Ge _1-xSn _xalloys 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 Lvalleys in energy can improve the optoelectronic properties of Ge _1-xSn _xalloys due to the significant differences in effective mass within the valleys. Thus inter-valley scattering mechanisms between the Γand Lvalleys in Ge _1-xSn _xalloys are of paramount importance for understanding the electronic transport and optical properties of Ge _1-xSn _xmaterial. This letter focuses on the theoretical analysis of inter-valley scattering mechanisms between Γand Lvalleys, and hence on the electron transmission dynamics in Ge _1-xSn _xalloys based on the phenomenological theory model.
Firstly, the 30th-order k·p perturbation theory is introduced to reproduce the band structure of Ge _1-xSn _x. Results show that effective mass of Lvalley is always about an order of magnitude higher than that of Γvalley, which will significantly influence the electron distributions between Γand Lvalleys.
Secondly, the scattering mechanism has been modeled in Ge _1-xSn _xalloys. Results indicate that scattering rate R_ΓLis about an order of magnitude higher than R_LΓ, while R_ΓLdecreases with the increase of Sn composition and tends to saturate when Sn component is greater than 0.1. And R_ΓLis almost independent of the Sn component.
Thirdly, kinetic processes of carriers between Γand Lvalleys have been proposed to analyze the electron transmission dynamics in Ge _1-xSn _xalloys. 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-Ge _1-xSn _xalloys is independent of the injected electron concentration, while the electron population ratio for Γ-valley in direct-Ge _1-xSn _xalloys 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 Ge _1-xSn _xalloys, and can provide theoretical value for the design of Ge _1-xSn _xalloys in the fields of microelectronics and optoelectronics.