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谷间电子散射机制对锗锡材料的电子输运及光电性能的影响至关重要. 本文构建了锗锡材料Γ和L能谷之间的谷间光学声子散射模型, 研究其谷间电子转移效应. 结果表明: 散射率RΓL高于RLΓ约一个数量级, 同时RΓL随Sn组分的增加而减小, 并在Sn组分大于0.1时趋于饱和; 而RLΓ几乎与Sn组分无关. 谷间电子转移模型表明, Γ能谷电子填充率随Sn组分的增大呈现先增大后趋于饱和的规律, 且与注入电子浓度关系不大. 不考虑散射模型时, 间接带Ge1–xSnx材料Γ能谷电子填充率与注入电子浓度关系不大; 直接带Ge1–xSnx材料Γ能谷电子填充率与注入电子浓度相关, 且电子浓度越低, Γ能谷电子填充率越大. 研究成果有助于理解锗锡材料的电子迁移率、电输运和光电转换等微观机制, 可为锗锡材料在微电子和光电子等领域提供理论参考价值.
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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 5. Relationship between electron transmission time and electron density in Γ, L valleys with various Sn compositions, the inset shows as a linear scale.
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