Thermoelectric (TE) materials and devices have demonstrated

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1 pubs.acs.org/nanolett Effect of Silicon and Sodium on Thermoelectric Properties of Thallium-Doped Lead Telluride-Based Materials Qinyong Zhang,, Hengzhi Wang, Qian Zhang, Weishu Liu, Bo Yu, Hui Wang, Dezhi Wang, George Ni, Gang Chen, and Zhifeng Ren*, School of Material Science and Engineering, Xihua University, Chengdu, Sichuan , P. R. China Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, United States Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ABSTRACT: Thallium (Tl)-doped lead telluride (Tl 0.02 Pb 0.98 Te) thermoelectric materials fabricated by ball milling and hot pressing have decent thermoelectric properties but weak mechanical strength. Addition of silicon (Si) nanoparticles strengthened the mechanical property by reducing the grain size and defect density but resulted in low electrical conductivity that was not desired for any thermoelectric materials. Fortunately, doping of sodium (Na) into the Si added Tl 0.02 Pb 0.98 Te brings back the high electrical conductivity and yields higher figure-of-merit ZT values of 1.7 at 770 K. The ZT improvement by Si addition and Na doping in Tl 0.02 Pb 0.98 Te sample is the direct result of concurrent electron and phonon engineering by improving the power factor and lowering the thermal conductivity, respectively. KEYWORDS: Thermoelectric materials, lead telluride, mechanical strength, silicon, sodium Thermoelectric (TE) materials and devices have demonstrated great potentials in solid state cooling and conversion of heat to electricity. 1,2 For TE device, higher efficiency comes from TE materials higher dimensionless figure-of-merit (ZT), ZT = (S 2 σ/κ)t, where S and σ are Seebeck coefficient and electrical conductivity, respectively, κ is the thermal conductivity (κ = κ L + κ e ), the sum of electron thermal conductivity κ e and lattice thermal conductivity κ L, and T is the absolute temperature. In the past a few years, most progress has been made on enhancing ZT to above 1 through decreasing κ L via phonon scattering by nanostructures, 3 5 while some advance also been achieved through power factor (S 2 σ) improvement. 6 9 Our previous work showed that ball milling plus hot pressing is a simple and scalable method to fabricate nanostructures with high performance bulk TE materials. 10,11 As one of the most studied intermediate temperature TE materials system, lead telluride (PbTe)-based materials retain the highest ZT that has ever been obtained in bulk TE materials. For example, by band engineering, 12 resonant states doping, 13 nanostructuring, 14 endotaxial precipitating, 15 and quantum nanodots, 16 peak ZTs of have been reached in p- and n-type, which shows good potentials in moderate temperature applications and attract much attention. Most recently, through combining the effects of resonant doping by Tl and alloy scattering by S partial substitution of Te, peak ZT of 1.6 at 700 K was achieved in the Na 0.01 Tl 0.02 Pb 0.97 Te 0.92 S 0.08 sample with higher average ZT. 17 However, materials based on PbTe suffer from weak mechanical strength. With an 8 at. % Si addition in PbTe, the sample was significantly strengthened, but the ZT was also degraded significantly to 0.9 at 660 K by PbI 2 doping. 18 In our previous work on Tl 0.02 Pb 0.98 Te by ball milling plus hot pressing, 11 the sample softens above 673 K as well. We report here, by addition of a smaller amount of Si and doping of Na, very strong samples of p-type Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 can be obtained through ball milling plus hot pressing, with peak ZT of 1.7 at 770 K. Si (99.99%, Alfa Aesar) chunk was first loaded into a ball mill jar with stainless steel balls and ball milled in a high energy ball mill SPEX 8000D (SPEX SamplePrep) for 30 h into Si nanopowder. Then, the obtained Si nanopowder, element Tl (granules, %, Alfa Aesar), Pb (granules, 99.99%, Alfa Aesar), Te (chunks, %, EZMetals Corp.), and Na 2 Te (powder, 99.99%, CERAC Inc.) were weighed according to the stiochiometry of Tl 0.02 Pb 0.98 TeSi x Na y (x = 0 or 0.02, while y = 0, 0.015, 0.02, and 0.025) and loaded into ball mill jar with balls for mechanical alloying by SPEX 8000D. The alloyed nanopowders were then compacted into dense bulk disks of 12.7 mm in diameter in a graphite die through direct current (dc)-induced hot pressing. An argon gas-filled glovebox was used in materials handling process to minimize contaminations. A laser flash system (NETZSCH LFA-457) and a DSC system (NETZSCH DSC 200-F3) were used to measure the thermal diffusivity and the specific heat of the disk samples, respectively. Thermal conductivity was then calculated as the Received: January 18, 2012 Revised: March 17, 2012 Published: April 11, American Chemical Society 2324

2 Nano s product of the thermal diffusivity, specific heat, and volumetric density that was determined by the Archimedes method. A four-point probe system (ULVAC ZEM-3) was used to measure the Seebeck coefficient and electrical conductivity of the bar samples with dimensions of about mm 3. Hall measurements were carried out on a Lakeshore system (Hall Effect System7712A) for thin disk samples of around 0.5 mm in thickness. The structures of the as-pressed samples were characterized by X-ray diffraction (XRD Bruker-AXS, G8 GAADS) using Cu radiation (Kα: 1.54 Å), field emission scanning electron microscopy (SEM, JEOL-6340F), and transmission electron microscopy (TEM, JEOL-2010F). Through ball milling and hot pressing, dense Tl 0.02 Pb 0.98 TeSi x Na y samples ( 97% relative to theoretical density) with different values of x and y were prepared, and all were crystallized in rock salt structure evidenced by X-ray diffraction patterns, shown in Figure 1a. Within the detection limit of XRD, there is no impurity found. One interesting phenomena is that after 770 K measurements of Seebeck coefficient and resistivity in ZEM-3 the bar samples without Si bend like a bow, shown in Figure 1b, which clearly shows the weak mechanical strength at that temperature. In our previous TEM work on PbTe-based materials, we found high density of defects, such as Pb-depleted disks, 19 after high energy ball milling and hot pressing. The bending of the sample without Si may be due to the high residual stress and strain in the sample made by high energy ball milling process, which will be detailed later. For mechanical strengthening, Si was added in the materials, inspired by its effects in the PbTe:I material to overcome brittleness. 18 With sufficient Si addition, the sample is strong enough to experience high temperature measuring, as shown in the photograph of Figure 1c. However, the electrical conductivity was degraded significantly. To bring back the electrical conductivity, we added Na to further dope the Si added Tl 0.02 Pb 0.98 Te samples, as suggested by Singh s calculation 20 and evidenced by Pei s experimental results 21 that heavy doping would help to improve thermoelectric properties of PbTe. Recent work by Wang et al. on reducing the thermal conductivity using TlSbTe 2 addition in Tl 0.02 Pb 0.98 Te also found the decrease of electrical conductivity, resulting in a lower ZT than the pure Tl 0.02 Pb 0.98 Te sample. 22 To understand the effects of the addition of Si and doping of Na in Tl 0.02 Pb 0.98 Te samples, extensive microscopy study was conducted by SEM, TEM, and HRTEM. The main results are shown in Figure 2. Analyzed by the linear intercept particle method 23 from the SEM image of Tl 0.02 Pb 0.98 Te sample (without Si and Na) shown in Figure 2a, the average grain size of this sample is 7 μm, much bigger than the ball milled starting nanopowder with particle size less than 50 nm, clearly indicating significant grain growth happened during hot pressing as shown in our previous work. 11 It is interesting to note that after a 2 at. % Si addition the grain size dramatically decreased to 200 nm, shown in Figure 2b. Although the mechanism of refinement by Si addition is not clear now, this dramatic decrease in grain size, certainly causes much stronger phonon scattering than that without Si addition, and leads to the reduction of lattice thermal conductivity. Like our previous results on PbTe, 19 there are Pb-depleted disks, and the strain caused by it, shown in Figure 2d,f. These features with dimensions of a few nanometers will also contribute to the lattice thermal conductivity reduction. By doping Na, the grains grow to an average of 500 nm, shown in Figure 2c. Figure 1. (a) XRD spectra of various samples: (1) Tl 0.02 Pb 0.98 Te, (2) Tl 0.02 Pb 0.98 TeSi 0.02, (3) Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.015, (4) Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02, and (5) Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.025, (b) Photograph of the softened sample Tl 0.02 Pb 0.98 Te after measurement up to 673 K. (c) Photograph of the strong sample Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 up to 770 K. Another interesting structure character discovered by TEM studies is that the defect density is significantly decreased by addition of Si. Our previous report on PbTe 19 showed that the sample without Si have many Pb-depleted disks lying in the 001 planes (the inset of Figure 2d shows the plane 2325

3 Nano s Figure 2. (a) SEM image of sample Tl 0.02 Pb 0.98 Te, (b) SEM image of sample Tl 0.02 Pb 0.98 TeSi 0.02, (c) SEM image of sample Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02, (d) TEM image of sample Tl 0.02 Pb 0.98 Te showing the very high density of Pb-depleted disks (the inset is the FFT of this image), (e) TEM image of sample Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 with low density of Pb-depleted disk, with the inset of FFT of this image, and (f) HRTEM of sample Tl 0.02 Pb 0.98 TeSi 0.02 Na orientation) with a volume density of cm 3, diameter of 2 5 nm, and thickness less than 0.5 nm. It is believed that these defects cause strain and stress near the disks leading to the sample bending at temperature higher than 673 K. It is surprising that with Si addition and Na doping the volume density of the Pb-depleted disks is greatly decreased, as shown in Figure 2e,f, which is believed to be one of the main reasons of the much higher mechanical strength in the sample with Si addition and leads the samples to endure temperature up to 770 K without bending. The Hall effect measurements show that the carrier concentration and mobility of Tl 0.02 Pb 0.98 Te samples prepared by ball milling and hot pressing are cm 3 and 72.7 cm 2 V 1 s 1, respectively, which are different from cm 3 and 50 cm 2 V 1 s 1 in the samples prepared by melting method reported by Heremans, 13 primarily due to the different fabricating processes. After a 2 at. % Si addition, these values turn into cm 3 and 44.4 cm 2 V 1 s 1, resulting in a much lower electrical conductivity (further discussed later). The decreasing of carrier concentration and mobility from Si addition is consistent with the results reported by Nemov. 24 By doping of 1.5, 2, and 2.5 at. % Na, the carrier concentration increased to 5.7, 8.9, and cm 3, respectively, while the mobility stayed as 42, 46, and 45.7 cm 2 V 1 s 1, respectively. The room temperature (RT) Seebeck coefficient dependence on carrier concentration (Pisarenko plot 25 ) of the samples is illustrated in Figure 3a, compared with the reported Tl 13 and Na 21,26 29 doped PbTe samples, as well as the recently reported PbTeS:Tl and PbTeSe:Tl data. 8 When the carrier concentration is higher than cm 3, the deviation of the reported Na-doped samples from the single parabolic band (SPB) model 30 (solid line in Figure 3a) clearly shows the 2326

4 Nano s Figure 3. (a) RT Seebeck coefficient dependence of carrier concentration (Pisarenko plot). The references are Jaworski, 8 Heremans, 13 Airapetyant, 26 Pei, 21 Crocker, 27 Alekseeva, 28 and Androulakis. 29 The solid line is calculated from single parabolic band model (SPB) 30 where acoustic scattering is assumed predominant and m* = 0.36m 0 as that adopted by Airapetyant. 26 (b) Seebeck coefficient dependence of temperature of the studied samples; the dashed line is reference data from Heremans. 13 failure of SPB model in PbTe, where there are actually two nonparabolic valence bands: a light one whose band edge lies at 0.3 ev under the bottom of conduction band and another heavy one whose band edge lies at 0.2 ev under the light one, as discussed in the reported theory 20,31 33 and experimental work. 26,34 39 When the carrier concentration is higher than cm 3, the Fermi level enters in the second band, and the heavy carrier contributes to higher thermopower, which leads to the deviation from the SPB model. 21,26 29 The Tl-doped PbTe samples, with the help of distortion of density of states (DOS) caused by resonant states from Tl, have much higher Seebeck coefficient than that without resonance enhancement 13 at the same carrier concentration. The research on the Tl effects was extended to PbTe x S 1 x and PbTe y Se 1 y in recent report, 8 which yielded a peak ZT 1.6 at 700 K, due to the Seebeck enhancement of resonant states created by Tl, illustrated also in Figure 3a. The RT Seebeck coefficient of our Tl 0.02 Pb 0.98 TeSi 0.02 Na x (x =0, 0.015, 0.02, 0.025) samples, shown in Figure 3a, confirms the resonant states created by Tl at even higher carrier concentration than that reported by Heremans. 13 One more interesting thing can be observed in Figure 3a is that in the Tldoped samples where resonant states exist in our study and other reports, 8,13 the Seebeck coefficients at RT decreased from 180 to 150 μv K 1 (about a 20%) when carrier concentration increased from cm 3 to cm 3, wherease the decrease is about 50% for the samples without resonant states, which agrees well with the recent theory prediction included resonant states effects. 17 The temperature dependence of Seebeck coefficient shown in Figure 3b clearly demonstrate that the sample of the lowest carrier concentration, Tl 0.02 Pb 0.98 TeSi 0.02, has the highest Seebeck coefficient, which may be possibly due to the carrier scattering from grain boundary and Si impurity. From Figure 2 and the discussions above, the Tl 0.02 Pb 0.98 TeSi 0.02 sample has the smallest grain size in the studied samples that would cause strongest carrier scattering by grain boundaries, resulting in higher Seebeck coefficient. This also can explain higher Seebeck coefficient than Tl-doped PbTe/Se/S samples 8 and theoretical prediction 17 in the same carrier concentration. In the range of K, the Seebeck coefficient of this sample shows independent relationship with temperature and begins to decrease with temperature at above 670 K, due to the presence of thermally excited minor carriers. In the three samples with Na doping, the sample of moderate Na doping and carrier concentration, 2 at. % and cm 3, respectively, has the highest Seebeck coefficient in the measured temperature, which may originate from the good alignment of Fermi level with the energy of the Tl impurity created resonant states, that would lead to higher Seebeck coefficient enhancement. 40,41 At temperature higher than 570 K, Seebeck coefficient stays almost the same for samples with 1.5 and 2 at. % Na doping primarily due to the bipolar effect, leading to lower Seebeck coefficient than the reference data. The electrical conductivity and power factor are demonstrated in Figures 4a and 4b, respectively, compared with reference data (dashed line) from Heremans. 13 The 2 at. % Si added Tl 0.02 Pb 0.98 Te sample has electrical conductivity of S m 1 at 300 K and 9000 S m 1 at 767 K, respectively, about half of the reference data, which is due to the low carrier concentration and high grain boundary scattering of carriers Figure 4. Electrical conductivities (a) and power factor (b) of the studied samples. The reference data (dashed line) is from Heremans

5 Nano s Figure 5. Thermal diffusivity (a), C p (b), thermal conductivity (c), and lattice thermal conductivity (d) of the studied samples, with the reference samples of Tl 0.02 Pb 0.98 Te from Heremans, 13 PbTe:Na from Pei, 21 and PbTe:Si from Sootsman. 18 caused by Si nanoparticles. To make up the loss of electrical conductivity by Si, Na as an effective p-type dopant in PbX (X = Te, Se, and S) 12,15,21,42,43 was doped into Tl 0.02 Pb 0.98 TeSi 0.02 samples. The results indicate that, first, the electrical conductivity is greatly improved and is even higher than the reference data when enough Na is used. Second, higher concentration of Na leads to higher electrical conductivity. The 2 at. % Na-doped Tl 0.02 Pb 0.98 TeSi 0.02 sample has electrical conductivity of S m 1 at 770 K, a little bit higher than that of reference data. This improvement of electrical conductivity is due to the increased carrier concentration by Na doping. The power factors of the measured samples, calculated from S 2 σ, are shown in Figure 4b. It can be seen that the Tl 0.02 Pb 0.98 TeSi 0.02 sample has the lowest power factor due to the lowest electrical conductivity, but Na doping increased the power factors significantly. The power factors are even higher than the reference data at temperatures lower than 525 K though lower than the reference data at temperatures higher than 525 K. The highest power factor at 770 K, 16.3 μw cm 1 K 2,ofTl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 sample is about 13% lower than that of the reference sample. 13 The total thermal conductivity was calculated using κ = ρdc p, where ρ is the volumetric density, D the diffusivity (Figure 5a), and C p the specific heat (Figure 5b). In calculating κ, the C p values of 2 at. % Na-doped sample were used for all Na-doped samples in a conservative way. The total (Figure 5c) and lattice thermal conductivity (Figure 5d) of our studied samples are plotted together with the Si added PbTe samples, 18 the only data we can find in the literature of Si added PbTe, as reference as well as that of samples PbTe:Na 21 and PbTe:Tl. 13 The lattice thermal conductivity is calculated by subtracting the electronic contribution from the total thermal conductivity (κ L = κ κ e = κ LσT, where L is the Lorenz number). Because the difficulty of accurate determination of Lorenz number due to the complex band structure and nonparabolicity of the light hole band, especially when presented with Tl created resonant states which has strong impact on the carrier transport, an assumption of one parabolic band, predominant acoustic scattering of phonons, and elastic mechanism of carriers scattering was used to estimate L, 44 where the reduced Fermi energy were deduced from the Seebeck coefficient in SPB model. 30 Despite the roughness in the estimation, the result of L V 2 K 2 at 770 K is consistent with the rigorous calculation based on multiband model having considered the nonparabolicity of the band, 44 quite lower than the widely used metal values of V 2 K 2. Also, the RT Lorenz number V 2 K 2 is about 11% off the results of Kaidanov, 45 who ascribed the reducing factor of 1.65 from full degenerate value to the resonant scattering by Tl in PbTe. This method of estimation was used to recalculate the Lorenz number of the PbTe:Si sample. 18 From Figure 5d, the lattice thermal conductivity of the studied samples is well below the reference data. The κ L of Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 sample at 770 K, 0.54 W m 1 K 1,is about 27% lower than that of PbTe:Tl sample, 13 and 45% lower than that of PbTe:Na sample, 21 which shows big increase of phonon scattering by the grain boundary and the point defects, directly from the fine Si particles. The sample without Na doping, having smallest grain size in this study (shown in Figure 2b), demonstrates the lowest κ L, confirming the size effects on lattice thermal conductivity reduction. It is interesting that the κ L of our 2 at. % Si added samples from RT to 580 K is about 40% 22% lower than the PbTeSi 0.08 sample fabricated by melting and quenching method, 18 which again suggests an effective way of κ L reduction by ball milling and hot pressing method. Because of the quite low lattice thermal conductivity by greatly increased grain boundary scattering of phonons, the Si added Na doped samples have much lower total thermal conductivity, shown in Figure 5c, leading to ZTs higher than the reference data shown in Figure 6. We achieved peak ZT value 1.7 at 770 K in samples Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02, close to the most recently reported 1.8 in samples PbSeTe:Na 12 and PbTe:Sr,Na. 15 In summary, Si was found to have dramatically increased the mechanical strength of samples Tl 0.02 Pb 0.98 TeSi 0.02 made by ball milling and hot pressing due to probably the dramatically decreased defect density of Pb-depleted disks and much smaller grains of 200 nm, but also much lower electrical conductivity 2328

6 Nano s Figure 6. Dimensionless figure-of-merit (ZT) dependence of temperature of the studied samples. for lower ZTs. However, a small amount of Na doping for samples Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 brings back the high electrical conductivity while keeping the enhanced Seebeck coefficient by Tl created resonant states and also produces low thermal conductivity, with the lowest lattice thermal conductivity of 0.54 W m 1 K 1 at 770 K. The highest ZT value reaches 1.7 at 770 K in mechanically strong samples Tl 0.02 Pb 0.98 TeSi 0.02 Na 0.02 involving resonant doping, nanograins, and high carrier concentration. AUTHOR INFORMATION Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work is funded by the Solid State Solar-Thermal Energy Conversion Center (S 3 TEC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Science, under Award DE- SC /DE-FG02-09ER46577 (G.C. and Z.F.R.). REFERENCES (1) Tritt, T. M. Annu. Rev. Mater. Res. 2011, 41, (2) Bell, L. E. Science 2008, 321, (3) Vineis, C. J.; Shakouri, A.; Majumdar, A.; Kanatzidis, M. G. Adv. Mater. 2010, 22, (4) Liu, W. S.; Yan, X.; Chen, G.; Ren, Z. F. Nano Energy 2012, 1, (5) Dresselhaus, M. S.; Chen, G.; Ren, Z. F.; Fleurial, J. P.; Gogna, P.; Tang, M. Y.; Vashaee, D.; Lee, H.; Wang, X. W.; Joshi, G.; Zhu, G. H.; Wang, D. Z.; Blair, R.; Bux, S.; Kaner, R. Thermoelectr. Power Gener. 2008, 1044, (6) Zebarjadi, M.; Joshi, G.; Zhu, G. H.; Yu, B.; Minnich, A.; Lan, Y. C.; Wang, X. W.; Dresselhaus, M.; Ren, Z. F.; Chen, G. Nano Lett. 2011, 11, (7) Heremans, J. P.; Thrush, C. M.; Morelli, D. T. Phys. Rev. B 2004, 70, (8) Jaworski, C. M.; Wiendlocha, B.; Jovovic, V.; Heremans, J. P. Energy Environ. Sci. 2011, 4, (9) Zhang, Q. Y.; Wang, H.; Liu, W. S.; Wang, H. Z.; Yu, B.; Zhang, Q.; Tian, Z.; Ni, G.; Lee, S.; Esfarjani, K.; Chen, G.; Ren, Z. F. Energy Environ. Sci. 2012, 5, (10) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y. C.; Minnich, A.; Yu, B.; Yan, X. A.; Wang, D. Z.; Muto, A.; Vashaee, D.; Chen, X. Y.; Liu, J. M.; Dresselhaus, M. S.; Chen, G.; Ren, Z. F. Science 2008, 320, (11) Yu, B.; Zhang, Q. Y.; Wang, H.; Wang, X. W.; Wang, H. Z.; Wang, D. Z.; Wang, H.; Snyder, G. J.; Chen, G.; Ren, Z. F. J. Appl. Phys. 2010, 108, (12) Pei, Y. Z.; Shi, X. Y.; LaLonde, A.; Wang, H.; Chen, L. D.; Snyder, G. J. Nature 2011, 473, (13) Heremans, J. P.; Jovovic, V.; Toberer, E. S.; Saramat, A.; Kurosaki, K.; Charoenphakdee, A.; Yamanaka, S.; Snyder, G. J. Science 2008, 321, (14) Poudeu, P. F. R.; D Angelo, J.; Downey, A. D.; Short, J. L.; Hogan, T. P.; Kanatzidis, M. G. Angew. Chem., Int. Ed. 2006, 45, (15) Biswas, K.; He, J. Q.; Zhang, Q. C.; Wang, G. Y.; Uher, C.; Dravid, V. P.; Kanatzidis, M. G. Nat. Chem. 2011, 3, (16) Hsu, K. F.; Loo, S.; Guo, F.; Chen, W.; Dyck, J. S.; Uher, C.; Hogan, T.; Polychroniadis, E. K.; Kanatzidis, M. G. Science 2004, 303, (17) Heremans, J. P.; Wiendlocha, B.; Chamoire, A. M. Energy Environ. Sci. 2012, 5, (18) Sootsman, J. R.; He, J. Q.; Dravid, V. P.; Ballikaya, S.; Vermeulen, D.; Uher, C.; Kanatzidis, M. G. Chem. Mater. 2010, 22, (19) Wang, H. Z.; Zhang, Q. Y.; Yu, B.; Wang, H.; Liu, W. S.; Chen, G.; Ren, Z. F. J. Mater. Res. 2011, 26, (20) Singh, D. J. Phys. Rev. B 2010, 81, (21) Pei, Y. Z.; LaLonde, A.; Iwanaga, S.; Snyder, G. J. Energy Environ. Sci. 2011, 4, (22) Wang, H.; Charoenphakdee, A.; Kurosaki, K.; Yamanaka, S.; Snyder, G. J. Phys. Rev. B 2011, 83, (23) Brieseck, M.; Lengauer, W.; Gneiss, B.; Wagner, K.; Wagner, S. Microchim. Acta 2010, 168, (24) Nemov, S. A.; Zhitinskaya, M. K.; Proshin, V. I. Sov. Phys. Semicond., USSR 1991, 25, (25) Ioffe, A. F. Semiconductor Thermoelements and Thermoelectric Cooling; Infosearch Ltd.: London, (26) Airapetyants, S. V.; Vinograd, M. N.; Dubrovsk, I. N.; Kolomoet, N. V.; Rudnik, I. M. Sov. Phys. Solid State,USSR 1966, 8, (27) Crocker, A. J.; Rogers, L. M. Br. J. Appl. Phys. 1967, 18, (28) Alekseeva, G. T.; Zemskov, B. G.; Konstantinov, P. P.; Prokofeva, L. V.; Urazbaeva, K. T. Sov. Phys. Semicond., USSR 1992, 26, (29) Androulakis, J.; Todorov, I.; Chung, D.-Y.; Ballikaya, S.; Wang, G.; Uher, C.; Kanatzidis, M. Phys. Rev. B 2010, 82, (30) May, A. F.; Toberer, E. S.; Saramat, A.; Snyder, G. J. Phys. Rev. B 2009, 80, (31) Hoang, K.; Mahanti, S. D.; Kanatzidis, M. G. Phys. Rev. B 2010, 81, (32) Bilc, D.; Mahanti, S. D.; Quarez, E.; Hsu, K. F.; Pcionek, R.; Kanatzidis, M. G. Phys. Rev. Lett. 2004, 93, (33) Wei, S. H.; Zunger, A. Phys. Rev. B 1997, 55, (34) Chernik, I. A.; Kaidanov, V. I.; Vinogradova, M. I.; Kolomoets, N. V. Sov. Phys. Semicond., USSR 1968, 2, (35) Vinogradova, M. N.; Kolomoets, N. V.; Smirnov, I. A.; Sysoeva, L. M. Sov. Phys. Semicond., USSR 1968, 9, (36) Allgaier, R. S.; Houston, B. B. J. Appl. Phys. 1966, 37, (37) Andreev, A. A.; Radionov, V. N. Sov. Phys. Semicond., USSR 1967, 1, (38) Sysoeva, L. M.; Vinograd, Mn.; Kolomoet, Nv.; Ravich, Y. I. Sov. Phys. Semicond., USSR 1970, 3, (39) Gruzinov, B. F.; Drabkin, I. A.; Ravich, Y. I. Sov. Phys. Semicond., USSR 1979, 13, (40) Kaidanov, V. I.; Ravich, Y. I. Sov. Phys. - Usp. 1985, 28, (41) Kaidanov, V. I.; Nemov, S. A.; Ravich, Y. I. Sov. Phys. Semicond., USSR 1992, 26, (42) Wang, H.; Pei, Y. Z.; LaLonde, A. D.; Snyder, G. J. Adv. Mater. 2011, 23, (43) Girard, S. N.; He, J. Q.; Zhou, X. Y.; Shoemaker, D.; Jaworski, C. M.; Uher, C.; Dravid, V. P.; Heremans, J. P.; Kanatzidis, M. G. J. Am. Chem. Soc. 2011, 133, (44) Smirnov, I. A.; Vinograd, Mn; Kolomoet, Nv; Sysoeva, L. M. Sov. Phys. Solid State, USSR 1968, 9,

7 Nano s (45) Kaidanov, V. I.; Nemov, S. A.; Ravich, Y. I.; Zaitsev, A. M. Sov. Phys. Semicond., USSR 1983, 17,