phases.

Crystec GmbH [133] ). Both substrates show stepped surfaces, however multiple different height steps are observed on the substrate. Additionally no sharp edges are seen in the AFM images. It was shown in the literature, that a substrate preparation technique is necessary to improve the quality of the substrates [168–170] . Approaches employing thermal annealing [171–173] , etching in buffered HF [168,169] and the combination of both approaches [170] are reported. A comprehensive review of the literature on substrate treatments and a summary of the experiments carried out in the framework of the present study can be found in Ref. [162] . For the preparation of the substrates used herein a combination of etching and annealing is employed, and the substrate is soaked in a water bath for 10 min prior to the etching step, as proposed in Refs. [174,175] . The annealing step was either carried out in a rapid thermal annealing chamber under an oxygen atmosphere of 700 mbar or in a conventional tube furnace in air. The annealing temperature was set to 1,000◦ C in both cases. The effects on the surfaces were investigated by AFM, 2 µm×2 µm images are shown in Fig. 3.24. In both cases vicinal substrates were prepared which show only steps of unit cell height. It is therefore concluded, that the substrates are only terminated by TiO2 layers, which gives ideal conditions for the epitaxy of perovskite thin films [169] . Additionally the morphology of (110) and (111) STO substrates 50

3.3. The perovskites BaTiO3 and SrRuO3 7,4 nm

2,6 nm

0,0 nm

0,0 nm

Figure 3.23: 2 µm×2 µm AFM images of untreated (100) STO substrates as received from (a) Crystal GmbH and (b) Crystec GmbH. (Courtesy of Stefan Schöche) 8,6 nm

7,2 nm

0,0 nm

0,0 nm

Figure 3.24: 2 µm×2 µm AFM images of STO substrates annealed in (a) a rapid thermal annealing chamber in 700 mbar O2 (b) a tube furnace in air. Both samples are annealed at 1,000◦ C. (Courtesy of Stefan Schöche)

is investigated in Ref. [162] . Both types of orientation will not be regarded in this study, as the ferroelectric polarization is parallel to the [001] direction in BTO layers at room temperature. The effects of the ferroelectric polarization at a heterointerfaces will therefore be maximal if the surface normal of the interface plane is parallel to this direction. Growth experiments summarized in Ref. [162] showed, that the optimal oxygen partial pressure for the growth of BTO thin films on STO substrates was 2 × 10−3 mbar, and the optimal temperature was 730◦ C. It has to be remarked, that the temperature is close to the attainable maximum in the PLD chamber employed, a higher structural quality could be possible, if the temperature was raised to even higher levels. Structural investigations indicated pseudomorphic growth for thin layers [176] . Within this study an evaluation of the asymmetric reflexes was not possible due to low reflection intensity, and therefore the growth mode had to be deduced from the sample morphology. Fig. 3.25 shows 2 µm×1 µm images of BTO thin films of different thicknesses grown on STO substrates under optimized growth conditions (2 × 10−3 mbar oxygen and 730 ◦ C). A transition from very well developed vicinal surfaces with unit cell height to surfaces without clear developed step edges takes place at a layer thickness of around 45–50 nm. It is concluded that the deterioration of the 51

3. Physical properties of materials employed

(a)

(c)

(e)

1,46 nm

1,02 nm

0,00 nm (b)

0,13 nm

2,48 nm

1,57 nm

0,00 nm (d)

0,70 nm

1,09 nm

3,21 nm

0,00 nm (f)

0,17 nm

Figure 3.25: 2 µm×1 µm AFM images of BTO thin films of (a) 15.9 nm, (b) 26.2 nm, (c) 43.4 nm, (d) 42.2 nm, (e) 53.9 nm, and (f ) 56.1 nm thickness grown on STO substrates. (Courtesy of Stefan Schöche)

surface is induced by the formation of misfit dislocation above the critical thickness, and that the critical thickness is roughly 45 nm, in concordance with Ref. [176] . As for the samples investigated in the following the BTO thickness is typically above 500 nm it is concluded, that the film is relaxed, and misfit dislocations exist inside the BTO films. Fig. 3.26 shows SRO thin films of roughly 30 nm thickness. A stepped surface with step edges of unit cell height can be seen for the highest deposition pressure of 0.1 mbarmbar, however holes in the films are visible. It is assumed, that these steps are parallel to the step edges of the substrate, and originate from incomplete substrate preparation [162] . More detailed work on the subject is required.

2,51 nm

9,6 nm

0,00 nm

7,3 nm

15,9 nm

10,5 nm

13,8 nm

8,4 nm

Figure 3.26: SRO thin films of roughly 30 nm thickness grown on STO substrates at 730◦ C and (a) 3 × 10−4 mbar (b) 2 × 10−3 mbar (c) 0.016 mbar and (d) 0.1 mbar. (Courtesy of Stefan Schöche)

52

3.4. Summary and conclusion

3.4

Summary and conclusion

The results of the present chapter can be summarized as follows: • The lattice constants a and c of Mgx Zn1−x O change linearly with the Mg content x in relaxed Mgx Zn1−x O layers, where a increases with x and c decreases with x. • It was shown that Mgx Zn1−x O can be grown pseudomorphically on ZnO. The c-axis lattice constant changes systematically with x. The linear relationship cps = c0 + kc,ps x with kc,ps = −0.064 Å was found from data obtained in the present study and in accordance with the literature [96,97] . • The mechanisms involved in the growth of ZnO on sapphire were investigated, a transition from initial 3D growth to 2D growth was revealed. A steady state is reached after roughly 100 nm film thickness, which allows determination of the growth rate. • The observation given in Ref. [81] that the morphology of Mgx Zn1−x O layers improves upon the introduction of a ZnO buffer layer was confirmed, and understood within the argumentation given in Refs [122–124] . The Mgx Zn1−x O layer grown on the ZnO buffer is compressively strained, which increases the surface diffusion length and therefore promotes step flow growth. • The state of the art ZnO substrate material available was reviewed, and the individual advantages discussed. Only hydrothermally grown material proved applicable in the light of transport investigations. A thermal pretreatment of the substrates necessary to produce surfaces suitable for epitaxy was discussed. • The mechanisms involved in the homoepitaxial growth of ZnO were investigated. Within the temperature range available layer by layer growth was observed rather than step flow growth. A significant reduction of the defect density was observed in comparison to ZnO grown on sapphire substrates. • The mechanisms involved in the growth of Mgx Zn1−x O on ZnO substrates were investigated. It was shown, that the temperature allowing step flow growth was lower than for pure ZnO. This was again explained by the presence of compressive strain in the films, in accordance with the argumentation given in Refs. [122–124] . Perfect vicinal surfaces were prepared, depending on the miscut of the substrate. • A substrate preparation routine was applied to commercially available STO substrates and produced perfect vicinal substrates with step edges of unit cell step height. • Vicinal BTO thin films with step edges of unit cell step height were grown up to a critical thickness of roughly 45 nm in concordance with Ref. [176] . 53

3. Physical properties of materials employed • Vicinal SRO thin films with step edges of unit cell step height were grown, however in the films investigated holes parallel to the steps of the substrate are visible. An improvement of the growth of this material will be necessary in the future.

54

Chapter 4 Properties of ZnO and MgxZn1−xO single layers For the fabrication of light emitting devices several conditions have to be satisfied. Primarily the design of the active region is of importance. High densities of electrons and holes have to be available to recombine in this region. For the sake of radiative recombination efficiency the density of defects in the active region has to be as low as possible. Further a low series resistance of the injection regions is required for high injection efficiencies. Hence, high conductivity of the layers adjacent to the active region is necessary. The photons generated in the active region have to leave the crystal, which demands additional optimization of the device. Reabsorption has to be low, and the extraction efficiency has to be high. Many of the considerations regarding this issue are of geometrical nature, but refinement in the material properties is also required. Again, low defect densities are required, as they act as absorption centers. One structure is most suitable to fulfill all the requirements listed above, a p–n heterodiode. The most simple structure applicable would be a doubleheterostructure with a higher bandgap in the injection regions than in the active region. Much more sophisticated structures can be designed, containing (multi-)quantum wells, graded injection regions, dielectric mirrors and lateral carrier confinement barriers. From these complicating device improvements only quantum wells will be regarded in the following. It is further important to know, that reliable reports on ZnO based heterostructure light emitting devices are sparse. p–n homodiodes are reported in the literature [66,177–179] , but show low recombination efficiency. Despite the inherent drawbacks in the structure itself, the low conductivity of the hole injection layer reduces the recombination efficiency. Another promising approach is the developement of more efficient heterodiodes [180] . It is therefore necessary to transfer the ability of p-type doping from ZnO to ternary systems, in the case of this study Mgx Zn1−x O. In the literature successful p-type doping of Mgx Zn1−x O with phosphorous was reported [181–184] . Like for pure ZnO numerous other dopants (all group I and all group V elements) are conceivable alternatives. Among them nitrogen and phosphorous are the most promising candidates [141,177,185] . Sucessful fabrication of p-type material employing arsenic and antimony are 55

4. Properties of ZnO and Mgx Zn1−x O single layers also reported [186,187] , but will not be regarded in the present study. Given the successful reports of p-doping of PLD grown Mgx Zn1−x O [188,189] with phosphorous and its much easier handling (it can be introduced into the target from solid powder) this route is followed in the present study.

4.1 4.1.1

Properties of homoepitaxial ZnO thin films Properties of nominally undoped homoepitaxial ZnO thin films

Structural properties The structural and morphological properties of typical homoepitaxial thin films were extensively discussed in Chap. 3.2.5. In the following section the electronic properties of nominally undoped and phosphorous doped thin films will be reported. Therefore four samples will be compared in the following. All samples were grown at 700◦ C but at four different oxygen partial pressures in the range between 3 × 10−4 and 0.1 mbar. The films were approximately 1µm in thickness. The results given in this section are partially reported in [190] . The sample morphology will not be discussed in detail here, as it is very similar to the morphology observed in Fig. 3.14 (b) and only shows a slight variation with the change in oxygen partial pressure. Figure 4.1 depicts the X-ray diffraction intensity measured on the films in the vicinity of the (002) reflection. All films show a common peak of high intensity, which is related to the substrate. The peak is shifted to zero angle for comparison of the strain in the individual layers. No peak splitting is visible for the two samples grown at the highest oxygen partial pressure. The presence of the thin film is evident from the Pendellösung oscillations best visible for the film grown at 0.016 mbar. It can therefore be concluded, that the two films grown at the highest oxygen partial pressures possess the same c-axis lattice constant as the substrate. No splitting can be seen for the in-plane reciprocal lattice vector from asymmetric reflexes, indicating pseudomorphic growth of all four thin films. Interestingly, the film peak is shifted towards lower angles for the two films deposited at the lower oxygen partial pressures. As the film is grown pseudomorphically, an increase in the c-axis lattice constant corresponds to a compressive strain. The relative change in the c-axis lattice constant is 4.3 × 10−3 and 2.3 × 10−3 for sample grown at 2 × 10−3 mbar and 3 × 10−4 mbar, respectively. The change in the lattice constant is most likely related to the increased incorporation of intrinsic defects. Several theoretical studies have shown, that the unit cell volume changes upon the incorporation of charged intrinsic defects [191–194] .

56

4.1. Properties of homoepitaxial ZnO thin films

Figure 4.1: 2Θ–ω X-ray diffraction patterns of the (002) reflection of homoepitaxial ZnO thin films grown at various oxygen partial pressures. The oxygen partial pressures during growth are marked in the graph. (Data acquired by Dr. Michael Lorenz, graphed by Alexander Lajn)

Recombination spectra Recombination spectra were detected by photoluminescence spectroscopy. The samples were subject to 325 nm excitation, as described in Chap. 2.5. The luminescence spectra of the near band edge region are graphed in Fig. 4.2. The recomination lines are labeled following the nomenclature given in Ref. [195] . In order to identify the features visible, and correlate them to their chemical origin, the spectrum obtained from the sample grown at 0.016 mbar will first be regarded, as the features are best visible in this sample. Identification of the respective lines is done by comparing the peak positions with the compilation given in Ref. [139] . The free exciton recombination is visible (labeled FXA ), along with the recombination features I0 , I3a and I6a . While the I6a line corresponds to an exciton bound to a neutral aluminum donor (Al0 X) [139] , the I0 line originates from the recombination of an exciton bound to an ionized Al donor (Al+ X) [196] . The I3a feature is related to the recombination of an exciton bound to a zinc atom on interstitial site (Zni X) [197] . The presence of this defect indicates a zinc rich stoichiometry, and a dependence on the oxygen partial pressure during growth is anticipated. For the aluminum donors, however, an extrinisic source has to exist. It is reported, that metallic impurities gather at the oxygen face of ZnO single crystals [150,153] . Also the ZnO target itself contains trace amounts of aluminium, which are most likely introduced during the sintering process. Therein the pressed ZnO powder is heated up to 1150◦ C under an 57

4. Properties of ZnO and Mgx Zn1−x O single layers

Figure 4.2: Near band edge recombination spectra of homoepitaxially ZnO thin films grown at various oxygen partial pressures. The labeling follows a nomenclature given in Ref. [195] . The chemical origin is given in the graph and explained in the text. (Spectra measured by Gabriele Benndorf, graphed by Alexander Lajn)

alumina cover. Despite the very high (2072◦ C) melting point of alumina, a finite mass transport might take place due to sublimation of the alumina. Finally a contamination of the powder used in the target preparation process can not be excluded. The chemical purity of the powder is analyzed by the supplier, and the aluminum concentration is below 2 ppm. It has however been found, that the concentration of shallow donors in homoepitaxially grown ZnO thin films is as low as 6 × 1014 cm−3 [146] , which is significantly below this level. Whatever the origin of the aluminum donors is, it is reasonable to assume, that the concentration does not change drastically with the oxygen partial pressure. A small spread might however exist, as the different atomic mass will lead to different scattering kinetics in the plasma plume compared to Zn and O. Also a stochastic scattering of the aluminum concentration is thinkable regarding the substrate material. The substrates employed in this study are however cut from nearby sectors of the same crystal, thus it seems reasonable to assume an equal distribution. Comparing the relative intensity of the I6a and I3a line, the sample grown at 0.016 mbar shows the lowest contribution from I3a which corresponds to nearly stoichiometric conditions. This is also supported by the sharper lineshape and the observation of the free exciton recombination line. In contrast the films grown at lower oxygen partial pressure show a relative increase of the I3a line, indicating Zn rich conditions. Further a blueshift of the spectra is observed for the samples grown at the lowest oxygen partial pressures. This can be understood by a shift of the fundamental band edge due to the compressive strain. In order to quantify the shift, the difference in the energetic position of the I6a line is taken with respect to the sample grown at 0.016 mbar. The blue-shifts are 2.2 meV and 1.3 meV for the sample grown 58

4.1. Properties of homoepitaxial ZnO thin films at an oxygen partial pressure of 2 × 10−3 mbar and 3 × 10−4 mbar, respectively. In order to clarify if the blue-shift is strain induced, the experimental shift is compared with theoretical values. Therefore the change in the energetic position of the free exciton emission E(XA ) is calculated following Ref. [198] : E(XA ) = EA0 + (D1 − D2 /µ)εc + b+ (D3 − D4 /µ)εc −b+ b− [(D3 − D4/µ)εc ]2 (EC0 − EA0 )−1

(4.1)

where EA0 = 3.3759 eV and EC0 = 3.4199 eV are the energies of the free A and C exciton transitions in unstrained bulk ZnO [139] . The deformation potentials used are D1 = −3.9 eV, D2 = −4.13 eV, D3 = −1.15 eV and D4 = −1.22 eV [199] ; the Poisson ratio µ = C13 /C33 is calculated using the elastic constants given in Ref. [99] . The b± are calculated following 2b± = 1 ± [δ1 − δ2 ][(δ1 − δ2 )2 + 8δ22 ]−1/2

(4.2)

where δ1 and δ2 are the crystal-field and spin–orbit-coupling splitting parameters δ1 = 38.3 meV and δ2 = −2.1 meV [199] . Taking the strain values determined from the XRD analysis, blue-shifts of 3.1 meV and 1.6 meV were calculated for the samples grown at a p(O2 ) of 2 × 10−3 mbar and 3 × 10−4 mbar, respectively. Both values a slightly above the experimentally observed blue-shift, which might relate to a partial relaxation of the films by misfit dislocations. Again PL measurements only probe a small fraction of the sample volume, approximately 100 nm from the surface, while XRD measures the whole thin film and part of the substrate. As the reduction of the strain due to misfit dislocations increases with the film thickness the results would be explained from this viewpoint.

Transport properties and defect states In order to further probe the electronic properties electric measurements were carried out. Hall-effect investigations are undertaken using the setup described in Chap.2.4. Ohmic gold contacts were sputtered onto the corners of the samples in argon. The temperature dependence of the free carrier concentration and the Hall-mobility are depicted in Fig. 4.3. Only three of the samples could be measured by means of temperature dependent Hall-effect. The sample grown at 0.016 mbar was too insulating to allow a meaningful determination of the free carrier concentration and Hall-mobility. Regarding the free carrier concentration, the samples can be phenomenologically divided into two subsets: one being dominated by rather shallow donors (group A), in this case the samples grown at lowest oxygen partial pressures, the other one with very deep dominant donors (group B), in this case the sample deposited at 0.1 mbar. For rigorousness groups A and B will be defined as the samples grown at pressures at and below 2 × 10−3 mbar and at and above 0.016 mbar respectively. The samples of group A can be measured over a wide range of temperatures and show rather high Hall-mobilities. The determination of the donor activation energy and donor and acceptor concentrations as well as an evaluation of the 59

4. Properties of ZnO and Mgx Zn1−x O single layers

1017

0.1 mbar 2×10-3 mbar 3×10-4 mbar

n (cm -3)

1016

1015

1014

1013 5

10

15 1000/T (1/K)

20

25

1.000 0.1 mbar 2×10-3 mbar 3×10-4 mbar

µH (cm 2/Vs)

800 600 400 200 0 50

100

150

200 T (K)

250

300

Figure 4.3: Temperature dependence of (a) the free electron concentration and (b) the Hall-mobility in nominally undoped homoepitaxial ZnO thin films deposited under various oxygen partial pressures. The solid lines represent fits to the data, as described in the text.

60

4.1. Properties of homoepitaxial ZnO thin films scattering processes limiting the Hall-mobility is possible in these samples. In contrast the samples with deep dominant donors can only be measured in a rather small range of high temperatures, revealing only a limited amount of data. While the determination of the donor activation energy is still possible, the scattering processes limiting the Hall-mobility can not be assessed in detail. Especially the influence of ionized impurity scattering which limits the mobility at low temperatures is not revealed. As described in Chap. 2.4 the determination of the acceptor concentration is only possible from the mobility if this low temperature region is measurable, and the mobility in this region is not affected by additionally complicating conductivity contributions. The determination of the donor and acceptor concentration is therefore limited to the evaluation of the temperature dependence of the free carrier concentration, which can only yield both values in certain cases (refer to Chap. 2.4). It is possible however to understand the mechanisms involved. As the PL measurements have shown, shallow donors like aluminum and interstitial zinc are present in all four samples, however in different concentrations. The fact that the shallow donors can be observed in the Hall-effect measurements in the samples of group A shows that they dominate the Fermi-level. In contrast, in the sample grown at 0.1 mbar only a deep donor is visible, the Fermi-level must therefore lie below the levels of the shallow donors at all temperatures. This can be explained by a significant increase in the compensation, the concentration of acceptors has to exceed the concentration of shallow donors. As discussed before, the concentration of aluminum donors is expected to be roughly constant in all four films. A change in the ratio between shallow donors and acceptors can therefore only be explained by a change in the sample stoichiometry. The sample grown at 0.016 mbar therefore shows a behaviour typical for the samples of group B. The conductivity in this sample is even lower than that in the sample grown at 0.1 mbar, most likely due to the higher compensation ratio. For the samples of group A the acceptor concentration was determined from the low temperature part of the Hall-mobility. The Hall-mobility in all samples was modeled employing the exact numerical solution of the Boltzmann-transport equation including inelastic scattering effects and the self consistently determined Hall-factor, as described in Chap. 2.4. All intrinsic scattering processes are left unaltered. The solid line shown in Fig. 4.3 (b) gives the best fit to the experimental data, with the acceptor concentration NA being the only free parameter. In an iterative sequence the drift mobility is calculated, and the experimental Hall-mobility is converted into the drift mobility by the Hallfactor obtained. This is repeated until a self consistent solution is obtained. Finally the Hall-mobility is calculated from the drift mobility and Hall-factor obtained. For the sample grown at 2×10−3 mbar an almost perfect coincidence between the experimental and theoretical data can be obtained, indicating that no additional scattering processes contribute to the mobility, and no parallel conduction takes place in layers with different material properties. The scattering mechanisms involved equal that present in a single crystal, indicating the superior quality of the film compared to heteroepitaxially grown ZnO thin films. The mobility in the film exceeds 855 cm2 /Vs. For the sample grown at 61

4. Properties of ZnO and Mgx Zn1−x O single layers Table 4.1: Donor activation energy, donor and acceptor concentration as obtained from Hall-effect investigations (index H), net dopant concentration Nt = ND − NA measured by capacitance voltage spectroscopy (index C) and donor activation energy and capture cross section (in cm2 ) as determined by Arrhenius evaluation of thermal admittance spectroscopy (index T) for homoepitaxial ZnO thin films grown at various oxygen partial pressure (given in mbar). Only the most shallow donor is tabulated as would be seen by Hall-effect measurements. All concentrations are given in 1017 cm−3 , activation energies in eV.

p(O2 )

ED,H

ND,H

0.1 0.016 2 × 10−3 3 × 10−4

350 ± 50

70 ± 30

29 ± 1 34 ± 6

3.4 ± 0.2 0.9 ± 0.2

NA,H

0.24 ± 0.01 0.25 ± 0.05

NN,C < 0.003 0.01 0.07 0.6

ED,T

σT

37 ± 1 42 ± 3

2 × 1016 1 × 1016

3 × 10−4 mbar an equally good fit is not possible, which gives rise to the assumption that additional scattering at crystal imperfections takes place which is not accounted for in the model. This is supported by the broadening of the XRD diffraction curve for this sample (compare Fig. 4.1), which might give a hint towards the presence of misfit dislocations. These would represent onedimensional scattering centers which impede the transport. Nevertheless the acceptor concentration could be estimated from the low temperature flank of the mobility. All values are summarizes in Tab. 4.1. The temperature dependence of the free carrier concentration was modeled using a simple one donor charge balance equation with compensation. The data for the sample grown at 2 × 10−3 mbar was corrected by the Hall-factor as obtained from the mobility fit, prior to the analysis. Solid lines in Fig. 4.3 (a) represent the modeled results. The donor activation energies and concentrations are summarized in Tab. 4.1. In order to apply capacitance spectroscopic methods rectifying PtOx contacts are formed on the four samples. Pt was reactively sputtered in and Ar/O2 mixture, as described in Chap. 2.6. The contacts were capped by a metallic Pt layer sputtered in pure Ar afterwards to form an equipotential surface. Capacitance–Voltage and thermal admittance spectroscopy measurements were performed on the contacts. From the C–V measurements the net dopant concentration was derived and is tabulated in Tab. 4.1. For the samples of group A the net dopant concentration can be very well explained by the shallow donor and the acceptor concentration as determined by Hall-effect, it equals there difference within the experimental error. The situation is significantly different for the sample grown at 0.1 mbar, where the values obtained differ by four orders of magnitude. Several facts have to be considered explaining this drastic difference. First of all the determination of both values is subject to large experimental error due to its low value in the C–V case and the low conductivity in the case of the Hall-effect measurement. Additionally the low number 62

4.1. Properties of homoepitaxial ZnO thin films

Figure 4.4: Temperature dependence of capacitance of PtOx Schottky diodes fabricated from homoepitaxial ZnO thin films. (Courtesy of Alexander Lajn)

of points obtained in the temperature dependent Hall-effect measurement increases the uncertainty of the results obtained from the numerical evaluation. It is also important to note, that the simple assumption of a one donor charge balance equation is not valid in the case discussed here, as at least two types of shallow donors are present additional to the deep donor observed. While this does not introduce a large error for the shallow donors in the samples of group A which influence the Fermi-level, the error is considerable in the samples of group B, where numerous donors are already ionized before the ionization of deep donors. Finally, the acceptor concentration could not be determined from the Hall-effect data. It is however anticipated that the compensation is very high, and values above 95% were reported [47,200] . The net dopant concentration will therefore be significantly reduced in comparisson with the donor concentration. Figure 4.4 depicts the temperature dependence of the capacitance of the Schottky diodes fabricated from the samples. Again a clear distinction between samples of group A and samples of group B is visible. While for the samples of group A two steps in the capacitance can be seen, only a single step is visible for the samples of group B. The first step, visible at temperatures around 50 K corresponds to a resonance between the excitation frequency and the emission rate of the shallow donors, while the second step corresponds to the resonance between the excitation frequency and the emission rate of the deep donors. A emission from the shallow donors is not observed in the samples of group B, as these donors are ionized at all temperatures, and no recharging takes place. The activation energy of the shallow donors and two deep donors were deter63

4. Properties of ZnO and Mgx Zn1−x O single layers mined for the samples of group A by a conventional Arrhenius evaluation (not depicted here) and are tabulated in Tab. 4.1. Additionally the activation energy of the deep donor in both samples could be evaluated and is 410±30 meV and 244±10 meV for the sample grown at 2 × 10−3 mbar and 3 × 10−4 mbar, respectively. The latter is similar to the previously reported defect L2 [201] . A donor with an activation energy of 410±30 meV has not been reported to the best of my knowledge, however considering the comparatively large error bar, it might be related to the level E3’ with an activation energy of roughly 370 meV [202] . Regarding the shallow donors a difference between the activation energy obtained by TAS and Hall-effect is observed. The activation energy determined by Hall-effect is always smaller than that from the TAS analysis. This might originate from an inhomogenous distribution of the donors within the sample. As TAS probes a rather small sample volume at the edge of the space charge region introduced by the Schottky contact, the Hall-effect measures essentially the whole sample. In Hall-effect, however, one measures a weighted average over the conductivities and magnetoelectric properties of the sample, with the largest contribution from layers with the highest conductivity. It is reported, that metallic impurities gather at the surface of ZnO single crystals, therefore inducing a layer of higher conduction, up to degeneracy [150,153] . In such a layer (assuming it not to be degenerate, as this would give clear signatures in the Hall-effect measurement), the donor activation energy might be reduced due to beginning overlap of the donor wave functions. This scenario receives additional support by the results of the PL measurements, which resolve the presence of both aluminum and zinc interstitial related donors, while only a single level is observed in TAS, most likely zinc interstitial related. Following Haynes rule, an activation energy of 38.1 meV is anticipated from the PL measurements [196] , being in very good agreement with the values determined by TAS.

4.1.2

Properties of phosphorous doped homoepitaxial ZnO thin films

As outlined before phosphorous in one of the most promising candidates for achieving reliable p-type conductivity. Several publications report on p-type doping with phosphorous [203–207] , and even ZnO homojunction diodes were reported [205,208,209] . The investigated nominally undoped homoepitaxial ZnO thin films show very high purity, significantly reducing the influence of background doping. These samples are therefore perfectly suited to perform a doping study. Phosphorous doped thin films were deposited from targets containing 0.01 wt.%, 0.1 wt.% and 1 wt.% P2 O5 added to the ZnO powder. From now on these samples will be labeled series I, series II and series III. For each target samples were grown at four different oxygen partial pressures, namely 3× 10−4 , 2 × 10−3 , 0.016 and 0.1 mbar, the same pressures as for the nominally undoped samples shown in the previous section. For all samples a thickness of 1µm was deposited. Some of the results presented in this section were published previously [210–213] . 64

4.1. Properties of homoepitaxial ZnO thin films Morphology Figure 4.5 shows AFM height images obtained from samples of series I grown at different oxygen partial pressures. A clear 2-dimensional growth is observed for all samples, however the actual growth mode differs. The samples grown at oxygen partial pressures below 0.1 mbar show the formation of islands of 200– 400 nm diameter. Island growth is present in this case. The height and shape of hillocks differs somewhat from the clearly hexagonal shapes observed in the case of undoped homoepitaxial ZnO films. For the sample grown 0.1 mbar a much flatter surface is observed and vicinal steps are visible. Meandering of this steps and the formation of nucleation islands of the next overlayer are visible. Nevertheless, as with a film thickness of 1µm no transition to island growth is observed, it is concluded, that the growth mode must be at the transition between layer by layer growth and step flow growth. Structural and chemical properties XRD and HR-XRD measurements were carried out to reveal the structural properties of phosphorous doped homoepitaxial ZnO thin films. Fig. 4.6 depicts reciprocal space maps of the (002) and (104) reflection of the sample grown at 0.1 mbar from series I. No peak splitting is observed in any of the reciprocal space maps. A small asymmetric broadening of the reflections is visible, which is ascribed to minor mosaicity and the finite crystallite size of the substrate. Results of 2Θ–ω X-ray diffraction measurements are graphed in Fig. 4.7. In Fig. 4.7 (a) the diffraction patterns from series I are compared. For all samples the substrate peak is visible. Only for the film deposited at 0.016 mbar a splitting between the film and the substrate peak is visible. The lattice constant of all other films in this series equals that of the substrate. Pendellösung oscillations are visible, proving that the film peak indeed overlaps with that of the substrate and allowing the determination of the film thickness, which equals 1 µm within the experimental error. For the film grown at 0.016 mbar an expansion of the c-axis lattice constant of 270±15 ppm can be determined. This gives indication that the incorporation of phosphorous expands the ZnO lattice. As the film is grown pseudomorphic an expansion of the c-axis lattice constant corresponds to an compressive in-plane strain. This is supported by a comparison of the lattice constants of the films of the individual series as depicted in Fig. 4.7 (b). It can be seen that the c-axis lattice constants expands further with increasing phosphorous content in the target. It is also visible that the lattice constant differs within series III, that one with the highest phosphorous content. The largest splitting is observed for the smallest oxygen partial pressure. This behavior infers a dependency of the phosphorous content on the oxygen partial pressure. Also, the growth mode changes from pseudomorphic to relaxed as the phosphorous content increases [212] . Both the a-axis and c-axis lattice constant are expanded with respect to the lattice constant of the substrate, giving clear evidence of the expansion of the lattice with increasing phosphorous content. 65

4. Properties of ZnO and Mgx Zn1−x O single layers

2 nm

(a)

0

µm

0 2 2 nm

0

µm

0 2 2 nm

0

µm

2

(b)

(c)

0

Figure 4.5: 2 µm×1 µm AFM height images for samples from series I. The samples were deposited at (a) 0.1 mbar (b) 0.016 mbar and (c) 2×10−3 mbar. (Data measured by Dr. Heidemarie Schmidt (now Forschungszentrum Rossendorf))

66

4.1. Properties of homoepitaxial ZnO thin films

(a) ZnO:P (0 0 2) 3.85

Log10(Intensity (counts)) 3.5 3 2.5

−1

q⊥ (nm )

3.845

3.84

2 1.5

3.835

1 0.5

3.83

−7

−6

−1

q⊥ (nm )

(b) ZnO:P (1 0 4)

−5

−1

−4

q|| (nm )

−3 −3 x 10

Log10(Intensity (counts))

7.684

3

7.682

2.5 2

7.68

1.5

7.678

1

7.676

0.5

7.674 3.55

3.552 3.554 3.556 3.558 −1

q|| (nm )

3.56

Figure 4.6: HR-XRD reciprocal space map of the (a) (002) and (b) (104) reflection of a homoepitaxial ZnO:P sample from series I deposited at 0.1 mbar. The color scale represents the log10 of the scattered X-ray intensity (counts). (Data obtained by Dr. Michael Lorenz)

67

4. Properties of ZnO and Mgx Zn1−x O single layers

Intensity [cps]

10,000

p(O2) [ mbar ] 0.1 mbar 0.016 mbar 2×10-3 mbar

1,000

3×10-4 mbar

100

34.30

34.35

34.40

34.45

34.50

Intensity [cps]

2Θ [°]

4

10

E1328 0.01?P E1320 0.1?P E1324 1? P E1325 1? P

3

10

2

10

1

10

34.0

34.1

34.2

34.3

34.4 34.5 2Theta [°]

Figure 4.7: (a) 2Θ–ω X-ray diffraction patterns of the (002) reflection of homoepitaxial ZnO:P thin films of series I grown at various oxygen partial pressures. The oxygen partial pressures during growth are marked in the graph. (b) 2Θ–ω X-ray diffraction patterns of the (002) reflection of homoepitaxial ZnO:P thin films from different series with different splitting in the film and substrate c-axis lattice constant. (Data obtained and (b) graphed by Dr. Michael Lorenz.)

68

4.1. Properties of homoepitaxial ZnO thin films Table 4.2: Summary of all impurities detected by the PIXE experiments in the samples of series I, and their apparent concentrations

p(O2 )(mbar) impurity

0.1

0.016 2 × 10−3 3 × 10−4 concentration in weight ppm

Al Fe Si P S Cl K Ca Cr Mn

1390 ± 530 3070 ± 130 3490 ± 490 320 ± 110 780 ± 170 170 ± 60

2980 ± 180 2530 ± 460 830 ± 280 1000 ± 300 310 ± 70

260 ± 60

130 ± 60

2200 ± 210 3140 ± 600 780 ± 290

90 ± 40 130 ± 70 240 ± 90

1450 ± 500 2480 ± 130 3020 ± 340 840 ± 140 350 ± 80 2080 ± 130 1500 ± 80 490 ± 40

RBS channeling experiments were carried out at the LIPSION ion beamline as described in Ref. [214] . For comparison the channeling spectrum of a thermally pretreated CT substrate was recorded. A channeling axis perpendicular to the sample surface was observed only for the substrate and the sample of series I deposited at 0.1 mbar oxygen partial pressure. This gives evidence for the single crystalline nature of this ZnO:P thin film. It further indicates a high density of lattice imperfections for the films grown at lower oxygen partial pressures, incorporated most likely due to the phosphorous doping. The spectra of the substrate and the sample grown at 0.1 mbar oxygen partial pressure are depicted in Fig. 4.8 (a). A χmin as low as 0.034 can be seen for the film grown at 0.1 mbar oxygen partial pressure which is comparable to the value obtained for the substrate (0.033), indicating very good crystal quality (cf. for pure single crystalline Si χmin = 0.03). Within this structural study the chemical composition of the samples of series I was also evaluated. The phosphorous content of the ZnO:P thin films of series I was determined by PIXE experiments and is graphed versus the oxygen partial pressure in Fig. 4.8 (b). The phosphorous content in the samples differs significantly from the nominal concentration in the target (nominally 0.01 wt% P2 O5 , thus ≈ 43 µg/g P in ZnO). PIXE investigations of the target revealed, that the concentration in the ablated region is 45±11 µg/g P in ZnO in line with the expected concentration. The concentration of phosphorous in the films is significantly higher, and further depends on the oxygen partial pressure. The actual concentrations are only slightly above the detection limit of the PIXE analysis and therefore subject to a relative large error, which is depicted in Fig. 4.8 (b) as well. The apparent concentration in the film exceeds that of the target by a factor of 5 to 20, in contradiction to a previous analysis [215] , which resulted in a constant phosphorous transfer ratio between the target and the film of 0.5. It has to be mentioned that the phosphorous 69

4. Properties of ZnO and Mgx Zn1−x O single layers

Sample thickness [µm] 12

8.4

4.8

1.2

0

0.8

p[O2] = 0.1 mbar substrate

0.6 0.4

sample surface

Channeling yield χ

1.0

0.2 0.0 200

300

400

500

600

Phosphorous content [µg/g]

Channel number

1,200 1,000 800 600 400 200 0 0.0001

0.0010

0.0100

0.1000

p(O2) [mbar]

Figure 4.8: (a) Channeling yield χ as extracted from RBS measurements on the homoepitaxial ZnO:P film from series I deposited at 0.1 mbar compared to a typical CT substrate after thermal pretreatment. (b) Phosphorous content of of the samples of series I as a function of the oxygen partial pressure applied during growth. (Data obtained by Christoph Meinecke)

70

4.1. Properties of homoepitaxial ZnO thin films concentrations in the previous analysis was at least by a factor of 20 larger than that in the present investigation. Further within this study the concentration of other impurities was deduced from the PIXE data, and several unintentionally introduced elements were found in the samples of series I. Among them the most prominent detected were Fe and Si. Further Al, S, Cl, K, Ca, Cr and Mn were detected in small concentrations, or not for all samples. Traces of Ti, V, Ni, Co and Cu were detected, but their concentration is below the detection limit. The concentrations of all the impurities are given in detail in Tab. 4.2. The results give further insight into the origin of the impurities. The high fluctuation of Al between the samples is unexpected. From the possible mechanisms of aluminum incorporation discussed in Chap. 4.1.1 the substrate therefore becomes the most likely source. Other origins are not excluded, but their contribution must be below the detection limit of the PIXE analysis. Rather high concentrations of both iron and silicon are observed. There incorporation can easily be understood. The silicon enters the target during the target preparation, where the powder is homogenized in an agate mill. Iron most likely originates from the substrate holder in the PLD chamber, which like most of the parts of the chamber consists of steel and is subject to the same temperatures as the substrate. This is also the most probable origin of Cr and Mn, which are used in steel refinement. For the other impurities, it is remarkable to note that all of these elements take share in biological processes, especially Cl, Ca and K and might therefore be introduced by the sample handling. Recombination spectra Photoluminescence spectra of the near band edge region of series I are depicted in Fig. 4.9 (a). Again, like in in the undoped series (see Chap. 4.1.1) the spectra are dominated by the lines I6a and I3a . Their ratio is very similar to that in the nominally undoped films. This indicates, that the film stoichiometry is not strongly altered by the P content in the films. It further shows, that the high aluminum concentrations measured by the PIXE analysis cannot be homogeneously distributed throughout the affected films, which would most likely change the height and shape of the I6a peak in the samples with high aluminum concentrations, namely the samples deposited at 0.1 mbar and 3 × 10−4 mbar. Further the spectrum of the sample deposited at 0.016 mbar is blueshifted by 1.9 meV. In principle the blue-shift can again be explained by the compressive strain in the sample (see Chap. 4.1.2). However the magnitude of the strain is to small to explain the blue-shift completely, it can only account for around 20%. It is also interesting to note that the features I0 and the free exciton recombination peak can not be observed for the sample grown at 0.016 mbar, which were present in the undoped sample grown at the same pressure (refer to Chap. 4.1.1). This is reasoned by the overall reduction of the luminescence intensity, which is reduced by over three orders of magnitude in the phosphorous doped samples of series I (not shown here) It has to be concluded that additional recombination centers are present in the phosphorous doped films. Therefore luminescence spectra of all three series including the visible re71

4. Properties of ZnO and Mgx Zn1−x O single layers I6

I3a

PL intensity [arb.u.]

0.1 mbar

0.016 mbar

2×10-3 mbar 3×10-4 mbar

3.34

3.35

3.36

3.37

3.38

Energy [eV]

0.01 wt.% P2O5 10 K

0.1 wt.% P2O5 10 K

10-1 mbar

10-1 mbar

1 wt.% P2O5 10 K

1.6 × 10-2 mbar 2 × 10-3 mbar

3×

2 × 10-3 mbar

3 × 10-4 mbar

2 × 10-3 mbar

3 × 10-4 mbar

10-4 mbar

a) 1.5

1.6 × 10-2 mbar

1.6 × 10-2 mbar

CL intensity (arb. u.)

CL intensity (arb. u.)

CL intensity (arb. u.)

10-1 mbar

b) 2.0

2.5

energy (eV)

3.0

3.5

1.5

c) 2.0

2.5

energy (eV)

3.0

3.5

1.5

2.0

2.5

3.0

3.5

energy (eV)

Figure 4.9: (a) Near band edge region of low temperature PL spectra of the samples of series I. (Data obtained by Gabriele Benndorf) (b) Near band edge and deep emission CL spectra of all three series. (Data obtained by Jan Zippel)

gion were obtained by means of cathoduluminescence and are depicted in Fig. 4.9 (b). Four main luminescence features are visible: the near band edge luminescence in the UV region (nbe), as discussed previously, a blue–violet luminescence band (b–v) centered between 2.8 and 3.0 eV, a green luminescence band (g) centered around 2.5 eV and a red–orange luminescence band (r–o) observed between 1.8 and 2.0 eV. All of these luminescence features were observed previously. The b–v luminescence was ascribed to a donor acceptor transition probably involving the zinc vacancy [206,216] . The green luminescence is commonly ascribed to two possible origins, copper on zinc site CuZn and the oxygen vacancy VO [217–219] . The r–o luminescence was proven to be acceptor related, and is tentatively assigned to oxygen on interstitial site Oi [220] . The 72

4.1. Properties of homoepitaxial ZnO thin films high intensity of the deep luminescence gives an explanation for the quenching of the nbe luminescence, as a number of alternative recombination channels is present. The r–o luminescence is observed in all of the samples investigated and almost independent of the oxygen partial pressure applied during growth. Again, like in the undoped samples, the samples of the three series discussed can be collected in two groups, group B grown at oxygen partial pressures of 0.016 mbar and above and group A grown at oxygen partial pressures of 2×10−3 and below. While in the samples of group A the b–v luminescence is dominant, the samples of group B are dominated by the nbe luminescence, apart from the samples of series III, which all show a significant contribution to the luminescence in the nbe region. The appearance of the b–v luminescence in the samples grown at the smallest oxygen partial pressures is somewhat disturbing, as if it is related to the zinc vacancy its formation should be favored under oxygen rich conditions. Nevertheless, regarding the broad luminescence it is most likely that this feature is related to a donor acceptor pair recombination. The observation of this defect therefore must be related with the formation of a more shallow acceptor which is not present in the samples of group B. This acceptor might be related to phosphorous, however the zinc vacancy cannot be ruled out completely, as this defect has the highest probability among acceptor defects to form upon a high Fermi-level especially under oxygen rich conditions [191–194,221,222] . Even under zinc rich conditions it is very likely to be formed if the Fermi-level is high, but results of ab-inito studies vary regarding this issue. Some studies identify the zinc vacany as the most probably formed defect under the presence of a high Fermi-level [191,193,194] . Such conditions are present in the samples of group A, as proven by the transport measurements and space charge region spectroscopy given in the following section. It is also evident, that phosphorous doping must play a role in the formation of the acceptor, as it is not present in the nominally undoped films. It however remains unclear, if phosphorous itself takes part in the acceptor on a microscopical level, or if the lattice distortion or the shift in the Fermi-level introduced by the phosphorous incorporation promotes the formation of the acceptor. More detailed investigations will be necessary to understand the behavior observed. Transport properties and defect states To further evaluate the influence of the incorporation of phosphorous on the electronic defect structure Hall-effect and TAS measurements were carried out on the samples. In order to validate the approach of Hall-effect measurements the conductivity of typical homoepitaxial ZnO:P thin films is compared to the conductivity of the substrate, as depicted in Fig. 4.10. It can be clearly seen, that the conductivity even of the film with the lowest conductivity exceeds that of the substrate by more than 3 orders of magnitude at room temperature. As the substrates are affected by a high degree of compensation the activation of deeper donors takes place in the substrate than in the films. This leads to a faster decrease of the substrate conductivity towards low temperatures compared with the thin films. The conductivity of the substrates further decreases by several orders of magnitude in the annealing process preceding the growth. 73

4. Properties of ZnO and Mgx Zn1−x O single layers 103

σ [Ω-1cm-1]

102 Thin film (high conductivity) Thin film (low conductivity) Substrate (as received)

101 100 10-1 10-2 10-3 10-4 2

4

6

8 10 1000/T [1/K]

12

14

16

Figure 4.10: Conductivity of two typical homoepitaxial ZnO:P thin films compared to the conductivity of a CT substrate. Two samples from series I were chosen, the one with the highest and the one with the lowest conductivity. Table 4.3: Donor and acceptor concentration and donor activation energy in ZnO:P thin films.

p(O2 )(mbar) ED (meV) ND (1016 cm−3 ) 0.1 0.016 2 × 10−3 3 × 10−4

>8 > 50 36 ± 4 34 ± 5

200 ± 50 >5 35 ± 3 43 ± 4

NA (1016 cm−3 )

ED (TAS) (meV)

unknown >1 2.6 ± 0.1 1.5 ± 0.1

unknown 25±5 19 ± 5 20 ± 5

It has to be pointed out however, that the composition of the substrates varies (as outlined in Chap. 3.2.3), between the batches and even within one individual batch. This of cause influences the transport properties. Therefore the substrates are measured at room temperature before growth of the thin films and compared to the data of the thin films. Hall-effect measurements revealed the mobility and free carrier concentration in the samples of series I, which are given in Fig. 4.11. A very good qualitative agreement exists between the transport properties of these films and the nominally undoped homoepitaxial thin films discussed in Chap. 4.1.1 (compare Fig. 4.3) for both the mobility (Fig. 4.11 (a)) and the free carrier concentration (Fig. 4.11 (b)). Maximum mobilities of more than 800 cm2 /Vs are reached in the film grown at 2 × 10−3 mbar. Again a modeling of the mobility was done employing an exact self consistent solution of the Boltzmann transport equation using the acceptor concentration in the films as only free parameter. However an equally good agreement of the calculated and measured data as 74

4.1. Properties of homoepitaxial ZnO thin films

1.000

µH [cm2/Vs]

1.000

µH [cm2/Vs]

800 600

100

10

1 30

50

70

100

200

300

T [K]

400

p(O2) [mbar]

3×10-4 2×10-3 0.016 0.1

200 0 0

100

200 T [K]

300

400

1018

nH (cm-3)

1017

p(O2) [mbar]

16

10

0.1 2×10-3

0.1 corrected

3×10-4

fit 3×10-4

0.016

fit 2×10-3

fit 0.1

1015

1014 0

5

10

15

20

25

1000/T (1/K)

Figure 4.11: Hall-mobility (a) and free carrier concentration (b) as a function of temperature in the thin films of series I.

75

4. Properties of ZnO and Mgx Zn1−x O single layers for the undoped film grown at 2 × 10−3 mbar was not achieved. The reasoning is comparatively simple, as the partial contribution of a highly conductive layer is observed for these samples. Its influence can be easily seen from the temperature dependence of the free electron concentration (see Fig. 4.11 (b)), where at low temperatures a higher free carrier concentration is observed from the experimental data than it would be theoretically expected. This behavior is most pronounced for the sample grown at 0.1 mbar, where a correction following Refs. [223,224] was employed to separate the characteristic transport parameters of the non degenerate layer. It is however visible, that a complete correction of the influence of the degenerate layer was not possible, which can be understood by the fact, that the dopant concentration does not drop sharply at a imaginary interface, as assumed in the model [223,224] . The dopant concentration will therefore be high enough in the bulk of the film, leading to an overlap of the donor wave functions and to a reduction of the apparent dopant concentration. For the films of series I grown at oxygen partial pressures below 0.1 mbar the correction scheme was not applied, as the determination of the properties of a degenerate layer was not unabigiously possible. Also, the influence of the correction would only be of minor importance for the determination of the donor ionization energy, as it contributed to the free carrier concentration measured only at low temperatures. A significant influence on the low temperature mobility however exists, which can not be corrected within the model and with the experimental data available. An overestimation of the acceptor concentration is therefore possible, which in turn will lead to an uncertainty in the donor concentration identified. The donor activation energies and cocentrations were determined from the free carrier concentration using a single donor charge balance equation and are given in Tab. 4.3. Also the donor activation energies as determined by TAS are tabulated. Remarkable differences are visible between these values indicating that again both methods do not probe the same sample regions. This again supports the assumption that the distribution of donors in the films is not homogeneous. Hall-effect measurements of the samples of series II and III revealed that these samples were degenerately doped in the 1019 cm−3 region. Temperature depended measurements were carried out on these samples and again revealed that the high dopant concentrations observed were not homogeneously distributed. A distinct temperature dependence of both the mobility (Fig. 4.12 (a)) and the free electron concentration (Fig. 4.12 (b)) is observed. Such a behavior is not expected if the whole layer is degenerately doped. Only a small layer in the sample can show this high carrier concentration, and its influence can be separated using the correction scheme discussed before [223,224] . Fig. 4.12 (a) shows the mobility and Fig. 4.12 (b) free carrier concentrations of the samples of series II group A as measured and after the application of the correction scheme. It is visible that the transport data of the bulk of the film can be largely reconstructed. The abilities of the correction scheme are particularly impressive regarding the mobility, which increases by one order of magnitude. Also, the free carrier concentration reduces by roughly one order of magnitude, 76

4.1. Properties of homoepitaxial ZnO thin films

1.000 2×10-3 2×10-3 corrected 2×10-3 annealed 3×10-4 3×10-4 corrected

µH (cm 2/Vs)

3×10-4 annealed

100

10 30

50

70 100 T (K)

200

300

1020

n (cm -3)

1019 1018

2×10-3 2×10-3 corrected 2×10-3 annealed

1017

3×10-4 3×10-4 corrected 3×10-4 annealed

1016 1015 1014 0

10

20 30 1000/T (1/K)

40

50

Figure 4.12: Hall-mobility (a) and free carrier concentration (b) as a function of temperature in the thin films of series II, group A.

77

4. Properties of ZnO and Mgx Zn1−x O single layers 101

ρannealed (Ωcm)

100 10-1 10-2 10-3 10-4 10-5 10-5

10-4

10-3

10-2

10-1

100

101

ρas-grown (Ωcm) Figure 4.13: Resistivity of homoepitaxial phosphorous doped ZnO thin film as grown and after annealing. Meaning of the symbols: Series I (red ), series II (blue) and series III (green). Oxygen partial pressures during growth 0.1 mbar (•), 0.016 mbar (N), 2 × 10−3 (H) and 2 × 10−3 ().

still remaining in the high 1018 cm−3 to 1019 cm−3 region, which should still be very close to the degenerate limit. Despite the remarkable success of the correction scheme, a full reconstruction of the bulk properties remains beyond its abilities. This is explained by the comparatively simple model used. Additional complicating elements like a temperature dependence of the mobility in the degenerate layer and a inhomogeneous distribution of the dopants in the degenerately doped region were considered [153,154,225] , however these approaches introduce further unknown parameters. The determination of these parameters is not trivial, if possible at all, from the Hall-effect data available in this study. Certain parameters, like the distribution of dopants in the film can not be determined unambiguously. It is therefore questionable if the data obtained by such an approach would give a better representation of the physical reality. Such a reasoning is also followed in the paper by D. C. Look introducing some of these improvements in the correction scheme [154] and it is concluded that a Hall-effect analysis alone can not yield the dopant profile. In the present work a different approach will be followed to improve the informative values of the Hall-effect measurements, refer to Chap. 4.2. As the aim of this study is the exploration of the properties of homoepitaxial phosphorous doped ZnO thin films, and the assertion of the applicability of phosphorous as a p-type dopant in this layers a short review of the literature will be given at this point. Several authors have reported the transition to p-type material with phosphorous doping, both in heteroepitaxial and homoepitaxial samples [205–207] . However, all of these samples showed n-type 78

4.2. Evaluation of the transport properties by mobility spectrum analysis conductivity in the as grown state. A thermal annealing step at temperature between 800◦ C and 900◦ C was necessary in all cases to activate the phosphorous related acceptors and transform the samples into p-type material. Such annealing experiments were likewise carried out within this study. The material was exposed to a 700 mbar oxygen atmosphere at 850◦ C for 5 minutes. The transport data measured after the annealing step are given for the samples of series II group A in Fig. 4.12. The degenerate layer was completely removed. However a transition to p-type conductivity is not observed. Also the concentration of acceptors can not be higher than the concentration of shallow donors, as can be inferred from their influence on the free carrier concentration. The influence of the annealing process on the transport properties was studied and is summarized in Fig. 4.13. The resistivity of the films prior to and after the annealing are depicted. No change of the carrier type is observed in any of the samples. The change is most distinct for the samples having a high initial resistance. In this case the resistance decreases by at least three order of magnitude, which must originate from the annealing of acceptor defects. For some samples a slight increase of the resistance is observed, however in this case the effect consists mostly of the annealing of the defects necessary to form the degenerate layer, as discussed for the samples of series II. If at all a tendency towards increased acceptor concentration is observed this occurs for the samples of group B, grown at high oxygen partial pressures.

4.2

Evaluation of the transport properties by mobility spectrum analysis

As outlined above, the determination of the mobility and free carrier concentration from Hall-effect measurements in ZnO samples can be complicated by the presence of several conducting paths with different mobilities. A separation of the individual contributions to the overall transport properties can be done from their different dependence on temperature [153,154,223–225] . This approach however requires detailed theoretical knowledge of the temperature dependence of the individual contributions. The applicability of this approach is typically limited to two-layer system, and even in this case several assumptions have to be made on the nature of the transport processes involved. Therefore other possibilities for the separation of multiple transport channels have to be considered. The most promising approach employed in order to extend the informational value of Hall-effect measurements in multilayer system is the application of magnetic field dependent measurements. All of these approaches rely on the fact that the components of the conductivity are weighted sums of the different conduction paths in the sample. Rather simple approaches include three distinct conduction paths with different mobilities and carrier concentrations (which are typically electrons and holes in different bands) [226,227] . However, following a seminal work of Beck and Anderson a mobility spectrum can be defined, which can in principle account for any finite number of carriers of different mobilities contributing to the total conductivity [228] . They 79

4. Properties of ZnO and Mgx Zn1−x O single layers

3000

−0.5 −1

2500 −1.5

µ [cm2 /Vs]

2000

−2 −2.5

1500 −3 1000

−3.5 −4

500 −4.5

30

35

40 45 50

60

70

80 105 120 Temperature [K]

145160 180

220

270

320

−5

Figure 4.14: Mobility spectra of a Mgx Zn1−x O layer grown on the (0001) face of a ZnO single crystal as obtained from the f-MEMSA algorithm. The color scale represents the log10 of the occupation probability at the respective mobility channel. Red dots indicate the mobility calculated from a conventional Hall-effect analysis. The solid red line gives the mobility as a function of temperature only limited by lattice scattering. (Data obtained by Danilo Bürger (Forschungszentrum Rossendorf), spectra deconvolved by Robert Heinhold)

showed, following the argumentation of Ref. [229] that if a relaxation time can be defined, and if that relaxation time is constant around a cyclotron orbit, the components of the conductivity tensor can be written as Z ∞ s(µ)dµ (4.3) σxx (B) = 2 −∞ 1 + (µB) and σxy (B) =

Z

∞ −∞

µBs(µ)dµ . 1 + (µB)2

(4.4)

The problem of the determination of the mobility spectrum now consists of the inversion of these integrals. Several approaches have been proposed in order to solve the problem, which will briefly be discussed. Apart from the original approach techniques such as quantitative mobility spectrum analysis (QMSA) [230] , improved quantitative mobility spectrum analysis (i-QMSA) [231] , maximum entropy mobility spectrum analysis (MEMSA) [232] and full maximum entropy mobility spectrum analysis (f-MEMSA) [233] have been developed. A brief summary of the advantages and disadvantages of the specific methods 80

4.2. Evaluation of the transport properties by mobility spectrum analysis is summarized in Ref. [234] by the authors of Ref. [232] . The main advantage of the MEMSA algorithms over the competing methods are that no additional corrections and manipulations of the measured data are necessary and no artificial ghost peaks are seen in the spectra. The f-MEMSA method introduces two additional advantages, namely a matrix based inversion algorithm, which both increases the speed of convergence and reduces the sensitivity to errors, and the evaluation of the full set of available measurement data. The MEMSA algorithm instead only includes 50% of the available data as constrictions to the inversion problem, which is justified by the fact that the components of the conductivity tensor are ideally odd or ideally even functions of the magnetic field in noise free experiment. An additional improvement to the MEMSA algorithm is given in Ref. [235] , where a more accurate treatment of the noise level involved is given. Several approaches have been implemented and tested on both synthetical and experimental data by R. Heinhold, indicating, that the most stable algorithm is indeed the f-MEMSA algorithm. It has to be noted however, that the f-MEMSA algorithm uses a data truncation algorithm in the matrix inversion problem. Herein Eigenvalues under a certain magnitude will be removed from the set of solutions, reducing the dimensionality of the problem. While this both increases the speed of convergence and reduces the influence of small disturbances, the actual solution now depends on the limit chosen. This again introduces some ambiguity to the solution. As outlined in the preceding section multiple parallel conduction paths can be found in ZnO thin films and single crystals. Further complications are possible in the presence of a polarization induced 2DEG which will be discussed in section 5.3. In principle at least three different transport channels can be found in a ZnO/Mgx Zn1−x O single heterostructure, namely bulk conduction, surface conduction and interface conduction, where the mobility will differ between the individual processes. The application of the MEMSA algorithm does in principle allow the separation of these individual conduction paths. In the present study a ZnO/Mgx Zn1−x O single heterostructure was grown on the Zn face of a hydrothermal ZnO single crystal. A 1 µm thick ZnO buffer layer was introduced below the 1.3 µm thick Mgx Zn1−x O layer, in order to reduce the density of impurities at the heterointerface, and to avoid structural defects influencing the interface conduction. Bulk conduction can therefore occur in the substrate, the ZnO buffer layer and the Mgx Zn1−x O layer. As the substrates show a very low conductivity after annealing (refer to Chap. 4.1.2), no significant contribution to the overall conductivity should be expected. The ZnO buffer layer is grown at an oxygen partial pressure of 0.016 mbar, which again results in a low conductivity of this layer (refer to Chap. 4.1.1). The Mgx Zn1−x O layer however is grown at 0.004 mbar, and therefore a significant contribution to the conductivity is assumed in this layer. However, due to the [0001] polarity of the sample, the formation of a 2DEG is assumed to take place at the heterointerface (see Fig. 5.1) partially draining free electrons from the Mgx Zn1−x O layer. Interface conduction can both occur at the heterointerface and the interface between the substrate and the buffer layer. At the heterointerface the mobility of the 2DEG should exceed that of the bulk electrons. The 81

4. Properties of ZnO and Mgx Zn1−x O single layers interface transport channel between the buffer layer and the substrate does only exist if a high density of impurities is found near the interface, resulting in a reduced mobility. An equal argumentation holds for the surface conduction channel. Figure 4.14 shows a compilation of the individual mobility spectra calculated from field dependent measurements at different temperatures. Magnetic fields between -8 and 8 T were applied with widths between 0.2 and 0.5 T. The mobility derived from standard Hall-effect analysis is given as well as the maximal mobility possible in bulk ZnO in the limit of dilute doping, as calculated from an iterative solution of the Boltzmann transport equation. Only positive mobilities are displayed, which in this case means that only electron transport is present. The determination of the mobility spectra was carried out allowing for the possibility of hole transport, which however was not found in the spectra. Some contribution can be seen below zero mobility, which is introduced by a broadening of the peak at low electron mobilities. The corresponding (here negative) values in the mobility are therefore omitted from the plot. The f-MEMSA evaluation allows the separation of two individual transport channels with different mobilities at almost all temperatures. The channel with low mobility corresponds to the degenerate layer either found at the surface or the buffer layer substrate interface. The channel with higher mobility most likely originates from bulk conduction, as the contribution from this transport mechanism is only seen above 35 K. It is therefore concluded, that the carriers contributing to the transport process freeze out at low temperatures, which is expected from bulk conduction, but does not take place in the case of a 2DEG. One might now speculate that a 2DEG is present, and this assumption will receive some support by the data given in Fig 5.7. Between 50 K and 120 K a third peak is visible in the spectra at higher mobilities. Though no systematic behavior is observed, most likely due to the high conductivity of the other two conduction processes, the values obtained from the spectra lie in a range which is physical reasonable. No contribution of the transport mechanism is however seen below 50 K, which is again consistent with the data given in Fig 5.7. Such a behavior is surprising as metallic conduction would be expected for the 2DEG. One possible explanation is, that the energetic states related to the degenerate layer are found lower than the quantized states at the heterointerface, and some mechanism exists which allows the relaxation of free electrons from the 2DEG into the degenerate layer. An influence of surface states on the properties of a 2DEG has indeed been seen in the related GaN/AlGaN system [236] . However the nature and position of the degenerate layer is still not fully known in ZnO, and more detailed investigations are required to support this assumption.

4.3

Properties of phosphorous doped MgxZn1−xO thin films grown on ZnO

In order to investigate the influence of phosphorous doping on the properties of Mgx Zn1−x O thin films two series of samples were grown from Mgx Zn1−x O:P 82

4.3. Properties of phosphorous doped Mgx Zn1−x O thin films grown on ZnO

4.5

magnesium concentration (at.%)

(a)

4 3.5 3 2.5 2 1.5 1 10-4

10-3

10-2

10-1

p(O2) (mbar) 0.8

phosphorous concentration (at.%)

(b)

0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 10-4

10-3

10-2

10-1

p(O2) (mbar) Figure 4.15: Magnesium (a) and phosphorous (b) content of the Mgx Zn1−x O thin films deposited on ZnO substrates as determined by PIXE versus the oxygen partial pressure applied during growth. (Data obtained by Christoph Meinecke, graphed by Dr. Holger von Wenckstern)

83

4. Properties of ZnO and Mgx Zn1−x O single layers targets with a nominal P2 O5 -content of 1 wt and a nominal MgO-content of 2 wt.%. The Mg- and P- content of the thin films was determined by PIXE and is depicted in Fig. 4.15 versus the oxygen partial pressure applied during growth. With increasing oxygen partial pressure, the concentration of both Mg and P decreases. This suggests, that the incorporation of both elements follows the same mechanism. It is known, that Mg replaces Zn. In concordance with a defect model for Sb and As doped samples [237] it was calculated, that phosphorous is incorporated mainly onto Zn site as well [238] . This hypothesis is supported by the present results. Further experimental indications are given in Ref. [206,216] . It is further interesting, that the incorporation of dopants on Zn site is found to be higher for lower oxygen partial pressure. A possible explanation for this behavior is the fact, that at the growth temperatures employed the vapor pressure of Zn is more than one order of magnitude higher than that of for example Mg [92] . The film composition is not only determined by the target composition and the background gas, but further controlled by dynamic processes on the sample surface. Zinc evaporates partially from the surface leading to an increase in the dopant concentration in the film. This behavior is experimentally observed for Mg [215] . It is also in accordance with recent theoretical calculations [159] . Further, the background pressure influences the spatial distribution of the plasma composition, as the atomic momentum depends on the actual atomic weight of the element, and therefore light elements (in this case the oxygen) are more affected by scattering processes in the plasma than heavier elements (as Mg, P and Zn) at the same kinetic energy [48] . The HR-XRD 2Θ–ω scans of the (002) reflex for the MgZnO:P samples are depicted in Fig. 4.16. On top of the reflexes Pendellösung oscillations are visible, indicating a very smooth interface between the substrate and the film. All samples, grown at an oxygen partial pressure > 0.1 mbar, show two peaks, one corresponding to the substrate and the other to the film. The c-axis of the films is expanded compared to that of the substrate. From relaxed films grown on sapphire [85,91] it is known, that with increasing Mg concentration the a-axis expands, while the c-axis shrinks. In the pseudormorphic growth mode the a-axis is fixed due to the in-plane lattice match of the film and the underlying ZnO substrate, resulting in an relative expansion of the c-axis. Therefore in Mgx Zn1−x O samples grown pseudomorphically the c-axis constant is reduced compared to the substrate but larger than that of a relaxed Mgx Zn1−x O thin film. For a detailed discussion refer to Chap. 3.1.2. It is concluded, that the incorporation of phosphorous expands the ZnO lattice significantly, as already observed for the homoepitaxial ZnO thin films doped with phosphorous, exceeding the reduction of the c-axis due to the Mg. For the sample grown at 0.1 mbar only a single peak is observed in the 2Θ–ω scans, suggesting a perfect, both in-plane and out-of-plane lattice match between the film and the substrate. Reciprocal space maps of the symmetric (002) (Fig. 4.17 (a)) and the asymmetric skew (101) (Fig. 4.17 (b)) reflex of the MgZnO:P sample with the highest Mg and P concentration are shown exemplarily. As can be seen, the peak positions only differ in the out-of-plane direction, but have the same in-plane value. 84

4.3. Properties of phosphorous doped Mgx Zn1−x O thin films grown on ZnO 0.1 mbar

Intensity (arb. units)

0.016 mbar

34.1

2 × 10-3 mbar 3 × 10-4 mbar

34.2

34.3

34.4

34.5

34.6

2 θ (°)

Figure 4.16: HR-XRD triple axis 2Θ–ω scans of the symmetric (002) reflex of Mgx Zn1−x O:P films grown at the indicated oxygen partial pressures. For the samples grown at oxygen partial pressures below 0.1 mbar thickness fringes are visible, indicating the very smooth interface between the substrate and the film. The peaks at 2Θ around 34.42◦ correspond to the ZnO substrate reflections. (Data obtained by Dr. Michael Lorenz, graphed by Dr. Holger von Wenckstern)

This indicates a pseudomorpic growth for all samples grown at oxygen partial pressures below 0.1 mbar. The a- and c-axis values for all films investigated are given in Tab. 4.4. The temperature dependence of the Hall-mobility is depicted in Fig. 4.18 (a), that of the free carrier concentration is shown in Fig. 4.18 (b). A minor influence of a degenerate layer is detected for some of the samples, and eliminated using the correction scheme outlined in Ref. [223] . High electron mobilities are observed in the MgZnO:P samples grown at oxygen partial pressures below 0.1 mbar, comparable to that in the previously discussed homoepitaxial ZnO:P samples underlining the very high structural quality of the samples. While for these homoepitaxial ZnO:P samples the maximal mobility was observed in the sample grown at 3 × 10−4 mbar, the maximal mobility in the homoepitaxial MgZnO:P was observed for the samples grown at 2 × 10−3 mbar for a nominal MgO content of 1 wt.% and 2 wt.% likewise. From the temperature dependence of the free carrier concentration the donor activation energy ED and concentration ND was determined using a single donor model. As the donor concentration is in the 1017 cm−3 range, the activation energy is reduced by the beginning overlap of the donor states. The donor activation energy then follows  1/3 ! ND ED = ED0 1 − , (4.5) NC as given e.g. in Ref. [98] . Here NC denotes the critical donor concentration, ED0 is the donor activation energy in the dilute limit. The donor activation energy versus donor concentration is depicted in Fig. 4.19 (a). A least squares routine 85

4. Properties of ZnO and Mgx Zn1−x O single layers

(a) MgZnO:P (0 0 2)

Log10(Intensity (counts)) 3.5

q⊥ (nm−1)

3.85

3 2.5

3.84

2

3.83

1.5 1

3.82

0.5 3.81 −10

−9

−8

−7

−1

q|| (nm )

(b) MgZnO:P (1 0 1)

−6

−5 −3 x 10

Log10(Intensity (counts)) 2.5

4.042

2

−1

q⊥ (nm )

4.04 4.038

1.5

4.036

1

4.034

0.5

4.032 4.03 −6

−4

−2

−1

q|| (nm )

0

2

−3

x 10

Figure 4.17: HR-XRD reciprocal space maps of (a) the symmetric (002) and (b) the asymmetric skew (101) reflex of a Mgx Zn1−x O:P film grown on ZnO at 2 × 10−3 mbar. The color scale represents the log10 of the scattered X-ray intensity (counts). The horizontal broadening of the reciprocal lattice points of both substrate (top reflection) and thin film (bottom reflection) is due to the mosaizity of the used ZnO substrate. The homoepitaxial film follows the substrate mosaizity, resulting in an equal broadening. (Data obtained by Dr. Michael Lorenz)

86

4.3. Properties of phosphorous doped Mgx Zn1−x O thin films grown on ZnO

1.000

1% MgO 1.6 × 10-2 2 × 10-3 3 × 10-4

800

µ (cm 2/Vs)

2% MgO 2 × 10-3 3 × 10-4

600 400 200 0 0

50

100

150

200

250

300

350

T (K)

1% MgO 1.6 × 10-2 2 × 10-3 3 × 10-4

1018

n (cm -3)

2% MgO 2 × 10-3 3 × 10-4

1017

1016

1015 0

5

10

15

20

25

1000/T (1/K) Figure 4.18: Electron mobility (a) and free electron concentration (b) versus temperature in selected Mgx Zn1−x O:P thin films grown on ZnO, prepared from targets with a nominal MgO-content of 1 wt.% and 2 wt.%, respectively, as labeled. (Graphed by Dr. Holger von Wenckstern)

87

4. Properties of ZnO and Mgx Zn1−x O single layers Table 4.4: Oxygen partial pressure p(O2 )during growth, Mg content x and P content cp both in atomic percent, lattice parameters, and room temperature electron concentration n and Hall-mobility µH of MgZnO:P thin films grown on ZnO. The lattice constants of a substrate are given for reference.

p(O2 ) (mbar) x (%) cp (%) 0.1 0.016 2 × 10−3 3 × 10−4 substrate

1.09 2.25 3.81 4.71

0.43 0.47 0.67 0.84

c (nm)

a (nm)

n (cm−3 )

µH (cm2 /Vs)

0.52070 0.52208 0.52305 0.52285 0.52069

0.32498 0.32500 0.32498 0.32499 0.32499

1.6 × 1017 1.8 × 1018 4.9 × 1017 1.3 × 1018

0.6 4.7 140 84

was applied to model the experimental data using Eqn. 4.5. From the fit, a critical concentration of NC = 8.3 × 1018 cm−3 and a donor activation energy of ED0 = 56 meV is derived, which is close to the activation energy of the effective mass donor [239] . In order to investigate effects of thermal activation of the phosphorus dopant, the Mgx Zn1−x O:P layers were annealed in a 700 mbar oxygen atmosphere at 850◦ C for 5 minutes, the same conditions as for the homoepitaxial ZnO:P samples. The resistivity of the samples prior to and after the annealing are compared in Fig. 4.19 (b). The change in resistivity strongly depends on the oxygen partial pressure during growth. The samples grown at the highest oxygen partial pressures p(O2 )= 0.016 mbar and p(O2 )= 0.1 mbar show the highest increase in resistivity by 6 and 4 orders of magnitude, respectively. This result is in concordance with that obtained on the homoepitaxial ZnO:P thin films were high resistivities are only achieved in the samples grown at high oxygen partial pressures. The change in the resistivities upon annealing, however, is much stronger in the Mgx Zn1−x O thin films. The samples of group A, having a higher phosphorous content show only slight changes in the resistivity. Again these results coincide with that obtained on the homoepitaxial ZnO:P thin films, where only a slight change is observed for these samples. It is concluded, that despite having the highest phosphorous concentrations, the conditions are not present in these films to form a high density of phosphorous related acceptors. One reason therefore might be the preferential incorporation of P on Zn site. The mechanism involving the formation of PZn -2VZn might not work completely in these samples due to a high density of interstitial Zinc, which is observed for the nominally undoped homoepitaxial ZnO thin films. For the samples grown at higher oxygen partial pressures a transition to p-type conductivity might well be possible from the high density of acceptors present in the sample, however the density of compensating donors is still to high for the transition to occur. One possible reason for that is the high density of iron and silicon impurities in the sample as determined by PIXE in the homoepitaxial ZnO:P samples of series I (see Tab. 4.2). While these impurities do not have a significant influence on the transport properties as the defect levels introduced 88

4.3. Properties of phosphorous doped Mgx Zn1−x O thin films grown on ZnO

70 60

ED (meV)

50 40 30 20 10 0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

ND1/3 (106 cm -1)

ρannealed / ρas-grown

107 106 105 104 103 102 101 100 10-1 10-4

10-3

10-2

10-1

p(O2) (mbar) Figure 4.19: (a) Donor activation energy versus donor concentration in ZnO:P of series I and Mgx Zn1−x O:P thin films. The red line is a least squares fit to Eqn. 4.5. (b) Ratio of the resistivities of Mgx Zn1−x O:P thin films grown on ZnO after and before annealing versus oxygen partial pressure during growth. Full and open symbols indicate films with a nominal MgO content of 1 wt.% and 2 wt.%, respectively.

89

4. Properties of ZnO and Mgx Zn1−x O single layers by them are deep, their high density will still compensate acceptors and prevent the creation of free holes. It is therefore necessary to reduce the density of these impurities. This however is not trivial in the PLD process as these impurities were already present in the target, being most likely introduced by the homogenisation and sintering process. The target preparation process is required to add the dopant, and in the case of Mgx Zn1−x O also to produce the host material. For ZnO the possibility exist to use single crystalline targets of much higher purity, and to add the dopants via an alternative route. Nitrogen for example was introduced from a plasma, which allows a very high purity of the doping agent and finally led to p-type conduction and the fabrication of LEDs [66] . This route however is not accessible for Mgx Zn1−x O or other ternary alloys which in turn are necessary for the fabrication of highly efficient devices. Therefore either complicating steps involving multiple single crystalline targets or different growth methods like MBE have to be considered. All these steps would result in a significant complication of the growth process. In order to maintain the advantages of the PLD process such as simplicity, scalability and comparatively cheap design, one of the most critical challenges is the production of highly pure target material.

4.4

Summary and conclusion

The results of the present chapter can be summarized as follows: • The properties of undoped and phosphorous doped ZnO and Mgx Zn1−x O thin films grown on ZnO are strongly influenced by the oxygen partial pressure during PLD growth. The oxygen partial pressure influences the growing films in more than one way. 1. The II–VI ratio in the films is controlled by the oxygen partial pressure. For films grown at low oxygen partial pressures an increased c-axis lattice constant is observed for both the ZnO and Mgx Zn1−x O thin films, most likely due to an increasing density of charged defects. The thesis of an increase of the density of intrinsic defects related to oxygen deficiency in the films is supported by an increase in the zinc interstitial related luminescence and the free electron concentration upon decrease of the oxygen partial pressure. It is concluded, that oxygen in the background gas atmosphere is necessary in order to grow stoichiometric ZnO and Mgx Zn1−x O film. 2. The composition of the group II constituents depends on the background pressure in the chamber. The concentration of the lighter Mg atoms compared to Zn atoms is reduced by almost a factor of three within the range of oxygen partial pressures available in the present growth setup. Interestingly the concentration of P does change accordingly. It is concluded, that the atomic mass (which differs between Mg and P by only 20%) of the individual element influences the kinetic scattering processes with the background gas and therefore the plasma composition at the substrate position. 90

4.4. Summary and conclusion • It is therefore concluded that the versatility of the growth setup can be improved if the influences of the background gas on the sample composition could be separated. Two modifications of the PLD setup would probably allow at least a partial realization of this goal. 1. The use of a non uniform gas atmosphere. The application of a gas mixture, for example oxygen and an inert gas, inside the growth chamber could probably allow a control of the composition of the group II constituent without changing the II–IV ratio, therefore maintaining stoichiometric growth. However, a minimum oxygen partial pressure is necessary in order to maintain stoichiometry. This limits the total pressure attainable to values above the oxygen partial pressure. 2. The introduction of a plasma source. During laser plasma formation only a small fraction of the available oxygen molecules is cracked. It is reasonable to assume in the light of literature work [240] , that molecular oxygen is only responsible for a vanishing fraction of the total oxygen incorporation. The range of available gas mixtures in the growth chamber can be further expanded, if the availability of ionic oxygen species can be controlled without changing the base chamber pressure. Such a approach could allow a chamber pressure virtually below the oxygen partial pressure, as the availability of activated oxygen increases. Additionally, it is found in the literature [241] that the incorporation of nitrogen is promoted by the activation in a plasma environment, eventually leading to p-type conductivity [66,242] . • The similarities of the incorporation of Mg and P indicate that P is like Mg mainly introduced into the ZnO host lattice on Zn site, in accordance with theoretical calculations [238] . • A degenerate contribution to the sample conductivity was found in homoepitaxial samples with a phosphorous concentration with 0.1% and above, which could partially be removed by annealing in oxygen, indicating that at least in this case the origin of the degenerate layer is a layer of intrinsic defects, likely to be formed at the surface. • It was shown that the separation of the conduction of the degenerate layer and the bulk of the film was partially possible in the evaluation of the Hall-effect measurements employing a correction scheme as proposed in Refs. [223,224] . A complete separation however was not possible without further assumptions, as the incorporation of the defects responsible for the formation of the degenerate layer is not homogeneous. • It was shown that the separation of the conduction of individual conductive paths is possible without any assumption about the distribution of the individual carriers from magnetic field dependent measurements by the maximum entropy mobility spectrum approach. The individual 91

4. Properties of ZnO and Mgx Zn1−x O single layers properties of bulk conduction and the conduction of the degenerate layer were revealed over a wide range of temperatures. Such a detailed study of the parallel conduction processes in ZnO has not been reported so far. • The critical donor concentration and activation energy in the dilute limit of the dominant donor in phosphorous doped ZnO and Mgx Zn1−x O layers grown on ZnO was determined to be of NC = 8.3 × 1018 cm−3 and ED0 = 56 meV, respectively. • Transport measurements on phosphorous doped homoepitaxial ZnO thin films showed high electron mobilities of up to 800 cm2 /Vs around 70 K and 170 cm2 /Vs at room temperature. Exact modeling of the transport properties using a numerical solution of the Boltzmann-transport-equation indicated, that the scattering processes involved equal that of ZnO single crystals [210] . • The thermal activation of phosphorous related acceptors was studied in ZnO and Mgx Zn1−x O thin films grown on ZnO. A transition to p-type conduction was never observed. However an increase of the resistivity by more than 6 orders of magnitude was observed in the Mgx Zn1−x O:P layers deposited at the highest oxygen partial pressures. It is concluded that high oxygen partial pressures are necessary if p-type conduction is to be achieved, as the compensation of acceptors is reduced by the low density of intrinsic donors. • From the chemical analysis of the sample composition it is concluded that concentrated efforts are necessary to improve the purity of the target material, as the purity of the films can not exceed the purity of the starting material.

92

Chapter 5 Quantum effects on carriers in ZnO/MgxZn1−xO heterostructures 5.1

Principle considerations

Free carriers in semiconductor heterostructures will be influences by the band gap discontinuities between the constituents. If the spatial dimensions involved are of the order of the carrier wavelength, quantum effects will become important in the vicinity of the heterointerface. Quantized energy levels can be found in potential minima, and tunneling processes can occur at potential maxima. A detailed compilation of the numberous effects observed can be found in Ref. [243] . Within this work only effects of quantization in potential minima in heterostructures will be regarded. Two classes of minima will be investigated and differentiated by the heterostructures where they occur in. First a single ZnO/Mgx Zn1−x O heterojunction represents a one sided potential barrier due to the band offset at the heterointerface. Secondly a double heterostructure introduces two energetic barriers. The ZnO/Mgx Zn1−x O material system allows the fabrication of type-I heterostructures [244] , therefore for both electrons and holes the potential energy is lower in the ZnO than in the Mgx Zn1−x O part of the junction. If the layer sequence is Mgx Zn1−x O/ZnO/Mgx Zn1−x O and the thickness of the ZnO layer is sufficiently small so that quantization occurs, such a structure can be regarded as a quantum well with finite barriers. Electron and holes will be confined in such a structure, leading to an increase of the carrier density and recombination efficiency. Such a behavior was observed in semiconductor junctions [245] . As both the ZnO and Mgx Zn1−x O constituent show a spontaneous polarization parallel to the c-axis which can be superimposed by a piezoelectric polarization likewise parallel to the crystallographic c-axis additional complicating aspects have to be regarded. High quality heterostructures, as investigated in the present study grow pseudomorphic, and therefore at least one of the layers is strained. The polarization necessarily contains a piezoelectric component, which is discontinuous at the heterointerface. Additionally the spontaneous polarization in Mgx Zn1−x O is a function of the Mg content x, and an additional discontinuity will be introduced by the change in x at the heterointerface. If the layer sequence is organized in 93

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

(0001) (a) ZnO

0

MgZnO

50

100

150

200

z (nm) 1020

ZnO

(b) MgZnO

1018

n (cm-3)

1019

1017

1016 0

50

100

150

200

z (nm)

(c)

MgZnO

ZnO

1020

MgZnO

1018

n (cm-3)

1019

1017

1016 195

200

205

210

z (nm)

Figure 5.1: Band diagram of ZnO/Mgx Zn1−x O heterostructures. Stacking sequence (a) ZnO/Mgx Zn1−x O, (b) Mgx Zn1−x O/ZnO, and (c) Mgx Zn1−x O/ZnO/Mgx Zn1−x O. Solid black lines show the respective conduction and valence bands, vertical black lines indicate heterointerfaces. Dotted black lines represent quantized energy levels of confined carriers. Solid green and blueish lines symbolize hole and electron wavefunctions, respectively. The density of electrons in the vicinity of the junctions is shown by a red solid line. In the QW structure only the lowest energy levels are indicated.

94

5.1. Principle considerations a fashion that the heterointerfaces are perpendicular to the crystallographic c-axis, an electric field forms due to the discontinuity of the polarization. Such a stacking sequence is very common due to the preferential growth of ZnO and its compounds along the c-axis [87–90] . All samples investigated in the present study have their growth direction z parallel to the crystallographic c-axis. The piezoelectric polarization counteracts the change in spontaneous polarization in c-axis oriented growth, and might in principle cancel its influence completely. Such a behavior is suggested in some studies for small Mg contents [35] , see the discussion in Chap. 1. However for x > 0.15 a finite change in the polarization at the heterointerface is evident from most studies [35–38] . The electric field introduced will add a linear change in the potential parallel to the growth direction. Therefore a triangular potential is formed in the vicinity of the heterointerface for single heterojunctions. Depending of the layer sequence this represents of a minimum in the E(z) relation for either electrons or holes, which leads to the accumulation of the respective carriers, and the formation of quantized states. The change in polarization will also produce an electric field across a quantum well, which leads to the occurrence of the quantum confined stark effect. In all cases the accumulation of carriers leads to the formation of a space charge incorporating an additional potential, which in turn influences the potential leading to the confinement of the carriers. Self consistent solutions of the Poisson- and Schroedinger equation are necessary to determine the actual distribution of carriers in position and energy space. The calculations were carried out using the poisson solver Beta8c developed by Gregory Snider [246,247] . The results of such calculations are shown exemplarily in Fig. 5.1. For the Mgx Zn1−x O layers an Mg content x of 0.2 was used. All layers were assumed to be n-type with a donor concentration of 1 × 1017 cm−3 . Figure 5.1 (a) and (b) illustrate the possible situations in single heterostructures at 300 K. A 2DEG will only form in a single heterostructure if the O-face of the Mgx Zn1−x O is adjacent to the Zn-face of the ZnO, due to a positive sheet charge at the interface. Such a situation is displayed in Fig. 5.1 (b). A significant increase in the electron concentration is visible in the vicinity of the heterointerface. Four quantized states are found in the triangular potential, as visualized in the inset of Fig. 5.1 (b). Nevertheless, depending on the doping level, free electrons can be found in the bulk of the thin films, which will additionally contribute to conductivity of the stacked sample. Hall-effect measurements will record a weighted average over the whole film, complicating the unambiguous determination of the properties of the 2DEG. It is therefore crucial to control the dopant concentration in the adjacent layers, in order to determine the properties of the 2DEG correctly. The problem is reduced at low temperatures, where the bulk carriers are frozen out, and transport is only possible via the 2DEG. In contrast a heterostructure in which the Zn-face of the Mgx Zn1−x O is adjacent to the O-face of the ZnO will lead to a negative sheet charge at the interface and the repulsion of free electrons. Such a situation is graphed in Fig. 5.1 (a). The structure would in principle allow the accumulation of free holes at the heterointerface, which would require the Fermi-level to be close to the valence band. The situation displayed in Fig. 5.1 (a) fulfills this 95

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures 40

1.6·1017

(a)

39

1.4·10

38

1.2·1017

37

Nd - Na (cm -3)

36

C (pF)

(b)

17

35 34 33

ZnMgO

32 31

ZnO:Al

30 29

-1

0.8·1017 0.6·1017

ZnO

0.4·1017

a-Al 2O3

0.2·1017 0.0·1017 220

28 -2

1.0·1017

0

1

U (V)

230

240

250

w (nm)

Figure 5.2: (a): Capacitance versus voltage dependence of a Schottky diode formed on a ZnO/Mgx Zn1−x O heterostructure grown on a-plane sapphire (b): Spatial distribution of the apparent dopant concentration in the heterostructure as calculated from Fig. 5.2 (a), the peak indicated by the solid rectangle corresponds to the 2DEG. The sheet charge concentration was calculated to be n2d = 9.0 × 1010 cm−2 , integrating over the range inside the solid box. (Courtesy of Dr. Holger von Wenckstern)

condition, it can however be argued, that such a situation is not very likely in real ZnO/Mgx Zn1−x O samples. A high density of deep donors is frequently observed [101] which will hinder the Fermi-level from sinking to the valence band. The observation of a free hole gas is therefore very unlikely. Deep donors and acceptors are purposely excluded from the calculations, as their density and energy levels are not exactly know. Any inclusion would be rather speculative. Fig. 5.1 (c) shows the situation of a Mgx Zn1−x O/ZnO/Mgx Zn1−x O QW structure at 2K. The well width is 4 nm. The influence of the electric field is clearly visible. Quantized states for both electrons and holes are found, and the lowest level and respective wave function are displayed in Fig. 5.1 (c). It is seen that the overlap of the wave functions is reduced by the electric field. Further, in an equilibrium situation only electrons are confined in the quantum well, leading to carrier densities similar to that in the single heterostructures. A low temperature reduces the influence of bulk conduction significantly, allowing in principle the determination of the transport properties of the 2DEG in Hall-effect measurements.

5.2

Carrier confinement in ZnO/MgxZn1−xO single heterostructures

The formation of a 2DEG was studied in heteroepitaxial ZnO/Mgx Zn1−x O samples by C–V measurements (Fig. 5.2) and temperature dependent Hall-effect investigations (Fig. 5.3). For the C–V measurements the heterostructures were 96

5.2. Carrier confinement in ZnO/Mgx Zn1−x O single heterostructures

1013

(a)

n 2D (cm -2)

ZnO/MgZnO single heterostructure

1012 0

10

20

30

40

1000/T (1/K) 350

(b)

ZnO/MgZnO single heterostructure ZnO thin film

µH (cm²/Vs)

300 250 200 150 100 50 0 0

100

200

300

T (K) Figure 5.3: (a) Free electron concentration versus inverse temperature and (b) mobility versus temperature in a ZnO/Mgx Zn1−x O heterostructure on a-plane sapphire as determined by temperature dependend Hall-effect, its sheet charge concentration was calculated to be n2d = 3×1012 cm−2 . The mobility of a bulk ZnO thin film grown on sapphire is shown for comparison. (Courtesy of Dr. Holger von Wenckstern)

97

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures deposited on a highly aluminum doped ZnO layer, which represents a backcontact to the structure. Thereby the series resistance of the films is reduced, allowing the application of higher measurement frequencies before cutoff occurs [57,101] . Additionally the field distribution is more homogeneous in the film, which leads to a more accurate determination of the spatial distribution of carriers. This is of special importance for the determination of the sheet charge density of the 2DEG. From the C–V characteristic (Fig. 5.2 (a)) the net dopant concentration was calculated (Fig. 5.2 (b)). The accumulation of electrons at the hetero-interface is visible (indicated by the solid rectangle in (Fig. 5.2 (b)). The sheet charge concentration was calculated using [61] to be n2d = 9.0 × 1010 cm−2 . The sheet charge density could be increased by doping of the Mgx Zn1−x O barrier, as reported in [248] . For Hall-effect investigations the heterostructures have been directly grown onto a-plane sapphire. A sheet carrier concentration of n2d = 3 × 1012 cm−2 was observed, which is almost independent of the temperature (Fig. 5.3 (a)). The mobility of the 2DEG exceeds that of a 3DEG in a ZnO thin film shown for comparison, especially at low temperatures (Fig. 5.3 (b)). As the ZnO buffer layer and the Mgx Zn1−x O barrier material are not fully depleted in the structure and the Hall-effect integrates over all parallel layers in the sample, a slight influence of the 3DEG on the mobility can be seen, as indicated by the circle in (Fig. 5.3 (b)). Further, a degenerate layer forming at the interface between the film and the substrate might generally contribute to the transport [101] . Indicative for the existence of such a layer is the steep drop in mobility in the ZnO reference sample at low temperatures (marked by the solid rectangle), and the fact, that the contribution of a 2DEG is only observed in a very small number of heterostructure samples grown on sapphire. This suggests, that if a degenerate layer is present, its conductivity exceeds that of the 2DEG at all temperatures. The presence of such a layer would at least result in an underestimation of the 2DEG mobility [249] . Although the low temperature mobility is higher and the influence of ionized impurity scattering on the transport in the 2DEG is reduced, the room temperature value of the mobility is below that of a single crystal. Possible reasons are scattering at the heterointerface, potential fluctuations in the barrier and charged dislocation lines as well as grain boundaries intersecting the quantum well.

5.3 5.3.1

Electron accumulation in ZnO/MgxZn1−xO quantum wells Single quantum wells grown on a-plane sapphire

An AFM image of a typical heteroepitaxial MgZnO/ZnO QW structure is shown in Fig. 5.4 (a). The sample shows two-dimensional growth in the Burton–Cabrera–Frank mode [106] , with a visible surface roughness of several c/2 steps, which is of the order of the QW thickness (rRSM = 0.394 nm, rA = 0.495 nm). The crystal growth is enhanced by threading dislocations 98

5.3. Electron accumulation in ZnO/Mgx Zn1−x O quantum wells with a screw component present in the center of each of the crystallites. It is anticipated, that the interfaces of the ZnO/Mgx Zn1−x O QWs grown on sapphire, as well as the heterointerface in the ZnO/Mgx Zn1−x O structures grown on sapphire shows similar roughnesses. This results in interface scattering of electrons reducing the mobility, and in inhomogeneous QW thickness, broadening the QW related luminescence. Fig. 5.5 shows the temperature dependent transport data as obtained by Hall-effect investigations. A monotoneous increase of the mobility is observed towards decreasing temperatures, indicative for the contribution of a 2DEG. However, in contrast to the data obtained from the single heterostructure (see Fig. 5.3) a monotonic decrease of the free carrier concentration is observed. This can be ascribed to the contribution of a 3DEG to the overall conductivity, as already seen for the single heterostructure sample grown on sapphire. In the case of the QW structure, the influence of the 3DEG is even more pronounced, and a temperature independent free carrier concentration is not seen, even not at low temperatures. However a slight decrease of the slope in log n versus 1, 000/T is seen, which hints to the reduction of the three-dimensional transport in comparison to the 2DEG. Further the temperature dependence of the mobility shows a µH ∝ T −3 behavior. As for the 2DEG the main scattering mechanism should be scattering at phonons, at the smallest exponent anticipated should be −3/2 for scattering at acoustic phonons via the deformation potential, this behavior is unexpected. As however the mobility in the three-dimensional transport process is lower than that in the 2DEG, the systematic increase of the contribution of two-dimensional transport can lead to an increase of the mobility, which is steeper than that observed in a isolated 2DEG. Again the overall mobility remains smaller than that observed in other ZnO/Mgx Zn1−x O heterostructures [37,250–252] . The presence of bulk transport and a degenerate layer are possible explanations, along with interface imperfections. In principle a high density of ionized impurities near the heterointerface is a possible explanation as well, however the monotonic increase of the mobility towards low temperatures indicates that this limitation is of minor importance.

5.3.2

Single quantum wells grown on ZnO substrates

Following the results obtained in the growth studies (see Chap. 3.2.6), the surface roughness can be significantly reduced by growth on ZnO substrate. An AFM image of a ZnO/Mgx Zn1−x O QW grown under optimized conditions (650◦ C, oxygen partial pressure of 4 × 10−3 mbar, substrate miscut of 0.36◦ ) is shown in Fig. 5.4 (b). Step flow growth mode is achieved, with perfect parallel alignment of subsequent layer steps [253] . The average terrace width of w = 43 nm corresponds to that expected for the present miscut w0 = 41 nm. The sample shown represents the minimal surface roughness possible for the given substrate miscut (rRSM = 0.121 nm, rA = 0.152 nm). Reciprocal space maps of the symmetric (00.2) (Fig. 5.6 (a)) and the asymmetric skew (10.1) (Fig. 5.6 (b)) reflex of a homoepitaxial MgZnO/ZnO sample are shown. The peak positions only differ in the out-of-plane direction, but have the same in99

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

(a)

(b)

Figure 5.4: (a) 4 µm×4 µm AFM image of a ZnO/Mgx Zn1−x O QW grown on sapphire. (b) 2 µm×2 µm AFM image of a ZnO/Mgx Zn1−x O QW grown on ZnO. (Top image obtained by Gregor Zimmermann)

100

5.3. Electron accumulation in ZnO/Mgx Zn1−x O quantum wells T (K)

20

40

60

80

muH (cm2/Vs)

250

1017

200

100

mu H~T-3

150

10 30

40

50

60

70

80

100

90

T (K)

muH (cm2/Vs)

n (cm-3)

1018

50

1016

ND =5.6x1017cm -3 ED =35 meV NA =1.0x1016cm -3

10

20

0

30

40

50

1000/T (1/K)

Figure 5.5: Temperature dependence of (Red ): the free carrier concentration and (Blue): the mobility in a ZnO/Mgx Zn1−x O quantum well structure grown on sapphire as determined by Hall-effect investigation. The upper right inset shows the temperature dependence of the mobility in double logarithmical plot. The donor concentration and activation energy is given along with the acceptor concentration in lower left corner.

plane value. This indicates a perfect match of the a-axis lattice constant, thus growth is pseudomorphic. The c-axis of the film is compressively strained with respect to the substrate by −2.36 × 10−3 . The temperature dependence of the mobility of selected samples grown on ZnO is depicted in Fig.5.7 along with the temperature dependence of the mobility of a single crystal grown by the skull-melting method (Cermet) [127,128] . The mobility data of a homoepitaxial ZnO film are presented, as well as that of a ZnO/Mgx Zn1−x O QW structure. The mobility measured on the QW structure exceeds that of the homoepitaxial ZnO thin film at all temperatures, which itself shows significantly higher mobility than any ZnO thin film grown on sapphire investigated within the present study. However, the mobility of the single crystal still exceeds that of both the homoepitaxial ZnO thin film and the ZnO/Mgx Zn1−x O QW structure. Further a pronounced increase of the mobility at low temperatures, as expected for a 2DEG, is not observed for the QW structure. It is also observed, that the mobility of the homoepitaxial ZnO thin film and especially that of the ZnO/Mgx Zn1−x O QW structure drop sharply for low temperatures (indicated by the solid box in Fig. 5.7). In literature this behavior is connected to the presence of a degenerate layer in the sample, dominating carrier transport at low temperatures [101,225] . Again the TDH experiment is sensitive only to the integral properties of all parallel layers in 101

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

(00.2)

(b)

(10.1)

q (nm -1 )

(a)

4.05 3 2.5

q (nm -1 )

4.045

2 4.04 1.5 1

4.035

0.5 4.03 -4

-3

-2

q (nm

-1

-1

)

0 x 10

-3

Figure 5.6: HR-XRD reciprocal space maps of (a) the symmetric (002) and (b) the asymmetric skew (101) reflex of a ZnO/Mgx Zn1−x O QW structure grown at 4 × 10−3 mbar on ZnO (0001). The color scale represents the log10 of the scattered X-ray intensity (counts). The topmost peaks in each of the plots are from the thin film and the stronger bottom peaks from the ZnO substrate. (Data obtained by Dr. Michael Lorenz)

102

5.3. Electron accumulation in ZnO/Mgx Zn1−x O quantum wells

µH (cm2/Vs)

103

ZnO single crystal homoepitaxial MgZnO/ZnO QW homoepitaxial ZnO thin film

102 30

50

70

100

200

300

T (K)

Figure 5.7: Electron mobility versus temperature in a homoepitaxial ZnO thin film, a ZnO/Mgx Zn1−x O QW structure grown on ZnO and a ZnO single crystal.

the sample. The dominance of the degenerate layer masks the presence of the 3DEG in the homoepitaxial ZnO thin film as well as the presence of the 2DEG in the ZnO/Mgx Zn1−x O QW structure and that of the most likely existing 3DEG in the Mgx Zn1−x O barrier material. However, the presence of the 2DEG in the ZnO/Mgx Zn1−x O QW structure can still be deduced from its mobility. At about 45 K a peak in the mobility versus temperature behavior is observed (marked by the circle in Fig. 5.7). This peak is neither present in the mobility versus temperature dependence of the homoepitaxial ZnO thin film nor in that of the single crystal, and should not appear for a 3DEG at all. The peak is attributed to the presence of a 2DEG in the ZnO/Mgx Zn1−x O QW structure. However, the sheet carrier density of the 2DEG must decrease towards lower temperatures, indicating that the electronic states of the degenerate layer are energetically preferred. Detailed investigations of this phenomena have to be carried out, as well as investigations on samples without the degenerate layer. Nevertheless the deducible mobility of the 2DEG in the ZnO/Mgx Zn1−x O QW grown on ZnO by far exceeds that in the heterostructures grown on sapphire in this study. This is even more remarkable, as the mobility is expected to further increase towards low temperatures and is most likely underestimated in the present structure due to the overlay with the 3DEG and the degenerate layer. The FWHM of the QW related PL peaks of ZnO/Mgx Zn1−x O QW structures grown on sapphire and ZnO is depicted in Fig. 5.8 a. The peak width is always slightly smaller for the ZnO/Mgx Zn1−x O QW structures grown on ZnO, and the difference is more pronounced for smaller thicknesses. This difference is attributed to the more homogeneous growth of the QWs on ZnO compared to the QWs grown on sapphire. 103

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

50

FWHM (meV)

40 30 20 QWs on a-sapphire QWs on c-ZnO

10 0 0

2

4

6

L w (nm) Figure 5.8: Peak width (FWHM) of the QW related PL peak versus QW thickness LW for ZnO/Mgx Zn1−x O QW structures grown on sapphire and ZnO substrates. (The data for the QWs grown on sapphire are taken from Ref. [81] )

5.4

The quantum confined Stark-Effect in the ZnO/MgxZn1−xO system

In the previous sections the principle physics involved in the acculumation and quantum confinement of free carriers in the vicinity of a ZnO/Mgx Zn1−x O heterojunctions were discussed. Morphological, structural and transport properties of single heterostructures and structures containing a ZnO QW were discussed. This section is devoted to a detailed study of the luminescence properties of ZnO/Mgx Zn1−x O QW well structures. All structures discussed in the following are grown along the c-axis direction, and will therefore be subject to an electric field forming inside the heterostructures due to the discontinuity in the electric polarization at the heterointerfaces. All samples discussed in the following are of very high crystalline quality. AFM investigations of the surfaces revealed step-flow-growth exclusively, though the interface roughness is different. For the samples grown on ZnO solely pseudomorphic growth is observed, and depending on the miscut, a perfect vicinal surface is observed as shown in Fig 3.21. It therefore seems reasonable to believe, that the interfaces defining the quantum well are of equal quality. Nevertheless, deterioration of the interfaces is possible. Among them, interdiffusion of the constituents has the most tremendous influence. While the surface of the samples remains perfect, the interfaces buried inside the junctions might degrade during growth, making the evaluation of the interface quality impossible from surface observation, even if the growth is stopped after the layer in question. The rate of interdiffusion depends on the kinetic energy of the particles that are about to diffuse. Apart from the inevitable thermal energy given to all atoms inside the 104

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system growing crystal at the growth temperature another source of kinetic energy becomes important in the case of PLD growth. The ablation of the target results in the formation of a high energy plasma with a plasma temperature of several 103 K [49,50] . This gives energies in the range of up to several hundreds of eV to the impinging adatoms [49] . This can be advantageous, as the surface diffusion is enhanced, which will lead to an improvement of the surface perfection. This does in principle allow lower growth temperature than in processes which involve incorporation of adatoms from a gas phase, such as CVD and MBE. In contrast, the high energies of impinging species does have significant drawbacks, as it can result in an ion implantation, and will damage the bulk of the film, at least the first few atomic layers [49,254] . While such a process is not disturbing in the growth of bulk films, it will dramatically reduce the attainable interface quality. The appearance of the quantum confined Starkeffect can be a measure for the interface quality, as it has been shown, that the influence of polarization discontinuities on the wave-function separation of electrons and holes can be reduced by smoothing the interfaces [255–257] . The authors showed that ion implantation of ZnO/Mgx Zn1−x O samples showing a pronounced QCSE resulted in a blueshift of the emission. They concluded, that softening of the interfaces changes the triangular well potential. The electron and hole wave-function therefore have an increases overlap, and their energy levels are closer.

5.4.1

Literature data on the QCSE in ZnO/Mgx Zn1−x O Quantum wells

In preceding studies [81,258] , luminescence properties of ZnO/Mgx Zn1−x O quantum wells were investigated. Luminescence spectra were recorded as a function of the well widths in different samples. The well width was extrapolated by the number of laser pulses required to grow a certain ZnO layer by PLD, and accurately measured by X-ray reflectometry. The quality of the interfaces was optimized employing AFM studies of the surfaces, and step flow growth was obtained, at least in the case of growth on a single crystal ZnO substrate. However, despite having thicknesses of up to 6.5 nm only a slight influence of the QCSE was seen. The lowest value of an QW related emission was observed at 3.36 eV, which is roughly the position of the donor bound transition line I6 typically observed in bulk ZnO. This line is present in the emission of all the samples discussed in these studies, as all samples are deposited onto a ZnO buffer layer introduced in order to improve the sample morphology. It is therefore not possible to judge, if a luminescence lower in energy than that of bulk ZnO occurs. In contrast, a strong redshift of the QW luminescence below the bulk ZnO luminescence emission energy due to the QCSE was observed in ZnO/Mgx Zn1−x O samples grown by MOCVD [259] , MBE [38,255,257,260–263] and Laser-MBE [264–267] (which is technically equal to PLD, with the difference, that the distance between the target and the substrate is much larger than the mean free path 105

Transition energy (eV)

3.8 3.6 3.4 3.2 3 0

2

4 6 QW width (nm)

8

10

Inverse Oscillator strength (arb. u.)

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

−10

10

−12

10

−14

10

−16

10

−18

10

0

2

4 6 QW width (nm)

8

10

2

4 6 QW width (nm)

8

10

−9

8 Exciton Bohr radius λ (m)

Exciton binding energy (eV)

0.05 0.04 0.03 0.02 0.01 0

2

4 6 QW width (nm)

8

10

x 10

7 6 5 4 3 2 0

Figure 5.9: Properties of an exciton in a c-oriented ZnO/Mgx Zn1−x O QW with x = 0.18 as function of the QW width obtained from variational calculations. (a) transition energy (b) inverse oscillator strength (c) exciton binding energy and (d) Exciton Bohr radius.

of the particles in the plasma). Interestingly the redshift associated with the QCSE is less pronounced in the samples grown by LMBE, compared to MBE and MOCVD grown samples for the same well width. Further the QCSE was observed in MBE grown ZnO/CdZnO QWs [268,269] .

5.4.2

Luminescence phenomena related to presence of the QCSE

In order to understand the luminescence phenomena to be expected in QWs subject to the QCSE numerical calculations have been performed. The wavefunction of the uncorrelated electrons and holes have been calculated using the poisson solver Beta8c developed by Gregory Snider [246,247] . The exciton binding energy and wave-function have been calculated in the envelope function approximation by a variational approach [270–273] . Herein the exciton is treated as 3-dimensional, which is required due to the strong electric field in the quantum well. While for small well widths a 2-dimensional approach would in principle be valid, this is not the case in broad quantum wells, which is however the case of interest here. The two-body exciton wave function is written 106

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system as Φ = Φe (ze )Φh (zh )Φr (r⊥ , |ze − zh |) ,

(5.1)

where Φe and Φh symbolize the uncorrelated electron and hole wave functions, respectively, and r2 + ζ 2 |ze − zh |2 Φr = exp − ⊥ λ 



,

(5.2)

where ζ is a dimensionless parameter describing the ‘dimensionality’ of the exciton, and λ is the exciton Bohr radius. Only the lowest electron and heavy hole eigenstates of the uncorrelated system are regarded in the following. The total energy of the exciton is minimized in the calculation, by variation of the parameters λ and ζ. The oscillator strength of the exciton is calculated with this parameters following Ref. [273] . The properties of a single exciton determined from these calculations are displayed in Fig. 5.9 as a function of the QW width. Figure 5.9 (a) shows the transition energy of the exciton, which is the energy of the photon observed in an luminescence experiment. Upon increase of the well width Lz the transition energy decreases, due to the lowering of the electron energy level (and the rise of the hole energy level) in the presence of the polarization induced electric field. This effect was observed in all publications cited in the previous section. In fact, the existence of a luminescence peak clearly lower in energy than the I6 transition, which is very often observed in bulk ZnO, and its dependence on the thickness was chosen as a criterion to list the specific publication. Likewise the overlap of electron and hole wave functions decreases due to the increasing spatial separation, and the inverse oscillator strength increases (see Fig. 5.9 (b)). This quantity is proportional to the luminescence decay time, and an increase of the luminescence decay time with increasing well width is frequently observed in the literature [255,257,260–263,267,268] . Further the separation of the electron and hole leads to an increase of the exciton Bohr radius (see Fig. 5.9 (d)) which results in a decrease of the exciton binding energy via the Coulomb interaction (see Fig. 5.9 (c)). In experiments this manifests in an increase of the exciton phonon coupling, and therefore an increase in the Huang–Rhys factor S [264–267] . All the considerations outlined here are drawn for a single exciton. In a real experiment however, the optical excitation will generate an electron hole plasma, which thermally relaxes into the respective minimum, accompanying exciton formation. During this process however additional radiative recombinations can take place, resulting in photons with higher energy than the characteristic luminescence. Additionally the high density of free carriers leads to a partial screening of the polarization induced interface charges in the system, and therefore a reduction of the electric field within the QW. The QCSE will therefore diminish, and a blueshift of the luminescence is expected with increasing excitation strength. Such a behavior has indeed been observed in the ZnO/Mgx Zn1−x O system [260] . 107

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

Figure 5.10: Schematics of ZnO/Mgx Zn1−x O QW samples investigated in the present study. (a) sample grown on sapphire substrate and (b) on ZnO (0001). As indicated the surface polarity of the samples differs in both cases. An additional ZnO buffer layer can be introduced for the sample grown on sapphire, in order to improve the morphology of the Mgx Zn1−x O film.

5.4.3

Observation of the QCSE in ZnO/Mgx Zn1−x O quantum wells grown by PLD

The samples grown for this study follow an idea outlined by Zhang et al. [274] . In spite of having multiple samples of a single thickness each, the sample shows a thickness gradient, result in different QW widths on one sample. This has the advantage of an exactly equal composition of the Mgx Zn1−x O barrier layer for all QW widths. This is not guaranteed if multiple samples of individual thickness are used, as the Mg content x of the layers deposited increases slightly during the lifetime of a ceramic target. The reason for this behavior is most likely a selective evaporation of Zn from the target, which has a much higher vapor pressure than Mg. The resulting films therefore have to be carefully compared regarding their composition. This complication is completely excluded by the present approach. The gradient of the thickness is small enough, that within the excitation spot of the PL experiment of 100 µm diameter a thickness variation of less than 0.1 nm occurs, even for the thickest QWs investigated. This results in a maximal change of a single unit cell height of the QW width, which is inevitable anyway, as the growth of an exact number of atomic layers can not be realized over the whole sample by conventional PLD. It has to be outlined, that introducing an in-situ RHEED analysis could in principle allow for such high accuracy, the realization itself however is demanding. As the growth setup employ does not include such equipment, no additional error sources are introduced by the shape of the sample in the PL experiment. An additional complication however arises, which is the determination of the QW width Lz at the individual point investigated in the experiment. This is much easier in a sample of uniform thickness as techniques like X-ray reflectometry or spectroscopic ellipsometry can be employed, which would be obscured by the thickness variation inside the detection spot. It has nevertheless been shown in a previous study [81] and also in this work, that the number of laser pulses relates linearly to the thickness of the film above a critical thickness. 108

CL-Intensity (arb. units)

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system

1000

100

10

1 3.0

3.1

3.2

3.3

3.4

Photon energy (eV)

CL-Intensity (arb. units)

1000

100

10

1 3.20

3.25

3.30

3.35

3.40

3.45

3.50

3.55

3.60

Photon energy (eV)

Figure 5.11: Low temperature CL spectra obtained from two otherwise equal Zno/Mgx Zn1−x O QWs deposited at two different laser fluences: (a) lense in position 2 (low fluence) (b) lense in position 1 (high fluence). The spectra are color coded, red corresponds to a high, blue to a low QW thickness. (Data obtained by Jan Zippel)

109

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

CL-Intensity (arb. units)

10000

1000

100

10

3.0

3.1

3.2

3.3

3.4

Photon energy (eV)

Figure 5.12: Excitation dependence of the CL spectra of a sample showing a pronounced QCSE. The excitation currents are 800 nA, 1600 nA, and 2,000–8,000 nA in steps of 1,000 nA. (Data obtained by Jan Zippel)

The error introduced by this approximate thickness determination is below the experimental error of the thickness determination by X-ray reflectometry or spectroscopic ellipsometry, as the coefficients can be determined from measurements of comparatively thick films by the same techniques, reducing the relative error by more than two orders of magnitude. Additionally, as discussed in Chap. 3.2.1, the error introduced by a 3-dimensional nucleation process in the beginning of the thin film growth is negligible allowing the exact determination of the growth rate from the absolute thickness of a film thicker than 100 nm. This leads to the conclusion that an equally exact determination of the QW thickness is possible from the total thickness of the layer stack in the individual spot investigated. The thickness of the whole stack was assessed for selected samples by scanning electron microscopy on a cross section prepared by in-situ ion milling in an focused ion beam microscope. Cross sections were prepared on both sides of the sample, and the thickness inside was assumed to show a linear gradient. As the QW thickness is not determined directly, for all evaluations, were this thickness is not required, the actual measured quantity, which is the position on the sample is given in the following. In the preceding sections it was shown, that the QCSE can in general be observed in ZnO/Mgx Zn1−x O QW structures. It became clear, that growth methods involving low energy atomic species, such as MBE and MOCVD are suitable for the growth of the sharp heterointerfaces required to see the QCSE. In contrast no convincing report has yet emerged showing the QCSE in PLD 110

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system grown samples. The occurrence of the QCSE in samples grown by the PLD related technique LMBE is much less pronounced than in the case of MBE and MOCVD. It has been speculated that the high energy of impinging adatoms leads to a damage of the topmost atomic layers of the sample, and therefore enhances the interdiffusion of ZnO and Mgx Zn1−x O. This thesis will be proven unambiguously by the experimental data given in the following. The mean to control the kinetic energy of the impinging particles is the fluence of the laser pulses used to ablate the target. In the setup employed in the present study, the fluence is controlled by the position of a focusing lense in the light path. The CL spectra shown in Fig. 5.11 have been obtained on two selected samples grown with different lense positions, noted as position 1 (corresponding fluence 2.4 J/cm2 ) and position 2 (corresponding fluence 1.75 J/cm2 ). The CL spectra were obtained at similar positions on the sample, covering the whole thickness gradient. A remarkable difference in the spectra is observed. For the sample grown at the lower laser fluence a pronounced redshift of the luminescence maximum below the I6 transition is observed (see Fig. 5.11 (a)), which systematically depends on the position investigated on the sample. In contrast, the luminescence spectra of the sample grown at the high laser fluence have their maximum either at the spectral position of the I6 line, or at even higher energy (see Fig. 5.11 (b)). The observation of the I6 luminescence originates in the ZnO buffer layer. A systematic shift is indeed observed, however the luminescence energy of the maximum is always at least 80 meV higher than in the sample grown at the lower laser fluence. This indicates, that the QCSE is significantly reduced in this sample, which is attributed to an interdiffusion of the ZnO and Mgx Zn1−x O layers in the vicinity of the interface. However, in principle another origin is thinkable. A high density of residual donors in the sample grown at higher laser fluence would result in an increase of the carrier density accumulating at the interface, and therefore in partial compensation of the polarization induced sheet charge at the heterointerfaces responsible for the electric field inside the QW. The free electron concentration was determined by Hall-effect measurements, and was roughly 1016 cm−3 in both samples. Although the density of free carriers in the vicinity of the QW can not be directly inferred from this value, it indicates that no significant differences exits between the samples. Numerical calculations show that the QCSE is as well expected in samples with a donor concentration of 1018 cm−3 . Therefore this alternative origin of the diminishing of the QCSE in samples grown at a high laser fluence is ruled out. In order to evaluate the magnitude of the change of the field induced carrier separation due to high carrier densities in the QW, CL experiments have been carried out with different excitation currents. The current has been varied between 800 and 8,000 nA at an acceleration voltage of 5 kV. The resulting spectra are depicted in Fig 5.12. A systematic blueshift with increasing excitation current is indeed visible, as has already been observed in Ref. [260] . The overall magnitude of the spectral shift is ≈ 60 meV in the range of currents employed in the present study. The luminescence intensity increases by more then a factor of 20, which is roughly equal to the increase in the excitation 111

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures power. The overlinear increase can be explained by the increase in the oscillator strength of the excitonic transition due to an increased overlap of electron and hole wave functions. Photoluminescence investigations have been carried out on samples of different Mg contents x. Both, samples grown on sapphire and on O-face ZnO were investigated. The spectra obtained on two selected samples are displayed in Fig. 5.13. The spectra depicted in Fig. 5.13 (a) are obtained from a sample directly deposited onto an a-plane sapphire substrate, without a buffer layer. The spectra given in Fig. 5.13 (b) are measured on a sample grown on a ZnO substrate. All spectra were normalized to the intensity of their QW luminescence. The measurement position is color coded where blue indicates low and red high QW thickness, respectively. A clear redshift of the QW luminescence with increasing QW thickness is observed for both samples. For the sample directly deposited onto sapphire an additional feature is observed for the high QW thicknesses at 3.379 eV. The spectral position is not a function of the QW thickness, which indicates that the origin of the luminescence feature is not the QW. A spectral feature labeled XI was observed in a previous work in the range of 3.39–3.4 eV in QW samples [81] . It has been speculated in this work, that this luminescence feature originates from the interface between the ZnO buffer and the Mgx Zn1−x O barrier layer in the samples discussed therein. This assertion can not be supported here, as no ZnO buffer layer is present in the sample in question. It however remains unclear, if the origin of the peak reported here is the same as in Ref. [81] . For the sample grown on ZnO additional to the QW luminescence contributions from the luminescence of the underlying substrate is visible. The spectral position of typical ZnO luminescence lines is indicated in Fig. 5.13 (b), namely the lines I6 , I3a , I0 and FX are given in the plot, corresponding to the luminescence from excitons bound to the neutral aluminum donor (Al0 X), the zinc interstitial donor (Zni X), the ionized aluminum donor (Al+ X) and the free A-exciton respectively. Interestingly, if the spectral position of the luminescence of the quantum well coincides with that of the ZnO luminescene, an absorption line is visible in the QW luminescence at the position of the free exciton, indication that • A sizeable fraction of the photons measured in the PL experiment are not directly emitted from the sample, but undergo a reflection, either at the back side of the substrate or at at the film–substrate interface. • An excitation in the substrate takes place via the formation of free excitons by the incident light from the QW luminescence. • The free excitons created in the substrate by the QW luminescence do not recombine instantly, but are likely to be bind to defects, and recombine there with a lower emission energy. The luminescence from the quantum well shows pronounced phonon replica, which indicate a strong exciton phonon coupling in the quantum well. It can be observed that 112

Normalized Intensity (arb. units)

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system

3.10

3,379 eV

3.15

3.20

3.25

3.30

3.35

3.40

Normalized Intensity (arb. units)

Photon energy (eV)

3.10

3.15

3.20

3.25

3.30

3.35

3.40

Photon energy (eV)

Figure 5.13: Normalized PL spectra of two samples with different Mg content x in the barrier (a) x = 0.23 and (b) x = 0.28. The sample shown in Fig. 5.13 (b) was grown on the O-face of a ZnO substrate. The measurement position is color coded: blue denotes low QW thickness, while red corresponds to high QW thickness. (Data obtained by Martin Lange)

113

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures • The exciton phonon coupling strength increases with increasing well width, as the intensity of the first phonon replica increases systematically with increasing well width. • The exciton phonon coupling strength of the QW well luminescence exceeds that of the donor bound excitons in bulk ZnO, which is seen for the thinnest QWs. There a significant peak is seen at the I6 position, exceeding the intensity of the QW luminescence by more than a factor of 5. In contrast for the first phonon replica the peak shape has changed and only a weak shoulder is observed corresponding to the replica of the I6 line. The spectral position of the maximum of the QW related emission was evaluated and is given in Fig. 5.14 (a) for different sample positions. The location on the sample was carefully controlled by an adjustable sample holder, and the 10x10 mm sample was scanned over the whole width. The spectral position of the ZnO luminescence is indicated. Though the thickness of the quantum well is not directly known, it can be inferred from the position on the substrate. The samples are all grown under the same conditions and employing the same pulse numbers. Electron micrographs for one of the samples allow to calculate a thickness variation of the QW from 2.9–4.3 nm. A systematic redshift is observed for all samples with increasing thickness. An increase in the shift is observed with increasing Mg content x. However a significant difference in spectral the position of the QW luminescence is seen between the samples grown an sapphire and these grown on ZnO. The QW emission energy measured in the samples grown on sapphire is always lower than that in the samples grown, typically by 20 meV. Several possible reasons for the change exist. First of all, in the samples grown on ZnO the Mgx Zn1−x O layer is compressively strained, while the ZnO layer is relaxed. This situation is reversed if the Mgx Zn1−x O layer is directly deposited onto sapphire. The Mgx Zn1−x O layer is relaxed, while the ZnO is under tensile strain, which induced a reduction of the band gap of the ZnO. The shift in the bandgap does however only account for x×16 meV, which is below the experimental observed values. Additional processes have to play a role here. It has to be remarked, that the different strain does not influence the change in polarization trough the piezoelectric polarization, which is proportional only to the change of the a-axis lattice constant in the strained layer. This change is exactly equal if either the Mgx Zn1−x O barrier layer or the ZnO QW layer is strained. Also a dependence of the QW thickness on the substrate chosen is unlikely, but can not be completely excluded. High resolution TEM investigations of the QW region should reveal the thickness of the QW in detail, and allow determination of the change in polarization in both cases. HR-XRD measurements and Raman investigations are required in order to unambiguously determine the strain of the barrier layer, and allow a calculation of the strain in the quantum well. Figure 5.14 (b) gives the dependence of the Huang–Rhys factor of the first phonon replica of the QW luminescence on the spectral position of the QW luminescence maximum. A systematic increase is observed with decreasing 114

QW Luminescence Energy [eV]

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system

3.40 3.38

FX

3.36

I6

3.34 3.32 x=0.23

3.30

x=0.22 x=0.28

3.28

x=0.27

3.26 0

2

4

6

8

10

Position on sample [mm]

I6

0.18

FX

Huang-Rhys Faktor S0

0.16 0.14 0.12 0.10 0.08 x=0.23

0.06

x=0.22

0.04

x=0.28

0.02

x=0.27

0.00 3.26

3.28

3.30

3.32

3.34

3.36

3.38

QW Luminescence Energy [eV]

Figure 5.14: (a) Position of the QW related luminescence maximum for two samples grown on sapphire (open symbols) and two grown on ZnO (full symbols) with different Mg content x measured at different positions on the sample. (b) Huang– Rhys factor S0 calculated from the main transition and the first phonon replica as a function of the spectral position of the main peak.  corresponds to samples grown on ZnO substrates, while • indicates the samples grown on sapphire. The position of important ZnO related emission lines is indicated. (Measurements performed by Martin Lange)

115

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

Decay-time [ns]

PL-Intensity [arb. units]

100

10

1

0.1 3.15

3.20

3.25

3.30

3.35

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3.45

3.7

10-3

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10-4

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3.4 3.3

10-6

3.2

10-7

3.1

10-8

Decay time [s]

QW Emission Energy [eV]

Energy [eV]

3.0 10-9

2.9

10-10

2.8 0

2

4

6

8

10

QW thickness [nm] Figure 5.15: (a) Pl maximum position (left scale) and decay time (right scale) as a function of the luminescence energy. (b) Dependence of the luminescence energy (left scale) and decay time (right scale) at the maximum of the QW luminescence on the QW widths. Full symbols give data obtained in this study, while open symbols are taken from Ref. [262] . Solid lines give the expected dependence from the variational calculations. (Spectra obtained and time constants determined by Marko Stölzel, QW thickness calculated from measurements by Jörg Lenzner)

116

5.4. The quantum confined Stark-Effect in the ZnO/Mgx Zn1−x O system transition energy, in accordance with previous publications [264–267] . In addition an increase in the luminescence decay time is observed from time dependent luminescence experiments. The dependence of the decay time on the emission energy is given in Fig. 5.15 (a). The spectrum chosen contains essentially three parts, which are, from left to right: the phonon replica of the QW luminescence (3.1–3.27 eV), the QW luminescence (3.27–3.35 eV) and a luminescence of unknown origin (3.35–3.45). While the luminescence decay time is as low as ≈ 300 ps for the luminescence of unknown origin, a systematic increase in the decay time is observed, for lower luminescence energies. Interestingly a maximum is reached at a transition energy where a minimum in the luminescence is observed. The QW luminescence dominates at higher energy, the phonon replica at lower energy. It is therefore concluded, that the QW luminescence itself does not consist of a single luminescence process with a single time constant, but represents a dynamic relaxations of the free carriers created by the excitation. After the excitation the free carriers screen the polarization induced sheet charges partially, which leads to a higher transition energy than in the dilute limit. However, carriers decay radiative and non radiative and additionally diffuse in the plane of the quantum well to areas which are not subject to the excitation. The overall density of carriers in the active region of the QW therefore decreases with time, and the luminescence red-shifts, as the screening of the polarization induced sheet charges by the free carriers is reduced. The luminescence shifts to lower energies while increasing the time interval after excitation, as the system approaches the dilute limit. In principle, the carrier dynamics can be understood from the present data already, but sophisticated models would be required to include the in-plane motion of the free carriers and excitons, exciton formation and radiative and non radiative recombination rates. Such an evaluation will not be performed in the present thesis. A detailed investigation of the luminescence energy versus time behavior is highly helpful to understand the recombination dynamics completely. Such data can be obtained employing a streak camera, which allows the observation of the time dependence of several energetic channels simultaneously. Additionally, the spatial dependence of the luminescence should be investigated, possibly by using a micro-luminescence setup as described in [275] or by observation of spatially masked samples, as described in Ref. [276] . Figure 5.15 (b) shows the luminescence energy of the maximum of the QW emission and the related decay time as a function of the QW thickness as calculated from the cross section micrographs and the position on the sample where the spectra were obtained. The Mg content x in the barriers was x = 0.18, the spectra at the individual positions are displayed in Fig 5.13 (a). Data from Ref. [262] is included for reference. The solid lines show the expected transition energy and a quantity proportional to the inverse oscillator strength as given by the variational calculations. This quantity was normalizes to the low thickness decay time obtained in Ref. [262] , as for the lowest QW thickness the influence of non radiative recombination is the smallest, assuming a thickness independent non radiative recombination rate. The coincidence of the values is remarkable, underlining, that the samples present in this study are 117

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures equal in both interface quality and density of non radiative defects to the MBE grown samples studied in Ref. [262] . It also shows, that a determination of the polarization as function of the Mg content is possible from the present samples, if the recombination properties of the excitons in the dilute limit are known. An estimation is already possible at present yielding a value of 0.24 C/cm2 in close agreement with previous studies. Further investigation will be required to improve the accuracy of this value, and could in principle help to accurately quantify further unknown material parameters as the conduction band offset in Zno/Mgx Zn1−x O heterostructures and the effective hole masses.

5.5

Summary and conclusion

The results of this chapter can be summarized as follows: • 2D growth in the Burton–Cabrera–Frank mode has been observed for the ZnO/Mgx Zn1−x O single heterostructures and ZnO/Mgx Zn1−x O quantum wells grown on a-sapphire. The effective surface roughness in these samples is of the order of the thickness of the quantum wells present in the structures. • In contrast, a significant improvement of the structural and morphological properties of the ZnO/Mgx Zn1−x O quantum wells grown on ZnO is observed. Step flow growth leading to perfect vicinal surfaces could be achieved for these samples as confirmed by atomic force microscopy. The Mgx Zn1−x O layers were confirmed to be grown pseudomorphic by high-resolution X-ray diffraction. • Electron accumulation layers have been observed for ZnO/Mgx Zn1−x O single heterostructures grown on sapphire by Capacitance–Voltage spectroscopy and temperature dependent Hall-effect measurements. • Indications for the presence of a 2DEG in ZnO/Mgx Zn1−x O quantum wells grown on ZnO were found by temperature dependent Hall-effect measurements. For a clear observation of the transport properties of the 2DEG further improvements is still necessary. The contributions of the degenerate layer have to be removed and the conductivity of the bulk material has to be reduced. • Quantum confinement effects have been confirmed previously by photoluminescence PL measurements [258] . A narrowing of the PL peak width is observed in quantum wells grown on ZnO, especially for low well width, due to the higher influence of the interface roughness on thinner quantum wells. • Careful control of the laser fluence applied to the PLD target resulted in a significant improvement of the quality of the heterointerface in ZnO/Mgx Zn1−x O heterostructures. A pronounced QCSE was observed in PLD grown samples for the first time. Comparison with data obtained 118

5.5. Summary and conclusion on MBE grown samples given in the literature revealed, that the samples discussed here equal the MBE grown samples both in interface quality and in density of non-radiative recombination centers. • The use of a slanted QW allowed the observation of quantum confinement effects in QW of different thicknesses in one sample with a well defined barrier composition. However, uncertainties in the thickness of the determination are present. The use of an in-situ RHEED observation would help to determine and control the thickness of individual layers.

119

5. Quantum effects on carriers in ZnO/Mgx Zn1−x O heterostructures

120

Chapter 6 Polarization related effects in ZnO/BaTiO3 heterostructures The preceding chapter discussed the influence of a change in the electric polarization at a semiconductor heterointerface on the locaization of free carriers. The interface was controlled to be atomically abrupt, which allowed the observation of quantization effects. While the change in polarization could be controlled via the Mg content x, and a determination of this change as a function of x was possible, it remained a constant value in one single structure. The effects on mobile carriers induced by the polarization where the same in equilibrium, regardless of the history of the sample. Nevertheless, the occupation of the individual accumulation layers can be modified by optical excitation (see Chap. 5.4), and the dynamics of the system approaching equilibrium was monitored. In principle the equilibrium configuration can be modified by the application of an electric field. This modification however is only effective as long the electric field is applied. This behavior is contrasted by the material class of ferroelectrics. As outlined in Chap. 3.3 BaTiO3 (BTO) will serve as a model ferroelectric within the present study. Upon the formation of heterostructures between ZnO and BTO interesting physical phenomena can be anticipated. First the polarization of the ZnO will, if aligned perpendicular to the interface between the layers, influence the polarization in the BTO. This polarization can be controlled by the external electric field, and will, at least to some extent remain in the state it was polarized to, even in the absence of the external field. Like in the case of the ZnO/Mgx Zn1−x O heterostructures the density of free carriers in the ZnO will be influenced by the change in polarization across the interface. Depending on the orientation of this difference either carrier accumulation or depletion is expected in the ZnO layer, again in accordance with the ZnO/Mgx Zn1−x O heterojunctions. This however will have a subtle influence on the value of the external electric field forming in the individual parts of the heterostructure, as a function of external voltage. This in turn will influence the polarization in the BTO layer. The behavior of the structure can therefore not be predicted from the applied voltage to the heterostructure alone, but is also a function of the history of applied voltages. 121

6. Polarization related effects in ZnO/BaTiO3 heterostructures Within the present thesis a detailed understanding of the behavior of ZnO/BTO heterostructures has been developed. The work was carried out in close collaboration with Venkata M. Voora and Prof. Dr. habil. Mathias Schubert from the University of Nebraska Lincoln. A description of the model employed to understand the properties of ZnO/BTO heterostuctures will be given in Chap. 6.2. Before that, the effects observed experimentally will be summarized in Chap.6.1. An application in the form of ZnO/BTO based ferroelectric thin film transistors will be presented in Chap.6.3.

6.1 6.1.1

Effects observed in ZnO/BTO heterostructures ZnO/BTO samples grown on Si

For the first investigations into ZnO/BTO heterostructures such junctions were grown by PLD on Si substrates. In order to form ohmic contacts to both sides of the heterojunction, Pt was used as a bottom and top electrode. The BTO and subsequently the ZnO were than deposited onto the bottom Pt contact, which was previously DC-sputtered on the Si substrate. ZnO grows highly textured polycrystalline on the polycrystalline BTO, with a preferred c-axis (002) orientation of the ZnO and multiple different orientations of the BTO [277] . The phase transition from the tetragonal ferroelectric phase to the cubic paraelectric phase was observed in such structures by Raman and C–V measurements [277] . Polarization measurements revealed a significant change in the ferroelectric hysteresis loop in the presence of a ZnO layer adjacent to the BTO [278] . While the S–T loop of a single BTO layer is highly symmetric, a strong asymmetry is observed in the ZnO/BTO heterojunctions. The actual shape depends strongly on the measurement parameters, as cycling frequency and voltage amplitude. This behavior was already reported in Ref. [278] , and is exemplified in Fig 6.1. In general the area surrounded by the loop increases with increasing voltage amplitude, indicative for the fact, that the polarization of the ferroelectric increases. This further shows, that the polarization of the ferroelectric in the investigated junction is not in saturation yet. Additionally the current flowing trough the heterostructure shows a hysteresic behavior as depicted in Fig. 6.2. The overall shape of the I–V dependence resembles that of a semiconductor diode. For such a structure the current voltage characteristic can be modeled following Eqn. 2.18. The determination of the barrier height and ideality factor is obscured by the presence of the hysteresis, however the parallel and series resistance can be estimated with high accurancy. Especially the parallel resistance can be easily calculated from the current in backwards direction. For the modeling the average of both parts of the hystersis loops was used. Therefore numerous heterojunctions were measured on a 3 inch wafer of Si. Maps of the parallel and series resistance are given in Fig. 6.3. The spread in the parallel resistance is almost 3 orders of magnitude, and the parallel resistance can be as low < 104 Ω for individual contacts. The series 122

6.1. Effects observed in ZnO/BTO heterostructures 100.00 Hz

1000.00 Hz

3

1

2

0.5

1

0

0

Vo

Vo

4

-1

-0.5 -1

-2 -1.5 -3 -2

-4 -5

0

5

-5

Vi

0

5

Vi

10000.00 Hz

100000.00 Hz

1 1

2V 3V 4V 5V 6V 7V 8V

0.5 0.5

Vo

Vo

0 -0.5

0

-0.5

-1

-1

-1.5 -2

-1.5 -5

0

5

-5

Vi

0

5

Vi

Figure 6.1: Sawyer–Tower-circuit response of a ZnO/BTO heterostructure grown on Si with Pt contacts measured at various cycling frequencies and voltage amplitudes as indicated. The data was obtained from selected contacts on the wafer shown in Fig. 6.3.

resistance has a much smaller spread, but remains of the order of 100 Ω. This value is much to small, if the BTO is to be considered as an insulator. The polycrystalline nature of the BTO introduces a high density of grain boundaries, which most likely serve as parallel conducting channels trough the BTO layer. Also the density of shunts trough the ZnO must be very high, resulting in the low parallel resistance. The structure is able to serve as a model to understand physics of ZnO/BTO heterojunctions, an application in an electrically driven device is unlikely in the present form, as parasitic power consumption would be huge.

123

current density (A/cm2)

6. Polarization related effects in ZnO/BaTiO3 heterostructures

10-2 10-3 10-4 10-5 10-6 -2

0

2

Voltage (V)

Figure 6.2: Current voltage characteristic of a ZnO/BTO heterojunction grown on Si with Pt contacts.

6.1.2

ZnO/BTO samples grown on lattice matched substrates

In order to improve the properties of the BTO layers, thin BTO films were grown on isostructural substrates, in this case STO substrates [279] . In order to form contacts to the back side of the BTO films, either a conductive SRO layer was deposited prior to the deposition of the BTto the samples grown on silicon. First of all, the structural properties differ largely. Figure 6.4 shows the 2Θ–ω scans of a sample grown on silicon and one deposited onto STO. The same angular range is chosen for better comparison. The peaks related to the ZnO and the BTO layers are encircled in blue and green respectively. While in both cases only one (002) ZnO reflex is found in the whole angular range due to the tendency of ZnO to grow c-axis oriented [87–90] , the situation is different for the BTO. Three different orientations of BTO crystallites are observed for the material grown on Si, while only the (001) orientation is present in the material grown on the STO substrates. Further, the peak width of both (002) ZnO and (001) BTO is reduced on the STO substrate. The peak intensity of the ZnO (002) reflection is increased by more the two orders of magnitude for the ZnO/BTO heterostructure grown on the STO substrate, indicating that a uniform, defined BTO (001) underlayer results in a much better orientation of the ZnO layer on top of it. While no in-plane epitaxial relationship between ZnO and BTO was found by XRD in ZnO/BTO heterostructures grown on Si, such a relationship is seen for the films grown on STO substrates. Figure 6.5 gives φ-scans of the STO substrate, and the BTO and ZnO layers. From the alignment of the four (103) BTO peak with the (310) STO peak it can be inferred, that the BTO grows with the [100] and [010] directions of the STO and the BTO aligning. In contrast, the (104) ZnO reflection shows a 12 fold in-plane symmetry, where none of the peaks coincide with that of the (103) BTO and (310) STO peak. Four of the 12 peaks are however shifted by 45◦ with respect to the (103) BTO and 124

6.1. Effects observed in ZnO/BTO heterostructures

3

> 5×10 W 4

> 1×10 W 4

> 2×10 W 4

> 5×10 W 5

> 1×10 W 5

> 2×10 W 5

> 5×10 W 6

> 1×10 W 6

> 2×10 W 6

> 5×10 W

> 40 W > 50 W > 60 W > 70 W > 80 W > 90 W > 100 W > 110 W > 120 W > 130 W

Figure 6.3: Maps of the (a) parallel and (b) series resistance of ZnO/BTO heterojunctions of a 3 inch silicon wafer. Individual contacts are color coded. Colors represent certain values of the parallel and series resistance, whereas gray contacts show an ohmic behavior.

125

6. Polarization related effects in ZnO/BaTiO3 heterostructures

Pt (111)

BTO(002)

BTO(111)

ZnO(002)

102

Pt/Si(011)

103

BTO(110)

104

BTO(001)

Intensity counts (arb.u.)

105

101 100 20

25

30

35

40

45

50

105

STO(200)

BTO(002) Au (111)

ZnO(002)

106

104

K

K

103 K?

Intensity counts (arb.u.)

107

BTO(001) STO(100)

2? (°)

102 101 100 20

25

30

35

40

45

50

2? (°) Figure 6.4: Wide angle 2Θ–ω scans of ZnO/BTO heterostructures grown on (a) Si/Pt and (b) STO/SRO. The Peaks corresponding to ZnO and BTO are encircled in blue and green, respectively. On Si/Pt, the BTO shows a polysrystalline orientation, whereas on STO/SRO the BTO is (001) oriented. (Data obtained by Aziz Abdullah and Dr. Michael Lorenz)

126

6.1. Effects observed in ZnO/BTO heterostructures

Intensity (cps)

STO:Nb (310) BTO (103)

ZnO (104)

103

102

101 -180

-90

0

90

180

ϕ (°) Figure 6.5: XRD φ-scans of a ZnO/BTO heterostructure grown on a STO:Nb substrate. The scans were performed using the asymmetric (104), (103), and (310) reflexes of ZnO, BTO, and STO, respectively on a wide-angle goniometer. (Data obtained by Dr. Michael Lorenz)

(310) STO peaks. This indicates an in-plane epitaxial relationship, where the [100] ZnO direction is parallel to the [110] BTO direction. As there exist four equivalent [110] direction in the BTO lattice, which are rotated by 90◦ each, and ZnO does not contain the 90 degree rotation as a symmetry element, two different types of ZnO crystallites must be present in the sample. As ZnO contains the 60◦ rotation as a symmetry element, both types of crystallites are rotated by 30◦ , giving a twelfefold reflex pattern. The presence of such 30◦ rotational domains is reported for ZnO grown on c-plane sapphire [280] . It has also been reported that these 30◦ rotational domains correspond to an inversion in the ZnO polarity [34] , in that case rendering a sample with both Zn- and O-polar crystallites. In addition to these changes in the crystal structure, the electrical properties of the ZnO/BTO heterostructures grown on STO improved compared to the samples grown on silicon. The leakage current reduced significantly, down to values in the nA range for BTO layers of roughly 1µm thickness. The leakage current is a function of the BTO thickness, and increases with decreasing thickness. Fig. 6.6 shows the current voltage characteristic of a ZnO/BTO heterostructure consisting of a 800 nm thick BTO and a 500 nm thick ZnO layer. A significant hysteresis is again observed, however the shape differs significantly from that in the heterojunctions grown on Si. This can be understood if the origin of the hysteresis is considered. In the ZnO/BTO heterostructures a depletion layer is formed, if a positive voltage is applied to the ZnO side 127

6. Polarization related effects in ZnO/BaTiO3 heterostructures

Current (nA)

2dBTOEC

t i (ms) 0.2 2 20 200 2000

6 4 2 0 -2

dZnOPZnO/ε

-4 0

5

10

15

20

Voltage (V) Figure 6.6: Current flowing into a ZnO/BTO heterostructure grown on a STO:Nb as function of applied voltage and integration time. The ZnO has a thickness of 500 nm, the BTO 800 nm.

of the junction, which is large enough to remove possible accumulation in the vicinity of the heterointerface caused by the difference in the electric polarization of ZnO and BTO. Such a depletion region will lead to the formation of a potential barrier, which impedes the transport of carriers. If the structure has a low series resistance, the transport is largely controlled by the presence of this potential barrier. The current flowing is controlled by the presence of the depletion layer, which in turn is also a function of the change in polarization at the interface between ZnO and BTO. This difference is a function of the polarization in the BTO, which shows a typical ferroelectric hysteresis. This case is present in the ZnO/BTO heterostructures grown on Si. In contrast, if the resistance of the heterostructure is very large, the current is mostly limited by the series resistance. The formation of the depletion layer will therefore only have a small influence on the transport properties, and no significant hysteresis will be observable related to the different extension of the space charge region and the difference in the polarization at the interface. The currents measured are not only currents flowing trough the structure, but also currents transporting the charge necessary to change the ferroelectric polarization. As the current trough the structure is now small enough, the polarization current determines the I–V characteristic. Such a behavior is also observed for highly insulating BTO single layers [281] . The current will be a function of time, as the charge necessary to switch the polarization of the ferroelectric domains is finite. This behavior is observed in Fig. 6.6, where two contribution of the 128

6.1. Effects observed in ZnO/BTO heterostructures current can be distinguished. The hysterestic part of the current decreases with increasing integration time. It is remarkable, that this current can be negative, even if the applied voltage is positive. This can be understood by the influence of the ZnO polarization, which can not be changed by the applied voltage. In a ferroelectric, the current transporting the charge necessary to change the polarization will show a maximum at the voltage position of the steepest inclination in the ferroelectric hysteresis loops [281] . At this point the largest change in polarization per unit voltage occurs. Assuming a constant voltage cycling rate (which can be controlled in the experiment), the rate of unit voltage per unit time is constant. Therefore, at the steepest point in the ferroelectric hysteresis the largest current will flow into the structure. In an ideal undisturbed ferroelectric, the hysteresis loop will be symmetric with respect to zero. In the presence of a ZnO layer, however, the BTO polarization will have a preferred orientation which is related to the magnitude of the polarization in the ZnO. The hysteresis loop will therefore be shifted along the voltage axis. The value of the ZnO polarization can be deduced from the magnitude of this shift, which in this case is PZnO = 0.2 ± 0.05 µC. Additionally, in an ideal ferroelectric, the steepest change in the polarization versus voltage occurs at the point where the polarization is zero. If the presentation of P (E) is considered, the electric field at this point is the coercive field. The maxima observed in the current voltage dependence can therefore be used to determine the coercive field, in this case EC = 12.5 ± 1 kV/cm. This value is comparable to typical values obtained from BTO thin films [282] . The ZnO polarization however, is about on order of magnitude smaller than in the literature [16,17,283,284] . Figure 6.7 shows the I–V curves obtained on two contacts of the same sample with a ZnO thickness of 50 nm and a BTO thickness of 800 nm. The leakage currents are again below 1 nA, and peaks are observed in the I–V curves. The separation of the peaks is much less pronounced in this case, and the peaks are significantly broadened. Also the mean value of the peaks lies at smaller voltage amplitudes, which is understood regarding the smaller film thickness. It has therefore to be pointed out, that the relative width of the peaks is larger compared with that measured in the sample with the 500 nm thick ZnO film. The experimental errors are therefore increased. It is nevertheless obvious, that differences exist in both curves. While in Fig. 6.7 (a) the center of gravity of curves is at a positive voltage, it is at a negative voltage in Fig. 6.7 (b). This indicates, that two different ZnO polarization orientations influence the transport properties of both contacts, which are on the same sample. This can be understood assuming the same situation is present in ZnO growth on BTO as it is on c-sapphire [34] . It has however to be remarked, that the origin of the two ZnO polarities might be slightly different. In the case of ZnO on c-plane sapphire, the reason for the existence of both polarities is that the first layer of ZnO might either be a O layer or a Zn layer, depending on the bonding partner in the topmost layer of the sapphire. The binding to aluminum atoms is energetically preferred considering a single bond, however the formation of crystallites of the Zn face polarity results in a high (31.8%) lattice mismatch. The bonding to oxygen atoms in the topmost layer is less favorable for a single 129

6. Polarization related effects in ZnO/BaTiO3 heterostructures

2

a) Current (nA)

1.5 1 0.5 0 -0.5 -1 -1.5 -5.0

-2.5

0.0

2.5

5.0

0

2

Voltage (V) b) Current (nA)

0.4 0.2 0 -0.2 -0.4 -0.6 -6

-4

-2

Voltage (V) Figure 6.7: Current–voltage characteristic of two selected contacts of a ZnO/BTO heterstructure grown on STO:Nb with a reduced ZnO thickness of 50 nm.

130

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures bond, however represents the global energy minimum. It is a question of the growth temperature if this global minimum is reached. Both growth orientations can coexiste in one sample [34,280] . The situation is different for the growth of ZnO on BTO. The existence of 30◦ rotational domains in ZnO is inherent to the symmetry of the BTO lattice. Nevertheless the topmost layer contains at least two species, Ba and O. If the BTO unit cell is not completely filled, Ti is also present in the topmost layer. Bonding sites therefore exist for both Zn and O, and the coexistence of both polarities is thinkable. In order to form high quality ZnO films on BTO the polarity of the ZnO has to be controlled. The presence of both 30◦ rotational and inversion domains will hinder in-plane transport in the ZnO, which is a key issue for the formation of devices such as field effect transistors.

6.2

Theory of coupling phenomena in ZnO/BTO heterostructures

From the experimental observations considerations about the nature of the coupling of the polarization of ZnO and BTO, and the formation of depletion layers within the heterojunctions arose. Those considerations do not only include the single ZnO/BTO heterostructures, as discussed in the previous section, but also double ZnO/BTO/ZnO heterostructures. No extension of the physical assumptions included in the model is required to predict the properties of such a structure, once single heterostructures are understood. The work was carried out in close cooperation with Venkata M. Voora and Prof. Dr. Mathias Schubert (University of Nebraska, Lincoln). Some of the results presented in this section were published previously [283,285,286] .

6.2.1

Derivation of a model describing the coupling phenomena

The properties of the heterostructures are derived from the distribution of charges within the individual layers. For simplification several assumptions are drawn in the beginning. 1. The BTO is treated as to be ideally insulating. As outlined in the preceding section, this is not self-evident. It can however be motivated, that upon adequate experimental conditions BTO layers of very high resistivity can be grown. For the best insulating layers the resistivity of the BTO layers was more then 12 orders of magnitude above that of the ZnO. Even for inferior samples, the assumption is still valid in the form that the conductivity of the BTO is negligible compared to that of the ZnO. This assumption however introduces a limitation to the model, that is, that the current passing through the heterojunctions will not be predictable. The model will therefore be limited to a capacitive response of the heterostructures. Nevertheless, a detailed understanding of the distribution 131

6. Polarization related effects in ZnO/BaTiO3 heterostructures of space charge regions will be gained from the model, which will prove valueable, at least for a qualitative understanding of the current flow in the structures where the space charge regions introduce the main limitation to the current flow. As a consequence, however, the current flowing through the structure must be zero. 2. Any charge transport within the junction will be instantaneous. No explicit time dependence exists for the ferroelectric response to an applied field, and for the ionization of the donors in ZnO upon formation of a depletion layer. Tough neither of these two facts is true in a real sample, the assumption introduces significant simplifications in the calculation of the properties as any explicit time dependence is removed from the quantities involved. Additionally, the experiment can be easily performed sufficiently slow that explicit time dependence of as well the ferroelectric response as the donor ionization does not play a role, and the assumption holds true. 3. The ZnO has a finite net donor concentration Nt , which can be removed 2 from sublayers of thickness w by an external voltage of size eN2εt wz , where e is the unit charge, and εz the permitivity of ZnO. This will lead to the formation of a space charge region. Additionally a voltage is required to drive carriers through the ZnO due to its finite conductance. This however will be neglected as a consequence of the first two assumption, due to the absence of steady state currents, and currents resulting from the redistribution of charge within the structure. Further, carriers can be accumulated within the ZnO layer, which also requires an external voltage. This will also be neglected, and the ZnO will be treated as ideally conductive. Even this is not the case in reality, the error introduced by this assumption is small. Following these assumption two possible responses of the heterojunctions to external excitations exist. First the ferroelectric component can be polarized by the external field. The response is described by a phenomenological electric field dependent polarization model [287]   Ef − EC + Psat (Ef ) = Ps tanh . (6.1) 2δ + Here the plus sign in the superscript indicates the saturation polarization Psat on the lower branch of the saturated polarization hysteresis loop at electric field Ef after a given electric field increment. EC denotes the coercive field. The quantity δ is obtained from   −1 1 + Pr /Ps δ = EC log , (6.2) 1 − Pr /Ps

where Pr denotes the remanent polarization and Ps is the maximum saturation − polarization. Psat after a given electric field decrement is obtained from Eq. 6.1 as follows − + Psat (Ef ) = −Psat (−Ef ) . (6.3) 132

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures For an unsaturated polarization loop Pd does not necessarily follow the saturation hysteresis loop. In order to calculate an unsaturated hysteresis loop an approach suggested by Miller et al. is employed [288] . In this model, the saturated and unsaturated polarizations at a given field Ef can be related by a factor Γ, which ensures smooth and monotonic approaching of the unsaturated polarization to the saturation polarization loop. This factor relates the first partial derivatives of both loops ∂Pd ∂Psat =Γ , ∂Ef ∂Ef and Γ = 1 − tanh



(6.4)

Pd − Psat ξPs − Pd



.

(6.5)

The factors ξ = +1 and ξ = -1 are for incrementing and decrementing fields Ef , respectively, and Pd is the ferroelectric polarization on the unsaturated hysteresis loop at Ef . Second, upon the appearance of a difference in the polarization at a heterointerface, a depletion layer can form in the ZnO layer adjacent to the interface. As discussed in the third assumption, for removing the mobile charge from 2 sublayers of thickness w by the potential of size eN2εt wz is required. The arrangement of space charge regions is exemplarily depicted in Fig. 6.8 for a double heterostructure. All further considerations will be developed for a double heterostructure, as the properties of a single heterostructure can be easily determined from setting the thickness of one of the ZnO layers to zero. In the following discussions the polarization will be counted positive, if it is oriented as given in Fig. 6.8, pointing from the ground contact of the structure towards the contact with the applied voltage. Further both the thickness and the magnitude of the polarization for the ZnO layers will be set to a single value. For the thickness any influence is canceled out, as the voltages applied are small, so that none of the layers will be fully depleted. As the non depleted ZnO is treated as ideal conductive, the part of the ZnO layers included in the calculations is only the depletion layer. Nevertheless care was taken during the deposition of the layers to ensure equal thicknesses, as the assumption of ideal conductive layers is not fulfilled, in real samples. For the polarization, fixing the amplitude to a certain value is explained by the fact, that it is a constant for ZnO, however the growth orientation of both layers can be different, therefore the sign will be left a variable. For further discussions, the ZnO layer adjacent to the ground contact will be denoted as layer 2, that adjacent to the excitation bias contact will be denoted as layer 1. The ferroelectric layer will be described as layer F. In order to calculate the polarization of the BTO the electric field distribution inside the sample has to be related to the applied voltage. The voltage drop across the sample is the sum of the voltage drops across the sublayers. Again, a voltage will only drop over the depleted parts of the ZnO layers. Z w1 Z w2 V = df Ef + E1 dx + E2 dx′ , (6.6) 0

0

133

6. Polarization related effects in ZnO/BaTiO3 heterostructures

ZnO BTO dz df w2

ZnO dz w1

ez

ef

ez

Psz

Pd

Psz

V

Figure 6.8: Schematic of the distribution of space charge regions within the heterojunctions. Here dz and df are the thicknesses of the ZnO and BTO layers, w1 and w2 are the extension of the space charge regions in layer 1 and 2, respectively. PZnO and Pd denote the electric polarization in the ZnO and BTO layers, respectively, while εz and εf represent their relative permittivity. (Courtesy of Venkata M. Voora)

where Ef is the electric field in layer F, E1 and E2 are the fields and PZnO1 and PZnO2 the spontaneous ZnO polarizations in layer 1 and layer 2, respectively. The depletion layers will be assumed to be abrupt (Schottky-approximation), and the concentration of donors will be treated independently, as the donor concentration Nt1 in layer 1 might differ from Nt2 in layer 2 due to slightly different growth conditions. The electric field will therefore be a linear function of x, and the voltage drop will become a quadratic function of the individual depletion width, as outlined before. The field in the part of the ZnO layer away from the junction will be zero, which results in different dependencies of E1 and E2 on x, E1 (x = 0) =

eNt1 w1 εz

E1 (x = w1 ) = 0

(6.7)

eNt2 w1 . εz

(6.8)

E1 (x′ = 0) = 0 E1 (x′ = w2 ) = −

With Eq. 6.7, and replacing Ef = ε−1 f (Df − Pd ) one obtains V =

df e (Df − Pd ) + (Nt1 w12 − Nt2 w22 ) , εf 2εz

(6.9)

where Pd , Df , εf are the ferroelectric polarization, displacement, and dielectric constant of layer F, respectively. Df is equal to the surface charge density on the left side of layer F, σb . Dielectric displacement continuity across interface 1–F requires eNt w1 + PZnO1 = Ef εf + Pd ,

(6.10)

Ef εf + Pd = −eNt w2 + PZnO2 .

(6.11)

and across F–2

134

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures Table 6.1: Operation schemes according to depletion layer formation, variables w1 , w2 , and corresponding junction conditions (forward-like ‘F’, reverse-like ‘R’ ) between layer 1 and layer F (1–F) and layer F and layer 2 (F–2), respectively.

Configuration (A) (B) (C) (D) (E) (F) (G) (H) (I)

w1 0 0 < w1 < dz1 0 0 < w1 < dz1 dz1 0 0 < w1 < dz1 dz1 dz1

w2 0 0 0 < w1 < dz1 0 < w1 < dz1 0 dz1 dz1 0 < w1 < dz1 dz1

Junction 1–F Junction F–2 ‘F’ ‘F’ ‘R’ ‘F’ ‘F’ ‘R’ ‘R’ ‘R’ ‘R’ ‘F’ ‘F’ ‘R’ ‘R’ ‘R’ ‘R’ ‘R’ ‘R’ ‘R’

The values w1 and w2 can be taken to distinguish different operation schemes the heterostructure is in, their labeling is summarized in Tab. 6.1. Operation schemes (E)–(I) are included for completeness, within the present study the driving voltage will be limited to values where a full depletion of the ZnO layers is not reached. Therefore only the schemes (A)–(D) will be of importance. In order to probe the properties of the samples Sawyer–Tower measurements where performed on them. Therein a sinusodial voltage is applied to the sample. In order to compare the experimentally obtained with the calculated loops, the time derivative of the charge transfered to the heterostructure, a current ji is required as a function of the time derivative of the excitation voltage. One of the basic assumptions of the present model is, that none of the internal charge transfer processes has a explicit time dependence. Nonetheless all internal quantities implicitly depend on time through the excitation voltage. In order to evaluate the charge transferred to the structure a new quantity will be defined, the charge on the virtual metal plate within layer 1 σm . The introduction of this virtual metal plate is required by assumption 3, wherein the ZnO is treated as ideal conductive (metallic), as long as no depletion region is present. The position of the virtual metal plate is not constant, but determined by the extension of the space charge region in layer 1. As long as no space charge region is present, the metal plate is situated at the interface between layer 1 and layer F. The charge density on the metal plate will be positive, and equal σb = Df . In this case, the current flowing into the structure directly equals the time derivative of the dielectric displacement at the interface 1–F dσf dDf ji = = . (6.12) dt dt As σb crosses zero and becomes negative, σm will not follow this response. The reason for that is that free electrons inside the ZnO are repelled by the negative sheet charge σb and withdrawn from layer 1. The virtual metal plate will wander towards the electrode. The negative sheet charge σb that would be required on a plate at the heterointerface 1–F is completely compensated by the positive space charge within the depletion layer. Nevertheless, a finite positive 135

6. Polarization related effects in ZnO/BaTiO3 heterostructures current will be flowing into the structure, in order to remove the electrons from the depletion layer. This current will equal the change of the charge stored in the depletion layer, as every change in the sheet charge density at the heterointerface 1–F is expressed by a change in the size of the depletion region ji =

dσf dDf d(eNt1 w1 ) = = . dt dt dt

(6.13)

For the theoretical case of full depletion a finite negative charge density will be found on the metal plate, which will we reduced in comparison to σb by the constant charge stored within the ZnO layer eNt1 dz1 . The current flowing into the structure will again be ji =

dσf dDf = . dt dt

(6.14)

This current can now be calculated via the dielectric displacement from the electric field and polarization within the BTO layer ji =

d dDf = (εf E + Pd ) . dt dt

(6.15)

Herein the time dependence of the Polarization is related to the time dependence of the electric field by the chain rule dPd dPd dE = , dt dE dt

(6.16)

giving 

dPd ji = γ ε f + dE



dV , dt

(6.17)

where gamma relates the external voltage and the electric field within the BTO layer   −1 w1 + w2 dPd γ = df + εf + , (6.18) εz dE

and therefore represents the inverse of the effective thickness of the sample, which can exceed the actual thickness of the BTO layer, whenever a depletion layer is present. The contribution of the depletion layer   width to the effective dPd 1 sample thickness is amplified by the term εz εf + dE which is typically much larger than 1, due to the different permitivities of ZnO and BTO. Within this framework of equations the extension of the space charge regions inside the ZnO layers can be calculated at all times. Following the approach of Miller et al. [287] , the response measured in the Sawyer–Tower circuit is given by the Kirschhoff rules d(Cst Vo ) Vo Vin − Vo j i Af − = − , (6.19) dt Rn Rs where Vin is the sinusodial voltage applied to the circuit, Vo is the voltage across the normal capacitor, Cst is the capacitance of the standard capacitor, and Rs and Rn are parallel resistances of the sample and standard capacitor 136

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures Table 6.2: Best-match model calculation parameters.

Parameter

Best-match model values BTO BTO–ZnO ZnO–BTO–ZnO

dz (µm) df (µm) Nt (cm−3 ) Vbi (V) εf εZnO EC (kV/cm) Ps (µC/cm2 ) Pr (µC/cm2 ) Rs (kΩ) PZnO (µC/cm2 )

– 1.5 – 0 202 – 11.5 7.54 1.39 1000 –

0.5 1.45 5.5×1016 -0.78±0.2 250 8 11 14.1 5.6 13 -4.1

0.5 1.4 2×1017 0 80 6 11 6 0.11 1000 -0.1

respectively. In order to predict the output measured in the experiment, the dependence of Vo on Vin has to be calculated. An iterative technique is applied following Ref. [287] . Herein the differential relation yielding Pd is integrated, and the change in Pd in step l is calculated using the slope obtained in the previous iteration step l − 1   dPd ∆Pd = ∆Efl . (6.20) dE l−1 After each differential change in the applied voltage the actual depletion widths w1 and w2 are calculated from the input voltage and the polarization obtained in the previous step. Only positive values for w1 and w2 ate taken into account. The field within the ferroelectric is then calculated following Eqn. (6.18). Finally the polarization of the ferroelectric is calculated after Eqn. (6.20).

6.2.2

Application of the model to experimental data

The predictions of the model have been tested on experimental data obtained from several samples. The model was applied to single BTO layers, ZnO/BTO single heterostructures and ZnO/BTO/ZnO double heterostructures. Representative S–T output loops are given for all three types of samples in Fig. 6.9. The parameters varied in order to match the experimental loops are summarized in Tab. 6.2. The frequency of the sinusodial excitation was fixed to 1.5 kHz, the capacitance and resistance of the normal capacitor were 1 µC and 1 MΩ, respectively. The thicknesses of the individual layers were measured by spectroscopic ellipsometry, and are not varied during the calculations. The quantity Vbi is introduced in the case of the ZnO/BTO heterostructure in order to account for the finite offset of the conduction band between ZnO and BTO. For all three structures a very good agreement between the calculated and the experimentally measured data was obtained. In the case of the single BTO layer (see Fig. 6.9 (a)), the voltage across the standard capacitor is propor137

6. Polarization related effects in ZnO/BaTiO3 heterostructures

(a)

(b)

(c)

Figure 6.9: Experimentally measured (dots) and model calculated (solid lines) Sawyer-Tower loops for (a) a single BTO layer, (b) a ZnO/BTO single heterostructure and (c) a ZnO/BTO/ZnO double heterostructure. The left panels give the voltage across the standard capacitor as a function of the sweep voltage, the right panels show the polarization of the ferroelectric as a function of the input voltage. (Courtesy of Venkata M. Voora, data partially obtained by Nurdin Ashkenov)

138

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures tional to the polarization in the ferroelectric layer. The values obtained for the coercive field and the remanent and saturation polarization agree well with the values estimated from the I–V measurements in Chap. 6.1.2 and literature values for polycrystalline BTO thin films [289,290] . They further agree exactly with what would be calculated from a conventional analysis of the S–T loops. The situation changes significantly in the case of the ZnO/BTO single heterostructures (see Fig. 6.9 (b)). Again a very good agreement between the measured and calculated loop is achieved, however in this case the polarization inside the ferroelectric and the voltage across the standard capacitor are not equal. A conventional analysis is not able to determine the parameters of the individual layers in this case. The difference in the shape of the S–T loop and the real voltage dependence of the ferroelectric polarization is of cause introduced by the presence of a space charge region within the ZnO. The calculations allow to determine the the voltage points at which the depletion layer starts to form, these points are marked by triangles in Fig. 6.9 (b). The depletion layer is present on the right side of the loops, and a significant fraction of the applied voltage now drops across this layer. The effective thickness of the sample in this case is larger than the thickness of the BTO layer, and the field within will be reduced Ef < V /df . The change in polarization per unit voltage will therefore also be reduced, as can be seen from the right panel of (see Fig. 6.9 (b)). Only a subloop of the possible ferroelectric hysteresis loop is therefore reached in this structure. The situation becomes more complicated in the case of the ZnO/BTO/ZnO double heterostructure, as seen in Fig. 6.9 (c). Here the depletion layer forms for both positive and negative voltages, and the pure ferroelectric response of the layer system is, if present at all, only observed for a small range of input voltages. The question for which part the hysteresis curve of a single BTO layer is still reached, is not trivially answered. Here the orientation of the ZnO polarization is important, and four different arrangements can be distinguished, giving the two possible orientations in both ZnO layers. The four possible arrangements are graphed in Fig. 6.10. For two of them the ZnO polarization vectors are aligned in parallel (arrangements P− FP− and P+ FP+ ). In this case there is always exactly one depletion layer present either in layer 1 or in layer 2. The effective sample thickness then always exceeds the BTO layer thickness. The attainable polarization of the BTO is therefore significantly reduced in such samples with respect to single BTO layers (compare the scales in the right panels of Fig. 6.9 (a) and (c)). Depending on the actual direction of the ZnO polarization vectors, the points where the transition from the depletion of layer 1 to the depletion of layer 2 occurs changes with respect to the input voltage. In the other two possible arrangements the ZnO polarization vectors are aligned antiparallel (arrangements P+ FP− and P− FP+ ). In order to understand the differences between both arrangements, it is helpful to consider the state of the heterostructure in the absence of a ferroelectric polarization. The sheet charge density at the heterointerface will then only be influenced by the ZnO polarization. As the individual polarization vectors are antiparallel, the sheet 139

6. Polarization related effects in ZnO/BaTiO3 heterostructures

-P

-0.1

140

1

2

-P

w

-0.2

w

V

70 0.2

o

o

0.3

[V]

sz

70 ZnO BTO ZnO

P

P

sz

0.1 10 -10

0 in

[V]

V

10

0

-10

in

ZnO BTO ZnO

w

V

10

0

[V]

in

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w

2

140

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1

2

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70

o

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w

70

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[V]

sz

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o

[V]

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[V]

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140

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[nm]

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(b) Arrangement P+ FP+

(a) Arrangement P− FP− 0.04

10 -10

0 V

[V]

in

sz

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[nm]

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140 1

-0.3

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sz

[nm]

[V]

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w

[nm]

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w

0.5

ZnO BTO ZnO

P

-0.04 -10

0 V

in

[V]

10 -10

0 V

in

10

sz

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0

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[V]

in

(c) Arrangement P+ FP−

[V]

-P

sz

10 -10

0 V

in

10

0

[V]

(d) Arrangement P− FP+

Figure 6.10: Model calculated Sawyer–Tower loops (left panels) and depletion layer widths (right panel ) in ZnO/BTO double heterostuctures for different arrangements of the ZnO polarizations in both layers, as explained in the text. (Courtesy of Venkata M. Voora)

charges on both sides will be equal, positive in the P+ FP− arrangement, and negative in the P− FP+ arrangement. It is clear, that regardless of the polarization of the BTO the sum of the depletion layer widths will be always larger in the P− FP+ arrangement than in the P+ FP− arrangement. The effective thickness is therefore always larger in the P− FP+ case, and the polarization has to remain smaller (this manifests also in smaller voltages across the standard capacitor, as seen in comparison between the left panels of Fig. 6.10(c) and Fig. 6.10(d). The accuracy of the parameters describing the ferroelectric properties derived from the model is therefore not as good as for the cases of a single BTO layer, or the ZnO/BTO heterostructure, especially the saturation polarization, as the structures are typically far away from saturation. From the model, further prediction of the capacitance of the structures is possible. The capacitance will be a function of the external voltage, through the depletion layer width within the ZnO layers. The capacitance of the BTO layer will be treated as a constant, which is not true for single BTO layers. As the structure represents a series of capacitances, the overall capacitance is determined by the smallest individual capacitance, which is that of the ZnO. The changes in the BTO capacitance will therefore be negligible compared to the changes introduced by the occurrence of the depletion layer. The ferroelec140

C [arbitrary units]

(c) P FP

-5

0 V

in

(d)

SFS

SIS

-

(b)

C [arbitrary units]

C [arbitrary units]

(a)

C [arbitrary units]

6.2. Theory of coupling phenomena in ZnO/BTO heterostructures

-

5

+

P FP

+

-5

0 V

[V]

in

5

[V]

Figure 6.11: Principle of C–V response of (a) a semiconductor–insulator– semiconductor (SIS) heterostucture (b) a semiconductor–ferroelectric–semiconductor (SFS) heterostructure and (c) and (d) of ZnO/BTO double heterostructures with two different parallel arrangements of the ZnO polarization. (Courtesy of Venkata M. Voora)

tric nature of the BTO will however be regarded, as it implicitly influences the depletion layer widths. From the previous considerations the depletion layer width is know as a function of the external voltage. Figure 6.11 depicts a model calculated C–V hysteresis curve for a semiconductor– insulator–semiconductor heterostructure without ferroelectric hysteresis. For semiconductor layers with equal donor concentrations and interface properties, the C–V curve is symmetric with respect to zero voltage (Fig. 6.11 (a)), and decreases monotonically for increasing voltages due to formation of identical space charge regions in either of the semiconductor layers depending on the sign of the applied voltage. The space charge region infers a series capacitance which decreases with increasing voltage, leading to an overall reduction of the total capacitance. Figure 6.11 (b) shows the C–V response if the insulator between the two semiconductor layers is a ferroelectric. In that case the C–V response is shifted along the voltage axis, depending on the actual polarization in the ferroelectric constituent. The ferroelectric polarization produces an additional interface charge, which offsets the space charge region formation depending on the sign of the charge. At certain external voltages, the electric field within the ferroelectric layer is sufficient to switch the polarization, iden141

6. Polarization related effects in ZnO/BaTiO3 heterostructures

ZnO

ZnO

-7

(b)

10

V

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in

sz

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sz

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10

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C [nf]

log|I| [A]

10

BTO

(a)

4 -5

0 V

in

5 -5

[V]

0 V

in

5

[V]

Figure 6.12: Experimental (a) I–V and (b) C–V characteristic of a ZnO/BTO/ZnO double heterostructure. (Courtesy of Venkata M. Voora)

tified by the maxima in the C–V response. A typical symmetric butterfly-type hysteresis is observed centered around zero voltage. Figure 6.11 (c) depicts the scenarios when the two semiconductor layers carry spontaneous polarizations with their associated polarization vectors parallel to each other (arrangements P− FP− and P+ FP+ ). As in the arrangements with parallel orientation of the ZnO polarization the contribution of the ZnO polarizations will generate sheet charges of different sign on both heterointerfaces, and the overall C–V response will be shifted with respect to the excitation voltage. The direction and magnitude of the shift depends on the arrangement and the size of PZnO . For antiparallel arrangement, P+ FP− and P− FP+ , identical sheet charges are located at both interface. While these charges still affect the formation of a space charge region, the changes are symmetric with respect to the applied external voltage, and the C–V response is qualitatively equivalent to the case depicted in Fig. 6.11 (b). The theoretical predicted curves were indeed seen in experiments. Figure 6.12 (b) gives the C–V response of a ZnO/BTO/ZnO heterostructure. The corresponding I–V curve is given in Fig. 6.12 (a). From the shift of the capacitance peaks with respect to the voltage axis and the relative peak height in both sweep directions it is concluded, that the arrangement of the ZnO polarizations in the heterostructure is of P− FP− type, thereas, both ZnO layers are grown in the Zn polar orientation. 142

6.3. ZnO/BTO based ferroelectric thin film transistors

Source

Drain

Au Au ZnO Channel

PLD 2

BTO Gate oxide

PLD 1

STO:Nb Substrate Gate Figure 6.13: Principle layout of ZnO/BTO MISFET transistors.

6.3

ZnO/BTO based ferroelectric thin film transistors

Additionally to theoretical understanding of the properties of ZnO/BTO heterojunctions, experimental investigations to exploit their unique properties for device application were performed within the present study. The ferroelectric polarization can be used to control the conductivity in the ZnO layer, enabling the fabrication of ferroelectric field-effect-transistors [291] . The first ferroelectric field effect transistors have been reported by Wu et al. [292] , and since than several reports emerged on such devices involving different materials materials. In the ZnO system metal–insulator–semiconductor field effect transistors (MISFET) have been demonstrated using different gate oxides [293,294] . Further, transparent metal–semiconductor field effect transistors (MESFET) have been demonstrated for the ZnO system [295] . Recently, it has been shown [296] that the fabrication of ZnO/Bax Sr1−x TiO3 (BST) thin film transistors is possible. However, the used BST was polycrystalline, and was not ferroelectric at room temperature, due to its composition. However a dielectric constant of around 500 was obtained, which, in principle, allows a rather thick gate insulator. The device discussed in this study was realized by the deposition of ZnO thin films of 50 nm thickness by pulsed laser deposition (PLD) at a substrate temperature of 670◦ C and an oxygen partial pressure of 0.002 mbar on ex-situ prepared BTO templates. These templates were likewise prepared by PLD by Dr. Jürgen Schubert from Forschungszentrum Jülich and consist of a BTO layer of a thickness of 800 nm, deposited on a lattice matched Nb doped SrTiO3 (100) (STO:Nb) substrate. The ZnO target was ablated using a KrF excimer laser with a pulse energy of 600 mJ and a repetition rate of 10 Hz. At first, a 300 pulse nucleation layer was deposited at a reduced ablation rate of 1 Hz. MISFET structures were patterned by photolithography. The ZnO was etched by phosphoric acid in order to form mesas acting as the ZnO channels. The 143

Source - Drain Current Isd (µA)

6. Polarization related effects in ZnO/BaTiO3 heterostructures

70 Ug =5V

60 50

Ug =4V

40 30

Ug =3V

20 Ug =2V

10

Ug =1V Ug =0V

0 0

2

4

6

8

10

Source - Drain Voltage Vsd (V) Figure 6.14: Output characteristics of a ZnO/BTO MISFET at different gate voltages. The dashed line is a guide to the eye, underlining the quadratic behavior of the position of the pinch-off-points.

channel length (L) is 30 µm and the channel width W = 430 µm. The conductive STO:Nb substrate was used as a back-gate electrode. The back gate geometry was chosen due to different etchability of ZnO and BTO. While ZnO is easily wet-etched, dry etching methods are typically employed in order to pattern BTO. Ohmic source and drain contacts, of 500 µm × 400 µm size were deposited by DC-sputtering of Au onto the ZnO, without overlapping onto the underlying BTO layer. The schematic layout of the device is given in Fig. 6.13. Metal–insulator–semiconductor (MIS) diodes have been fabricated as a reference, by DC-sputtering of circular Au contacts on the ZnO with a diameter of 2 mm. One necessary condition for the fabrication of high quality MISFETs is a low leakage current of the gate insulator material. As discussed in Chap. 6.1.2 the use of lattice matched substrates reduces the leakage current significantly. Current–Voltage measurements on reference samples with circular contacts of 2 mm diameter revealed leakage currents as low as 6 nA at 20 V gate voltage, giving a leakage current density of 200 nA/cm2 . The leakage current density was significantly smaller for lower gate voltages (jl < 10−9 A/cm2 at 5 V). Field-effect measurements on the samples show a linear region and a typical saturation behavior of the source–drain-current upon an increase of the source–drain-voltage in the output characteristic (Fig. 6.14). The pinch-off points follow the theoretically expected quadratic behavior [98] . The transfer characteristic is shown in Fig. 6.15. The MISFETs are normally-on with a 144

10-5

0.30

10-6

0.25

10-7

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10-8

0.15

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10-11

0.00 -4

-2

0

2

4

Channel mobility µch (cm 2/Vs)

Source - Drain Current Isd (A)

6.3. ZnO/BTO based ferroelectric thin film transistors

Gate Voltage Vg (V) Figure 6.15: Transfer characteristics and calculated channel mobility of a ZnO/BTO MISFET at a fixed source–drain-voltage of VSD = 2V.

threshold voltage of VT = −2.4V, and the source–drain-current can be varied by at least 6 orders of magnitude within a change in VG of 7V, reaching values of up to 10 µA. This results in a sub-threshold slope of 400 mV per decade. The field effect mobility was calculated from the output and the transfer characteristic, following ∂ID L 1 µch = × , (6.21) ∂VD VD →0 W Ci (VG − VT )

and is depicted in Fig. 6.15. The insulator capacitance was determined by quasi-static-C–V measurements (not depicted here), to be Ci = 7nF, yielding a dielectric constant of the BTO of 197. The field effect mobility reaches a maximum of 0.27, which is significantly below the mobility in bulk ZnO at room temperature, and even significantly below the mobility in high quality heteroepitaxial ZnO thin films [297] , however, the value is close to that reported in literature for bottom gate ZnO MISFETs [298,299] . Three important scattering effects might contribute: First, the density of defects at the interface can be large, accounting for a significant interface scattering [300] , and these defects might create a high density of dislocation lines in the thin film, especially due to the small thickness. Further, charged grain boundaries will also contribute to carrier scattering, and a high density of these is likewise probable, due to the low film thickness. This assumption is supported by the existence of the 30◦ rotational domains (see for detailed explanation Chap 6.1.2). It has to be remarked, that the scattering at the 30◦ rotational domain barriers and at inversion domain barriers, if they are present in the material, will have a more dramatic effect on the mobility than scattering at low angle grain boundaries, 145

a)

Source - Drain Current Isd (A)

6. Polarization related effects in ZnO/BaTiO3 heterostructures

10-8 10-9 10-10

Isd (A) (switched on) Isd (A) (switched off) Vsd = 2V

10-11 10-12 1.5

2.0

2.5

3.0

3.5

4.0

3.5

4.0

Gate Voltage Vg (V) 1.000

Isd(on) / Isd(off)

b)

100

10

1 1.5

2.0

2.5

3.0

Gate Voltage Vg (V) Figure 6.16: (a) Transfer characteristics of a ZnO/BTO MISFET after applying a for- and backwards pulse, respectively. (b) Ratio of the current in the permanent ‘on’ and the permanent ‘off’ state.

146

6.4. Summary and conclusion as typically treated in literature [301] . In sum, a high density of charged crystal imperfections is the most likely reason for the rather low mobility. In order to improve the performance of the field-effect transistor the mobility has to be improved significantly. Inversion of the transistor structure might solve the problem, especially if the ZnO is grown homoepitaxially. One has to be aware, however, of the fact that this might reduce the quality of the gate oxide leading to increased leakage currents. The transistor structures have been poled by exposure to increased gate voltages (VG ≈ 20V) and the transfer characteristic was recorded between VG = 0 V and VG = 5 V. After that, a sufficiently large negative ‘erase’ voltage (e.g. VG = −7V) was applied and the transfer characteristic was recorded again. The process was repeated multiple times in order to check for reproducibility. The results of these experiments have been depicted in Fig. 6.16 (a). The transistor can be switched into two polarization states, and the transfer characteristics in both states differ largely. The ratio of the source–drain-current between these states is depicted in Fig. 6.16 (b). A positive gate voltage polarizes the BTO with the positive side towards the ZnO, creating an electron depletion therein. A negative gate voltage causes a polarization in the BTO, with the negative side facing the ZnO, leading to the formation of an accumulation layer. The ratio of the currents in the both operation schemes can reach values of up to 1,000, depending on the gate voltage. However, the source– drain-current is larger following the negative voltage pulse, which cannot be explained assuming a simple ferroelectric polarization model. An equal behavior has already been reported for ferroelectric field effect transistors and was assigned to interface defects between the channel and the ferroelectric [292] . The mechanism involved in the formation of these interface defects will have to be studied in detail, before a commercial application of the device becomes an option. Nevertheless, as the process is reversible and reproducible, the structure forms a transparent nonvolatile memory element, allowing a resistive readout process. Such a method is always advantageous compared to capacitive readout, as the information stored on the ferroelectric is not destroyed, and will not have to be rewritten.

6.4

Summary and conclusion

The results of this chapter can be summarized as follows: • ZnO/BTO heterojunctions have been successful synthesized on both Si and STO substrates. The structural and electrical properties of the structures grown on the lattice matched STO substrates are by far superior to that of the samples grown on Si. • From the I–V curves measured on ZnO/BTO heterostructures grown on STO the polarization of the ZnO layer PZnO = 0.2 ± 0.05 µC and the coercive field of the BTO EC = 12.5 ± 1 kV/cm were estimated. • A detailed model was developed in close cooperation with Venkata M. 147

6. Polarization related effects in ZnO/BaTiO3 heterostructures Voora and Prof. Dr. Mathias Schubert (University of Nebraska Lincoln) to understand the coupling of the ZnO and BTO polarization and the formation of depletion layers in the ZnO introduced by the sheet charge related to the offset of the polarization at a ZnO/BTO heterointerface. • Employing the aforementioned model, the Sawyer–Tower loops of single BTO layers, ZnO/BTO single heterojunctions and ZnO/BTO double heterojunctions could be accurately described, and the material parameters of the individual layer were extracted. Qualitative description of the C–V loops of ZnO/BTO double was also possible from the model. • Ferroelectric thin film transistors have been demonstrated on the basis of ZnO/BTO heterostructures. The transistors were normally-on and show output currents of up to 10 µA, which could be controlled over more than 6 orders of magnitude by the gate voltage. A reproducible nonvolatile memory effect was observed due to the ferroelectric polarization in the BTO.

148

Chapter 7 Summary and outlook 7.1

Summary and conclusion

The results of the present study can be summarized as follows: • The lattice constants a and c of Mgx Zn1−x O systematically change with the Mg content x in relaxed Mgx Zn1−x O layers, where a increases with x and c decreases with x. • It was shown that Mgx Zn1−x O can be grown pseudomorphically on ZnO. The c-axis lattice constant changes systematically with x. The linear relationship cps = c0 + kc,ps x with kc,ps = −0.064 Å was found from data obtained in the present study and in accordance with the literature [96,97] . • The mechanisms involved in the growth of ZnO on sapphire were investigated, a transition from initial 3D growth to 2D growth was revealed. A steady state is reached after roughly 100 nm film thickness, which allows determination of the growth rate. • The observation given in Ref. [81] that the morphology of Mgx Zn1−x O layers improves upon the introduction of a ZnO buffer layer was confirmed, and understood within the argumentation given in Refs [122–124] . The Mgx Zn1−x O layer grown on the ZnO buffer is compressively strained, which increases the surface diffusion length and therefore promotes step flow growth. • The state of the art ZnO substrate material available was reviewed, and the individual advantages discussed. Only hydrothermally grown material proved applicable in the light of transport investigations. A thermal pretreatment of the substrates necessary to produce surfaces suitable for epitaxy was discussed [146] . • The mechanisms involved in the homoepitaxial growth of ZnO were investigated. Within the temperature range available layer by layer growth was observed rather then step flow growth. A significant reduction of the defect density was observed in comparison to ZnO grown on sapphire substrates. 149

7. Summary and outlook • The mechanisms involved in the growth of Mgx Zn1−x O on ZnO substrates were investigated. It was shown, that the temperature allowing step flow growth was lower than for pure ZnO. This was again explained by the presence of compressive strain in the films, in accordance with the argumentation given in Refs. [122–124] . Perfect vicinal surfaces were prepared, depending on the miscut of the substrate. • A substrate preparation routine following Ref. [174,175] was applied to commercially available STO substrates and produced perfect vicinal substrates with step edges of unit cell step height. • Vicinal BTO thin films with step edges of unit cell step height were grown up to a critical thickness of roughly 45 nm in concordance with Ref. [176] . • Vicinal SRO thin films with step edges of unit cell step height were grown, however in the films investigated holes parallel to the steps of the substrate are visible. An improvement of the growth of this material will be necessary in the future. • The properties of undoped and phosphorous doped ZnO and Mgx Zn1−x O thin films grown on ZnO are strongly influenced by the oxygen partial pressure during growth. The oxygen partial pressure influences the growing films in more than one way. 1. The II–VI ratio in the films is controlled by the oxygen partial pressure. For films grown at low oxygen partial pressures an increased c-axis lattice constant is observed for both the ZnO and Mgx Zn1−x O thin films, most likely due to an increasing density of charged defects. The thesis of an increase of the density of intrinsic defects related to oxygen deficiency in the films is supported by an increase in the zinc interstitial related luminescence and the free electron concentration upon decrease of the oxygen partial pressure. It is concluded, that oxygen in the background gas atmosphere is necessary in order to grow stoichiometric ZnO and Mgx Zn1−x O film. 2. The composition of the group II constituents depends on the background pressure in the chamber. The concentration of the lighter Mg atoms compared to Zn atoms is reduced by almost a factor of three within the range of oxygen partial pressures available in the present growth setup. Interestingly the concentration of P does change accordingly. It is concluded, that the atomic mass (which differs between Mg and P by only 20%) of the individual element influences the kinetic scattering processes with the background gas and therefore the composition of the plasma at the substrate position. • The similarities of the incorporation of Mg and P indicate that P is like Mg mainly introduced into the ZnO host lattice on Zn site, in accordance with theoretical calculations [238] . 150

7.1. Summary and conclusion • A degenerate contribution to the sample conduction was found in homoepitaxial samples with a phosphorous concentration with 0.1% and above, which could partially be removed by annealing in oxygen, indicating that at least in this case the origin of the degenerate layer is a layer of intrinsic defects, likely to be formed at the surface. • It was shown that the separation of the conduction of the degenerate layer and the bulk of the film was partially possible employing a correction scheme as proposed in Refs. [223,224] . A complete separation however was not possible without further assumptions, as the incorporation of the defects responsible for the formation of the degenerate layer is not homogeneous. • It was shown that the separation of the conduction of individual conductive paths is possible without any assumption about the distribution of the individual carriers from magnetic field dependent measurements by the maximum entropy mobility spectrum approach. The individual properties of bulk conduction and the conduction of the degenerate layer were revealed over a wide range of temperatures. Such a detailed study of the parallel conduction processes in ZnO has not been reported so far. • The critical donor concentration and activation energy in the dilute limit of the dominant donor in phosphorous doped ZnO and Mgx Zn1−x O layers grown on ZnO was determined to be of NC = 8.3 × 1018 cm−3 and ED0 = 56 meV, respectively. • The thermal activation of phosphorous related acceptor was studied in ZnO and Mgx Zn1−x O thin films grown on ZnO. A transition to p-type conduction was never observed. However an increase of the resistivity by more than 6 orders of magnitude was observed in the Mgx Zn1−x O layers deposited at the highest oxygen partial pressures. It is concluded that high oxygen partial pressures are necessary if p-type conduction is to be achieved, as the compensation of acceptors is reduced by the low density of intrinsic donors. • 2D growth in the Burton–Cabrera–Frank mode has been observed for the ZnO/Mgx Zn1−x O single heterostructures and ZnO/Mgx Zn1−x O quantum wells grown on a-sapphire. The effective surface roughness in these samples is of the order of the thickness of the qunatum wells present in the structures. • A significant improvement of the structural and morphological properties of the ZnO/Mgx Zn1−x O quantum wells grown on ZnO is observed. Step flow growth leading to perfect vicinal surfaces could be achieved for these samples as confirmed by atomic force microscopy. The Mgx Zn1−x O layers were confirmed to be grown pseudomorphic by high-resolution X-ray diffraction. 151

7. Summary and outlook • Electron accumulation layers have been observed for ZnO/Mgx Zn1−x O single heterostructures grown on sapphire by Capacitance–Voltage spectroscopy and temperature dependent Hall-effect measurements. • Indications for the presence of a 2DEG in ZnO/Mgx Zn1−x O quantum wells grown on ZnO were found by temperature dependent Hall-effect measurements. For a clear observation of the transport properties of the 2DEG further improvements is still necessary. The contributions of the degenerate layer have to be removed and the conductivity of the bulk material has to be reduced. • Quantum confinement effects have been confirmed previously by photoluminescence PL measurements [258] . A narrowing of the PL peak width is observed in qunatum wells grown on ZnO, especially for low well width, due to the higher influence of the interface roughness on thinner quantum wells. • Careful control of the laser fluence applied to the PLD target resulted in a significant improvement of the quality of the heterointerface in ZnO/Mgx Zn1−x O heterostructures. A pronounced QCSE was observed in PLD grown samples for the first time. Comparison with data obtained on MBE grown samples given in the literature revealed, that the samples discussed here equal the MBE grown samples both in interface quality and in density of non-radiative recombination centers. • The use of a slanted QW allowed the observation of quantum confinement effects in QW of different thicknesses in one sample with a well defined barrier composition. However, uncertainties in the thickness of the determination are present. The use of an in-situ RHEED observation would help to determine and control the thickness of individual layers. • ZnO/BTO heterojunctions have been successful synthesized on both Si and STO substrates. The structural and electrical properties of the structures grown on the lattice matched STO substrates are by far superior to that of the samples grown on Si. • From the I–V curves measured on ZnO/BTO heterostructures grown on STO the polarization of the ZnO layer PZnO = 0.2 ± 0.05 µC and the coercive field of the BTO EC = 12.5 ± 1 kV/cm were estimated. • A detailed model was developed to understand the coupling of the ZnO and BTO polarization and the formation of depletion layers in the ZnO introduced by the sheet charge related to the offset of the polarization at a ZnO/BTO heterointerface. • Employing the beforementioned model the Sawyer–Tower loops of single BTO layers, ZnO/BTO single heterojunctions and ZnO/BTO double heterojunctions could be accurately described, and the material parameters of the individual layer were extracted. Qualitative description of the C–V loops of ZnO/BTO double was also possible from the model. 152

7.2. Outlook • Ferroelectric thin film transistors have been demonstrated on the basis of ZnO/BTO heterostructures. The transistors were normally-on and show output currents of up to 10 µA, which could be controlled over more than 6 orders of magnitude by the gate voltage. A reproducible nonvolatile memory effect was observed due to the ferroelectric polarization in the BTO.

7.2

Outlook

From the present work further questions arise which should be addressed in the future. • The versatility of the setup could be improved if the influences of the background gas on the sample composition could be separated. Two constructive changes of the setup would allow at least a partial realization of this goal. 1. The use of a non uniform gas atmosphere. The application of a gas mixture, for example oxygen and an inert gas, inside the growth chamber will allow a control of the composition of the group II constituent without changing the II–IV ratio, therefore maintaining stoichiometric growth. However, a minimum oxygen partial pressure is necessary in order to maintain stoichiometry. This limits the total pressure attainable to values above the oxygen partial pressure. 2. The introduction of a plasma source. During laser plasma formation only a small fraction of the available oxygen molecules is cracked. It is reasonable to assume in the light of literature work [240] , that molecular oxygen is only responsible for a vanishing fraction of the total oxygen incorporation. The range of available gas mixtures in the growth chamber can be further expanded, if the availability of ionic oxygen species can be controlled without changing the base chamber pressure. Such an approach could allow a chamber pressure virtually below the oxygen partial pressure, as the availability of activated oxygen increases. Additionally, it is found in the literature [241] that the incorporation of nitrogen is promoted by the activation in a plasma environment, eventually leading to p-type conductivity [66,242] . 3. The use of an in-situ RHEED analysis A LMBE chamber has been set up recently by members the semiconductor physics group. This device will become a very valuable tool for the analysis of growth phenomena and the very precise evaluation of layer thicknesses during the growth process. 4. From the chemical analysis of the sample composition it is concluded that concentrated efforts are necessary to improve the purity of the target material, as the purity of the films can not exceed the 153

7. Summary and outlook purity of the starting material. New zirconia and tungsten carbide mills have become available only recently. A study on the impurity introduction in the homogenization process is motivated. • A degenerate layer is often seen in ZnO and Mgx Zn1−x O samples in this study. While the properties of such layer were investigated in transport measurements in great detail, the microscopical origin remains unclear. Further investigations are necessary, regarding the localization of the degenerate layer. Chemical investigation of the substrate surfaces could help to understand if the substrate introduces a high density of point defects at the film substrate interface as speculated. A plasma treatment of the substrate could help to remove impurities creating these defects. • Removal of the degenerate layer would allow more detailed measurements on the 2DEG found in several samples. In that case low temperature studies in high magnetic fields would be interesting, in order to observe quantum transport phenomena. • In principle, the carrier dynamics can be understood from the present data on the QCSE. Sophisticated models are required to include the inplane motion of the free carriers and excitons, exciton formation and radiative and non radiative recombination rates. A detailed investigation of the luminescence energy versus time behavior is highly helpful to understand the recombination dynamics completely. Such data can be obtained employing a streak camera, which allows the observation of the time dependence of several energetic channels simultaneously. Additionally, the spatial dependence of the luminescence should be investigated, possibly by using a micro-luminescence setup as described in [275] or by observation of spatially masked samples, as described in Ref. [276] . • More detailed studies on the growth of SRO on STO will be necessary in order to produce perfect vicinal surfaces as a starting point for BTO growth. • The use of STO/BTO superlattices is a promising approach in order to increase the effective critical thickness of BTO on STO and to enhance certain material properties, as the dielectric constant [302] and the ferroelectric polarization. • The mechanisms involved in the growth of ZnO on BTO should be studied in more detail. Especially the polarity of the ZnO layers is of interest here, and CBED measurements are perfomed at present. Also the formation of interface defects is of high interest in order to improve the properties of nonvolatile memory elements based on ferroelectric ZnO/BTO FETs.

154

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List of own publications zel, M. Brandt, H. von Wenckstern, and M. Grundmann, J. Vac. Sci. Technol. B 27, 1693 (2009). [14] M. Brandt, H. Frenzel, H. Hochmuth, M. Lorenz, M. Grundmann, and J. Schubert, J. Vac. Sci. Technol. B 27, 1789 (2009). [15] H. Frenzel, H. von Wenckstern, A. Lajn, M. Brandt, G. Biehne, H. Hochmuth, M. Lorenz, and M. Grundmann, AIP conference proceedings 1199, 469 (2009). [16] H. von Wenckstern, J. Zippel, A. Lajn, M. Brandt, G. Biehne, H. Hochmuth, M. Lorenz, and M. Grundmann, AIP conference proceedings 1199, 99 (2009). [17] H. von Wenckstern, M. Brandt, H. Schmidt, G. Benndorf, J. Zippel, H. Hochmuth, M. Lorenz, and M. Grundmann, Proc. SPIE 6895, 689505 (2008). [18] B. Q. Cao, M. Lorenz, H. von Wenckstern, C. Czekalla, M. Brandt, J. Lenzner, G. Benndorf, G. Biehne, and M. Grundmann, Proc. SPIE 6895, 68950V (2008). [19] V. Voora, T. Hofmann, M. Brandt, M. Lorenz, M. Grundmann, N. Ashkenov, and M. Schubert, J. Electron Mater. 37, 1029 (2008). [20] G. Brauer, W. Anwand, W. Skorupa, J. Kuriplach, O. Melikhova, J. Cizek, I. Prochazka, H. von Wenckstern, M. Brandt, M. Lorenz, and M. Grundmann, Phys. Status Solidi C 4, 3642 (2007). [21] M. Brandt, H. von Wenckstern, H. Schmidt, A. Rahm, G. Biehne, G. Benndorf, H. Hochmuth, M. Lorenz, C. Meinecke, T. Butz, and M. Grundmann, J. Appl. Phys. 104, 013708 (2008). [22] M. Lorenz, G. Wagner, A. Rahm, H. Schmidt, H. Hochmuth, H. Schmid, W. Mader, M. Brandt, H. von Wenckstern, and M. Grundmann, Phys. Status Solidi C 5, 3280 (2008). [23] H. Frenzel, A. Lajn, M. Brandt, H. von Wenckstern, G. Biehne, H. Hochmuth, M. Lorenz, and M. Grundmann, Appl. Phys. Lett. 92, 192108 (2008). [24] H. von Wenckstern, M. Brandt, H. Schmidt, C. Hanisch, G. Benndorf, H. Hochmuth, M. Lorenz, and M. Grundmann, J. Korean Phys. Soc. 53, 3064 (2008). [25] B. Q. Cao, M. Lorenz, M. Brandt, H. von Wenckstern, J. Lenzner, G. Biehne, and M. Grundmann, Phys. Status Solidi RRL 2, 37 (2008). [26] V. M. Voora, T. Hofmann, M. Brandt, M. Lorenz, M. Grundmann, and M. Schubert, Phys. Status Solidi C 5, 1328 (2008). [27] H. von Wenckstern, R. Pickenhain, H. Schmidt, M. Brandt, G. Biehne, M. Lorenz, M. Grundmann, and G. Brauer, Superlattices Microstruct. 42, 14 (2007). [28] H. von Wenckstern, H. Schmidt, C. Hanisch, M. Brandt, C. Czekalla, 172

List of own publications G. Benndorf, G. Biehne, A. Rahm, H. Hochmuth, M. Lorenz, and M. Grundmann, Phys. Status Solidi RRL 1, 129 (2007). [29] M. Lorenz, M. Brandt, J. Schubert, H. Hochmuth, H. von Wenckstern, M. Schubert, and M. Grundmann, Proc. SPIE 6474, 64741S (2007). [30] H. von Wenckstern, M. Brandt, G. Zimmermann, J. Lenzner, H. Hochmuth, M. Lorenz, and M. Grundmann, Proc. MRS 957, 23 (2007). [31] H. von Wenckstern, R. Pickenhain, H. Schmidt, M. Brandt, G. Biehne, M. Lorenz, M. Grundmann, and G. Brauer, Appl. Phys. Lett. 89, 092122 (2006). [32] H. von Wenckstern, G. Benndorf, S. Heitsch, J. Sann, M. Brandt, H. Schmidt, J. Lenzner, M. Lorenz, A. Y. Kuznetsov, B. K. Meyer, and M. Grundmann, Appl. Phys. A 88, 125 (2007). [33] H. von Wenckstern, M. Brandt, H. Schmidt, G. Biehne, R. Pickenhain, H. Hochmuth, M. Lorenz, and M. Grundmann, Appl. Phys. A 88, 135 (2007). [34] I. Konovalov, L. Hartmann, M. Brandt, and L. Makhova, Phys. Status Solidi C 3, 2891 (2006). [35] M. Lorenz, H. Hochmuth, J. Lenzner, M. Brandt, H. von Wenckstern, G. Benndorf, and M. Grundmann, Wissenschaftlich-Technische Berichte des FZ Rossendorf FZR-433, 57 (2005).

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174

List of own conference contributions [1] M. Brandt, H. von Wenckstern, M. Stölzel, M. Lange, C. P. Dietrich, A. Müller, G. Benndorf, J. Zippel, J. Lenzner, M. Lorenz et al.. “Observation of a strong polarization induced quantum-confined Stark effect in Mgx Zn1−x O/ZnO quantum wells”. 52st Electronic Materials Conference, Notre Dame, IN, 2010 (2010). [2] M. Brandt, H. von Wenckstern, M. Lorenz, H. Frenzel, G. Benndorf, M. Lange, M. Stölzel, C. Dietrich, J. Zippel, and M. Grundmann. “Complex oxide heterostructures grown by pulsed laser deposition”. 2010 SPIE Photonics West, San Francisco, 2010 (2010). [3] M. Brandt, H. Frenzel, H. Hochmuth, M. Lorenz, and M. Grundmann. “Ferroelectric thin film field-effect transistors based on ZnO/BaTiO3 heterostructures”. 51st Electronic Materials Conference, Penn State University, 2009 (2009). [4] M. Brandt, H. Frenzel, H. Hochmuth, M. Lorenz, and M. Grundmann. “Transparent non-volatile memory devices based on ZnO/BaTiO3 ferroelectric FETs”. 2009 MRS Spring Meeting, San Francisco, 2009 (2009). [5] M. Brandt, H. von Wenckstern, G. Benndorf, J. Zippel, J. Lenzner, H. Hochmuth, M. Lorenz, and M. Grundmann. “Formation of a 2DEG in ZnO/MgZnO single heterostructures and quantum wells”. 2009 MRS Spring Meeting, San Francisco, 2009 (2007). [6] M. Brandt, H. Frenzel, H. Hochmuth, M. Lorenz, and M. Grundmann. “Ferroelectric thin film transistors based on ZnO/BaTiO3 heterojunctions”. German Physical Society Spring Meeting, Dresden, March 2009 (2009). [7] M. Brandt, H. von Wenckstern, H. Hochmuth, M. Lorenz, J. Zippel, J. Lenzner, G. Benndorf, and M. Grundmann. “Accumulation of carriers in ZnO/MgZnO heterostructures and quantum wells”. 2nd International Symposium on Transparent Conducting Oxides, Hersonissos, Crete, 2008 (2008). [8] M. Brandt, H. von Wenckstern, C. Dietrich, G. Benndorf, J. Zippel, A. Abdullah, C. Meinecke, T. Butz, H. Hochmuth, M. Lorenz et al.. “Dopant activation in homoepitaxial ZnO:P and ZnMgO:P thin films”. The 5th 175

List of own conference contributions International Wokshop on ZnO and Related Materials, Ann Arbor, Michigan, 2008 (2008). [9] M. Brandt, H. Frenzel, H. Hochmuth, M. Lorenz, J. Schubert, and M. Grundmann. “Ferroelectric thin film field-effect transistors based on ZnO/BaTiO3 heterostructures”. The 5th International Wokshop on ZnO and Related Materials, Ann Arbor, Michigan, 2008 (2008). [10] M. Brandt, H. Hochmuth, M. Lorenz, M. Grundmann, N. Ashkenov, V. Voora, and M. Schubert. “Ferroelectric properties of BaTiO3 – ZnO heterojunctions”. German Physical Society Spring Meeting, Berlin, March 2008 (2008). [11] M. Brandt, H. von Wenckstern, H. Hochmuth, M. Lorenz, G. Biehne, G. Benndorf, C. Meinecke, T. Butz, H. Schmidt, A. Rahm et al.. “Homoepitaxial growth of ZnO thin films by pulsed laser deposition (PLD)”. German Physical Society Spring Meeting, Berlin, March 2008 (2008). [12] M. Brandt, H. Hochmuth, M. Lorenz, M. Grundmann, M. Schubert, T. Hofmann, V. M. Voora, N. Ashkenov, and J. Schubert. “Electrical and electro-optical investigations of the polarization coupling in epitaxial ferroelectric BTO/ZnO heterostructures”. 2007 MRS Fall Meetingg, Boston, Fall 2007 (2007). [13] M. Brandt, H. von Wenckstern, C. Hanisch, H. Hochmuth, M. Lorenz, H. Schmidt, and M. Grundmann. “Homoepitaxial growth of ZnO thin films by pulsed laser deposition (PLD)”. German Physical Society Spring Meeting, Regensburg, March 2007 (2007). [14] M. Brandt, H. von Wenckstern, H. Hochmuth, M. Lorenz, M. Grundmann, J. Schubert, V. Voora, and M. Schubert. “Ferroelectric properties of BaTiO3 - ZnO heterojunctions”. German Physical Society Spring Meeting, Regensburg, March 2007 (2007). [15] M. Brandt, H. Schmidt, H. von Wenckstern, C. Henkel, H. Hochmuth, M. Lorenz, and M. Grundmann. “Charge carrier profiling of ZnO”. The 4th International Wokshop on ZnO and Related Materials, 03.-06.10.2006, Giessen, Germany P – 221 (2006). [16] M. Brandt, H. von Wenckstern, G. Benndorf, J. Lenzner, H. Schmidt, M. Lorenz, M. Grundmann, G. Braunstein, and G. Brauer. “Optical and microelectrical characterization of ZnO single crystals implanted with group V elements”. German Physical Society Spring Meeting, Dresden, March 2006 HL14 – 4. [17] M. Brandt, H. von Wenckstern, G. Zimmermann, S. Heitsch, G. Benndorf, H. Hochmuth, M. Lorenz, and M. Grundmann. “Hall effect measurements on ZnO thin films”. German Physical Society Spring Meeting, Berlin, 2005 HL 17.4 (2005).

176

List of Symbols Variable a, c a0 , c 0 b B β βBH C C13 , C33 Ci cl cp cps Cst cx Dn Df df dz δ1 , δ2 E e EC ED ED0 Ef epz ε ε0 ε∞ ǫ⊥ ǫk εf εz F f Φb Φe , Φh Φx , Φy Φr γ ~ η I ji ka , kc

Meaning First Occurrence Lattice constants in a hexagonal crystal . . . . . . . . . . . . . . . . . 16 Lattice constants of an unstrained pure ZnO substrate . . 18 Burgers vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Magnetic induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 inverse thermal energy β = kB1T . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Brooks-Herring correction factor . . . . . . . . . . . . . . . . . . . . . . . . . 8 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Elastic constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Insulator Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Longitudinal elasticity constant . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Phosphorus content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 c-axis lattice constant under pseudomorphic strain . . . . . . 18 Capacitance of standard capacitor . . . . . . . . . . . . . . . . . . . . . 136 c-axis lattice constant as function Mg content x . . . . . . . . . 18 Deformation potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Dielectric displacement in ferroelectric . . . . . . . . . . . . . . . . . 134 Thickness of ferroelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Thickness of individual ZnO layers . . . . . . . . . . . . . . . . . . . . . 134 Crystal-field and Spin-Orbit splitting parameters . . . . . . . . 59 Electron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Elementary charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Coercive field strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Donor activation energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Donor activation energy in the dilute limit . . . . . . . . . . . . . . 85 Electric field in the ferroelectric . . . . . . . . . . . . . . . . . . . . . . . . 132 Isotropic piezoelectric coefficient . . . . . . . . . . . . . . . . . . . . . . . . . .8 Relative permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Permittivity of free space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8 High frequency permittivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Strain perpendicular to the substrate . . . . . . . . . . . . . . . . . . . .17 Strain parallel to the substrate . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Relative permittivity of ferroelectric layer . . . . . . . . . . . . . . 134 Relative permittivity of ZnO layer . . . . . . . . . . . . . . . . . . . . . 134 Electric field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Distribution function of electrons . . . . . . . . . . . . . . . . . . . . . . . . . 7 Barrier height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Electron and Hole wave function . . . . . . . . . . . . . . . . . . . . . . . 107 Perturbation terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Exciton radial wave function . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Surface energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Plancks constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Ideality factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Current density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Change of lattice constant with magnesium content . . . . . 16 177

List of symbols kx , ky kB kc,ps L LD Lc λ λi λo Lz me µ µH NA NC ND NI Npo Nt n νel ωo ωc P Pd Pr Ps Psat PZnO p(O2 ) r RS RP Sn Si So s σb , σf , σm σij σT T t Θ τ V VD

Components of the electron wave vector . . . . . . . . . . . . . . . . . . 7 Boltzmann constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Pseudomorphic c-axis lattice constant . . . . . . . . . . . . . . . . . . . 18 Channel length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Debye length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Collision operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Exciton radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Differential rate of scattering in . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Differential rate of scattering out . . . . . . . . . . . . . . . . . . . . . . . . . 8 Quantum well width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Effective electron mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Rigidity modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Hall-mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 Acceptor concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62 Critical donor concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Donor concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Concentration of ionized impurities . . . . . . . . . . . . . . . . . . . . . . .8 Phonon occupation number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Net dopant concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Free electron concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 Elastic scattering rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Phonon frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Cyclotron frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Electromechanical coupling coefficient . . . . . . . . . . . . . . . . . . . . 8 Polarization of the ferroelectric . . . . . . . . . . . . . . . . . . . . . . . . 132 Remanent polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Spontaneous polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Saturation polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Spontaneous polarization of the individual ZnO layer . . .134 Oxygen partial pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Radius of a depression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Series resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 Parallel resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Huang–Rhys factor of n-th phonon replica . . . . . . . . . . . . . 107 Rate of scattering into a specific state . . . . . . . . . . . . . . . . . . . . 7 Rate of scattering out of a specific state . . . . . . . . . . . . . . . . . . 7 Mobility distribution function . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Charge at individual interfaces of a heterojuction . . . . . . 134 Components of the conductivity tensor . . . . . . . . . . . . . . . . . . . 9 Effective capture cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Absolute temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Debye temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Scattering time of elastic scattering . . . . . . . . . . . . . . . . . . . . . . 7 Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Drain voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 178

List of symbols VG VT W w x XC ζ

Gate voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Threshold voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Channel width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Depletion layer width in the individual ZnO layer . . . . . . 132 Magnesium content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Acoustic deformation potential . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Exciton dimensionality parameter . . . . . . . . . . . . . . . . . . . . . . 107

179

List of symbols

180

List of Figures 1.1

Change in the spontaneous polarization vs Mg content x. . . . .

2.1

Schematics of the Sawyer Tower measurement circuit. (Courtesy of Venkata M. Voora) . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 3.2 3.3 3.4

Possible orientantions of the wurtzite material ZnO. . . . . . . . Peak position of photoluminescence spectra vs Mg content x. . . Principle of pseudomorphic growth. . . . . . . . . . . . . . . . . Reciprocal space maps of (002) and (104) reflection of a Mgx Zn1−x O thin film grown on a CT substrate. . . . . . . . . . . . . . . . . Reciprocal space maps of (002) and (104) reflection of a Mgx Zn1−x O thin film grown on a CT substrate. . . . . . . . . . . . . . . . . Change in the c-axis lattice constant vs. Mg content x in pseudomorphic Mgx Zn1−x O thin films. . . . . . . . . . . . . . . . . . 2 µm×2 µm AFM images of ZnO thin films grown on a-plane sapphire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example for double spirals and islands present on one ZnO sample. 2 µm×2 µm AFM images and film thickness of ZnO thin films after 100, 300, 1,000, 3,000 and 10,000 pulses. . . . . . . . . . . 2 µm×2 µm AFM images of Mgx Zn1−x O thin films grown on sapphire substrates. . . . . . . . . . . . . . . . . . . . . . . . . . Free electron concentration and mobility in various ZnO substrates versus temperature. . . . . . . . . . . . . . . . . . . . . . Comparison of reciprocal space maps of the (002), (101) and (104) reflexes obtained on a TD substrate and two selected CT substrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 µm×2 µm AFM height images of ZnO substrates purchased from CrysTec GmbH before and after thermal annealing. . . . . 2 µm×1 µm AFM height images of homoepitaxial ZnO thin films grown at various temperatures. . . . . . . . . . . . . . . . . . . Reciprocal space maps of the (002) and (104) reflex of a homoepitaxial ZnO thin film. . . . . . . . . . . . . . . . . . . . . . Cross section TEM bright field images of a homoepitaxial ZnO thin film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CBED diffraction patterns as obtained on an O-polar homoepitaxial ZnO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12

3.13 3.14 3.15 3.16 3.17

181

3

14 16 18 19 20 22 25 26 29 32 35

37 39 40 42 43 43

List of Figures 3.18 Cross section HR-TEM image of the interface between a homoepitaxial thin film and the substrate. . . . . . . . . . . . . 3.19 2 µm×0.5 µm AFM height images of homoepitaxial ZnO thin films of different thickness. . . . . . . . . . . . . . . . . . . . . 3.20 AFM height images of Mgx Zn1−x O thin films grown on ZnO. . 3.21 2 µm×2 µm AFM height images of Mgx Zn1−x O samples with various Mg contents grown on substrates of different miscuts. . 3.22 Perovskite unit cell (ABO3 ). . . . . . . . . . . . . . . . . . . . 3.23 2 µm×2 µm AFM images of untreated (100) STO substrates as received from (a) Crystal GmbH and (b) Crystec GmbH. (Courtesy of Stefan Schöche) . . . . . . . . . . . . . . . . . . . . . . 3.24 2 µm×2 µm AFM images of annealed STO substrates. . . . . . 3.25 2 µm×1 µm AFM images of BTO thin films. . . . . . . . . . . 3.26 SRO thin films of roughly 30 nm thickness grown on STO substrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 4.2 4.3

4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12

4.13 4.14 4.15

. 44 . 45 . 46 . 48 . 50

. 51 . 51 . 52 . 52

2Θ–ω X-ray diffraction patterns of the (002) reflection of homoepitaxial ZnO thin films. . . . . . . . . . . . . . . . . . . . . Near band edge PL spectra of homoepitaxially ZnO thin films. . Temperature dependence of the free electron concentration and the Hall-mobility in nominally undoped homoepitaxial ZnO thin films. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature dependence of capacitance of PtOx Schottky diodes fabricated from homoepitaxial ZnO thin films. . . . . . . . . . . 2 µm×1 µm AFM height images for homoepitaxial ZnO:P samples. HR-XRD reciprocal space map of the (002) and (104) reflection of a homoepitaxial ZnO:P sample. . . . . . . . . . . . . . . . . . 2Θ–ω X-ray diffraction patterns of the (002) reflection of homoepitaxial ZnO:P thin films. . . . . . . . . . . . . . . . . . . . Channeling yield χ and phosphorous content of homoepitaxial ZnO:P thin films as extracted from RBS and PIXE measurements. Low temperature recombination spectra of homoepitaxial ZnO:P samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conductivity of two typical homoepitaxial ZnO:P thin films compared to the conductivity of a CT substrate. . . . . . . . . . Hall-mobility and free carrier concentration as a function of temperature in homoepitaxial ZnO:P thin films. . . . . . . . . . . . Hall-mobility and free carrier concentration as a function of temperature in homoepitaxial ZnO:P thin films before and after annealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistivity of homoepitaxial phosphorous doped ZnO thin film as grown and after annealing. . . . . . . . . . . . . . . . . . . . Mobility spectra of a Mgx Zn1−x O layer grown on the (0001) face of a ZnO single crystal as obtained from the f-MEMSA algorithm. Magnesium and phosphorous content of the Mgx Zn1−x O thin films deposited on ZnO substrates as determined by PIXE. . . . 182

57 58

60 63 66 67 68 70 72 74 75

77 78 80 83

List of Figures 4.16 HR-XRD triple axis 2Θ–ω scans of the symmetric (002) reflex of Mgx Zn1−x O:P films. . . . . . . . . . . . . . . . . . . . . . . . 4.17 HR-XRD reciprocal space maps of the symmetric (002) and the asymmetric skew (101) reflex of a Mgx Zn1−x O:P film grown on ZnO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.18 Electron mobility and free electron concentration versus temperature in selected Mgx Zn1−x O:P thin films grown on ZnO. . . 4.19 (a) Donor activation energy versus donor concentration in ZnO:P and Mgx Zn1−x O:P films grown on ZnO. (b) Ratio of the resistivities of Mgx Zn1−x O:P thin films grown on ZnO after and before annealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 5.2

5.3 5.4 5.5 5.6 5.7

5.8

5.9

5.10 5.11

5.12 5.13

85

86 87

89

Band diagram of ZnO/Mgx Zn1−x O heterostructures investigated. 94 Capacitance versus voltage dependence and apparent dopant concentration of a Schottky diode on a ZnO/Mgx Zn1−x O heterostructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Free electron concentration and mobility versus temperature in a ZnO/Mgx Zn1−x O heterostructure. . . . . . . . . . . . . . . . . 97 AFM images of a ZnO/Mgx Zn1−x O QW grown on sapphire and ZnO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Temperature dependence of the free carrier concentration and the mobility in a ZnO/Mgx Zn1−x O quantum well structure. . . . 101 HR-XRD reciprocal space maps of the symmetric (002) and the asymmetric skew (101) reflex of a ZnO/Mgx Zn1−x O QW. . . . . 102 Electron mobility versus temperature in a homoepitaxial ZnO thin film, a ZnO/Mgx Zn1−x O QW structure grown on ZnO and a ZnO single crystal. . . . . . . . . . . . . . . . . . . . . . . . . 103 Peak width (FWHM) of the QW related PL peak versus QW thickness LW for ZnO/Mgx Zn1−x O QW structures grown on sapphire and ZnO substrates. . . . . . . . . . . . . . . . . . . . . . 104 Properties of an exciton in a c-oriented ZnO/Mgx Zn1−x O QW with x = 0.18 as function of the QW width obtained from variational calculations. . . . . . . . . . . . . . . . . . . . . . . . . . 106 Schematics of ZnO/Mgx Zn1−x O QW samples investigated in the present study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Low temperature CL spectra obtained from two otherwise equal Zno/Mgx Zn1−x O QWs deposited at two different laser fluences: (a) lense in position 2 (low fluence) (b) lense in position 1 (high fluence). The spectra are color coded, red corresponds to a high, blue to a low QW thickness. (Data obtained by Jan Zippel) . . 109 Excitation dependence of the CL spectra of a sample showing a pronounced QCSE. . . . . . . . . . . . . . . . . . . . . . . . . . 110 Normalized PL spectra of two samples with different Mg content x in the barrier. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 183

List of Figures 5.14 (a) Spectral maximum of QW related luminescence in various QW samples (b) Huang–Rhys factor as a function of the spectral position of the main peak. . . . . . . . . . . . . . . . . . . . . . 115 5.15 PL maximum position and decay time as a function of the QW thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.1

6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16

Sawyer–Tower-circuit response of a ZnO/BTO heterostructure grown on Si with Pt contacts measured at various cycling frequencies and voltage amplitudes as indicated. The data was obtained from selected contacts on the wafer shown in Fig. 6.3. . 123 Current voltage characteristic of a ZnO/BTO heterojunction grown on Si with Pt contacts. . . . . . . . . . . . . . . . . . . . 124 Maps of the parallel and series resistance of ZnO/BTO heterojunctions of a 3 inch silicon wafer. . . . . . . . . . . . . . . . . . 125 XRD Wide angle 2Θ–ω scans of ZnO/BTO heterostructures grown on Si/Pt and STO/SRO. . . . . . . . . . . . . . . . . . . 126 XRD φ-scans of a ZnO/BTO heterostructure grown on an STO substrate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Current flowing into a ZnO/BTO heterostructure grown on a STO:Nb as function of applied voltage and integration time. The ZnO has a thickness of 500 nm, the BTO 800 nm. . . . . . . 128 Current–voltage characteristic of two selected contacts with a reduced ZnO thickness of 50 nm. . . . . . . . . . . . . . . . . . . 130 Schematic of the distribution of space charge regions within the heterojunctions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Experimentally measured and model calculated Sawyer-Tower loops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Model calculated Sawyer–Tower loops and depletion layer widths in ZnO/BTO double heterostuctures. . . . . . . . . . . . . . . . 140 Principal of C–V response of a SIS, a SFS and of ZnO/BTO double heterostructures with two different parallel arrangements of the ZnO polarization. . . . . . . . . . . . . . . . . . . . . . . 141 Experimental (a) I–V and (b) C–V characteristic of a ZnO/BTO/ZnO double heterostructure. . . . . . . . . . . . . . . . . . . . . . . . 142 Principle layout of ZnO/BTO MISFET transistors. . . . . . . . 143 Output characteristics of a ZnO/BTO MISFET at different gate voltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Transfer characteristics and calculated channel mobility of a ZnO/BTO MISFET at a fixed source–drain-voltage of VSD = 2V.145 (a) Transfer characteristics of a ZnO/BTO MISFET after applying a for- and backwards pulse, respectively. (b) Ratio of the current in the permanent ‘on’ and the permanent ‘off’ state. . . 146

184

List of Tables 3.1 3.2 4.1 4.2 4.3 4.4

6.1 6.2

Change of lattice constants of Mgx Zn1−x O thin films with increasing magnesium content for various growth methods on different substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Suppliers and growth methods of ZnO single crystals investigated. 34 Donor activation energy, donor and acceptor concentration and capture cross section homoepitaxial ZnO thin films. . . . . . . Impurity concentration as detected by PIXE in homoepitaxial ZnO:P samples. . . . . . . . . . . . . . . . . . . . . . . . . . . Donor and acceptor concentration and donor activation energy in ZnO:P thin films. . . . . . . . . . . . . . . . . . . . . . . . Mg and P content, lattice parameters and room temperature electron concentration and Hall-mobility in MgZnO:P thin films grown on ZnO. . . . . . . . . . . . . . . . . . . . . . . . . . .

. 62 . 69 . 74 . 88

Operation schemes of a ZnO/BTO/ZnO heterostructure. . . . . 135 Best-match model calculation parameters. . . . . . . . . . . . . 137

185

List of Tables

186

Acknowledgement First of all, I acknowledge the guidance by my supervisor Prof. Dr. Marius Grundmann and the countless opportunities he gave me to ask questions and to improve my knowledge. Without the discussions, seminars, invited talks and conferences he organized or enabled me to visit the thesis certainly would not be what it is today. I am indebted to PD Dr. habil Michael Lorenz, who is the supervisor of the A2 project of the Sonderforschungsbereich 762, for numerous discussions and extensive support especially in regard to PLD related questions. I’m very grateful for the scientific freedom he admitted to me and for providing the means of realization of these ideas wherever possible. I want to thank Dr. Holger von Wenckstern for all the support in the past years, starting from supervising my diploma thesis. I always benefited from his respectable knowledge on the matter of electrical characterization, and was highly influenced by his encouraged and encouraging support. Thank you for the always open door, and the friendship that developed. I also want to thank Gabriele Benndorf for her help regarding optical and luminescence related questions, her accurate and critical comments, and countless nightly discussions on scientific problems. I deeply appreciate the personal relation to her, her warm hearted attitude and the help she provided on any personal matter. Danke Gabi! I am greatly indebted to all the people who helped in carrying out the work discussed in this thesis, namely • Holger Hochmuth for the help regarding the growth of the films studied, RHEED measurements as well as technical support in multiple ways. I appreciate his patience on the topic of ‘mysteriously disappearing’ tools. • Helena Hilmer and Martin Lange for mutual help in sample growth and company during nights and weekends. • Hannes Münch for the help regarding sample growth and metalization. • Dr. Jürgen Schubert (Forschungszentrum Jülich) for providing BTO templates. 187

. Acknowledgement • Gisela Biehne and Monika Hahn for the help in sample processing. Besonderen Dank an Gisela für die Hilfe außerhalb aller Arbeitszeiten. • Jörg Lenzner for several microscopy and CL measurements and extensive help regarding technical questions. • Gabriele Ramm for the preparation of the target material used in the study and technical help. • PD Dr. habil Michael Lorenz, Christof Dietrich, Stefan Schöche and Jan Zippel for XRD measurements. • Dr. Heidemarie Schmidt (now Forschungszentrum Rossendorf), Helena Hilmer, Stefan Schöche and Gregor Zimmermann for AFM investigations. • Gabriele Benndorf, Christian Czekalla, Chistof P. Dietrich, Martin Lange, Alexander Müller, Marko Stölzel, Jan Zippel and Johannes Kupper for the various luminescence spectroscopy measurements. • Roswitha Riedel for various technical help. • Dr. Holger von Wenckstern and Robert Heinhold for various Hall-effect measurements. • Dr. Heidemarie Schmidt and Danilo Bürger (both Forschungszentrum Rossendorf) for the magnetotransport measurements. • Robert Heinhold for the MEMSA evaluation. • Dr. Holger von Wenckstern, Martin Ellguth, Alexander Lajn, Matthias Schmidt, Kerstin Brachwitz, Florian Schmidt and Stefan Müller for numerous measurements on rectifying contacts, including I–V, C–V, TAS and DLTS measurements. • Heiko Frenzel and Peter Schwinkendorf for the help regarding the characterization of field effect transistors. • Dr. Rüdiger Schmidt-Grund, Helena Hilmer, Philipp Kühne, Stefan Schöche, Chris Sturm and David Schumacher for numerous ellipsometry measurements. • Christoph Meinecke for the RBS and PIXE measurements discussed in this work. • Dr. Gerald Wagner, Prof. Dr. Werner Mader, Dr. Herbert Schmid (both Universität Bonn) and Dr. Jesús Dr. Zúñiga-Pérez (Centre de Recherche sur l’Hétéro-Epitaxie et ses Applications) for the TEM measurements. • Nurdin Ashkenov and Venkata M. Voora for ST, I–V and C–V measurements on ZnO/BTO heterostructures. 188

• Venkata M. Voora and Mathias Schubert (University of Nebraska, Lincoln) for the cooperation in developing the model of ZnO/BTO coupling and for numerous mutual visits. • PD Dr. habil. Rainer Pickenhain for helpful discussions. • Anja Heck and Birgit Wendisch for help with all administrative issues. • Prof. Dr. Kremer for providing his AFM instrument. • Dr. Atsushi Tsukazaki for the inspiring opportunity to visit his lab. • My room members Matthias Schmidt, Venkata M. Voora, Thomas Lüder, Zhipeng Zhang, Michael Lorenz, Robert Heinhold, Heiko Frenzel and Martin Lange for various invaluable help and exciting discussions. • My ‘librarians’ Annika Brandt (Universität Halle) and Stefanie Benkwitz (Universität Jena) for the help in acquiring various scientific articles and their kind motivation. • Gregor Zimmermann for the help with LATEXrelated questions. • PD. Dr. habil. Michael Lorenz, Dr. Holger von Wenckstern, Dr. Gerald Wagner, Gabriele Benndorf and Andreas Kraus for help in proofreading the present work. I acknowledge the financial support in the framework of the Forschergruppe 404 and the Sonderforschungsbereich 762. I am very grateful for the opportunity to work in the semiconductor physics group at the Universität Leipzig and will always remember the outstanding teamwork which is both scientifically and personally inspiring. Thank you all! Last but not least I want to acknowledge the ongoing support, help and motivation I received through my friends and family. Vielen Dank!

189

. Acknowledgement

190

Curriculum Vitae Address Matthias Brandt Mierendorffstr. 52 04318 Leipzig Germany Tel: +49 341 97 32 642 Fax: +49 341 97 32 668 Email: [email protected]

Personal Details Surname

Brandt

Given Name

Matthias, Andreas

Date of Birth

10th of May, 1981

Place of Birth

Hohenmölsen

Nationality

German

Education early 2010

Award of the doctorate

end 2009

Completion of PhD thesis, prospective title: "Influence of the electrical polarization on carrier transport and recombination dynamics in ZnO-based heterostructures"

since 07/2006

Multiple monthly visits in Lincoln, Nebraska, USA, in the group of Prof. M. Schubert

since 07/2006

Postgraduate student, Universität Leipzig, Fakultät für Physik und Geowissenschaften, Semiconductor physics group of Prof. M. Grundmann 191

. Curriculum Vitae 30.06.2006

Award of the Diplom, title of the thesis: "Elektrische Eigenschaften von Zinkoxid bei erhöhten Temperaturen" ("Electrical properties of zinkoxide at elevated temperatures")

2003–2004

Semester abroad, University of Leeds, UK

2000–2006

Physics study program, Universität Leipzig

1999–2000

Civilian Service in a public hospital, "Kreiskrankenhaus", Altenburg

1997–1999

Secondary school: "Friedrichgymnasium", Altenburg, Award of the Abitur

1991–1997

Secondary school: "Veit Ludwig von Seckendorff Gymnasium", Meuselwitz

1987–1991

Primary school: "Polytechnische Oberschule Rosa Luxemburg", Meuselwitz

Language Skills German English French

native near native basic knowledge

192