Journal of ELECTRONIC MATERIALS, Vol. 43, No. 6, 2014
DOI: 10.1007/s11664-014-3101-x Ó 2014 TMS
Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics S.V. NOVIKOV,1,4 A.T. BURKOV,1,2 and J. SCHUMANN3 1.—Ioffe Physical-Technical Institute, Saint Petersburg, Russia. 2.—St. Petersburg National Research University of Information Technologies, Mechanics and Optics, Saint Petersburg, Russia. 3.—Leibniz Institute for Solid State and Materials Research, Dresden, Germany. 4.—e-mail:
[email protected]
We studied the thermoelectric properties, crystallization, and stability of amorphous and nanocrystalline states in Cr-Si composite films. Amorphous films, prepared by magnetron sputtering, were transformed into the nanocrystalline state by annealing with in situ thermopower and electrical resistivity measurements. We have found that the amorphous state is stable in these film composites to about 550 K. Prior to crystallization, the amorphous films undergo a structural relaxation, detected by peculiarities in the temperature dependences of the transport properties, but not visible in x-ray or electron diffraction. The magnitude and temperature dependences of electrical conductivity and thermopower indicate that electron transport in the amorphous films is through extended states. The amorphous films are crystallized at annealing temperatures above 550 K into a nanocrystalline composite with an average grain size of 10–20 nm. Key words: Nanocrystalline composite, thermoelectric properties , electronic transport
INTRODUCTION Nanostructuring is regarded as a promising route to a new generation of efficient thermoelectric materials.1,2 Technologically, nanocrystalline (NC) composites are the simplest representatives of nanostructured materials and are therefore very important from application perspective. Preparation of NC composite by crystallization from amorphous state features a low level contamination by environment impurities, which may have a decisive impact on the thermoelectric performance of NC material. In our recent article,3 we have demonstrated that NC CrSi2 and MnSi2 compounds, prepared by crystallization from amorphous state, have 2 a higher thermoelectric power factor (P ¼ Sq , where S is the thermopower coefficient, and q the electrical resistivity) in comparison with polycrystalline counterparts. Figure 1 shows the power factor of a CrSi2 thin film in NC and polycrystalline states. (Received October 28, 2013; accepted February 27, 2014; published online March 20, 2014)
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Considering the generally observed decrease of thermal conductivity upon nanocrystallization,4,5 this result implies an essential increase of thermoelectric performance in NC materials. Understanding of underlying mechanisms of nanocrystallization and of the electronic transport in different structural phases is of crucial importance for the development of practically useful nanostructured thermoelectrics. In this article, we present results of a systematic investigation of the electrical resistivity and thermopower of Cr1x Six thin film composites in amorphous state and data on the stability of this state as a function of the film composition and thickness. We use specific features of the qðTÞ and SðTÞ dependences and high sensitivity of the electronic transport properties to structural changes as a tool for investigation of the mechanism of electronic transport and of the structural state of the compounds. The crystalline CrSi2 is a semiconductor with band gap of about 0.35 eV.6 The main characteristic features of amorphous state are the absence of longrange order and large number of dangling bonds, which can act as donors or acceptors. Furthermore,
Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics
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with the resistivity temperature dependence follows the activation type: E2 ; (3) q ¼ D exp kT
Fig. 1. Power factor of a CrSi2 thin film in different structural states: 1 nanocrystalline state, 2 polycrystalline state. Note, the power factor of NC state is higher then the power factor of polycrystalline state.
in amorphous semiconductors, due to high degree of structural disorder, long tails of localized states appear in the band gap of the electronic structure. Due to a strong scattering on structural disorder potential, the charge carrier mobility is low, while the mean free path can be comparable to the de Broglie wavelength.7 Depending on the position of the Fermi energy relative to the band edges, different conduction mechanisms can be realized in amorphous semiconductors:7–9 – Hopping conduction via localized states, when the Fermi level is fixed in the narrow band of localized states near the middle of the band gap. Resistivity in this regime follows the activation type temperature dependence: E0 ; (1) q ¼ A exp kB T m here E0 is the activation energy, m < 1, kB is the Boltzmann constant. Thermopower is a nonlinear function of temperature and large. – When the Fermi level is near to the top of the valence band or near to the bottom of the conduction band, the conduction is due to diffusion of charge carriers, thermally activated into extended states. Resistivity temperature dependence is also of the activation type: E1 ; (2) q ¼ C exp kT where E1 —activation energy, E1 =EF EV , EF is the Fermi level, EV is the top of the valence band. Thermopower magnitude is strongly dependent of the Fermi level position and is generally nonlinear in temperature. – When the Fermi level is in the tail of localized states close to the band edges, some charge carriers can be excited into the extended states while others can hop over through the localized states. This is the regime of mixed conduction,
here E2 ¼ EF Eb þ H, where H is hopping activation energy, Eb is the position of the localized state levels. Thermopower can be large and nonlinear as a function of temperature. – In case of highly degenerate semiconductors, when EF is located in the valence or in conduction band, the physical properties of semiconductors are similar to the properties of metals. The resistivity temperature dependence follows a power law dependence: qðTÞ ¼ q0 þ BT y ;
(4)
Here, the factor B can be either positive or negative. The resistivity has a weak temperature dependence and is determined by the charge carrier scattering. For an amorphous metal, it is given by:10 q
Z2kF
IðqÞWðqÞq3 dq; 4kF
(5)
0
where kF is the Fermi wave vector, WðqÞis the structure function, IðqÞis the scattering crosssection, and q the scattering wave vector. Resistivity depends on temperature through the change of the structure factor WðqÞ with temperature. At higher temperatures, the atomic correlations become weaker and so the WðqÞ becomes broader, its magnitude in the main maximum decreases. If 2kF is in the neighborhood of WðqÞ maximum, then qðTÞ decreases with temperature due to the temperature smearing of WðqÞ.8,11 Thermopower is small and can be expressed via the Mott formula: 2 2 p k T dðln rÞ S¼ (6) 3eEF dðln EÞ E¼EF The logarithmic derivative on the right-hand side is of the order of unity for amorphous metals.12 These theoretical results form the basis for the analysis of experimental results on the temperature dependences of q and S. EXPERIMENTAL PROCEDURES The amorphous films were deposited by magnetron sputtering of composite targets onto unheated Si/SiO2 substrates. The deposition procedures were carried out in a high-vacuum chamber equipped with a turbo-molecular pump and with a mass flow controller for maintaining Ar working pressure at 4103 mbar. The deposition rate was in the range 20–60 nm/min. Cr1x Six films in composition range 0.51 < x < 0.9 with thickness from 20 to 500 nm were prepared. The films were further transformed
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RESULTS AND DISCUSSION
(b)
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ρ
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It has been shown that structural changes in conductors have a profound impact on the electronic transport. For this reason, the transport properties can be used as sensitive probes to detect and to monitor structural transformations. The lower panel of Fig. 2 presents temperature dependences of thermopower and electrical resistivity of a Cr0:28 Si0:72 film. There are well-defined temperatures, where both properties undergo sudden changes as the temperature increases. Comparing with x-ray data, shown in the upper panel of Fig. 2, one can conclude that the sharp increase of both q and S at T2 reflects the onset of crystallization. It has been shown that amorphous Cr1x Six films crystallize into nanocrystalline composite with average grain size about 10–20 nm; this state is stable to about 1,000 K.14 In this article, we focus on the transport properties of the amorphous state and its stability range; the properties of the nanocrystalline composites will be discussed elsewhere. Figure 3 shows the resistivity and Fig. 4 the thermopower temperature dependences of Cr1x Six amorphous films. The resistivity increases with temperature up to 150 K while it slowly decreases at higher temperatures, having a maximum at 150 K. The maximum is unusual for amorphous metals and requires additional investigation. qðTÞ at higher temperatures is typical of amorphous metal. Thermopower has low values and is, to a first approximation, linear in the temperature. The thermopower and the resistivity magnitude and resistivity temperature coefficient (Fig. 5) show variation with x. However, these changes have a purely quantitative nature, and the general features of qðTÞ and SðTÞ are common for all studied Cr1x Six amorphous compounds. They indicate that conduction in the amorphous Cr1x Six films is via extended states,7 the film being highly degenerate semiconductors with the Fermi level located within the valence band near its top. We have found that the as-deposited amorphous state is stable up to T ¼ T1 420 K. The heating and cooling curves of the resistivity and thermopower temperature dependences are reproducible if the highest heating temperature is less than T1 (see Fig. 3 cycle 1). Abrupt change of qðTÞ versus T slope
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into nanocrystalline state by annealing with in situ thermopower and electrical resistivity measurements. The resistivity and thermopower were measured simultaneously. A 4-point, DC procedure was used in the resistivity measurements, while a differential method was employed for the measurement of the thermopower. The measurements of temperature dependences were performed with a continuous variation of temperature with rate of 5 K/min, on heating and on cooling. The measurement set-up has been described elsewhere.13 The measurements were done in an inert helium gas atmosphere.
0.4 0.2
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T, K Fig. 2. (a) X-ray diffraction spectra of a Cr0:28 Si0:72 film measured in situ at different temperatures in high-temperature diffractometer. Measurement temperatures are indicated to the right of each trace; (b) temperature dependences of electrical resistivity qðT Þ and thermopower SðT Þ of Cr0:28 Si0:72 film. T1 and T2 indicate the temperature of structural relaxation in the amorphous state and the crystallization temperature of the NC phase, respectively.
(Fig. 3) at about 420 K indicates a change of shortrange order in the amorphous state (structural relaxation). This relaxation is not detected by x-ray diffraction. The structural relaxation during annealing is accompanied by an irreversible increase of the resistance and by a smaller change of thermopower. The rate of the resistivity increase depends on the annealing temperature. Successive annealing cycles result in a parallel q(T) curve shift ( Fig. 3). Each annealing cycle in this figure consists of a heating to a temperature Tann with following cooling to 100 K. Figure 3 shows 4 cycles. In the first cycle, the highest temperature was less than T1 , heating and cooling curves are fully reproducible. At heating to a temperature higher than T1 in the second cycle, the resistivity irreversibly increased, therefore the cooling curve does not coincide with the heating. The relaxation continues in the following cycles. The structural relaxation drives the as-deposited amorphous system towards a more ordered, quasi-equilibrium state.Correspondingly, the structure function WðqÞ narrows and the magnitude of its main maximum
Crystallization and Transport Properties of Amorphous Cr-Si Thin Film Thermoelectrics 1.05
(a) 0.47 4
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Fig. 5. Temperature dependence of normalized electrical resistivity for amorphous Cr1x Six films. The vertical line shows the approximate position of the structural relaxation temperature Tsro .
0.436
Temperature
350
0.424
0
500
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annealing time, min Fig. 3. (a) Resistivity temperature dependences of a CrSi2 ðx ¼ 0:67Þ amorphous film measured in the course of several heating-cooling cycles. The numbers indicate the sequence of the cycles. Changes of short-range order start at T1 , T2 is the temperature of onset of crystallization. (b) Resistivity of a CrSi2 ðx ¼ 0:67Þ amorphous film in dependence on the annealing time at the annealing temperature Tann = 440 K. Also shown is the variation of temperature during the annealing cycle. Note, the sharp decrease of the resistivity at the beginning of the annealing cycle is related to the increase of temperature from 300 K to the annealing temperature of 440 K.
Fig. 4. Thermopower temperature dependences of Cr1x Six amorphous films.
increases.15 Due to these changes, the resistivity increases during annealing at T > T1 , see Eq. 5. Since the mechanism of the resistivity temperature
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0.428
Crystallisation temperature, K
400
0.432
T, K
ρ, mΩ cm
x=0.67
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ρ(T)/ρ(300)
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d=21 nm d=41 nm d=100 nm d=208 nm
40
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Si content, at. % Fig. 6. The crystallization temperature of the amorphous Cr1x Six in dependence of film composition. The inset shows the thermopower of Cr0:15 Si0:85 composite films of different thicknesses.
dependence remains unchanged during the structural relaxation, the main features of qðTÞ dependence are preserved. It was found that the temperature of structural relaxation does not depend on the Si/Cr ratio (Fig. 5). The structural relaxation precedes the crystallization which starts at T2 of about 550 K. The crystallization temperature T2 increases with Si/Cr ratio; however, it is hardly dependent on the film thickness in the whole investigated range from 21 to 208 nm (Fig. 6). In contrast, thermopower magnitude reveals a clear size dependence below 41 nm in both the amorphous and the nanocrystalline states. Similarly, the resistivity is independent of film thickness d, when d > 40 nm, however the resistivity increases for thinner films. CONCLUSIONS The transport properties of amorphous Cr1x Six thin films were studied in the temperature range
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100–600 K. It was found from the analysis of the temperature dependences of the resistivity and thermopower that the amorphous composites are degenerate semiconductors, in which the main electronic transport mechanism is charge carrier diffusion over extended states. The as-deposited amorphous state is stable up to about 420 K. At higher temperatures, structural relaxation was observed. The relaxation temperature does not depend on the Cr/Si ratio. Crystallization temperature increases with Si content; however, it is independent of film thickness. Thermopower and resistivity show a dependence on film thickness below 40 nm. ACKNOWLEDGEMENTS This work in a part was supported by Government of Russian Federation, Grant 074-U01, and by the Russian Foundation for Basic Research under Grant No. 14-08-31177 mol_a. S.N.V. gratefully acknowledges financial support by Stipend of the President of the Russian Federation SP-543.2012.1.
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