An Approach to Optimize the Thermoelectric Properties of III–V

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

An Approach to Optimize the Thermoelectric Properties of III−V Ternary InGaSb Crystals by Defect Engineering via Point Defects and Microscale Compositional Segregations Velu Nirmal Kumar,*,† Yasuhiro Hayakawa,‡ Haruhiko Udono,§ and Yuko Inatomi*,†,∥ †

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, Sagamihara, Japan Research Institute of Electronics, Shizuoka University, Hamamatsu, Japan § Faculty of Engineering, Ibaraki University, Hitachi, Japan ∥ School of Physical Sciences, SOKENDAI (The Graduate University for Advanced Studies), Sagamihara, Japan

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‡

ABSTRACT: Thermoelectric power generators require semiconductor materials with controlled phonon and free charge carrier transport properties. This could be achieved by changing their molecular and lattice dynamics through introducing/ controlling structural imperfections (defects engineering). The structural imperfections such as point defects and compositional segregations in a multicomponent alloy are observed experimentally, and their impact on electron and phonon transport properties was explained. The thermoelectric properties of a III− V ternary alloy InGaSb was improved by the presence of point defects and compositional segregations. The compositions were segregated randomly, and they had a major impact on the phonon contribution to the thermal conductivity. The point defects affected electrical resistivity, and the Seebeck coefficient was influenced by carrier concentration. The figure of merit (ZT) of In0.95Ga0.05Sb is enhanced to 0.62 at 573 K, and it is the highest among any other reported values of binary/ternary III−V semiconductor alloys. The enhancement in the ZT of InGaSb from the viewpoints of point defects and compositional segregations are explained. This experimental defect engineering study could be helpful to understand and improve the thermoelectric properties of many other crystalline materials.

1. INTRODUCTION Thermoelectric (TE) materials have the potential to convert heat into electrical energy without any harmful radiation or emissions. The performance of TE generators depends on the thermoelectric figure of merit (ZT) of semiconductor materials used for fabrication. ZT is a dimensionless numberhaving direct proportionality with the thermoelectric power factor and an inverse proportionality with thermal conductivityas explained elsewhere.1−3 Thus, enhancement of the power factor and a reduction in thermal conductivity are preferred to obtain a high ZT in TE materials. To utilize the TE conversion process more effectively, much research has been developed by employing various experimental processes and theoretical assumptions to determine the best TE performance in different material systems.4−7 The experimental techniques are focused mostly to reduce the thermal conductivity in a multicomponent system by controlling their lattice thermal conductivity through various phonon scattering processes. It is possible to achieve the high ZT by controlling phonon transport because phonons contribute more than 80% of the total thermal conductivity in many semiconductor materials.8−10 A major issue in controlling the phonon transport is a reduction of the power factor (which results from electron © XXXX American Chemical Society

transport) because electron and phonon transport properties are interrelated to each other, which affects the ZT. As the phonons can be considered virtual atomic positions arising from thermal agitation in a crystal lattice, controlling those atomic positions could affect electron transport as well. To avoid this, the lattice sites should behave as a “crystal” for electrons and “glass/amorphous” for phonons. Though the concept of “electron crystal-phonon glass” was proposed and achieved in some materials experimentally,4,11−13 it is quite challenging to achieve this condition in many other materials. To overcome this issue, it is important to understand the change in lattice dynamics through the variations in molecular dynamics of crystalline materials. A way to observe this effect experimentally is through understanding and engineering the defects in materials because various imperfections/defects can affect the electron and phonon transports, and their effect depends on the nature of defects in crystalline materials. Recently, various reports explained the achievement of high ZT through the presence of point defects and lattice disorders Received: May 16, 2019

A

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. A schematic of the effects of charged and structural defects on the electron and phonon transport properties in crystalline materials.

in nanostructured materials by defect engineering.14−16 Though those works explain the reason for achieving a higher ZT, it was not clear that how to optimize/control the defects in nanostructured materials experimentally and analyze their impact on TE properties for a particular material system. For this purpose, a study on bulk crystalline materials could be helpful to understand and improve the impact of various defects on the TE properties. The crystalline imperfections can be differentiated as (i) charged and (ii) structural defects, in order to understand and improve the TE properties of materials. The point defects can be considered as “charged defects,” and other lattice imperfections such as grain boundaries, lattice strain, slip planes, twinning, etc. can be considered “structural defects,” in crystalline materials. On the basis of this consideration, the effects of charged and structural defects on the electron and phonon transport properties are schematically shown in Figure 1. The point defects affect charge carrier transport highly, though they have an important role in reducing the phonon wavelengths, because they are charged and serve as compensation centers for the electrons and holes, which reduces the electrical performance of a material. However, the lattice strains behave as a scattering center to the phonon transport, and they do not affect the carrier transport much. Thus, the charged and structural defects dominate the electron and phonon transport properties in a crystal lattice, respectively. This reveals that the understanding and control over the density of point defects and lattice strains is a possible way to improve the TE performance of crystalline materials. An understanding of the formation of defects in crystalline materials requires a knowledge of nucleation kinetics during their growth process. Our research group performed various growth experiments under normal and microgravity conditions

to understand the nucleation kinetics of InGaSb ternary alloys.17−20 InGaSb is a III−V ternary alloy whose thermoelectric properties are yet to be understood well. The thermal conductivities of some significant III−V semiconductors such as InSb, InAs, GaSb, GaAs, and AlAs were around 17.5, 30, 36, 45, and 91 W/mK, respectively.8,21 However, the highly efficient TE materials (ZT > 1) possess thermal conductivity less than 1 W/mK.22−24 Thus, the III−V semiconductors have at least one order of higher magnitude of thermal conductivity when compared to other efficient TE materials. Their higher thermal conductivity results from the ease of phonon propagation through their cubic zincblende lattice. InSb had the higher ZT (0.5) among the III−V semiconductors because of its very high charge carrier mobility and relatively lower thermal conductivity. However, a ZT value close to 1 is preferred for the fabrication of TE devices. Thus, the III−V semiconductors were considered not suitable for TE applications. Upon understanding the growth kinetics of the In−Ga−Sb system, we tried to reduce the lattice thermal conductivity by utilizing natural segregation phenomena that occur during the growth process, to reveal the possibilities for this system to be used for TE applications. This was achieved in our previous work, and the thermal conductivity was reduced (above 66%) in the In−Ga−Sb system, successfullyby the change of phonon vibrations from out of phase optical mode to in phase acoustic modeby forming InxGa1−xSb ternary alloys between InSb and GaSb binaries.8 However, the highest ZT achieved in In0.8Ga0.2Sb (0.29) is lower than that in binary InSb (0.51) because the segregations affected the electron transport as well, which resulted in a reduced power factor of In−Ga−Sb. To overcome this issue in the In−Ga−Sb system, we studied and reported the effects of In/Ga doping with GaSb/InSb binaries. The segregations in the In−Ga−Sb system were avoided, and B

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry the ZT of Ga doped (1 × 1021) InSb (0.56) surpassed the ZT of binary InSb (0.51), for the first time.25 It was also revealed that the TE properties of the In−Ga−Sb system could further be enhanced by optimizing Ga content with a higher indium composition, to reduce the segregations for improving their power factor. With these understandings, this work explains the improvement in the thermoelectric properties of the In−Ga−Sb ternary system by optimizing point defects and compositional segregations through varying Ga content in indium-rich InGaSb. This work would be helpful to understand the defect engineering process, and it could be applicable to many other bulk-crystalline multicomponent systems, experimentally.

2. EXPERIMENT InGaSb ternary alloys with indium compositions of 0.85, 0.90, and 0.95 were grown by a melt solidification process using a radio frequency heating furnace (hereafter, the samples will be indicated as InxGa1−xSb, a common name that represents the three compositions (x = 0.85, 0.90, and 0.95) studied in this work). In, Ga, and Sb elements of 6N purity were loaded in a quartz crucible, and a temperature profile was applied for the growth of InxGa1−xSb under a hydrogen flowing atmosphere. The furnace was heated at a rate of 10 °C/min up to 650 °C and kept hold at this temperature for 2 h. After a holding process, a cooling rate of 10 °C/min was applied to grow the InxGa1−xSb crystals. The grown crystals were cut and polished for analyzing their properties. The X-ray diffraction (XRD) patterns of InxGa1−xSb crystals were recorded by a Rigaku RINT Ultima II X-ray diffractometer. The compositional distribution of InxGa1−xSb was analyzed by electron probe microanalysis (EPMA) using an electron probe microanalyzer JEOL-JXA 8530F. The composition was measured in-plane using the wafer cut across the crystal. As the growth of InxGa1−xSb is affected by segregation phenomena, the measurement was made at five random positions with a spot size of 10 μm, in a 1 cm2 area of each sample. The binding energies of the elements were measured by X-ray photoelectron spectroscopy (Shimadzu - ESCA 3400 electron spectrometer). The defects in the grown crystals were revealed by an optimized etching process using an etchant in a 1:3:1 ratio of HF/ KMnO4/CH3COOH. The compositional segregations and etch pits were observed, and their images were taken by a digital optical microscope. The phonon vibration modes in the grown crystals were analyzed by a laser Raman spectrometer (JASCO NRS-7100). The carrier concentration was measured at room temperature by a Hall effect measurement system (Accent HL 5500). Temperature (T) dependent electrical resistivity (ρ) and the Seebeck coefficient (S) were measured by an Ulvac Rico ZEM3 instrument. The thermoelectric (TE) power factor of the crystals was calculated from the measured values using the formula S2/ρ. The thermal diffusivity (α) and specific heat (Cp) were measured by the laser flash method using a NETZSCH-LFA 447 instrument. The thermal conductivity (κ) was calculated using the formula κ = αρCp, where ρ is the density of the samples. The crystals were cut along the growth direction, and both the Seebeck and thermal diffusivity measurements were performed in the same direction. In0.95Ga0.05Sb had a low melting point of 823 K among the analyzed samples. The InxGa1−xSb crystals were stable before and after the TE measurements because the studies were carried up to 573 K, well below (at least 250 K) their melting point.

Figure 2. XRD pattern of InxGa1−xSb crystals.

be 6.4529, 6.4635, and 6.4779 Å, respectively. Because the broad nature of the peaks was observed to be similar, and their lattice parameters had close values, the phase segregations were not differentiated in this study. 3.2. Compositional Analysis. The indium and In + Ga (cation) compositions are given in Table 1, and the distribution of cation composition at various places in the InxGa1−xSb crystals is shown in Figure 3. The indium composition was calculated from the atomic percentage with respect to cation composition. However, the cation composition was calculated with respect to both the cations (In + Ga) and anion (Sb). The average composition had some deviation from the expected value, and it was decreased with the increase of indium composition. It revealed that the compositions were not uniform in the grown crystals because of the segregation during the solidification process. The segregations were arising from the variations in liquidus and solidus temperatures of In−Ga−Sb solid solution. The degree of variation of composition in the grown crystals was revealed by calculating the standard deviation (SD) of compositions measured by EPMA. The SD of indium composition gradually decreased with increase in the source composition (from x = 0.85 to 0.95). However, the SD of the cation composition (In + Ga) was random, which revealed In and Ga elements were segregated in InxGa1−xSb as observed in our earlier experiment.8 It was inferred from Table 1 and Figure 3 that the SD of cation composition in In0.90Ga0.10Sb was very low, and In0.95Ga0.05Sb had a moderately high value among the three samples. The equilibrium segregation coefficients (k = Cs/Cl, where Cs and Cl are respective solidus and liquidus compositions of indium in the In−Ga−Sb melt) for InxGa1−xSb crystals (x = 0.85, 0.90, and 0.95) were obtained, from the phase diagram values, to be 0.86, 0.91, and 0.95, respectively. This suggests that In0.95Ga0.05Sb should have had the lowest segregation among the other crystals. However, the segregation effect (SD

3. RESULTS AND DISCUSSION 3.1. Structural Analysis. The XRD patterns of InxGa1−xSb crystals are shown in Figure 2. The peaks were broad in nature, which indicated a lattice strain from compositional segregations that was inconsistent with our earlier report.8 The crystals had a cubic zincblende structure, and the lattice parameters of In0.85Ga0.15Sb, In0.90Ga0.10Sb, and In0.95Ga0.05Sb were calculated, from the high intensity of the peak position, to C

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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Table 1. Indium and Cation Compositions, Standard Deviation, and Deviation from Expected Composition in InxGa1−xSb Crystals standard deviation (no unit) sample

position

In composition in InxGa1−xSb

cation (In + Ga) composition in InxGa1−xSb

In composition

cation composition

average In composition (deviation)

In0.85Ga0.15Sb

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.885 0.972 0.929 0.988 0.956 0.927 0.931 0.935 0.924 0.989 0.977 0.954 0.988 0.981 0.988

0.458 0.505 0.483 0.514 0.486 0.469 0.478 0.489 0.475 0.475 0.515 0.489 0.434 0.536 0.516

0.040

0.021

0.946 (0.096)

0.027

0.007

0.941 (0.041)

0.014

0.039

0.978 (0.028)

In0.90Ga0.10Sb

In0.95Ga0.05Sb

3.3. XPS Analysis. The binding energies of In 3d, Ga 2p, and Sb 3d energy levels of InxGa1−xSb are shown in Figure 4. The In 3d and Sb 3d levels were split into 3/2 and 5/2 energy levels because of their spin−orbital coupling. The intensity of the Ga 2p energy level peak is observed to be low because of its lower composition in InxGa1−xSb. The peak positions of all the energy levels were the same, and it indicated that the binding nature between the elements of InxGa1−xSb is similar for indium-rich compositions. Unlike doping of In/Ga with GaSb/InSb binaries, in which the binding energies of In 3d, Ga 2p, and Sb 3d levels were changed,25 the binding energy among the constituent elements did not change with the formation of In−Ga−Sb ternary alloy. The charge neutrality is disturbed when In/Ga was doped with GaSb/InSb because the ratio between the cations and the anion was changed. However, in In−Ga−Sb ternary alloys, the charge neutrality between the cations (In and Ga) and anion (Sb) was not changed irrespective of the segregations of In and Ga elements. Moreover, as both the In and Ga elements were tetrahedrally bonded with Sb, the valence states between the cations and anion were maintained constant when formed as a ternary alloy. 3.4. Raman Analysis. The Raman spectra of InxGa1−xSb are shown in Figure 5. Peaks corresponding to longitudinal and

Figure 3. Distribution of cation (In + Ga) composition at various places that represent segregations in InxGa1−xSb crystals.

of cation composition) was observed to be more in In0.95Ga0.05Sb than that of crystals with indium compositions 0.85 and 0.90. The variation among segregations could result from various factors including segregation coefficient, temperature, cooling rate, and chemical potential of each constituent.

Figure 4. Binding energies of In 3d, Ga 2p, and Sb 3d energy levels in InxGa1−xSb crystals. D

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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segregations in the grown crystals. Both the segregations and etch pit densities (EPD) were observed simultaneously using an optimized etching process for the first time. In addition to the point defects, other crystalline defects such as dislocations, grain boundaries, and stacking faults were possibly present in crystalline materials. Because of the complexity involved in scaling and analyzing those line and planar defects experimentally for a three-dimensional bulk crystal, their effect on the thermoelectric performance is unclear yet. However, this observation of EPD and compositional segregations by a simple etching process could be an efficient method to understand the functional properties of various material systems upon varying their molecular dynamics, experimentally. As the size and shapes of the segregated areas are random, they were not comparable. However, the cross sections of segregated areas were varying from a few micrometers to around 50 μm. The segregations were observed to be less in In0.90Ga0.10Sb than the other samples, and the result was inconsistent with the SD values of cation compositions (segregations) calculated from the EPMA data. The EPD or point defects were calculated to be 74, 51, and 50 × 106/cm2 for InxGa1−xSb with compositions of 0.85, 0.90, and 0.95, respectively. The EPD of In0.85Ga0.15Sb was higher than those of the other samples, and it was decreased with Ga composition. Our previous studies on pure and doped InSb and GaSb crystals revealed that the shape of etch pits in InSb was observed to be symmetric circular/triangle, and GaSb crystals had nonsymmetric oval/elongated-circular etch pits.8,25 In the present study, the shapes of etch pits were changing from elongatedcircular to a triangular shape upon a decrease in Ga content. It should be noted that, though In0.95Ga0.05Sb had more segregations than In0.90Ga0.10Sb samples, its EPD was low. Considering the segregations can increase the point defects and also the shape of the etch pits, it was observed that in indium-rich InxGa1−xSb, Ga content is a major factor that affects the point defects. 3.6. Thermoelectric Properties. 3.6.1. Charge Transport Properties. The carrier concentrations of InxGa1−xSb (x = 0.85, 0.90, and 0.95) crystals were measured to be 12.9, 6.74, and 5.30 (× 1017/cm3) at room temperature, respectively. The Hall effect measurement revealed that charge carriers had a high mobility of 5156, 5485, and 7506 cm2/(V s) at 300 K in InxGa1−xSb crystals. The mobility was increased with indium composition because of their decreased carrier concentration and point defects. The electrical resistivity, Seebeck coefficient, and power factor values of InxGa1−xSb with respect to temperature are given in Figure 7. The electrical resistivity was decreased with temperature, which is a typical tendency of undoped semiconductors (Figure 7a). Among the three samples, In0.85Ga0.15Sb had a higher electrical resistivity, and it was decreased with increased indium composition. The density of point defects (EPD) had a similar tendency with the electrical resistivity, i.e., decreased with increased indium composition. This indicates that the point defects affected the charge carrier transport through the crystal lattice, with a nonlinear relation. The point defects may either scatter or neutralize the charge carriers during their propagation, which depends on their nature and charge of the carriers (e− or h+). The Seebeck coefficient (Figure 7b) had negative values that indicate electrons are the majority charge carriers in the grown

Figure 5. Raman spectra of InxGa1−xSb crystals.

transverse optical phonon (LO + TO) vibration modes were observed in the grown crystals. The positions of LO + TO modes in In0.95Ga0.05Sb and In0.90Ga0.10Sb are around 180 cm−1, close to the bulk InSb, and they appeared around 220 cm−1 in In0.85Ga0.15Sb, similar to GaSb. In addition to the optical phonon modes, a broad peak with low intensity was present in In0.85Ga0.15Sb, and it was not observed in In0.90Ga0.10Sb and In0.95Ga0.05Sb crystals. Though broad peaks were observed around a similar position of Sb−Sb vibrational modes, as observed in InxGa1−xSb with the compositions x = 0.2 to 0.8,8 they were not dominant over optical phonons in In0.85Ga0.15Sb. Additionally the higher carrier concentration of In0.85Ga0.15Sb suggests that the broad peak was resulting from longitudinal optical phonon-plasmon coupled modes (LOPCMs) that could be observed in multicomponent III−V alloys.26,27 3.5. Etching Analysis. An etching study of a crystal is useful to remove a few atomic layers at the surface, and it could provide a direct observation of structural defects by variations in their etching rate. The etched surfaces of the InxGa1−xSb crystals are shown in Figure 6. It was clear that the etchant revealed not only the point defects but also the compositional

Figure 6. Digital microscopic images on the etched surfaces of InxGa1−xSb crystals, showing segregations and point defects. E

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 7. (a) Electrical resistivity, (b) Seebeck coefficient, and (c) power factor values of InxGa1−xSb with respect to temperature.

Figure 8. (a) Total thermal conductivity, (b) Lorentz number, (c) electron contribution (ke), and (d) phonon contribution (kl) to total thermal conductivity, in InxGa1−xSb crystals.

Seebeck coefficient with temperature cannot be predicted by these standard theories.28 In our present work, the Seebeck coefficient values are increasing with carrier concentration in InxGa1−xSb (x = 0.95 to 0.85) from 350 K. This tendency is opposite the general equation for the Seebeck coefficient because the bandgap of In0.85Ga0.15Sb (0.206 eV) is larger than that of In0.95Ga0.05Sb (0.181 eV) and the difference between the band edge and Fermi level becomes large. The bandgap values were calculated using the bowing parameter value of 0.415 eV for InxGa1−xSb ternary alloys.29 The Seebeck coefficients of InxGa1−xSb had a similar tendency with electrical resistivity (with increased indium composition), i.e., it decreases with decreased point defects.

crystals. Among the three samples, In0.90Ga0.10Sb had the highest value of a Seebeck coefficient, and it reached a maximum of 358 μV/K at 300 K. The general formula for the Seebeck coefficient S=

8π 2kb2T 2

3eh

iπ y m × jjj zzz k 3n {

2/3

was predicted for metals and degenerate semiconductors with a parabolic band approximation. Though this approximation can be successful in explaining the thermo power of many materials, it cannot explain the behaviors of intrinsic semiconductors and intermetallic materials. For example, the nonlinear temperature dependency and sign-reversal of the F

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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The value of ke could be estimated by the Wiedemann− Franz law, ke = LσT (where L is the Lorentz number, σ is the electrical conductivity, and T is the temperature). Here, L is considered as a proportionality constant (2.44 × 10−8 WΩ/K2) for metals considering that their charge carriers are free electrons. In most of the TE studies on semiconductor materials, the constant value of L is used to estimate ke by an assumption that they are degenerate in nature. However, the value of L is a variable depending on various factors for semiconductor materials, unlike metals. As this classical approach gives the maximum possible value of ke, the kl value is estimated to be minimum. Thus, the error associated with the estimation of kl is more, and it is necessary to make a correction for the L value. The Wiedemann−Franz law holds good for metals and can also be applicable to semiconductor materials with the correction for L, based on various linear response theories. However, many degenerate and nondegenerate semiconductor materials had deviations in the calculated L values. Takeuchi et al. mentioned in their report that most of the standard theories ignored the fine electronic structure near the chemical potential, which plays an essential role in explaining the thermoelectric behaviors of semiconductors. They employed electronic structure models with high resolution photoemission spectroscopy measurements and found that the effect of chemical potential on the thermoelectric power is low below 100 μV/K. When it exceeds around 200 μV/K, the chemical potential becomes a significant factor that affects the temperature dependent Seebeck coefficient (S) values.28 As the parameters L and S are functions of chemical potential in a single parabolic band model, it is possible to determine L from the S value. Kim et al. made an approximation for the estimation of L, using a single parabolic band model with an acoustic phonon scattering process, which is given by32 ÄÅ É Å |S| ÑÑÑ ÑÑ L = 1.5 + expÅÅÅÅ− ÅÇÅ 116 ÑÑÖÑ (2) −8 2 where L is in 10 WΩ/K and S in μV/K. Though this approximation is not so accurate for the determination of L, it gives a close accurate value within the error of 5% for materials with a dominant acoustic scattering process and less than 20% for complex, multicomponent alloys which possess various scattering mechanisms. This approximation was used to calculate the L values in the present study, because InxGa1−xSb is a multicomponent alloy semiconductor that has multibands33,34 and exhibits both the optical and acoustic phonon scattering processes.8 The L values (Figure 8b) were calculated for InxGa1−xSb using eq 2, and they were varied between 1.54 × 10−8 and 1.71 × 10−8 WΩ/K2. Those L values lied in between the degenerate (1.49 × 10−8 WΩ/K2) and nondegenerate (2.45 × 10−8 WΩ/ K2) limits of semiconductor materials.35 The lower L of InxGa1−xSb indicates that it could be a potential material for TE applications.36 The calculated L was used for the estimation of ke (Figure 8c), and it was observed that the ke of InxGa1−xSb was gradually increased with indium composition (from x = 0.85 to 0.95). The In0.85Ga0.15Sb crystal had the lowest ke even though it had a higher carrier concentration when compared with the other samples. It also should be noted that the EPD was more in In0.85Ga0.15Sb, which revealed that point defect scattering changes the momentum of the electron, thereby a decrease in kewas observed.

Considering the level of segregations was similar between In0.85Ga0.15Sb and In0.95Ga0.05Sb, the reduction in Seebeck coefficient (of In0.95Ga0.05Sb) with increased indium composition indicate that the change in temperature difference is getting more than the change in potential difference across the hot and cold junctions. If the point defects have had a similar effect to that of electrical resistivity, the Seebeck coefficient should have been increased in In0.95Ga0.05Sb through an increase in potential difference across its junctions. Though the point defects are less in In0.95Ga0.05Sb, the Seebeck coefficient was reduced because the number of charge carriers is less than that of In0.85Ga0.15Sb. Recently, Wang et al. made a first principle calculation based on a rigid band approximation for determination of the Seebeck coefficient from the electron density of states.30 It was considered that each point of a nonuniform system in space was a thermodynamic system in which the gradient in chemical potential of electrons is the thermodynamic driving force for establishing a potential difference upon inducing a temperature gradient. Thus, the density of electronic states was used to compute the change in chemical potential of electrons, by which it was established that the Seebeck coefficient is a thermodynamic quantity. On the basis of this approach, the Seebeck coefficient of n-PbTe was determined, and it was observed that the Seebeck coefficient was reduced with a decrease in carrier concentration. Though this phenomenon was not explained in that work, based on their approach it was clear that the electron density of states has a major influence on the Seebeck coefficient. As the electron density of states in an intrinsic semiconductor depends on the number of charge carriers, the reason for the reduction of the Seebeck coefficient with decreased carrier concentration might be because of the decreased density of states in InxGa1−xSb upon increasing the indium composition. This revealed that the carrier concentration had a major influence on the Seebeck coefficient compared to the density of point defects. The power factor was calculated from the measured electrical resistivity and Seebeck coefficient (Figure 7c). The maximum power factor recorded by In0.95Ga0.05Sb, 5.94 mW/ mK2 at 573 K, is similar to that of the InSb crystal heavily doped with Ga atoms.25 Though the Seebeck coefficient of In0.85Ga0.15Sb was high, it recorded a lower power factor because of its higher resistivity. This revealed that the point defects affected electrical resistivity and the Seebeck coefficient was influenced mainly by carrier concentration. Thus, reducing point defects and increasing carrier concentration would be an efficient way to enhance the TE power factor of crystalline materials. 3.6.2. Thermal Transport Properties. The thermal conductivity of InxGa1−xSb is shown in Figure 8a. In0.90Ga0.10Sb had higher thermal conductivity than In0.85Ga0.15Sb and In0.95Ga0.05Sb crystals. The total thermal conductivity (k) of a semiconductor crystalline material is given by k = kl + ke + k r

(1)

where kl is the lattice thermal conductivity by phonon propagation, ke is the electronic thermal conductivity, and kr is the thermal conductivity due to phonon radiation at high temperatures. Among these factors, the kr could be negligible because it is contribution to k is much lower when compared to kl and ke.31 G

DOI: 10.1021/acs.inorgchem.9b01430 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry The contribution of kl to k was calculated from ke and is shown in Figure 8d. Unlike ke, which was gradually increased with indium composition, the kl was not gradual, and some random variations were observed. However, the kl of all the samples was decreased with temperature, like other semiconductors, because of enhanced phonon scattering processes at high temperature.37,38 The kl was higher for In0.90Ga0.10Sb, which had less segregation of its elements, than for the other samples. Though the point defects in In0.85Ga0.15Sb were higher than in In0.95Ga0.05Sb (about 32%), the lattice thermal conductivities of In0.85Ga0.15Sb and In0.95Ga0.05Sb were nearly the same, and it should be noted that they had a similar level of compositional segregation. It revealed that the ionized point defects did not have a major influence on the phonon transport process, though they influenced electron transport. The compositional segregation on the microscale is a major reason to reduce the lattice contribution to thermal conductivity through the random distribution of cations for reducing phonon propagation through a crystal lattice. Thus, it is possible to control the electron and phonon transport properties by controlling segregations and point defects in a bulk crystalline material, to enhance the TE properties of multicomponent alloy semiconductors. The ZT of InxGa1−xSb was calculated and shown in Figure 9. Among the samples, In0.95Ga0.05Sb recorded a higher ZT of

Table 2. ZTs of Various III−V Materials temperature (k)

power factor (mW/ mK2)

thermal conductivity (W/mK)

ZT

ref

In0.95Ga0.05Sb

573

5.94

5.49

0.62

InSb Ga doped (1 × 1021) InSb In0.8Ga0.2Sb In0.9Ga0.1Sb InGaN(thin film) In0.86Ga0.2Sb Al0.83In0.17N (thin film) In0.36Ga0.64Sb In0.98Ga0.02Sb

550 573

7.56 5.95

8.1 6.33

0.51 0.56

this work 8 25

770 600 873

2.5 ∼4.5 ∼0.6

4 4 ∼1.8

0.52 0.54 0.34

39 40 41

600 300

∼4.5 8.6

∼4.5 4.87

0.59 0.53

42 43

450 600

0.15

3.9

0.23 0.17

44 45

material

It is expected that the ZT of In0.95Ga0.05Sb could further be enhanced by reducing point defects, increasing carrier concentration, and optimizing compositional segregations so that enhancement in electrical conductivity, power factor, and reduction of thermal conductivity could be achieved, respectively. We are in progress to understand the crystal growth conditions and kinetics for the formation of point defects and compositional segregations in InxGa1−xSb, to further enhance its TE properties for future power generation applications.

4. CONCLUSION InxGa1−xSb (x = 0.85, 0.90, and 0.95) crystals were grown by melt solidification processes, and their TE properties were studied to understand the effects of point defects and microscale compositional segregations in multicomponent semiconductor alloys. The segregations were random, and they were scaled by standard deviation of measured compositions in the grown crystals. The point defects and compositional segregations were observed simultaneously, using an optimized etching process. The Seebeck coefficient was affected mainly by carrier concentration rather than point defects, even though the point defects affected their electrical resistivity. Thus, (i) reducing point defects and (ii) increasing carrier concentration are efficient ways to enhance the TE power factor of crystalline materials. Though the electron contribution to the thermal conductivity was affected, the lattice contributions were not affected much by the presence of point defects. The compositional segregations on the microscale are a major reason to reduce the lattice contribution to thermal conductivity by altering the lattice dynamics through random distribution of cations. The highest ZT of 0.62 at 573 K was recorded by In0.95Ga0.05Sb for the first time among any other III−V semiconductors, through improved power factor and reduced thermal conductivity. This study revealed that the interrelated electron and phonon transport properties in crystalline materials could be enhancedwithout much affecting the electron transport propertiesby defect engineering via point defects and compositional segregations. Thus, changing the molecular dynamics through point defects and microscale compositional segregations is an efficient way to alter the lattice dynamics for enhancing the TE properties of bulk crystalline multicomponent alloys.

Figure 9. ZT (300−573 K) of InxGa1−xSb crystals.

0.62, which is thus far the highest at 573 K of any reported values of III−V binary or ternary semiconductors (Table 2). In the present study, the TE performance was measured up to 573 K because of the limitation in the operating temperature of the instrument. The literature data were collected for various temperatures ranging from 300 to 770 K, based on availability. The data were compared at around 573 K and above for most of the materials, and the temperature, at which the ZT is compared, is given in Table 2. The ZT of In0.80Ga0.20Sb was achieved to be 0.29 at 600 K, in our previous study.8 In this study, the ZT of InxGa1−xSb not only surpasses the binary InSb, but also it was enhanced from 0.29 to 0.62 by improved power factor and reduced lattice thermal conductivity. Considering the tendency of electron and phonon transport as explained above, the higher ZT is achieved because of the compositional segregations on the microscale and moderately lower point defects. H

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected], [email protected]. *E-mail: [email protected]. Address: Department of Interdisciplinary Space Science, Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan. ORCID

Velu Nirmal Kumar: 0000-0002-2179-7608 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grant Number JP16K14238. The authors thank Mr. Dai Kaneda, Ibaraki University, Hitachi, for his help in thermoelectric measurements. We also thank Mr. Tadanobu Koyama and Dr. S. Harish for their assistance in measurements and Centre for Instrumental Analysis, Shizuoka University, Hamamatsu, Japan, for extending the characterization facilities.

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