GaN quantum wells for

Pseudo-square AlGaN/GaN quantum wells for terahertz absorption M. Beeler, C. Bougerol, E. Bellet-Amalric, and E. Monroy Citation: Applied Physics Letters 105, 131106 (2014); doi: 10.1063/1.4896768 View online: http://dx.doi.org/10.1063/1.4896768 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/105/13?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Terahertz intersubband absorption in non-polar m-plane AlGaN/GaN quantum wells Appl. Phys. Lett. 105, 021109 (2014); 10.1063/1.4890611 Terahertz absorbing AlGaN/GaN multi-quantum-wells: Demonstration of a robust 4-layer design Appl. Phys. Lett. 103, 091108 (2013); 10.1063/1.4819950 Terahertz intersubband transition in GaN/AlGaN step quantum well J. Appl. Phys. 113, 154505 (2013); 10.1063/1.4802496 Improvement of near-infrared absorption linewidth in AlGaN/GaN superlattices by optimization of delta-doping location Appl. Phys. Lett. 101, 102104 (2012); 10.1063/1.4751040 Terahertz intersubband absorption in GaN/AlGaN step quantum wells Appl. Phys. Lett. 97, 191101 (2010); 10.1063/1.3515423

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.168.10.36 On: Tue, 30 Sep 2014 14:26:46

APPLIED PHYSICS LETTERS 105, 131106 (2014)

Pseudo-square AlGaN/GaN quantum wells for terahertz absorption M. Beeler,1,2 C. Bougerol,1,3 E. Bellet-Amalric,1,2 and E. Monroy1,2 1

Universit e Grenoble Alpes, 38000 Grenoble, France CEA-Grenoble, INAC/SP2M/NPSC, 17 avenue des Martyrs, 38054 Grenoble, France 3 Institut N eel-CNRS, 25 avenue des Martyrs, 38042 Grenoble Cedex 9, France 2

(Received 12 July 2014; accepted 17 September 2014; published online 29 September 2014) THz intersubband transitions are reported down to 160 lm within AlGaN/GaN heterostructures following a 4-layer quantum well design. In such a geometry, the compensation of the polarizationinduced internal electric field is obtained through creating a gradual increase in polarization field throughout the quantum “trough” generated by three low-Al-content layers. The intersubband transitions show tunable absorption with respect to doping level as well as geometrical variations which can be regulated from 53 to 160 lm. They also exhibit tunnel-friendly designs which can be easily C 2014 AIP Publishing LLC. integrated into existing intersubband device architectures. V [http://dx.doi.org/10.1063/1.4896768] Wide-bandgap AlGaN/GaN heterostructures are intensively studied as a promising alternative to replace GaAs in solid-state THz optoelectronics. GaAs-based quantum cascade lasers operating in this spectral range are limited by intrinsic material properties, namely, the longitudinal-optical (LO) phonon, which exists at 36 meV. On the contrary, the large energy of the GaN LO phonon (92 meV) opens prospects for GaN-based high-temperature THz quantum cascade lasers1–5 and intersubband (ISB) devices covering the 5–10 THz band, inaccessible to As-based technologies. ISB transitions in GaN/AlGaN multi-quantum-wells (MQWs) can be tuned from 1.0 lm to 10 lm by reducing the Al mole fraction in the barriers and increasing the quantum well (QW) width6–12 (see Ref. 13 for a review). This strategy faces a roadblock at longer wavelengths because of the quantum confined Stark effect. The polarization-induced internal electric field results in QWs with a sawtooth profile and with lower electronic levels confined to a small fraction of the QW, so that changes in well width do not induce proportional changes in ISB energy. Therefore, to shift the absorption towards longer wavelengths in polar structures, it is necessary to engineer the conduction band to reduce the effect of the internal electric field within the QWs. Polarization effects can be eliminated by growing on a nonpolar crystallographic plane14 or using cubic nitride heterostructures,15 but such approaches must face additional growth challenges. In the well-known (0001) orientation, attempts to reduce the electric field have led to 3-layer stepQW architectures, where ISB transitions in the THz region have been reported,16 and a THz photodetector has been demonstrated around this principle.17 However, the 3layered design in Ref. 16 suffers from issues with reproducibility and the inability to easily predict the ISB transitional energy.18 Alternative geometries have been proposed which increase the robustness of the ISB transition to accommodate errors in growth rate and interfacial roughness.18 This was accomplished by introducing a complex barrier system which sacrifices tunability and does not completely compensate the internal electric field. Furthermore, the width of the complex barrier inhibits electron tunneling transport, which complicates the 0003-6951/2014/105(13)/131106/4/$30.00

incorporation of such QWs in an electrically driven device structure. In this work, we introduce an AlGaN-based pseudosquare QW design for ISB devices operating in the THz spectral range. The proposed geometry achieves THz ISB absorption thanks to the compensation of the polarizationinduced internal electric fields, and the potential barriers are thin enough to facilitate tunneling at low bias. These QWs exhibit wave functions which are much more symmetric than previous designs, which translate to higher oscillator strengths. Pseudo-square QWs fabricated by plasma-assisted molecular-beam epitaxy (PAMBE) present ISB absorption at 160 lm, which blue shifts to 50 lm with increasing doping level, and can be tuned from 100 to 75 lm by changing the width of a quantum trough. AlGaN-based pseudo-square QWs have been simulated using the self-consistent nextnano3 8-band kp Schr€odingerPoisson solver.19 Calculations were performed using the material parameters in Ref. 20, and assuming the structure strained on GaN. The proposed band structure in Fig. 1(a) consists of four compositionally different AlGaN layers with nominal Al concentrations of 12%, 0%, 5%, and 7% for the barrier, GaN, A, and B layers, respectively. The highest Al concentration (the concentration of the barrier) is chosen as the sum of the other two, so that the structure can be realized by PAMBE using two Al effusion cells. In this pseudo-square QW, the electric field is compensated by creating a gradual increase in polarization field throughout the quantum “trough” formed by the 3 low-Al-content layers. Because of this gradual increase, the electron density function is delocalized from a single layer and is quantum confined across all three layers by the effective size of the trough and not by the polarization field. Simulations show that the oscillator strength of the pseudosquare QW is the same as the 4-layered MQW system,18 and an order of magnitude greater than that of the step-QW configuration.16 The ISB energy of this design is nominally targeted at 25 meV, and can be tuned by changing the width of the A layer of the quantum trough. At zero bias, the second electronic level, e2, is localized in the QW, but the tunneling probability of electrons in e2 increases by biasing in the h0001i direction.

105, 131106-1

C 2014 AIP Publishing LLC V


131106-2

Beeler et al.

FIG. 1. (a) Band profile of a pseudo-square QW where the first and second confined electronic levels are indicated as e1 and e2, respectively. The nominal compositions of the layers are indicated above. (b) Schematic description of the structure which was grown on an AlN-on-sapphire substrate. (c) Illustration of the robustness of the pseudo-square QWs. The dashed lines indicate the nominal transition wavelengths. The error bars represent the minimum and maximum values attributed to the uncertainties associated to growth (geometries changed by 60.5 nm and alloys changed by 610%). Similar data for step-QWs and 4-layer QWs are included for comparison (after Ref. 18).

The ISB transition in this pseudo-square system has been tested against the uncertainties associated to PAMBE growth with the results described in Fig. 1(c). There are 7 degrees of freedom within the superlattice, namely, the thickness of each layer and the Al mole fraction in each AlxGa1xN layer. Each of these parameters were varied considering 62 monolayers (ML) as the error bar for thicknesses, and 610% of the nominal concentration as the error bar for the aluminium mole fraction in AlxGa1xN. The 10% variation in alloy is roughly equivalent to a temperature difference of 64 C for the Al effusion cells in the compositional range of this design. Figure 1(c) shows that the variation of most of the layer thicknesses results in ISB wavelength differences of nearly 5 lm, conversely parameters such as the “B alloy” and the “A width” are almost insensitive to changes. The results of this robustness assessment are compared to the previously reported data for step QWs and 4-layer QWs,18 also in Fig. 1(c). The ISB transition deviations in the pseudo-square design are generally smaller than those induced within the step QW, although larger than those of the 4-layer QW. For a fair comparison of the structures, it is important to consider that they are engineered to operate at different wavelengths. Defining the relative errors as Dk/k, the average wavelength variation that can be induced by growth uncertainties is 10%, 8.8%, and 25%, for pseudo-square QWs, 4-layer QWs, and step-QWs, respectively. AlGaN/GaN 40-period superlattices following the pseudo-square design in Fig. 1 were synthesized by PAMBE on GaN templates deposited on float-zone Si(111).7 These

Appl. Phys. Lett. 105, 131106 (2014)

templates use a complex buffer layer to minimize the effects of the lattice mismatch between GaN and Si(111), as well as mitigate the effects of thermal expansion. Identical samples were simultaneously grown on 1-lm-thick AlN-on-sapphire templates to simplify the structural characterization. During deposition, the growth rate was 0.32 ML/s and the substrate temperature was 720 C. The structure was grown uninterrupted under self-regulated Ga-rich conditions.20,21 To populate the ground conduction band level in the quantum trough, e1, 1.5 nm of each GaN layer was doped with Si. The structural parameters and doping level of the samples under study are summarized in Table I. A first set of samples (series I in Table I) was synthesized following the geometry in Fig. 1(b) with different doping concentrations in the GaN layer. Then, a second set of samples (series II in Table I) with a slightly modified geometry was used to determine the experimental effect of trough size, which was varied by changing the width of the Al0.05Ga0.95N layer (layer A). Figure 2(a) shows a high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image of three periods of sample I.2 obtained in an FEI Titan 80–300 microscope at 200 kV. An average background subtraction filter was used to increase the atomic contrast between the layers. The interfaces appear straight and sharp, and the difference in gray scale indicates the alloy concentration, confirming the nominal chemical sequence. Furthermore, energy dispersive x-ray spectroscopy performed on a (S)TEM FEI-Osiris microscope operated at 200 kV render Al compositions very close to nominal values, namely, 11.9%, 0%, 5.6%, and 7.3% for the barrier, GaN, A, and B layers, respectively, with an estimated standard deviation of 60.4%. The periodicity of the samples was analyzed by highresolution x-ray diffraction (HRXRD) using a Seifert XRD 3003 PTS-HR system with a beam concentrator before a Ge(220) four-bounce monochromator, and a Ge(220) twobounce analyzer in front of the detector. Figure 2(b) depicts the x2h scans of the (0002) reflections of samples II.1 and II.2 grown on AlN-on-sapphire templates. From these measurements, we extracted the superlattice periods summarized in Table I. The experimental measurements in Fig. 2(b) are juxtaposed to simulated curves assuming nominal Al concentrations and a superlattice misfit compressive strain relaxation of 93.5% and 94.5%, respectively,22 which is in accordance with previous observations of relaxation processes stating that GaN/AlGaN superlattices tend to relax towards their average aluminum concentration independent of the layer underneath.21 All samples grown on GaN-on-Si templates were polished at the Brewster angle of 60 to form multipass waveguides allowing 3–4 interactions with the active region. These samples were measured by Fourier Transform Infrared spectroscopy (FTIR) in transmission mode using a farinfrared polarizer to discern between the transverse-electric (TE) and transverse-magnetic (TM) polarized light. All measurements were performed at 5 K. Taking the selection rules into account, the ISB absorption peaks are identified by dividing the transmission spectra for TE polarization by the TM transmission. Figure 3(a) shows the low-temperature far-IR absorption spectra of TM-polarized light for samples


131106-3

Beeler et al.

Appl. Phys. Lett. 105, 131106 (2014)

TABLE I. Structural parameters, doping level in the GaN layer, superlattice period measured by HRXRD, and peak ISB absorption wavelength of the samples under study. (*) Thickness extrapolated from I-1, consistent with HAADF-STEM. (**) Thickness extrapolated from I-1. Sample

GaN layer (nm)

A (nm)

B (nm)

Barrier (nm)

[Si] (cm3)

Period (nm)

Absorption (lm)

Series I

I-1 I-2 I-3

3.1 3.1 3.1

10.7 10.7 10.7

5.3 5.3 5.3

3.1 3.1 3.1

3.3 1017 1.3 1018 1.3 1019

22.2 6 0.2 (*) (**)

160 83 53

Series II

II-1 II-2 II-3

3.5 3.5 3.5

6.0 8.0 10.0

6.0 6.0 6.0

3.5 3.5 3.5

4.8 1018 4.8 1018 4.8 1018

19.5 6 0.2 21.2 6 0.2 23.4 6 0.2

77 87 95

from series I, which displays a peak assigned to the ISB transition from the first to the second electronic levels in the QWs. Maximum interaction of light with the active layer occurred for an angle of incidence of 55 –65 . At lower angles of incidence, the ISB absorption peak decreases as illustrated in Fig. 3(c). Samples with doping level of 3.0 1017, 1.3 1018, and 1.3 1019 cm3 exhibit ISB absorption at 160, 83, and 53 lm, respectively, as summarized in Table I. Unintentionally doped samples, grown as a reference, do not show significant absorption across the spectrum. This blue shifting ISB absorption with higher dopant level indicates that many-body effects (depolarization shift,

FIG. 2. HAADF-STEM image of sample I.2, which follows the architecture in Fig. 1. The nominal concentrations of each layer are shown above, where 5% represents Al0.05Ga0.95N. Layer thicknesses of 41 ML Al0.05Ga0.95N/22 ML Al0.07Ga0.93N/12 ML Al0.12Ga0.88N/12 ML GaN are seen in the image. (b) HRXRD x2h scans around the (0002) reflection of samples II.1 (top) and II.3 (bottom). The simulations assume nominal Al concentrations and a superlattice relaxation of 93.5% and 94.5%, respectively.

exchange interaction) play a large role in determining the ISB energy. The depolarization shift, estimated from,23,24 is negligible for the architectures under study due to the small ISB transition energies under consideration. On the contrary, calculations of the exchange interaction following pffiffiffiffiffiffiffiffiBandara et al.,25 assuming the wave vector k ¼ 0, k ¼ 2pr with r being the two-dimensional electron density in the QW, and with a k-independent equation, give absolute values comparable to the energy of the ISB transition itself, as illustrated in Fig. 3(d). This is in accordance with Helm24 and Guo et al.26 which show that with large well widths, and small ISB energies (