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Ge1–xSnx alloys have aroused great interest in silicon photonics because of their compatiblity with complementary metal-oxide-semiconductor (CMOS) technology. As a result, they are considered potential candidate materials. Owing to the significant differences in effective mass within the valleys, the unique dual-valley structure of Γ valley and L valley in energy can improve the optoelectronic properties of Ge1-xSnx alloys. Therefore, inter-valley scattering mechanisms between the Γ and L valley in Ge1–xSnx alloys are crucial for understanding the electronic transports and optical properties of Ge1–xSnx materials. This work focuses on the theoretical analysis of inter-valley scattering mechanisms between Γ and L valley, and hence on the electron transmission dynamics in Ge1–xSnx alloys based on the phenomenological theory model. Firstly, the 30th-order k·p perturbation theory is introduced to reproduce the band structure of Ge1–xSnx. The results show that the effective mass of L valley is always about an order of magnitude higher than that of Γ valley, which will significantly influence the electron distributions between Γ and L valley. Secondly, the scattering mechanism is modeled in Ge1–xSnx alloys. The results indicate that scattering rate RΓL is about an order of magnitude higher than RLΓ, while RΓL decreases with the increase of Sn composition and tends to saturate when Sn component is greater than 0.1. And RΓL is almost independent of the Sn component. Thirdly, kinetic processes of carriers between Γ and L valley are proposed to analyze the electron transmission dynamics in Ge1–xSnx alloys. Numerical results indicate that the electron population ratio for Γ-valley increases and then tends to saturation with the increase of Sn composition, and is independent of the injected electron concentration. The model without the scattering mechanism indicates that the electron population ratio for Γ-valley in indirect-Ge1–xSnx alloys is independent of the injected electron concentration, while the electron population ratio for Γ-valley in direct-Ge1–xSnx alloys is dependent on the injected electron concentration, and the lower the electron concentration, the greater the electron population ratio for Γ-valley is. The results open a new way of understanding the mechanisms of electron mobility, electrical transport, and photoelectric conversion in Ge1–xSnx alloys, and can provide theoretical value for designing Ge1–xSnx alloys in the fields of microelectronics and optoelectronics. -
图 1 Ge1–xSnx材料的能带参数 (a) Γ能谷与L能谷的能量差值与Sn组分之间的关系; (b)导带电子状态密度与Sn组分之间的关系
Figure 1. Parameters of Ge1–xSnx: (a) The energy difference of Γ and L valley and (b) the parameters for electron density of states (DOS) effective masses at Γ and L valley extracted from 30-band k ⋅ p mode in Ge1–xSnx.
图 2 Ge1–xSnx材料的谷间散射率 (a) Γ能谷到L能谷的散射率与能量的关系; (b) L能谷到Γ能谷的散射率与能量的关系
Figure 2. Inter-valley scattering rate (a) from Γ to L valleys and (b) from L to Γ valley with different Sn compositions.
图 3 谷间散射率与注入电子之间的关系 (a) Γ能谷到L能谷的谷间散射率; (b) L能谷到Γ能谷的散射率
Figure 3. Relationship between inter-valley scattering rate and inject electron density with different Sn compositions: (a) From Γ to L valleys scattering; (b) from L to Γ valley scattering.
图 4 谷间光学声子散射率与Sn组分之间的关系
Figure 4. Inter-valley scattering rate from Γ to L valleys scattering and from L to Γ valley scattering under different Sn compositions.
图 5 Ge1–xSnx材料注入电子浓度与电子转移时间的关系(对数坐标), 插图为线性坐标
Figure 5. Relationship between electron transmission time and electron density in Γ, L valleys with various Sn compositions, the inset shows as a linear scale.
图 6 散射时间常数与Sn组分的关系
Figure 6. Relationship between composition and time-delay.
图 7 考虑与不考虑散射模型的情况下, Γ能谷、L能谷电子填充率与Sn组分的关系
Figure 7. Simulated electron population ratio for Γ and L valleys as a function of Sn compositions, with and without the scattering model.
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[1] Miao Y H, Wang G L, Kong Z Z, Xu B Q, Zhao X W, Luo X, Lin H X, Dong Y, Lu B, Dong L P, Zhou J R, Liu J B, Radamson H H 2021 Nanomaterials 11 2556
Google Scholar
[2] Oka H, Mizubayashi W, Ishikawa Y, Uchida N, Mori T, Endo K 2021 Appl. Phys. Express 14 096501
Google Scholar
[3] Zhang D, Song J J, Xue X X, Zhang S Q 2022 Chin. Phys. B 31 068401
Google Scholar
[4] Wang H J, Han G Q, Jiang X W, Liu Y, Zhang J C, Hao Y 2019 IEEE Trans. Electron Devices 66 1985
Google Scholar
[5] Wang P C, Huang P R, Ghosh S, Bansal R, Jheng Y T, Lee K C, Cheng H H, Chang G E 2024 ACS Photonics 11 2659
Google Scholar
[6] Reboud V, Concepción O, Du W, El Kurdi M, Hartmann J M, Ikonic Z, Assali S, Pauc N, Calvo V, Cardoux C, Kroemer E, Coudurier N, Rodriguez P, Yu S Q, Buca D, Chelnokov A 2024 Photon. Nanostruc. Fundam. Appl. 58 101233
Google Scholar
[7] Zheng J, Liu Z, Xue C L, Li C B, Zuo Y H, Cheng B W, Wang Q M 2018 J. Semicond. 39 061006
Google Scholar
[8] Zhou Y Y, Dou W, Du W, Pham T, Ghetmiri S A, Al-Kabi S, Mosleh A, Alher M, Margetis J, Tolle J, Sun G, Soref R, Li B, Mortazavi M, Naseem H, Yu S Q 2016 J. Appl. Phys. 120 023102
Google Scholar
[9] Ghetmiri S A, Du W, Margetis J, Mosleh A, Cousar L, Conley B R, LucasDomulevicz, Nazzal A, Sun G, Soref R A, Tolle J, Li B, Naseem H A, Yu S Q 2014 Appl. Phys. Lett. 105 151109
Google Scholar
[10] Wirths S, Geiger R, von den Driesch N, Mussler G, Stoica T, Mantl S, Ikonic Z, Luysberg M, Chiussi S, Hartmann J M, Sigg H, Faist J, Buca D, Grützmacher D 2015 Nat. Photonics 9 88
Google Scholar
[11] Arakawa Y, Nakamura T, Urino Y, Fujita T 2013 IEEE Commun. Mag. 51 72
[12] Wu S T, Zhang L, Wan R Q, Zhou H, Lee K H, Chen Q M, Huang Y C, Gong X, Tan C S 2023 Photonics Res. 11 1606
Google Scholar
[13] Liu X Q, Zhang J, Niu C Q, Liu T R, Huang Q X, Li M M, Zhang D D, Pang Y Q, Liu Z, Zuo Y H, Cheng B W 2022 Photonics Res. 10 1567
Google Scholar
[14] Ghosh S, Sun G, Yu S Q, Chang G E 2025 IEEE J. Sel. Top. Quantum Electron. 31 1
[15] 黄诗浩, 谢文明, 汪涵聪, 林光杨, 王佳琪, 黄巍, 李成 2018 物理学报 67 040501
Google Scholar
Huang S H, Xie W M, Wang H C, Lin G Y, Wang J Q, Huang W, Li C 2018 Acta Phys. Sin. 67 040501
Google Scholar
[16] Huang S H, Zheng Q Q, Xie W M, Lin J Y, Huang W, Li C, Qi D F 2018 J. Phys. Condens. Matter 30 465701
Google Scholar
[17] Murphy-Armando F, Murray É D, Savić I, Trigo M, Reis D A, Fahy S 2023 Appl. Phys. Lett. 122 012202
Google Scholar
[18] Wang C, Wang H, Chen W, Xie X, Zong J, Liu L, Jin S, Zhang Y, Yu F, Meng Q, Tian Q, Wang L, Ren W, Li F, Zhang H, Zhang Y 2021 Nano Lett. 21 8258
Google Scholar
[19] Stern M J, René de Cotret L P, Otto M R, Chatelain R P, Boisvert J P, Sutton M, Siwick B J 2018 Phys. Rev. B 97 165416
Google Scholar
[20] Huang P, Zhang Y, Hu K, Qi J, Zhang D, Cheng L 2024 Chin. Phys. B 33 017201
Google Scholar
[21] Rogowicz E, Kopaczek J, Kutrowska-Girzycka J, Myronov M, Kudrawiec R, Syperek M 2021 ACS Appl. Electron. Mater. 3 344
Google Scholar
[22] Rideau D, Feraille M, Ciampolini L, Minondo M, Tavernier C, Jaouen H, Ghetti A 2006 Phys. Rev. B 74 195208
Google Scholar
[23] Song Z, Fan W, Tan C S, Wang Q, Nam D, Zhang D H, Sun G 2019 New J. Phys. 21 073037
Google Scholar
[24] Lever L, Ikonić Z, Valavanis A, Kelsall R W, Myronov M, Leadley D R, Hu Y, Owens N, Gardes F Y, Reed G T 2012 J. Appl. Phys. 112 123105
Google Scholar
[25] Liu S Q, Yen S T 2019 J. Appl. Phys. 125 245701
Google Scholar
[26] Wang X, Li H, Camacho-Aguilera R, Cai Y, Kimerling L C, Michel J, Liu J 2013 Opt. Lett. 38 652
Google Scholar
[27] Claussen S A, Tasyurek E, Roth J E, Miller D A B 2010 Opt. Express 18 25596
Google Scholar
[28] Zhou X Q, van Driel H M, Mak G 1994 Phys. Rev. B 50 5226
Google Scholar
[29] Mak G, van Driel H M 1994 Phys. Rev. B 49 16817
Google Scholar
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