High Power Factor of Ga-Doped Compositionally Homogeneous Si0

Article pubs.acs.org/crystal

High Power Factor of Ga-Doped Compositionally Homogeneous Si0.68Ge0.32 Bulk Crystal Grown by the Vertical Temperature Gradient Freezing Method Muthusamy Omprakash,† Mukannan Arivanandhan,†,‡ Tadanobu Koyama,† Yoshimi Momose,† Hiroya Ikeda,†,‡ Hirokazu Tatsuoka,‡ Dinesh K. Aswal,§ Shovit Bhattacharya,§ Yasunori Okano,∥ Tetsuo Ozawa,⊥ Yuko Inatomi,# Sridharan Moorthy Babu,∇ and Yasuhiro Hayakawa*,†,‡ †

Research Institute of Electronics, Shizuoka University, Hamamatsu 432-8011, Japan Faculty of Engineering, Shizuoka University, Hamamatsu 432-8011, Japan § Bhaha Atomic Research Center, Mumbai 400094, India ∥ Graduate School of Engineering Science, Osaka University, Osaka 565-0871, Japan ⊥ Shizuoka Institute of Science and Technology, Fukuroi, Shizuoka 437-8555, Japan # Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, Kanagawa 229-8510, Japan ∇ Crystal Growth Centre, Anna University, Chennai 60025, India ‡

ABSTRACT: Compositionally homogeneous Ga-doped Si0.68Ge0.32 bulk crystals were grown with two different doping concentrations, i.e., 1 × 1018 cm−3 (GSG1) and 1 × 1019 cm−3 (GSG2), using a vertical gradient freezing method. The growth was carried out under a mild temperature gradient of 0.57 °C/ mm using a sandwich structured sample, i.e., Si(seed)/Gadoped Ge/Si(feed). The grown crystals were cut along the growth direction to study the compositional variations, etch pit densities (EPDs), and thermoelectric characteristics. Electron backscatter diffraction analysis indicated that the (111) orientation has a larger area compared with other orientations in the grown crystal. The electrical resistivity decreased along the growth direction, although the carrier concentrations and mobility of the crystals were unchanged, possibly because of the variation in EPDs. Moreover, the electrical resistivity was found to be large at the high EPD region of the crystal. The electrical resistivity of all the samples gradually increased with temperature. The maximum values of Seebeck coefficients in GSG1 and GSG2 samples were 466 μV/K at 818 K and 459 μV/K at 892 K, respectively. The calculated power factors of GSG1 and GSG2 were higher than previously reported values (1416 μW m−1 K−2) for Si0.81Ge0.19. where Z is the figure of merit, T is the absolute temperature, S is the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity, and σS2 is the power factor. The thermoelectric conversion efficiency of Si1−xGex is strongly dependent on the composition of the material.5 Therefore, compositionally homogeneous Si1−xGex crystals are required to enhance the ZT. However, it is very difficult to grow a Si1−xGex bulk crystal with a homogeneous composition because of the large separation between the liquidus and solidus lines in the Si−Ge binary phase diagram, as well as the difference in densities, lattice parameters, and melting temperatures of Si and Ge.6 Although bulk growth of Si1−xGex with a homogeneous composition still remains a challenging task, several researchers have attempted to grow a homogeneous Si1−xGex bulk crystal.7−18 To grow a homogeneous crystal, the understanding

1. INTRODUCTION The amount of waste heat is drastically increasing from various sources, such as automobiles, incinerators, nuclear power plants, thermal power plants, and factories. This leads to environmental pollution.1 A thermoelectric device is a reliable device that can convert waste heat into electrical energy and thereby suppress environmental pollution. Si1−xGex alloy is one of the most prominent thermoelectric materials for hightemperature applications. It has been used in radioisotope thermoelectric generators powering NASA spacecrafts since 1976.2 In addition to high mechanical strength, its high melting point, low vapor pressure, and resistance to atmospheric oxidation makes SiGe an attractive material for device applications. Moreover, Si1−xGex alloy shows high power generating efficiency.3,4 The performance of a thermoelectric device is determined by the dimensionless figure of merit (ZT)

Received: December 6, 2014 Revised: January 16, 2015

σS 2 ZT = T κ © XXXX American Chemical Society

A

DOI: 10.1021/cg501776h Cryst. Growth Des. XXXX, XXX, XXX−XXX

Article

Crystal Growth & Design

approximately 10−4 Pa and sealed under high vacuum. The temperature profile of the furnace was measured repeatedly using an R-type thermocouple to find a consistent mild temperature gradient position inside the furnace. The ampule was kept inside the furnace at the appropriate position and heated at a predetermined heating rate under a mild temperature gradient of 0.57 °C/mm. The temperature was kept constant at 1200 °C for about 300 h for the growth of the Si1−xGex bulk crystal, after which it was cooled at a rate of −6 °C/h. A schematic diagram of the VGF method is shown in Figure 1. Two Si1−xGex crystals with initial Ga doping concentrations of 1 × 1018 and 1 × 1019 cm−3 were grown, denoted as GSG1 and GSG2.

of solute transport in the solution is necessary. Armour et al. reported that the dissolution of silicon into the germanium melt was slightly higher with an applied magnetic field compared with that without a field.19−23 In the vertical gradient freezing method, as the crystal growth proceeds, the growth interface shifts toward the high-temperature region, which causes a gradual increase in the temperature of the growth interface; the corresponding composition varies along the solidus line of the Si−Ge binary phase diagram. Thus, control of the temperature at the growth interface is required and is the key factor in obtaining a homogeneous crystal. Azuma et al. developed an automatic feedback control system to visualize the crystal−melt interface. The corresponding image was captured by a CCD camera, and the height of the ampule was adjusted to control the temperature at the growth interface.24 Our group reported the growth of compositionally homogeneous Si1−xGex (x = 0.3, 0.5, 0.7) bulk crystals by the vertical temperature gradient freezing (VGF) method.25,26 Compositionally homogeneous Mg2Si1−xGex (x = 0.3, 0.5, 0.7) samples were also synthesized using grown Si1−xGex as a source material, and the thermoelectric properties of prepared samples were analyzed as a function of temperature. Because the thermoelectric properties depend on the doping concentration and composition of the Si1−xGex crystal, the impact of doping concentration on the thermoelectric properties should be studied. Various attempts have been made to improve the power factor of nano Si1−xGex, such as doping modulation.27−29 Recent reports on nano thermoelectric materials show that increasing phonon scattering at grain boundaries (GBs) can reasonably control the thermal conductivity and the electron transport can be enhanced as a result of the quantum confinement effect.29−31 However, in the nanomaterial, the phonons may scatter at the GBs, but at the same time, electron transport may be degraded because of recombination at charged defects and GBs as the number of GBs increases in sintered nanomaterials. Therefore, despite the better ZT resulting from low thermal conductivity, the power factor is relatively low for nano thermoelectric (TE) materials compared with their bulk counterparts.31 Nevertheless, it is necessary to improve the power factor of the bulk material for the enhancement of ZT. In the present work, compositionally homogeneous Gadoped Si1−xGex alloy crystals were grown with two different doping concentrations by setting up a mild temperature gradient between the seed and feed interfaces (0.57 °C/mm), and their thermoelectric properties were analyzed. Attempts were made to control the defect density of Si1−xGex by modifying the radial temperature distribution, and defect density variations in the form of etch pits and their impact on the power factor of the material were studied.

Figure 1. Principles of vertical temperature gradient freezing method. After the growth experiments, the crystals were removed from the ampules. The samples were cut along the growth direction, and the surface was polished using alumina abrasive powder for further analysis. One half of the samples were used to measure the Si composition distribution by electron probe microanalysis (EPMA). The remaining half of the samples were used to analyze etch pit density (EPD) and cut into rectangular samples to investigate the thermoelectric properties such as carrier concentration, electrical resistivity, Seebeck coefficient, and thermal conductivity.

3. RESULTS AND DISCUSSION At high processing temperatures, Si seed and feed crystals started to dissolve once Ge was completely melted at its melting point (938 °C). The dissolved Si at the seed interface was transported toward the feed by solutal convection originating from the density difference between Si (2.33 g/ cm3) and Ge (5.323 g/cm3). At the same time, the dissolved solutes from the feed interface were transported toward the seed interface primarily by diffusion originating from the concentration gradient between the feed and seed interfaces. As time increased, solutal convection became weak and Si transport from the feed interface to the seed interface was dominated by diffusion. Thus, the solution near the seed interface became supersaturated, which provided the necessary driving force to initiate the growth of SiGe at the seed interface. The Si composition of the GSG1 crystal was measured along the growth direction in the center region, as indicated by the red line in Figure 2a (i). The shapes of the seed and feed interfaces were concave toward the solution because of the effect of inhomogeneous radial temperature distribution, as indicated by the white solid line in Figure 2a (i). The Si composition profile revealed that the crystal was grown from seed to feed interface with a homogeneous composition of Si0.68Ge0.32 with a grown length of approximately 15.5 mm, as shown in Figure 2a (ii). The Si composition gradient was

2. EXPERIMENTAL SECTION Polycrystalline Si and Ga-doped Ge were polished into a cylindrical shape using alumina abrasive powder. Prior to the growth experiment, Ga-doped Ge polycrystals were prepared with two different doping concentrations, i.e., 1 × 1018 and 1 × 1019 cm−3, by adding the appropriate amount of Ga to the 6 N purity Ge slurry. The Ga-added Ge slurry was heated to its melting temperature and kept for 3 h for homogenization. Subsequently, the Ga-doped Ge melt was quenched to avoid Ga segregation. Samples were etched in an acid mixture of HF:HNO3 (1:1) for Si and HF:H2O2 (1:1) for Ge. The etched samples with a sandwich structure of Si(seed)/Ga-doped Ge/Si (feed) were packed into a boron nitride (BN) crucible under a nitrogen atmosphere to avoid oxidation of the sample during packing. The BN crucible was inserted into a quartz ampule at a pressure of B


Article


Figure 2. (a) GSG1 bulk crystal (i) cross-sectional view of grown crystal and (ii) Si composition profile of grown crystal. (b) EPMA mapping of Si composition distribution (the horizontal bar shows the variation of X-ray counts per second).

direction of the GSG1 crystal was investigated by electron backscattered diffraction analysis, which revealed that the (111) oriented grain has a larger area compared with the other orientations in the grown crystal. The average grain sizes of GSG1 samples S(A) and S(B) (sliced near the seed interface and center of the GSG1) were 1.17 and 1.22 mm, respectively, as shown in Figure 4. The defect distribution in the grown crystals was studied by etching the samples using Wright-Jenkins etchant.32,33 The etching time was 15 min for all the samples. Figure 5a (i) shows a cross-sectional view of the grown crystal; the position of EPD measurement in the vertical direction is indicated by the dotted line. The etch pits were carefully counted in the optical microscope images of the etched sample to calculate the EPD along the growth direction. As shown in Figure 5a (ii), the EPDs were higher at both seed and feed interfaces compared with the center region of the crystal. Figure 5b shows the (i) optical microscope images of GSG1 along the radial direction 2 mm above the seed interface, at the center, and 2 mm below the feed interface. The distribution of EPDs can be clearly seen from the optical microscope image. The EPD slightly increased from periphery (Ph1) to periphery (ph2) because of inhomogeneous radial temperature distribution, possibly originating from misalignment of the ampule with the center axis of the furnace. The twin boundary and grain boundary are indicated by the dotted line in the optical microscope images. The lattice mismatch between Si and Si0.68Ge0.32 (1.3%)

calculated to be 0.001/mm. Because of the cracks generated near the seed and feed interfaces, the Si composition was slightly scattered at the interfaces. The formation of cracks at the seed and feed interfaces was possibly due to the lattice mismatch between Si and the Si0.68Ge0.32 grown crystal. The homogeneous distribution of Si in the GSG1 crystal was further confirmed by EPMA mapping analysis. Figure 2b shows the homogeneous distribution of Si in the crystal. During mapping analysis, the color bar variation shows X-ray counts/second. The Ge-rich residual solution solidified at the periphery region of the feed interface because of the inhomogeneous radial temperature distribution, as indicated by the red arrow line in Figure 2b. Figure 3a (i) and (ii) show cross-sectional views of the GSG2 crystal and Si composition profile along the growth direction in the center region of the crystal. The compositionally homogeneous Si0.68Ge0.32 bulk crystal was grown from seed to feed interface with a length of 10.6 mm, and the Si composition fluctuated near the feed interface because of the solidified residual Ge-rich solution, as shown in Figure 3a (ii). The Si composition gradient was calculated to be 0.005/mm. The homogeneous distribution of Si in the GSG2 crystal was further confirmed by EPMA mapping analysis, as shown in Figure 3b. Moreover, the residual Ge-rich solution was evenly solidified at the feed region compared with previous samples, as indicated by the red arrow line in Figure 3b, because of the improvement in the radial temperature distribution. The grain distribution of the specimen sliced parallel to the growth C


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Figure 3. (a) GSG2 bulk crystal (i) cross-sectional view of grown and (ii) Si composition profile of grown crystal. (b) EPMA mapping of Si composition distribution (the horizontal bar shows the variation of X-ray counts per second).

Figure 4. Orientation and grain size analysis of GSG1 bulk crystal.

A cross-sectional scanning electron microscope (SEM) image (i) and EPD variation of the GSG2 bulk crystal along the growth direction (iii) are shown in Figure 6a. The EPD decreased along the growth direction, and the EPD is low at the feed interfaces in the center region of the crystal. As can be seen from the SEM image of the sample cross section [Figure 6a (i)], no cracks were observed near the feed interface and the shape of the feed interface was more symmetric compared with

generated stresses in the grown crystals. The stresses are released by crack formation during postgrowth cooling of the grown crystals. During the propagation of cracks, large numbers of dislocations were generated around the cracks, as indicated by the solid arrow line. Thus, higher EPD concentrations were observed near the interfaces compared with the center region of the crystal. D


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Figure 5. Etch pit density (EPD) profile of GSG1 crystal along the (a) vertical and (b) radial directions: (i) cross-sectional view of sample and (ii) EPD profile.

the previous sample. This may be due to improvement in the radial temperature distribution during the experiment. Therefore, the Ge-rich residual solution was solidified evenly across the feed interface, unlike the previous sample. As a result, cracks were not generated in the grown crystal near the feed interface and the EPD was lower compared with the previous sample. The EPD was almost evenly maintained along the radial direction in the center region of the crystal because of the homogenization of the radial temperature distribution, as shown in Figure 6b. 3.1. Thermoelectric Properties. The carrier concentrations of the GSG1 and GSG2 bulk crystals were measured at room temperature using the van der Pauw method. To study the carrier concentration variation along the growth direction, the samples were cut within 10 mm of the crack-free region, and the GSG1 bulk crystal was cut perpendicular to the growth direction every 3 mm, as shown in Figure 7a. The cut samples were named S(A), S(B), S(C), and S(D), as shown in Figure 7a. Ohmic contacts were made in the polished samples to measure the carrier concentrations. Table 1 shows the carrier concentration and mobility of the grown crystal every 3 mm

along the growth direction. From the results, it is clear that the carrier concentration was almost the same for the three samples along the growth direction. Moreover, the mobility of the three samples was measured, and the values are nearly identical, as shown in Table 1. The carrier concentration of the GSG2 bulk crystal was measured along the growth direction by cutting the grown sample similarly to the method used for GSG1. The crystal was cut into four parts every 3 mm to study the dopant concentration variation along the growth direction, and samples were named S(a), S(b), S(c), and S(d). The measured carrier concentration and mobility values of these are given in Table 2. It is clear that the carrier concentration and mobility showed little variation from the seed to feed interfaces for all samples. From the GSG1 crystal, four samples were cut for measuring the carrier concentration and mobility. However, samples S(A) and S(D) were broken because of the cracks in the samples. Therefore, the carrier concentrations of S(B) and S(C) of GSG1 and S(b) and S(c) of GSG2 were comparatively analyzed. The carrier concentration of S(B) (8.5 × 1018 cm−3) was lower than that of S(b) (1.2 × 1019 cm−3). E


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Figure 6. Etch pit density (EPD) profile of GSG2 crystal along the (a) vertical and (b) radial directions: (i) cross-sectional view of sample and (ii) EPD profile.

Moreover, the mobility of S(B) (58.6 cm2/V·s) was higher than that of S(b) (46.4 cm2/V·s) because of the high carrier concentrations in the GSG2 sample. However, variations in the carrier concentrations and mobility within each crystal (GSG1 and GSG2) were very small, possibly because of the compositional homogeneity in the grown crystals. This is useful for thermoelectric applications, as all parts of the grown ingot can be used for device fabrication without yield wastages. The rectangular-shaped sample was cut to dimensions of 10 × 4 × 3 mm3 for Seebeck coefficient and electrical resistivity measurements. The electrical resistivities of GSG1 and GSG2 samples increased with temperature, as shown in Figure 7b,c, because of the decrease in mobility at high temperatures. Moreover, the overall resistivity of S(C) was smaller than that of S(B). Sample S(C) was sliced at the center region of the GSG1 crystal where the EPD was low compared with the region that contained sample S(B) (Figure 5), i.e., near the interface. On the other hand, the resistivity of GSG2 crystals decreased from S(a) to S(d), which shows that the resistivity of the crystal decreased along the growth direction. Although the carrier concentration and mobility of the ingot were almost the same as those of GSG1, the electrical resistivity of the samples decreased along the growth direction because of decreasing EPD along the growth direction (Figure 6). It was inferred that low defect density in the crystals led to low electrical resistivity.27 Figure 8 shows a schematic view of phonon and electron transport in the near-seed interface and center region

of the crystal. It is possible that phonon scattering occurs in the EPD region while phonons propagate through the crystal. Because electrons are trapped in the etch pits, the EPD region may act as a recombination center. Thus, electron transport is unfavorable in highly dense etch pit regions in the crystal. Conversely, electron transport is favorable in low-density etch pit regions. Thus, electrical resistivity decreased along the growth direction. Figure 9a,b shows the Seebeck coefficient variations of GSG1 and GSG2 bulk crystals as a function of temperature from 325 to 1100 K. The Seebeck coefficient is positive for both crystals, which indicates the p-type nature of the materials. The Seebeck coefficient increased with increasing temperature, and the maximum values of the Seebeck coefficient for GSG1 and GSG2 samples were 466 μV/K, at 818 K, and 459 μV/K, at 892 K, respectively (Figure 9a,b). The Seebeck coefficients of all samples decreased at higher temperatures as a result of carrier− carrier and carrier−phonon scattering.34 The Seebeck coefficients of GSG1 (346 μV/K) and GSG2 (371 μV/K) at room temperature were higher than the reported value (274 μV/K) for Ga-doped Si0.81Ge0.19.35 Figure 10a,b shows the calculated power factors of GSG1 and GSG2 bulk crystals as a function of temperature. The power factors of S(B) and S(C) were calculated from the measured electrical resistivity and Seebeck coefficient as a function of temperature, and the power factor of S(C) was slightly higher than that of S(B). The relatively high power factor of S(C) was F


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Figure 7. Electrical resistivity as a function of temperature: (a) schematic view of cuts made to the crystals along the growth direction; (b) GSG1; and (c) GSG2.

Table 1. Carrier Concentration and Mobility of GSG1 Bulk Crystal S. no

sample

mobility (cm2/V·s)

carrier concentration (×1018 cm−3)

1 2 3

S (A) S (B) S (C)

62.1 58.6 57.3

8.0 8.5 8.7

Table 2. Carrier Concentration and Mobility of GSG2 Bulk Crystal S. no 1 2 3 4

sample S S S S

(a) (b) (c) (d)

mobility (cm2/V·s)

carrier concentration (×1019 cm−3)

49.2 46.4 48.6 51.7

1.1 1.2 1.1 1.1

Figure 8. Schematic view of phonon and electron transport near the seed interface and in the center region of the crystal.

coefficients at high temperatures. The power factor of the GSG2 crystal (1820 μW m−1 K−2) at room temperature was slightly higher than that of the GSG1 crystal (1440 μW m−1 K−2). The obtained power factors for GSG1 and GSG2 were higher than previously reported values (1416 μW m−1 K−2).35 This may be due to the composition and dopant concentration of the crystal.

due to the low resistivity of the sample, as the resistivity is inversely proportional to the power factor of a material. The power factor of S(d) was relatively higher (1820 μW m−1 k−2) than those of S(a), S(b), and S(c) at 325 K. The low resistivity of sample S(d) causes the highest power factor compared with all other samples. For both GSG1 and GSG2, the power factors remained unchanged from 325 to 900 K. Above 900 K, the power factors decreased because of the decrease in the Seebeck G


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Figure 9. Seebeck coefficient variation as a function of temperature for (a) GSG1 and (b) GSG2.

Figure 10. Power factor as a function of temperature for (a) Ga-doped (1 × 1018 cm−3) Si0.68Ge0.32 and (b) Ga-doped (1 × 1019 cm−3) Si0.68Ge0.32 bulk crystals.

were higher than a previously reported value (1416 μW m−1 K−2).

4. CONCLUSION Compositionally homogeneous Ga-doped Si0.68Ge0.32 bulk crystals were grown under a mild temperature gradient of 0.57 °C/mm with two different doping concentrations, i.e., 1 × 1018 and 1 × 1019 cm−3. The EPD was low at the center region of crystal GSG1 compared with that at the seed and feed interfaces. The high EPD at the interfaces originated from the lattice mismatch between Si and Si0.68Ge0.32 bulk crystal, which caused stress in the grown crystal, inducing defects that are revealed as etch pits around the cracks. The electrical resistivities of the samples varied along the growth direction despite the nearly identical carrier concentrations and mobilities of the samples. The electrical resistivity variation may be due to EPD variations in the crystal, as high EPD was observed where the electrical resistivity was high (near the interface of the GSG1 crystal). The Seebeck coefficient gradually increased with increasing temperature. At high temperatures, the Seebeck coefficient decreased as a result of carrier−carrier and carrier−phonon scattering processes. The Seebeck coefficients of GSG1 (346 μV/K) and GSG2 (371 μV/ K) crystals were higher than the reported value (274 μV/K) for Ga-doped Si0.81Ge0.19 at room temperature. The power factor of the GSG2 crystal (1820 μW m−1 K−2) was slightly higher than that of the GSG1 crystal (1440 μW m−1 K−2) at room temperature. The obtained power factors of GSG1 and GSG2

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AUTHOR INFORMATION

Corresponding Author

*Tel/Fax: +81-053-478-1310. E-mail: [email protected]. jp (Y.H.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Portions of this work were financially supported by the Japan Society for the Promotion of Science and Department of Science and Technology (DST) under the Japan-India Science Cooperative Program (Joint Research Project), the cooperative research project of the Research Institute of Electronics, Shizuoka University, a Grant-in-Aid for Scientific Research (B) (nos. 22360316, 25289270, 25289087), and a Grant-in-Aid for Young Scientist C (no.22760005) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. We also thank the Center for Nanodevice Fabrication and Analysis for use of the EPMA facility.

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REFERENCES

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High Power Factor of Ga-Doped Compositionally Homogeneous Si0

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