Power Factor Enhancement by Modulation Doping in Bulk

May 10, 2011 - Only a few strategies have been proposed to enhance the power factor, ..... for the Si100B5 single-phase sample with a measured ZT of a...
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LETTER pubs.acs.org/NanoLett

Power Factor Enhancement by Modulation Doping in Bulk Nanocomposites Mona Zebarjadi,†,|| Giri Joshi,‡,|| Gaohua Zhu,‡ Bo Yu,‡ Austin Minnich,† Yucheng Lan,‡ Xiaowei Wang,‡ Mildred Dresselhaus,§ Zhifeng Ren,*,‡ and Gang Chen*,† †

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, United States § Department of Physics and Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States ‡

bS Supporting Information ABSTRACT: We introduce the concept of modulation doping in three-dimensional nanostructured bulk materials to increase the thermoelectric figure of merit. Modulationdoped samples are made of two types of nanograins (a two-phase composite), where dopants are incorporated only into one type. By band engineering, charge carriers could be separated from their parent grains and moved into undoped grains, which would result in enhanced mobility of the carriers in comparison to uniform doping due to a reduction of ionized impurity scattering. The electrical conductivity of the two-phase composite can exceed that of the individual components, leading to a higher power factor. We here demonstrate the concept via experiment using composites made of doped silicon nanograins and intrinsic silicon germanium grains. KEYWORDS: Electrical transport, thermoelectrics, modulation doping, nanocomposites

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hermoelectric cooling and power generation are solid-state technologies for the direct energy conversion between heat and electricity. The performance of thermoelectric devices depends on the materials’ dimensionless thermoelectric figureof-merit ZT = (S2σ/k)T, where S is the Seebeck coefficient, σ the electrical conductivity, k the thermal conductivity, and T the absolute temperature at which the properties are measured. The numerator S2σ is called the power factor. In recent years, significant improvements in ZT has been achieved particularly via size effects to reduce the phonon thermal conductivity in superlattices,13 nanocomposites4,5 and by incorporating nanoparticles into the bulk matrix.68 Even though there are no theoretical limits on the power factor,9,10 it has been experimentally observed that most of the enhancement in the performance of materials thus far achieved has been due to lowering of the thermal conductivity. Only a few strategies have been proposed to enhance the power factor, mostly based on increasing the Seebeck coefficient by increasing the slope of the differential conductivity. Hicks and Dresselhaus proposed to use quantum size effects in low-dimensional materials to create sharp features in the density-of-states and to enhance the Seebeck coefficient.11 Introducing resonant energy levels due to doped impurities into the bulk band-structure also modifies the electronic density-of-states and therefore modifies the r 2011 American Chemical Society

Seebeck coefficient.1214 On the other hand, one can create sharp features in the relaxation times versus energy by thermionic emission at interfaces, for example,15,16 which in principle make similar enhancements in the Seebeck coefficient. Despite all these efforts, only resonant energy levels have demonstrated an increased power factor in bulk materials. New approaches to increase the power factor are expected to further stimulate thermoelectrics research. Here, we develop a modulation-doping approach that uses an enhancement of the carrier mobility to increase the electrical conductivity. Modulation doping is widely used in microelectronics and photonic devices, and some recent experiments on SrTiO317 may benefit from a similar effect. In modulation doping, charge carriers are spatially separated from their parent impurity atoms to reduce the influence of impurity scattering and thereby increase the mobility of the charge carriers.18,19 For example, dopants are incorporated only into the barrier regions of a quantum well. Modulation doping has only been used in thin-film structures for electron transport along the film plane. The active layer of the modulation-doped structure usually consists of an undoped channel for the mobile carriers, an Received: January 18, 2011 Published: May 10, 2011 2225

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Nano Letters undoped spacer layer that separates the ionized dopants from the conducting channel, and a doping layer. The heterointerface is located between the channel and the spacer and separates the two regions energetically.20 Carriers then travel parallel to the film with much reduced impurity scattering and therefore with an enhanced mobility. Here, we use a similar concept but now we apply it to nanocomposite-based bulk thermoelectric materials. It has been demonstrated that nanograined materials can have a higher figure of merit compared to their stoichiometrically equivalent regular bulk material due to a significant reduction in the phonon thermal conductivity caused by interfacial scattering.4,2123 Here we show that using two types of grains introduces another strategy to enhance the performance of the bulk material through enhancing the power factor in addition to reducing the thermal conductivity. We incorporate dopants only into one type of minority nanograin, which we here refer to as the “nanoparticles”. These grains are then mixed with another type of majorityundoped nanograin, which we refer to as the “host”. Finally, the mixture of these types of grains is pressed to form a bulk material. By energy band engineering the grains, one can force the charge carriers to spill over from the nanoparticles into the surrounding host matrix, while the ionized dopant atoms remain spatially segregated within the nanoparticles. By using the modulationdoping concept, the ionized impurity scattering rate can be decreased, leading to increased carrier mobility and a larger power factor. The strategy is not as effective as that of thin films since there is no spacer between the channel and the doping region as there is in the thin film geometry. Instead, the doped nanograins are randomly distributed inside the host channel. Therefore, the free carriers inside the host do not experience impurity scattering, but they still scatter from grain interfaces and charged ionized nanograins. Some of the carriers might be trapped at interfaces between the doped nanoparticles and the host matrix and do not contribute to the transport. However, as long as the scattering at the interfaces between the host and the nanoparticle phases is not as effective as that among the homogeneously distributed dopants, our approach should work to increase the power factor. We demonstrate modulation doping for thermoelectrics in this paper by mixing two types of semiconducting nanoparticles: undoped Si80Ge20 (9050%) nanoparticles mixed with Si100B5 or Si100P3 (1050%) nanoparticles, and we compact the two types of nanoparticles to form a bulk composite. In the past, it has been shown that metallic/semimetallic nanoinclusions inside a host matrix2427 can contribute electrons. However, the nanoinclusion volume fraction is small and the main role of the nanoparticles is the reduction of the thermal conductivity, although it has been shown that uniform size nanoparticles scatter electrons less than their equivalent ionized impurities and therefore improve the carrier mobility significantly.27 The intentional modulation doping we introduce here uses semiconducting nanoparticles. The advantage of using semiconducting nanoparticles instead of metallic nanoparticles, is the ability to control the doping level. Moreover, the band offset between the nanoparticle and the host matrix could be tuned via alloying. Therefore, we have a controlled way to tune the Fermi level in order to optimize the thermoelectric performance. This strategy is very similar to the modulation doping used in semiconducting thin films to enhance carrier mobilities. We use a mixture of two semiconducting nanograins, each having a relatively large volume fraction. Since both types of

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grains have similar sizes, the transport properties not only come from the host matrix grains but they are also determined by the average properties of the two components (nanoparticles and host grains). It has been elegantly proven by Bergman28 that the ZT of a composite can never exceed the largest value of the ZT for any component of the composite if the properties of the constituent materials are identical to those of their parent bulk materials. The effects of interfaces and of charge transfer, however, were neglected in their argument. We show that these two effects are crucial in micro to nanoscale systems and that by considering these two effects, the figure of merit of a composite can be made to exceed that of its constituent components. In what follows, we first present experimental data showing an increased power factor and an increased mobility based on the modulation-doping strategy discussed above, and we then show that the experimental data can be explained based on a simplified effective-media model. The nanostructured SiGe alloy and the B-doped Si nanoparticles are separately prepared by ball milling the appropriate raw materials for at least 10 h. Then the SiGe alloy and the borondoped Si nanoparticles are mixed in the milling jar for a short time of about 1030 min. The powder mixture is loaded into graphite dies with a 12.7 mm central cylindrical opening diameter and is immediately pressed at temperatures of 11001250 °C by a dc hot press method for rapid compaction of the nanopowders.2931 The samples were characterized by high-resolution transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS). The mass densities of these samples were measured using an Archimedes’ kit. All samples have similar volume mass densities. The measured value for the reported modulation-doped sample in the manuscript is 2.78 g/cm3. The specimens used for TEM were prepared by dicing, polishing, and ion milling of the dc hot pressed bulk samples. Samples are cut into 2 mm  2 mm  12 mm bars for fourprobe electrical conductivity and Seebeck coefficient measurements and into 12.7 mm diameter discs with appropriate thickness for thermal conductivity measurements. The electrical conductivity and Seebeck coefficient were measured by commercial equipment (Ulvac, ZEM-3) from room temperature to 900 °C; the thermal diffusivity was measured by a laser flash system (Netzsch LFA 457) from room temperature to 900 °C; the specific heat capacity was measured by a differential scanning calorimetry (DSC) method from room temperature to 600 °C. The specific heat capacity is also calculated from room temperature to 900 °C by using the Debye approximation with anharmonic corrections. We compare the results for three samples. The first sample is the state-of-the-art bulk crystalline SiGe material that was used in past NASA flights (RTG sample).30 The second sample is the uniformly doped single-phase nanostructured sample and the third sample is the modulation-doped sample (Si80Ge20)70(Si100B5)30. The uniformly doped single-phase sample has similar doping levels and the same overall composition Si86Ge14B1.5. Both the uniformly doped and modulation-doped samples consist of grains with an average size of about 20 nm (see Supporting Information for the TEM image of the samples). Both samples have higher ZT values compared to the state-ofthe-art, RTG bulk sample (Figure 1f). While for the uniform sample, the main enhancement is coming from the reduction of the thermal conductivity (Figure 1e), for the modulation doped sample the main enhancement is from the improved power factor (Figure 1c). In Figure 2, we report the corresponding set of data 2226

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Figure 1. Temperature dependence of the (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor S2σ, (d) thermal diffusivity and specific heat capacity, (e) thermal conductivity, and (f) ZT of the twophase nanocomposite sample (Si80Ge20)70(Si100B5)30 (black-filled squares) in comparison to the uniformly alloyed single-phase nanocomposite sample Si86Ge14B1.5 (red-filled circles) and to the p-type SiGe bulk alloy used in RTGs for space power missions (solid line).30

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Figure 2. Temperature dependence of the (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor S2σ, (d) thermal diffusivity and specific heat capacity, (e) thermal conductivity, and (f) ZT of the twophase nanocomposite sample (Si80Ge20)80(Si100P3)20 (black-filled squares) in comparison to the uniformly alloyed single-phase nanocomposite sample Si84Ge16P0.6 (red-filled circles) and to the n-type SiGe bulk alloy used in RTGs for space power missions (solid line).31 2227

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Nano Letters for n-type samples. Similar to Figure 1, we compare the state-ofthe-art n-type bulk SiGe with the uniformly doped nanostructured sample Si84Ge16P0.6 and the modulation-doped sample (Si80Ge20)80(Si100P3)20. It is clear from Figures 1a and 2a that the electrical conductivity of the modulation-doped samples is much higher than that of their equivalent uniformly doped nanostructured samples in both n-type and p-type materials. In contrast to the large difference observed in the electrical conductivity, the difference between the Seebeck coefficient for the two types of samples is relatively small (Figures 1b and 2b). Thus, the modulationdoped samples have higher power factors than the uniformly doped nanocomposite samples and also than the bulk crystalline SiGe samples (Figures 1c and 2c), suggesting the effectiveness of the modulation-doping strategy. We further used Hall measurements to extract the carrier concentration and mobility of the two samples. At room temperature, the p-type uniform sample has a carrier concentration of 2.87 ( 0.13  1020 cm3 while the modulation-doped sample has a slightly lower carrier concentration of 2.61 ( 0.2  1020 cm3. The mobility of the modulationdoped sample, however, is clearly larger than that of the uniformly doped sample, 30.5 ( 3 versus 22.8 ( 1 cm2/V s. The 34% improvement in the mobility validates the modulationdoping concept. The thermal conductivity of the modulation-doped sample in most of the temperature range is lower than the thermal conductivity of the RTG sample because of the presence of the more numerous interfaces in the modulation-doped samples. However, the thermal conductivity is higher than that of the uniformly doped nanostructured sample (Figures 1e and 2e), mainly due to the presence of silicon grains which have high lattice thermal conductivities. The other possible explanations for the higher thermal conductivity are the larger electronic thermal conductivity and the absence of dopants in the host grains. These issues are discussed in detail in the Supporting Information. It is also interesting to look at this from the composite point of view and to compare the properties of the two-phase composite with those of the individual components. Almost in all of the fabricated nanocomposites, ZT of the two-phase composite is higher than the ZT of the individual single-phase components. For example in the reported (Si80Ge20)70(Si100B5)30 sample, the maximum ZT is around 0.92 at 900 °C, which is higher than that for the Si100B5 single-phase sample with a measured ZT of about 0.35 at 900 °C and ZT is obviously higher than that in the intrinsic Si80Ge20 single-phase sample, which contradicts Bergman’s theory. We recognize that we cannot treat the nanoparticles as scattering centers, as has been done in the past,32,33 because (1) the nanoparticles have a large volume fraction, and (2) the nanoparticle diameters (∼20 nm) are much larger than the electron mean free paths (12 nm34,35). Instead, we need to consider the materials as a composite material in which charge transfer happens inside both the host and the nanopartricles. Rigorous modeling of the thermoelectric properties of such complex nanocomposites is not feasible at this stage. Here, we develop a simple picture to investigate the potential of the modulation-doping approach and to understand the experimental results that were measured. Let us call the modulation-doped sample the sAB sample, which means that we mix type A grains and type B grains with volume fractions of vA and vB, respectively, and we then hot press them together to form the modulation-doped

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sample sAB. To find the properties of sAB, we fabricate two more samples, sample sA, which is made by hot pressing type A grains together, and sample sB, which is made by hot pressing type B grains together. We measure the properties of the sA and sB samples and we extract the properties of sAB by averaging over the measured values. The averaging process is discussed in the following. Note that in the modeling we only discuss room-temperature characteristics, unless otherwise explicitly mentioned. We compare the modeling with experimental data measured for different nanoparticle volume fractions. In a two-phase nanocomposite, the most important factor in the calculation of electronic transport is the consideration of the charge transfer between the grains. If we simply average over the single-phase resistances with their volume fraction weights to find the resistance of the twophase composites, the results are an order of magnitude lower than the measured values. This is because electrons redistribute themselves inside the two materials, which is the main idea behind modulation doping. Therefore, instead of simply averaging over the resistance of each phase, we estimate the electrical conductivity of the composites from eq 1 1 vA vB ¼ þ σAB qnA μA qnB μB

ð1Þ

in which nA and nB are the modified carrier densities and μA and μB are the carrier mobilities in grains A and B, respectively. Because of the charge transfer between the grains, the carrier density in grain A of the modulation-doped sample sAB is different from that of the single-phase nanocomposite sA. To find the correct charge distribution in each grain, we solve the Poisson equation self-consistently, assuming a local Fermi-Dirac distribution for the charge carriers (see Supporting Information for details). The carrier densities thus obtained, which we refer to as the modified carrier densities, are used in eq 1 for the averaging process. Unlike the electrons, which are moving to the intrinsic host grains, the ion positions are fixed inside the nanoparticles; therefore, the mobility in each phase is the same as that of the equivalent single-phase composite at the ionized impurity concentration predicted by the starting materials (e.g., the carrier mobility in grain A of the sample sAB is the same as the carrier mobility of sample sA). In other words, we are still averaging over the resistances of the two types of grains. But the resistance of each grain is now different from that of the single-phase one. We refer to 1/qnAμA as the modified resistance of grain A. The Seebeck coefficient of each grain is estimated from the modified resistance, using the measured relationship between the Seebeck coefficient and the resistivity of the single-phase uniform nanostructured samples. To obtain the Seebeck coefficient of the two-phase composite, we assume that the two grains are connected in series. The Seebeck coefficients add up with the thermal resistance weight as

SAB

S A vA S B vB þ k k ¼ vAA vB B þ kA kB

ð2Þ

in which SA and SB are the Seebeck coefficients of grains A and B, respectively, and kA and kB are their corresponding thermal conductivities. The results are summarized in Figure 3 and listed in Table S1 of the Supporting Information. One should note that no fitting parameters are used in this modeling. All the inputs are 2228

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(Si100B5)30 composite is 1.81  105 S m1 which is the main reason for the increased power factor of the modulation-doped sample. Figure 3b shows the calculated Seebeck coefficients compared to the experimental values. Interfaces have two additional effects on the Seebeck coefficient, which are neglected in our modeling. First, due to the thermal boundary resistance between the grains, a part of the temperature drop is over the interfaces and their effect therefore reduces the effective Seebeck coefficient. On the other hand, electron-filtering effects might occur at the interfaces, which would enhance the value of the Seebeck coefficient.37 The previous experimental results have shown that the Seebeck coefficient of the nanostructured SiGe materials is almost the same as that of the bulk.30,31 This means that either the two effects are small or somehow the two effects cancel each other. Therefore, in our discussion of the Seebeck coefficient, we are ignoring these two additional interface effects. However, we still take into account the possibility of charge transfer between the grains as was described above. Finally, the thermal conductivities of our samples obey the mixture law (eq 3). However, in order to include the interfaces, one has to use the thermal conductivity of the single-phase nanocomposites and not those of the equivalent bulk values (Figure 3c) 1 vA vB ¼ þ kAB kA kB Figure 3. Calculated and measured electrical conductivity (a) and Seebeck coefficient (b) of modulation-doped samples at room temperature versus the silicon nanograin volume fraction. Host grains are made of intrinsic Si80Ge20 and the nanoparticle samples are made of Si100P3 and Si100B5 for n-type and p-type samples, respectively. Here for the intrinsic mobility of Si80Ge20 we used 530 and 277 cm2 V1 S1 for the electrons and holes, respectively, and for the heavily doped silicon; we used 70 and 32 cm2 V1 S1 for n- and p-type materials, respectively.36 (c) Thermal conductivity at room temperature for different modulationdoped samples versus the silicon nanograin volume fraction. The solid line refers to averaging over the bulk values of the host and nanoparticle materials. Dashed lines are calculated from eq 3 by averaging over the single-phase host and the single-phase nanoparticle nanocomposites. The bulk thermal conductivity of Si is above 100 W/mK, while our measured value for the single-phase composite is only 12.67 and 26.37 W/mK for heavily doped n- and p-type Si, respectively. For Si80Ge20, the bulk thermal conductivity is around 6 W/mK, and our measured value for the nanostructured material is 2.9 W/mK.

either from experiment or from literature data. The agreement between the modeling results and the experimental values thus achieved is about 20%, which is surprisingly good, considering the simplicity of the model. The main idea of the modulation doping is to increase the carrier concentration without changing the mobility. The good agreement between theory and experiment suggests that this goal has been achieved in these samples. In other words, the carrier concentration in the intrinsic host matrix is increased to more than 1019 cm3, while the mobility is the same as the intrinsic mobility of Si80Ge20. It is interesting to note that due to the charge transfer effect, the electrical conductivity of the mixture can be higher than the conductivity of both of the components separately. For example, the measured electrical conductivity of Si100B5 is 1.16  105 S m1 and that of the Si80Ge20 is on the order of 103 S m1. The mixture, however, has a higher electrical conductivity than both grains. The high electrical conductivity of the (Si80Ge20)70-

ð3Þ

As can be seen from Figures 1e and 2e, the thermal conductivity of the modulation-doped samples is higher than that of the uniformly doped samples. The increase of the thermal conductivity can be prevented, for example, by alloying the nanoparticles and thus reducing their lattice thermal conductivities (see Supporting Information). On the basis of the above modeling, to get the maximum benefit from the modulation-doping strategy, we suggest several criteria. First, both types of grains in the modulation-doped samples should be made of good thermoelectric materials with low-lattice thermal conductivities. Second, the band edge of the conduction/valence band of nanoparticles should be higher/ lower than that of the host so that carriers can move from the nanoparticle to the host. We suggest using a host matrix with a larger effective mass compared to that of the nanoparticles, to increase the number of available states inside the host matrix and therefore to promote the flow of charge from the nanoparticles into the host matrix. If one can engineer the Fermi level and find the right materials, the modulation doping approach could have a significant potential to enhance the figure of merit of thermoelectric materials. In summary, we have demonstrated that using the modulation doping approach, one can enhance the power factor significantly. The power factor of the p-type Si86Ge14B1.5 uniform sample was improved by 40% using the modulation-doping approach, and this was achieved by using a thirty percent volume fraction of boron doped silicon nanoparticles in the intrinsic silicon germanium host matrix to make a modulation-doped sample with the same overall composition (Si80Ge20)0.7(Si100B5)0.3. A smaller improvement of about 20% was observed in the power factor of n-type samples and this in turn resulted in a 10% increase in the figure of merit. The increase in the power factor signifies a new strategy to improve the electron performance in bulk materials. Enhancement of the power factor is attributed to the 2229

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Nano Letters enhancement of the mobility by separating the carriers spatially from their parent impurity atoms. By eliminating impurities as scattering centers, the carrier scattering rates are reduced, which results in higher mobilities. We developed a simple model based on mixture rules to interpret the experimental data. Without any fitting parameters, we were able to explain the experimental data within a maximum uncertainty of (20%. We anticipate that similar modulation-doping strategies can be applied to other thermoelectric materials following the general guidelines developed.

’ ASSOCIATED CONTENT

bS Supporting Information. Additional information, figures, and tables. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: (G.C.) [email protected]; (Z.F.R.) [email protected]. )

Author Contributions

These authors made equal contributions.

’ ACKNOWLEDGMENT This material is based upon work supported as part of the “Solid State Solar-Thermal Energy Conversion Center (S3TEC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-FG02-09ER46577 (G.C. and Z.F.R.). M.Z. would like to thank Keivan Esfarjani for fruitful discussions. ’ REFERENCES (1) Chen, G. Phys. Rev. B 1998, 57, 14958–14973. (2) Koga, T.; Cronin, S. B.; Dresselhaus, M. S.; Liu, J. L.; Wang, K. L. Appl. Phys. Lett. 2000, 77, 1490. (3) Zeng, G. H.; Bahk, J. H.; Bowers, J. E.; Lu, H.; Gossard, A. C.; Singer, S. L.; Majumdar, A.; Bian, Z. X.; Zebarjadi, M.; Shakouri, A. Appl. Phys. Lett. 2009, 95, 083503. (4) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y. C.; Minnich, A.; Yu, B.; Yan, X.; Wang, D. Z.; Muto, A.; Vashaee, D.; Chen, X.; Liu, J. M.; Dresselhaus, M. S.; Chen, G.; Ren, Z. F. Science 2008, 320, 634. (5) Jiang, J.; Chen, L. D.; Bai, S. Q.; Yao, Q.; Wang, Q. Scr. Mater. 2005, 52 (5), 347. (6) 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 (5659), 818. (7) Kim, W.; Singer, S. L.; Majumdar, A.; Zide, J. M. O.; Klenov, D.; Gossard, A. C.; Stemmer, S. Nano Lett. 2008, 8, 2095. (8) Mingo, N.; Hauser, D.; Kobayashi, N. P.; Plissonnier, M.; Shakouri, A. Nano Lett. 2009, 9, 711. (9) Mahan, G. D.; Sofo, J. O. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 7436. (10) Humphrey, T. E.; Linke, H. Phys. Rev. Lett. 2005, 94, 096601. (11) Hicks, L. D.; Dresselhaus, M. S. Phys. Rev. B 1993, 47, 12727. (12) Heremans, J. P.; Jovovic, V.; Toberer, E. S.; Saramat, A.; Kurosaki, K.; Charoenphakdee, A.; Yamanaka, S.; Snyder, G. F. Science 2008, 321, 554. (13) Ahn, K.; Han, M. K.; He, J. Q.; Androulakis, J.; Ballikaya, S.; Uher, C.; Dravid, V. P.; Kanatzidis, M. G. J. Am. Chem. Soc. 2010, 132, 5227.

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