利用密度泛函理論開發高效率矽鍺錫熱電合金

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：61

、訪客IP：3.146.176.214

姓名

林俐玟(Li-Wen Lin) 查詢紙本館藏

畢業系所

化學工程與材料工程學系

論文名稱

利用密度泛函理論開發高效率矽鍺錫熱電合金
(Designing SiGeSn Alloys for Thermoelectric Applications Using Density Functional Theory)

相關論文

★ 使用機器學習決定不鏽鋼耐腐蝕性的關鍵因素	★ 多孔材料的BET表面積測定：限制和改進
★ 二維凡德瓦材料和異質結構中熱傳輸的計算研究	★ 利用密度泛函理論探討鐵合金中間隙元素的影響
★ 使用分子動力學模擬探討甲烷/二氧化碳/氮氣混合水合物的成核與生長	★ 研究多孔材料的孔徑分布：BJH方法的探討與機器學習方法的應用潛力
★ 利用密度泛函理論計算探討元素摻雜對g-C3N4光催化效率的提升

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

隨著綠色能源需求的持續增加，尋找有前景的綠色能源材料至關重要。熱電(TE)材料能夠有效地將廢熱轉換為電能，這不僅可以提高能源利用效率，還能減少對傳統能源資源的依賴。為了評估熱電材料的能量轉換效率，可以通過品質因數(zT)來確認，而提升zT值的方法包括提高Seebeck coefficient、電導率(Electrical conductivity)或降低熱導率(Thermal conductivity)。其中，SiGe合金以其出色的熱電轉換效率著稱，尤其是含有20% Ge的SiGe合金，在高溫熱電應用中表現出色。此外，研究發現，若在SiGe合金中添加Sn，會造成成分無序和晶格變形，導致強烈的非簡諧聲子-聲子散射，從而大幅降低熱導率，使得SiGeSn合金成為一種非常有前景的熱電材料。

本研究使用密度泛函理論(DFT) 探討添加Sn元素於SiGe合金對熱電性質的影響，並找尋具有最佳熱電轉換效率的Si4Ge1Snx合金比例。在保持Si/Ge比例為4的狀況下，通過計算改變了Sn元素組成比例，從0到4，建立了一系列Si4Ge1Snx合金。透過以下這些計算研究了Si4Ge1Snx合金的電子特性，包括Seebeck coefficient、電導率、熱導率和功率因數(Power factor)來評估它們的熱電性能。研究發現，當Sn含量(x)在0到4之間時會表現出n型熱電半導體的特性，且隨著溫度的升高，該合金的zT值也會增加，特別是在1300K的高溫下，Si4Ge1Sn1合金的zT值達到了 2.05，且同時具有優異的機械穩定性和動態穩定性，顯示出Si4Ge1Sn1合金作為熱電材料的應用前景。此外，隨著Sn含量的添加，晶格熱導率降低，但同時保持電導率不變，進一步影響了zT值。另外，隨著溫度升高，電子熱導率的影響變得更加顯著。最後，從研究中可以發現，添加Sn確實可以提升材料的熱電性能，並在Sn含量為1且溫度為1300K時達到最佳效果。然而，當Sn含量超過1時，zT 值會逐漸下降。總結來說，本研究證實了Si4Ge1Sn1合金在熱電材料方面的巨大潛力，特別是作為高溫熱電材料，展示出優異的性能和應用前景。

摘要(英)

With the increasing demand for clean energy sources, finding promising energy alternatives is crucial for society. Thermoelectric (TE) materials offer a green energy solution by enabling the reversible conversion between thermal and electrical energy. The figure of merit (zT) can be used to evaluate the energy conversion efficiency of thermoelectric materials, and methods to enhance zT include increasing the Seebeck coefficient, electrical conductivity, or decreasing thermal conductivity. SiGe alloys, known for their effective waste heat recovery, especially those containing 20% Ge content, exhibit excellent properties for high-temperature TE applications. Moreover, the addition of Sn to SiGe alloys can further reduce thermal conductivity because it causes compositional disorder and lattice distortion, leading to strong anharmonic phonon-phonon scattering. These characteristics make SiGeSn alloys promising candidates for thermoelectric materials.

In this study, density functional theory (DFT) was applied to search for the optimal composition of Si4Ge1Snx alloys for thermoelectric applications. A series of SiGeSn alloys were constructed by varying the composition, with the Sn ratio ranging from 0 to 4 while maintaining the Si/Ge ratio at 4. Electronic characteristics of SiGeSn alloys were calculated, and their thermoelectric properties, including the Seebeck coefficient, electronic conductivity, thermal conductivity, and power factor, were assessed. The conversion efficiency of TE materials was determined using the figure of merit (zT). Compositions with Sn content (x) ranging from 0 to 4 exhibited n-type thermoelectric behavior. Particularly, The Si4Ge1Sn1 alloy is found to have the optimal composition with the highest zT value of 2.05 with excellent mechanical stability, revealing the promising applications of SiGeSn alloys as thermoelectric materials. It is also found that the zT value is mainly determined by their thermal conductivity. In addition, while increasing the Sn content, the lattice thermal conductivity decreases while the electrical conductivity remains unchanged, thereby affecting the zT value. Furthermore, as temperature rises, the contribution of electronic thermal conductivity becomes more significant. Research indicates that with the addition of Sn, the power factor increases and reach to its maximum at x = 1 at temperature of 1300K. However, when the Sn > 1, the zT value gradually declines.This work confirms the significant potential of Si4Ge1Sn1 alloy as thermoelectric materials, particularly for high-temperature applications, showcasing excellent performance and promising prospects.

關鍵字(中)

★ 密度泛函理論
★ 熱電材料
★ 矽鍺錫合金
★ 品質因數
★ 熱導率
★ 半導體

關鍵字(英)

★ DFT
★ thermoelectric material
★ SiGeSn alloys
★ figure of merit
★ thermal conductivity
★ semiconductor

論文目次

摘要i
Abstract iii
Acknowledgement v
Contents vii
List of Figures ix
List of Tables xii
1 Introduction 1
1.1 Thermoelectric materials 1
1.2 Thermoelectric Devices Based on Semiconductors 4
1.3 SiGeSn alloys 7
1.4 Motivation 9
2 Methods and Simulation Settings 11
2.1 Density functional theory 11
2.2 Special quasi-random structure (SQS) modeling 13
2.3 Boltzmann transport equation (BTE) 14
2.4 Phonon dispersion and group velocity 16
2.5 Mechanical properties 17
2.6 Calculations 18
2.6.1 SiGeSn random alloys 18
2.6.2 Calculation settings 20
3 Results and Discussions 22
3.1 Lattice parameters 22
3.2 Formation energy 24
3.3 Band gap 26
3.4 Local density of states (LDOS) 28
3.5 Thermoelectric-related properties of binary alloys 30
3.6 Thermoelectric-related properties of Si4Ge1Snx alloys 33
3.7 Phonon dispersion and group velocity 48
3.8 Mechanical properties 50
4 Conclusion 53
5 Future Work 55
Bibliography 56

參考文獻

1. Koumoto, K. & Mori, T. Thermoelectric Nanomaterials. Materials Design and Applications, Springer
Series in Materials Science 182, 1–382 (2013).
2. Elsheikh, M. H. et al. A review on thermoelectric renewable energy: Principle parameters that
affect their performance. Renewable and Sustainable Energy Reviews 30, 337–355 (2014).
3. Zheng, X., Liu, C., Yan, Y. & Wang, Q. A review of thermoelectrics research–Recent developments
and potentials for sustainable and renewable energy applications. Renewable and Sustainable
Energy Reviews 32, 486–503 (2014).
4. Shu, G. et al. A review of waste heat recovery on two-stroke IC engine aboard ships. Renewable
and Sustainable Energy Reviews 19, 385–401 (2013).
5. Qin, Z., Zhang, H. & Qin, G. A Brief Perspective to the Development of Emerging Thermoelectric
Materials 2022.
6. Snyder, G. J. & Snyder, A. H. Figure of merit zT of a thermoelectric device defined from materials
properties. Energy & Environmental Science 10, 2280–2283 (2017).
7. Arivazhagan, N., Singh, S., Prakash, S. & Reddy, G. Investigation on AISI 304 austenitic stainless
steel to AISI 4140 low alloy steel dissimilar joints by gas tungsten arc, electron beam and friction
welding. Materials & Design 32, 3036–3050 (2011).
8. Snyder, G. J. & Toberer, E. S. Complex thermoelectric materials. Nature Materials 7, 105–114
(2008).
9. Zhao, L.-D., Dravid, V. P. & Kanatzidis, M. G. The panoscopic approach to high performance
thermoelectrics. Energy & Environmental Science 7, 251–268 (2014).
10. Shakouri, A. Recent developments in semiconductor thermoelectric physics and materials. Annual
Review of Materials Research 41, 399–431 (2011).
11. Possanzini, C. et al. Diffusion thermopower of a two-dimensional hole gas in SiGe in a quantum
Hall insulating state. Physical Review Letters 90, 176601 (2003).
12. Garg, J., Bonini, N., Kozinsky, B. & Marzari, N. Role of disorder and anharmonicity in the thermal
conductivity of silicon-germanium alloys: A first-principles study. Physical Review Letters 106,
045901 (2011).
13. Shi, H., Parker, D., Du, M.-H. & Singh, D. J. Connecting thermoelectric performance and topologicalinsulator
behavior: Bi2Te3 andBi2Te2Se from first principles. Physical Review Applied 3, 014004
(2015).
14. Li, G. et al. Superstrengthening Bi2Te3 through Nanotwinning. Physical Review Letters 119,
085501 (2017).
15. Skelton, J. M. et al. Anharmonicity in the High-Temperature Cmcm Phase of SnSe: Soft Modes
and Three-Phonon Interactions. Physical Review Letters 117, 075502 (2016).
16. Aseginolaza, U. et al. Phonon collapse and second-order phase transition in thermoelectric SnSe.
Physical Review Letters 122, 075901 (2019).
17. Nishimura, T. et al. Large enhancement of thermoelectric efficiency due to a pressure-induced
lifshitz transition in SnSe. Physical Review Letters 122, 226601 (2019).
18. Dusastre, V. Materials for sustainable energy: a collection of peer-reviewed research and review
articles from Nature Publishing Group (World Scientific, 2010).
19. Johnsen, S. et al. Nanostructures boost the thermoelectric performance of PbS. Journal of the
American Chemical Society 133, 3460–3470 (2011).
20. Dusetty, V. Numerical Simulation of Thermoelectric Transport in Bulk and Nanostructured SiSn
Alloys (2020).
21. Newman, R. A review of the growth and structure of thin films of germanium and silicon. Microelectronics
Reliability 3, 121–138 (1964).
22. Balk, P. Surface Properties of Oxidized Germanium-Doped Silicon. Journal of the Electrochemical
Society 118, 494 (1971).
23. Steele, M. & Rosi, F. Thermal conductivity and thermoelectric power of Germanium-Silicon alloys.
Journal of Applied Physics 29, 1517–1520 (1958).
24. He, R. et al. Thermoelectric properties of silicon and recycled silicon sawing waste. Journal of
Materiomics 5, 15–33 (2019).
25. Basu, R. & Singh, A. High temperature Si-Ge alloy towards thermoelectric applications: A comprehensive
review. Materials Today Physics 21, 100468 (2021).
26. Lee, H. et al. Effects of nanoscale porosity on thermoelectric properties of SiGe. Journal of Applied
Physics 107 (2010).
27. Bhandari, C. & Rowe, D. Boundary scattering of phonons. Journal of Physics C: Solid State
Physics 11, 1787 (1978).
28. Savvides, N. & Rowe, D. Altering the thermal conductivity of phosphorus-doped Si-Ge alloys by
the precipitation of dopant. Journal of Physics D: Applied Physics 15, 299 (1982).
29. Perez-Taborda, J. A., Muñoz Rojo, M., Maiz, J., Neophytou, N. & Martin-Gonzalez, M. Ultra-low
thermal conductivities in large-area Si-Ge nanomeshes for thermoelectric applications. Scientific
Reports 6, 32778 (2016).
30. Lee, Y., Pak, A. J. & Hwang, G. S. What is the thermal conductivity limit of silicon germanium
alloys? Physical Chemistry Chemical Physics 18, 19544–19548 (2016).
31. Ravindra, N. et al. Thermoelectric Properties of Silicon-Germanium Alloys. Thermoelectrics:
Fundamentals, Materials Selection, Properties, and Performance, 49–67 (2019).
32. D’costa, V. R. et al. Optical critical points of thin-film Ge1 – ySny alloys: a comparative Ge1 – ySny/Ge1 – xSix
study. Physical Review B 73, 125207 (2006).
33. Moontragoon, P. et al. Electronic properties calculation of Ge1 – x – ySixSny ternary alloy and nanostructure.
Journal of Non-Crystalline Solids 358, 2096–2098 (2012).
34. Soref, R. A. & Perry, C. H. Predicted band gap of the new semiconductor SiGeSn. Journal of
Applied Physics 69, 539–541 (1991).
35. Basu, R. et al. Improved thermoelectric performance of hot pressed nanostructured n-type SiGe
bulk alloys. Journal of Materials Chemistry A 2, 6922–6930 (2014).
36. Rowe, D., Shukla, V. & Savvides, N. Phonon scattering at grain boundaries in heavily doped
fine-grained silicon–germanium alloys. Nature 290, 765–766 (1981).
37. Lee, Y. & Hwang, G. S. Molecular dynamics investigation of the thermal conductivity of ternary
silicon-germanium-tin alloys. Journal of Physics D: Applied Physics 50, 494001 (2017).
38. Moontragoon, P., Ikonić, Z. & Harrison, P. Band structure calculations of Si-Ge-Sn alloys: achieving
direct band gap materials. Semiconductor science and technology 22, 742 (2007).
39. Wang, D., Liu, L., Chen, M. & Zhuang, H. Electrical and thermal transport properties of mediumentropy
SiyGeySnx alloys. Acta Materialia 199, 443–452 (2020).
40. Hahn, K. R., Melis, C., Bernardini, F. & Colombo, L. Intrinsic thermoelectric figure of merit of
bulk compositional SiGe alloys: A first-principles study. Physical Review Materials 5, 065403
(2021).
41. Madsen, G. K., Carrete, J. & Verstraete, M. J. BoltzTraP2, a program for interpolating band structures
and calculating semi-classical transport coefficients. Computer Physics Communications
231, 140–145 (2018).
42. Kestyn, J. & Polizzi, E. From Fundamental First-Principle Calculations to Nanoengineering Applications:
A Review of the NESSIE Project. IEEE Nanotechnology Magazine 14, 52–C3 (2020).
43. Dirac, P. A. M. Quantum mechanics of many-electron systems. Proceedings of the Royal Society
of London. Series A, Containing Papers of a Mathematical and Physical Character 123, 714–733
(1929).
44. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Physical Review 136, B864 (1964).
45. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects.
Physical Review 140, A1133 (1965).
46. Sholl, D. S. & Steckel, J. A. Density functional theory: a practical introduction (John Wiley &
Sons, 2022).
47. Mattsson, A. E., Schultz, P. A., Desjarlais, M. P., Mattsson, T. R. & Leung, K. Designing meaningful
density functional theory calculations in materials science—a primer. Modelling and Simulation
in Materials Science and Engineering 13, R1 (2004).
48. Simón, L. & Goodman, J. M. How reliable are DFT transition structures? Comparison of GGA,
hybrid-meta-GGA and meta-GGA functionals. Organic & Biomolecular Chemistry 9, 689–700
(2011).
49. Lin, I.-C., Seitsonen, A. P., Tavernelli, I. & Rothlisberger, U. Structure and Dynamics of Liquid
Water from ab Initio Molecular Dynamics Comparison of BLYP, PBE, and revPBE Density Functionals
with and without van der Waals Corrections. Journal of Chemical Theory and Computation
8, 3902–3910 (2012).
50. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations
using a plane-wave basis set. Physical Review B 54, 11169 (1996).
51. Van de Walle, A. et al. Efficient stochastic generation of special quasirandom structures. Calphad
42, 13–18 (2013).
52. Zunger, A., Wei, S.-H., Ferreira, L. & Bernard, J. E. Special quasirandom structures. Physical
Review Letters 65, 353 (1990).
53. Hass, K., Davis, L. & Zunger, A. Electronic structure of random Al0.5Ga0.5 As alloys: Test of the
‘‘special-quasirandom-structures’’description. Physical Review B 42, 3757 (1990).
54. Shin, D., Arróyave, R., Liu, Z.-K. & Van de Walle, A. Thermodynamic properties of binary hcp
solution phases from special quasirandom structures. Physical Review B 74, 024204 (2006).
55. Shin, D., Van De Walle, A., Wang, Y. & Liu, Z.-K. First-principles study of ternary fcc solution
phases from special quasirandom structures. Physical Review B 76, 144204 (2007).
56. Van de Walle, A., Ceder, G. & Waghmare, U. First-principles computation of the vibrational entropy
of ordered and disordered Ni3Al. Physical Review Letters 80, 4911 (1998).
57. Shin, D. & Liu, Z.-K. Enthalpy of mixing for ternary fcc solid solutions from special quasirandom
structures. Calphad 32, 74–81 (2008).
58. Jiang, C., Stanek, C., Sickafus, K. & Uberuaga, B. First-principles prediction of disordering tendencies
in pyrochlore oxides. Physical Review B 79, 104203 (2009).
59. Van De Walle, A. Multicomponent multisublattice alloys, nonconfigurational entropy and other
additions to the Alloy Theoretic Automated Toolkit. Calphad 33, 266–278 (2009).
60. Singh, D. J. & Du, M.-H. Density functional study of LaFeAsO1 – xFx: a low carrier density superconductor
near itinerant magnetism. Physical Review Letters 100, 237003 (2008).
61. May, A. F., Singh, D. J. & Snyder, G. J. Influence of band structure on the large thermoelectric
performance of lanthanum telluride. Physical Review B 79, 153101 (2009).
62. Ouardi, S. et al. Electronic transport properties of electron-and hole-doped semiconducting C1b
Heusler compounds: NiTi1 – xMxSn(M––
Sc, V). Physical Review B 82, 085108 (2010).
63. Parker, D., Chen, X. & Singh, D. J. High three-dimensional thermoelectric performance from
low-dimensional bands. Physical Review Letters 110, 146601 (2013).
64. Hong, A. et al. Full-scale computation for all the thermoelectric property parameters of half-
Heusler compounds. Scientific Reports 6, 22778 (2016).
65. He, J. et al. Ultralow thermal conductivity in full Heusler semiconductors. Physical Review Letters
117, 046602 (2016).
66. Zhang, J. et al. Designing high-performance layered thermoelectric materials through orbital engineering.
Nature Communications 7, 10892 (2016).
67. Ho, C. & Powell, R. u. Liley, PE: Thermal Conductivity of the Elements: A Comprehensive Review.
Journal of Physical and Chemical Reference Data 3 (1974).
68. Khatami, S. & Aksamija, Z. Lattice thermal conductivity of the binary and ternary group-IV alloys
Si-Sn, Ge-Sn, and Si-Ge-Sn. Physical Review Applied 6, 014015 (2016).
69. Togo, A., Chaput, L., Tadano, T. & Tanaka, I. Implementation strategies in phonopy and phono3py.
J. Phys. Condens. Matter 35, 353001 (2023).
70. Togo, A. First-principles Phonon Calculations with Phonopy and Phono3py. J. Phys. Soc. Jpn. 92,
012001 (2023).
71. Hill, R. The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society.
Section A 65, 349 (1952).
72. Voigt, W. Lehrbuch der kristallphysik:(mit ausschluss der kristalloptik) (BG Teubner, 1910).
73. Reuss, A. Mittelung von Fließgrenze und elastischen Eigenschaften. Z. angew. Math. Mech. Bd 9,
49 (1929).
74. Marmier, A. et al. ElAM: A computer program for the analysis and representation of anisotropic
elastic properties. Computer Physics Communications 181, 2102–2115 (2010).
75. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Physical
Review Letters 77, 3865 (1996).
76. Perdew, J. P. Density functional theory and the band gap problem. International Journal of Quantum
Chemistry 28, 497–523 (1985).
77. Tran, F. & Blaha, P. Accurate band gaps of semiconductors and insulators with a semilocal exchangecorrelation
potential. Physical Review Letters 102, 226401 (2009).
78. Molski, K. & Glinka, G. A method of elastic-plastic stress and strain calculation at a notch root.
Materials Science and Engineering 50, 93–100 (1981).
79. Madsen, G. K. & Singh, D. J. BoltzTraP. A code for calculating band-structure dependent quantities.
Computer Physics Communications 175, 67–71 (2006).
80. Hao, S., Dravid, V. P., Kanatzidis, M. G. & Wolverton, C. Research Update: Prediction of high
figure of merit plateau in SnS and solid solution of (Pb, Sn) S. Apl Materials 4 (2016).
81. Zhou, J.-J. & Bernardi, M. Ab initio electron mobility and polar phonon scattering in GaAs. Physical
Review B 94, 201201 (2016).
82. Ding, G., Gao, G. & Yao, K. High-efficient thermoelectric materials: The case of orthorhombic
IV-VI compounds. Scientific reports 5, 9567 (2015).
83. Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scripta Materialia
108, 1–5 (2015).
84. Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and
morphology data. Journal of Applied Crystallography 44, 1272–1276 (2011).
85. Windl, W. & Chien, S.-C. Free-Energy Parameterization and Thermodynamics in Si–Ge–Sn
Alloys. Physica Status Solidi (b) 259, 2100590. eprint: https://onlinelibrary.wiley.com/doi/pdf/
10.1002/pssb.202100590. https://onlinelibrary.wiley.com/doi/abs/10.1002/pssb.202100590
(2022).
86. Holland, M. Analysis of lattice thermal conductivity. Physical review 132, 2461 (1963).
87. Dorner, F., Sukurma, Z., Dellago, C. & Kresse, G. Melting Si: beyond density functional theory.
Physical Review Letters 121, 195701 (2018).
88. Domenicali, C. Thermoelectric Power and Resistivity of Solid and Liquid Germanium in the Vicinity
of Its Melting Point. Journal of Applied Physics 28, 749–753 (1957).
89. Fraizier, E., Nadal, M.-H. & Oltra, R. Noncontact determination of the elastic moduli of β-Sn up
and through the melting point. Journal of Applied Physics 93, 649–654 (2003).
90. Shimura, Y., Okado, M., Motofuji, T. & Tatsuoka, H. SiSn mediated formation of polycrystalline
SiGeSn. Japanese Journal of Applied Physics 61, SC1008 (2022).
91. Peng, Y. et al. Realizing high thermoelectric performance in p-type Si1 – x – yGexSny thin films at
ambient temperature by Sn modulation doping. Applied Physics Letters 117 (2020).
92. Tomita, M., Ogasawara, M., Terada, T. & Watanabe, T. Development of interatomic potential of
Ge(1−x−y)SixSny ternary alloy semiconductors for classical lattice dynamics simulation. Japanese
Journal of Applied Physics 57, 04FB04. https://dx.doi.org/10.7567/JJAP.57.04FB04 (Mar. 2018).
93. Togo, A., Chaput, L. & Tanaka, I. Distributions of phonon lifetimes in Brillouin zones. Phys. Rev.
B 91, 094306 (9 Mar. 2015).
94. Sajjad, M., Mahmood, Q., Singh, N. & Larsson, J. A. Ultralow Lattice Thermal Conductivity in
Double Perovskite Cs2PtI6: A Promising Thermoelectric Material. ACS Applied Energy Materials
3, 11293–11299. eprint: https://doi.org/10.1021/acsaem.0c02236. https://doi.org/10.1021/acsaem.
0c02236 (2020).
95. Mouhat, F. & Coudert, F.-X. Necessary and sufficient elastic stability conditions in various crystal
systems. Physical Review B 90, 224104 (2014).
96. McSkimin, H. Measurement of elastic constants at low temperatures by means of ultrasonic waves–
data for silicon and germanium single crystals, and for fused silica. Journal of Applied Physics
24, 988–997 (1953).
97. McSkimin, H. & Andreatch Jr, P. Elastic moduli of silicon vs hydrostatic pressure at 25.0˚C and-
195.8˚C. Journal of Applied Physics 35, 2161–2165 (1964).
98. Kang, K. & Cai, W. Brittle and ductile fracture of semiconductor nanowires–molecular dynamics
simulations. Philosophical Magazine 87, 2169–2189 (2007).
99. Wortman, J. & Evans, R. Young’s modulus, shear modulus, and Poisson’s ratio in silicon and
germanium. Journal of Applied Physics 36, 153–156 (1965).
100. Murugasami, R., Vivekanandhan, P., Kumaran, S., Tharakan, J., et al. Synergetic enhancement of
thermoelectric and mechanical properties of n-type SiGe-P alloy through solid state synthesis and
spark plasma sintering. Materials Research Bulletin 118, 110483 (2019).

指導教授

簡思佳(Szu-Chia Chien)

審核日期

2024-8-14

推文