role of nanoscale precipitates for enhancement of
TRANSCRIPT
Role of Nanoscale Precipitates for Enhancement of Thermoelectric Properties of Heavily P-Doped Si-Ge Alloys
Aikebaier Yusufu1,*, Ken Kurosaki1,*, Yoshinobu Miyazaki1, Manabu Ishimaru2, Atsuko Kosuga3, Yuji Ohishi1, Hiroaki Muta1 and Shinsuke Yamanaka1,4
1Graduate School of Engineering, Osaka University, Suita 565–0871, Japan2Graduate School of Engineering, Kyushu Institute of Technology, Fukuoka 804–8550, Japan3Nanoscience and Nanotechnology Research Center, Osaka Prefecture University, Osaka 599–8570, Japan4Research Institute of Nuclear Engineering, University of Fukui, Tsuruga 914–0055, Japan
Thermoelectric (TE) devices can save energy by generating electricity from waste heat. For industrial application of TE power generation, TE materials with high conversion ef�ciency and that are non-toxic and inexpensive are required. The nanostructured silicon-germanium (Si-Ge) alloy is one possible candidate for such TE materials. Nanostructuring is an effective way to improve the conversion ef�ciency of materials because it dramatically reduces the lattice thermal conductivity (κlat). Here, we experimentally demonstrate effective phonon blocking without carrier mobility deterioration in bulk Si-Ge alloys containing phosphorous-rich nanoscale precipitates connected coherently or semi-coherently with the matrix phase. When the Ge content was less than 5%, the nanoscale precipitates effectively scattered heat-carrying phonons, leading to a suf�cient reduction in κlat. However, at higher Ge content compositions, phonon scattering by Ge substitution with Si was more predominant than phonon scattering by nanoscale precipitates for the reduction of κlat. As a result, signi�cant enhancement of zT was achieved at low Ge contents. [doi:10.2320/matertrans.E-M2016805]
(Received November 9, 2015; Accepted January 23, 2016; Published April 22, 2016)
Keywords: thermoelectric, nanostructuring, nano-Si, thermal conductivity, electrical conductivity
1. Introduction
Huge amounts of energy are exhausted as waste heat from the primary energies1) used in all �elds, including industry, agriculture, and everyday life. Thermoelectric (TE) energy conversion could lead to signi�cant energy savings by gener-ating electricity from waste heat.2–4) The conversion ef�cien-cy of a TE energy conversion device depends on the proper-ties of the TE material used and the temperature difference applied across the device. The effectiveness of a TE material is represented by the dimensionless �gure of merit, zT = (S 2σ)T/(κel + κlat), where S, σ, T, κel, and κlat are the Seebeck coef�cient, electrical conductivity, absolute temperature, and electronic and lattice components of the thermal conductivity (κ), respectively.3) S, σ, and κel depend on the carrier concen-tration of the material, and there exists an optimized carrier concentration for maximizing S 2σ, meaning that zT can be effectively increased by decreasing κlat. At the present mo-ment, the best bulk TE materials are bismuth telluride (Bi2Te3) and lead telluride (PbTe) materials, whose zT values are around unity, corresponding to device ef�ciencies of several %. Although these conventional materials exhibit relatively high zT values, they contain highly toxic and/or rare ele-ments; thus, high-ef�ciency TE materials made from ele-ments that are non-toxic, less expensive, and more Earth abundant need to be developed.
Because silicon (Si) is a non-toxic, cost effective, and nat-urally abundant semiconductor, it has many compelling ad-vantages, which make it an ideal TE material. However, its only disadvantage for use as a TE material is that the bulk Si has a very high κlat (>100 Wm−1 K−1 at room temperature),5,6) leading to a maximum zT value of 0.2.6) Therefore, many ef-
forts have focused on reducing the κlat of bulk Si. The κlat of Si can be greatly decreased by forming a solid solution with ger-manium (Ge), and the best composition, Si100-xGex (x = 20~30), shows the highest zT value, of approximately 0.7–0.8.7–10) However, issues such as the still low zT and the high cost of Ge have limited the industrial applications of these materials. Recently, it has been experimentally proven that nanostructring also reduces the κlat and hence greatly im-proves the zT of various materials,11–15) including bulk Si and Si-Ge alloys.6,16–19) Indeed, very recently, our group has demonstrated that nanostructured bulk n-type Si heavily doped with phosphorous (P) containing a small amount of Ge, less than 3 at.%, shows a maximum zT of 0.6 at 1050 K,20) three times higher than that of non-nanostructured, i.e., tradi-tional, bulk Si. In our nanostructured bulk Si, P-rich nanoscale precipitates can be naturally formed by optimizing the heat treatment conditions of the samples. Because the nanoscale precipitates connect coherently or semi-coherently with the Si matrix, they effectively scatter heat-carrying phonons without signi�cantly in�uencing the electron transport prop-erties, leading to high zT values.20) It is thought that further improvement of zT is possible if the Ge content could be op-timized. As described before, the optimized Ge content in Si-Ge alloys is 20–30 at.%. Thus, in the present study, we at-tempted to synthesize heavily P-doped Si-Ge alloys containing naturally formed nanoscale precipitates and investigated the role of the precipitates in the enhancement of the TE proper-ties of Si-Ge alloys. The nominal sample compositions stud-ied here were Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20).
2. Experiment
The starting materials, Si chunks (11N), Ge shots (5N), and P chunks (4N), were weighed and mixed to the desired com-positions and melted by arc melting in an Ar atmosphere. The
* Corresponding author, E-mail: [email protected], [email protected]
Materials Transactions, Vol. 57, No. 7 (2016) pp. 1070 to 1075 Special Issue on Recent Progress in Thermoelectrics -New Analyses and New Materials- (Thermoelectric Conversion Materials IX) ©2016 The Thermoelectrics Society of Japan
ingots produced by arc melting were then crushed into micro-powders, which were placed in a graphite die for spark plas-ma sintering (SPS) at 1353 K for 3 min under an axial pres-sure of 100 MPa in an Ar atmosphere. The bulk samples produced by SPS were characterized using powder X-ray diffraction (XRD; Rigaku RINT2000) with Cu-Kα radiation at room temperature. The microstructure and chemical com-position of the samples were studied using scanning electron microscopy (SEM; Hitachi S-2600H) and energy-dispersive X-ray spectroscopy (EDX; Horiba EX-200). The density (d) of each bulk sample was calculated based on its measured weight and dimensions.
Nanoscale structures were characterized by transmission electron microscopy (TEM). For each TEM observation, each thin specimen was prepared by crushing the bulk sample into powders and then collecting the powders on a perforated amorphous carbon �lm supported by a copper grid. TEM was performed at an accelerating voltage of 200 kV in bright-�eld mode (Hitachi HF2000), with an ultrahigh-sensitivity energy dispersive X-ray spectroscopy instrument.σ and S were measured simultaneously in a He atmosphere
at 323–1073 K (Ulvac ZEM-3). The Hall coef�cient (RH) was measured (Toyo Resitest8300) at room temperature by the van der Pauw method in vacuum under an applied magnetic �eld of 0.5 T. The Hall carrier concentration (nH) and Hall mobility (μH) were calculated from RH by assuming a sin-gle-band model and a Hall factor of 1; i.e., nH = 1/(eRH) and μH = σRH, where e is the elementary electric charge. κ was evaluated from the thermal diffusivity (α), heat capacity (Cp), and d by κ = αCpd. α was measured at 323–1073 K by the laser �ash diffusivity method (Netzsch LFA-457).
Cp data for pure Si were used to calculate the κ for samples of Si1-xGexP3 (x = 0, 1, and 3) and the Cp data estimated from those of pure Si and pure Ge based on the Kopp–Neumann rule were used to calculate the κ for samples of Si1-xGexP3 (x = 5, 10, and 20).
3. Results and Discussion
The phase state of the samples was characterized by pow-der XRD. As shown in Fig. 1(a), all samples were con�rmed to have a single phase with a diamond structure21) (Fd-3m space group) without any noticeable secondary phases within the detection limit of our XRD equipment. In addition, all the XRD peaks were shifted to lower angles with increasing x in Si100-xGex, implying that the unit cell volume slightly ex-
pands. Figure 1(b) shows the lattice parameters (a) calculated from the XRD patterns as a function of Ge content. The a values are also summarized in Table 1. The a should increase with increasing Ge content because the atomic radius of Ge is larger than that of Si.22) In contrast, a should decrease by P-doping because the atomic radius of P is smaller than those of Si and Ge.22) The results in Fig. 1(b) show that the a values of the samples were slightly lower than the line for pure Si-Ge alloys predicted by Vegard’s law.
Table 1 summarizes the properties of the samples. All the samples exhibited very high d, corresponding to above 98% of the theoretical value. All samples exhibited high Hall nH, on the order of 1020 cm−3. The nH showed a tendency to de-crease with increasing Ge content. This behavior can be ex-plained by the solubility limit of P in Si-Ge alloys, which decreases with increasing Ge content.23) All samples exhibit-ed similar values for the (μH, at approximately 50 cm2V−1s−1. Figure 2(a) and 2(b) show the temperature dependences of S and σ, respectively. As expected, all samples exhibited nega-tive S over the entire temperature range, indicating n-type conduction, meaning that electron doping by adding P into Si-Ge alloys was performed successfully. As the temperature increased, the absolute S increased, while the σ decreased, showing the typical behavior of degenerate semiconductors. Above approximately 900 K, the temperature dependency of absolute S and σ tended to change, likely related to the in-creased carrier concentration caused by the increased solubil-ity limit of P for Si-Ge alloys at high temperatures. Fig. 2(c) shows the theoretical Pisarenko line, calculated using eqs. (1), (2), and (3). Under the single-parabolic-band model, S can be expressed as follows:
Fig. 1 (a) Powder XRD patterns of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20). The powder samples were produced by crushing parts of the sintered pel-lets prepared by SPS. (b) Lattice parameters of Si100-xGexP3 as a function of Ge content. A line describing the lattice parameters of pure Si-Ge al-loys determined by Vegard’s law is shown for comparison.
Table 1 Lattice parameter a, density d, Hall carrier concentration nH (300 K), Hall mobility μH (300 K), Seebeck coef�cient S (300 K), electrical conductiv-ity σ (300 K), lattice thermal conductivity κlat (300 K), and maximum zTmax (1070 K) of samples with nominal compositions of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20).
a d nH μH S σ κlat zTmax
nm g cm−1 %T.D. 1020 cm−3 cm2 V−1 s−1 μVK−1 105 S m−1 Wm−1K−1
Si100P3 0.54237 2.30 98 3.84 43 −77 2.52 25 0.35
Si99Ge1P3 0.54243 2.35 98 3.54 45 −75 2.31 12 0.44
Si97Ge3P3 0.54343 2.40 98 2.09 53 −87 2.12 9 0.60
Si95Ge5P3 0.54377 2.44 98 2.10 53 −85 2.13 8 0.63
Si90Ge10P3 0.54466 2.60 97 2.18 49 −90 1.89 5 0.68
Si80Ge20P3 0.54738 3.00 98 1.93 48 −100 1.39 4 0.78
1071Role of Nanoscale Precipitates for Enhancement of Thermoelectric Properties of Heavily P-Doped Si-Ge Alloys
S =kB
eη −
(2 + λ)F(1+λ)(η)
(1 + λ)Fλ(η), (1)
nH = 4π2m∗kBT
h2
3/2
F1/2(η), (2)
F(η)i =∞
0
xidx1 + exp(x − η) , (3)
where η, m*, kB, h, F(η), and λ are the reduced Fermi level (= EF/kBT, where EF is the Fermi level), carrier effective mass (= 1.08m0,24) where m0 is the free electron mass), Boltzmann constant, Planck constant, Fermi integral, and scattering pa-rameter, respectively. λ is a parameter associated with the en-ergy dependence of the charge-carrier mean free path, where we obtained λ = 0.65 by �tting the literature data for bulk Si and Si-Ge alloys.7,15) This value is reasonable because it has been reported that values of λ between 0 and 1 are a good �t to experimental S values for Si-Ge alloys.8) As can be seen in Fig. 2(c), our data existed on the theoretical Pisarenko line. The μH versus nH relationship for the samples at 300 K is shown in Fig. 2(d), together with the calculated curves using the literature data for single crystalline Si26) and polycrystal-line n-type Si70Ge30.8) The μH data for samples of Si100P3 and Si99Ge1P3 existed on the Si curve, while with increasing Ge content, e.g., for samples of Si100-xGexP3 (x = 3, 5, 10, and 20), the μH data existed on the Si70Ge30 curve. This behavior implies that the point-defect scattering caused by Ge substitu-tion with Si is dominant for carrier scattering and is the pri-mary factor that determines the magnitude of μH. The results shown in Fig. 2(c) and 2(d) indicate that the electrical trans-port properties of our samples are similar to those reported for traditional bulk Si and Si-Ge alloys.
The microstructures of the samples were characterized by SEM and TEM. From the SEM analysis, it was con�rmed that all samples were dense, with no remarkable cracks and pores, and that their grain sizes ranged from several microm-
eters to a few dozen micrometers (for example, see Support-ing Information of Ref. 20). Quantitative analysis using EDX spectroscopy equipped with the SEM revealed that Ge was uniformly distributed in the samples and that the samples’ contents were nearly the same as their starting compositions. However, we could not obtain accurate P contents because it was within the error range of the EDX.
Figure 3 shows the TEM images of samples with composi-tions of Si100-xGexP3 (x = 0, 1, 3, and 20). In the present study, the TEM observation was carried out for the sample of Si80Ge20P3. The TEM images for the samples of Si100-xGexP3 (x = 0, 1, and 3) were obtained in our previous study.20) In all the TEM images, nanoscale precipitates with various sizes under a few dozen nanometers can be clearly observed. As described in our previous paper,20) two types of nanoscale precipitates naturally form in the grains of the polycrystalline Si-Ge alloys. One is plate-like P-rich precipitates with sizes of a few dozen nanometers; the other is spherical precipitates with diameters of several nanometers.20) As reported in Ref. 20, we have con�rmed that the plate-like and spherical precipitates had P-rich compositions by using the TEM/EDX analysis and a lattice image modelling. Similar nanostruc-tures have been observed in a Cu-Al alloy, in which Cu-rich nanoinclusions naturally precipitate in the Al matrix and harden the alloys, called precipitation hardening or age hard-ening.27–30) In Si-Ge alloys, it has been con�rmed that plate-like and spherical precipitates are semi-coherently and coher-ently connected with the matrix phase, respectively.20) As shown in Fig. 3, there are no remarkable differences in the sizes and distribution of the precipitates among the samples with different Ge contents.
The temperature dependences of κ of the samples are plot-ted in Fig. 4(a). As the Ge content increased, the κ decreased throughout the whole measured temperature range. κlat was obtained by subtracting κel from κ. The electronic part was
Fig. 2 Temperature dependences of (a) Seebeck coef�cient S and (b) elec-trical conductivity σ of samples with nominal compositions of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20). Relationships between (c) the Seebeck coef�cient S and Hall carrier concentration nH and (d) Hall carri-er mobility μH and Hall carrier concentration nH of the samples, together with the literature data. The values were obtained at 300 K.
Fig. 3 TEM images of samples with nominal compositions of Si100-xGexP3. (a), (b), (c), and (d) correspond to x = 0, 1, 3, and 20, respectively. All scale bars are 100 nm.
1072 A. Yusufu, et al.
calculated by the Wiedemann–Franz relationship, i.e., κel = LσT, where L is the Lorenz number and can be calculated with the following expression:
L = −k2
B
e2
(1 + λ)(3 + λ)Fλ(η)F2+λ(η) − (2 + λ)2F1+λ(η)2
(1 + λ)2Fλ(η)2, (4)
where η values were obtained by �tting the temperature de-pendence of experimental S using eq. (1). As shown in Fig. 4(b), the calculated L values for all samples are lower than that of the metallic limit of 2.45 × 10−8 V2 K−2, and de-crease with increasing temperature throughout the entire tem-perature range. As can be seen in Fig. 4(c), the κlat decreased with increasing Ge content throughout the whole temperature range because of the enhancement of point-defect scattering of phonons caused by Ge substitution of Si. Additionally, the κlat of the samples were rather �at, slightly decreased with temperature, and did not follow the T −1 or T −0.5 relationship. This temperature dependence of κlat implies that complex phonon scatterings caused by not only Umklapp scattering but also other scatterings occur in this system. Figure 4(d) shows a comparison of experimental and theoretically calcu-lated κlat at 330 K for the samples. The theoretical lines were
calculated using a Born–von Karman dispersion model in-cluding frequency-dependent expressions for grain-boundary scattering.31) In this model, κlat can be expressed as:
κlat =p
13
C · υ2 · τc · dω, (5)
where C, υ, τc, and ω are the speci�c heat capacity, group velocity, relaxation time, and frequency, respectively. When calculating κlat, we considered four types of phonon scatter-ing: Umklapp scattering (phonon-phonon scattering), pho-non-impurity scattering (in other words, point-defect scatter-ing), phonon-grain boundary scattering, and phonon-electron scattering. Thus, we estimated τc as follows:
τ−1c = τ
−1umkl + τ
−1imp + τ
−1bdy + τ
−1ep , (6)
where τumkl, τimp, τbdy, and τep are the relaxation times deter-mined by Umklapp scattering, phonon-impurity scattering, phonon-grain boundary scattering, and phonon-electron scat-tering, respectively. All of the scattering parameters have been summarized in Table S1 in the Supporting Information of Ref. 20. In Fig. 4(d), for nondoped Si100-xGex, the experi-mental data obtained from the literature32) are consistent with
Fig. 4 Temperature dependences of (a) total thermal conductivity κ, (b) Lorenz number L, and (c) lattice thermal conductivity κlat. (d) Comparison of exper-imental and theoretically calculated κlat values at 330 K for samples with nominal compositions of Si100-xGexP3 (x = 1, 3, 5, 10, and 20). (e) Temperature dependence of dimensionless �gure of merit zT of samples with nominal compositions of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20). (f) Comparison of max-imum zT values of nanostructured and non-nanostructured Si-Ge alloys with nominal compositions of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20).
1073Role of Nanoscale Precipitates for Enhancement of Thermoelectric Properties of Heavily P-Doped Si-Ge Alloys
the theoretical line. The theoretical line was calculated when Umklapp scattering, phonon-impurity scattering (in this case, impurity means Ge), and phonon-grain boundary scattering were taken into account. Conversely, the theoretical line, cal-culated when Umklapp scattering, phonon-impurity scatter-ing (in this case, impurity means both Ge and P), grain-bound-ary scattering, and phonon-electron scattering were taken into account, was clearly higher than those of the experimental κlat for Si100-xGexP3, especially for low Ge content. However, the calculated values decreased with increasing Ge content, and almost completely agreed with the experimental values, when the Ge content was up to 20%. This means that additional phonon scatterings should be taken into account to under-stand the experimental κlat of Si100-xGexP3, especially at low Ge content. This additional scattering may be caused by the nanoscale precipitates observed in the TEM images (Fig. 3).
It has been demonstrated in various materials that nano-structuring reduces κlat, but in many cases, the nanostructur-ing also deteriorates carrier mobility to some degree.33–35) However, as shown in Fig. 2(d), the Si-Ge alloys containing nanoscale precipitates prepared in the present study exhibit values of carrier mobility similar to those of traditional Si-Ge alloys that do not contain nanostructures. This means that, in this system, the nanoscale precipitates scatter phonons effec-tively but scatter electrons very little. Indeed, in our samples, it has been con�rmed that the nanoscale precipitates coher-ently or semi-coherently connect with the matrix phase,20) and these types of matched interfaces have little in�uence on the electron transport properties.36–38) As can be con�rmed in Fig. 4(d), the contributions of this additional scattering de-crease with increasing Ge content in Si-Ge alloys. Thus, when the Ge content is low, the additional phonon scattering by nanoscale precipitates is predominant and effectively re-duces the κlat. However, when the Ge content increases and reaches approximately 20%, the point-defect scattering caused by substitution of Ge for Si becomes more predomi-nant in the determination of κlat than the additional phonon scattering caused by the nanoscale precipitates.
Figure 4(e) shows the temperature dependence of zT of the samples with nominal compositions of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20). The zT of the samples increased with both temperature and Ge content. As a result, the maximum zT of 0.8 was obtained for the sample with x = 20 at 1073 K. Fig-ure 4(f) shows the relationship between the maximum zT val-ue and Ge content of the samples. In this �gure, the zT values of non-nanostructured Si-Ge alloys calculated theoretically are shown for comparison. In the low Ge content region, the maximum zT values of nanostructured Si-Ge alloys are ap-proximately three times larger than that of non-nanostruc-tured Si, while, in the high Ge content region (e.g., the sample with x = 20), the nanostructured Si-Ge alloys exhibit almost the same zT values as that of non-nanostructured Si-Ge al-loys. This means that as the Ge content increases, the contri-bution of nanoscale precipitates is reduced but the point-de-fect scattering caused by substitution of Ge for Si becomes predominant in the determination of κlat. Therefore, it can be concluded that the nanoscale precipitates enhance the zT of Si-Ge alloys only when the Ge content is low.
4. Conclusions
Polycrystalline samples of Si100-xGexP3 (x = 0, 1, 3, 5, 10, and 20) with nominal compositions were prepared, and the TE properties were examined. The following conclusions were obtained. In heavily P-doped Si-Ge alloys, two types of P-rich nanoscale precipitates, semi-coherent plate-like pre-cipitates with sizes of a few dozen nanometers and coherent spherical precipitates with diameters of several nanometers, naturally form. There are no remarkable differences in the sizes and distribution of the precipitates among the samples with different Ge contents. The nanoscale precipitates have negligible in�uences on the electron transport properties, while effectively scattering heat-carrying phonons, leading to a signi�cant reduction in κlat while maintaining a high power factor. With low Ge content, phonon scattering caused by the nanoscale precipitates is the predominant factor in the reduc-tion of κlat, while at high Ge content, point defect phonon scattering caused by Ge substitution for Si is predominant. As a result, the nanoscale precipitates effectively enhance the zT of Si-Ge alloys when the Ge content is small, i.e., less than 5%.
Acknowledgments
This work was supported in part by a Grant-in-Aid for Sci-enti�c Research (No. 25289220) from the Ministry of Educa-tion, Culture, Sports, Science, and Technology and by the ALCA (Advanced Low Carbon Technology Research and Development Program) of the Japan Science and Technology Agency. Additional support was kindly provided by the Pro-gram for Creating Future Wisdom, Osaka University, selected in 2014.
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1075Role of Nanoscale Precipitates for Enhancement of Thermoelectric Properties of Heavily P-Doped Si-Ge Alloys