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Ge1-xSnxalloys have attracted great interest as a possible candidate for silicon photonics by its compatible with complementary metal-oxide-semiconductor (CMOS) technology. The unique dual-valley structure of Γand L valleys in energy can improve the optoelectronic properties of Ge1-xSnxalloys due to the significant differences in effective mass within the valleys. Thus inter-valley scattering mechanisms between the Γand L valleys in Ge1-xSnx alloys are of paramount importance for understanding the electronic transport and optical properties of Ge1-xSnx material. This letter focuses on the theoretical analysis of inter-valley scattering mechanisms between Γand L valleys, 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. Results show that effective mass ofL valley is always about an order of magnitude higher than that of Γvalley, which will significantly influence the electron distributions between Γand L valleys.
Secondly, the scattering mechanism has been modeled in Ge1-xSnx alloys. 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 Γand L valleys have been 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 of the injected electron concentration, and the lower the electron concentration, the greater the electron population ratio for Γ-valley.
Results open a new way to understanding the mechanisms of electron mobility, electrical transport, and photoelectric conversion in Ge1-xSnx alloys, and can provide theoretical value for the design of Ge1-xSnx alloys in the fields of microelectronics and optoelectronics. -
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