Electron transmission dynamics in Ge<sub>1-<i>x</i></sub>Sn<i><sub>x</sub></i> alloys based on inter-valley electrons transferring effect

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 <i>Γ</i>and <i>L</i> valleys 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 <i>Γ</i>and <i>L</i> valleys in Ge_1-<i>x</i>Sn<i>_x</i> alloys are of paramount importance for understanding the electronic transport and optical properties of Ge_1-<i>x</i>Sn<i>_x</i> material. This letter focuses on the theoretical analysis of inter-valley scattering mechanisms between <i>Γ</i>and <i>L</i> valleys, and hence on the electron transmission dynamics in Ge_1-<i>x</i>Sn<i>_x</i> alloys based on the phenomenological theory model.<br>Firstly, the 30th-order k·p perturbation theory is introduced to reproduce the band structure of Ge_1-<i>x</i>Sn<i>_x</i>. Results show that effective mass of<i>L</i> valley is always about an order of magnitude higher than that of <i>Γ</i>valley, which will significantly influence the electron distributions between <i>Γ</i>and <i>L</i> valleys.<br>Secondly, the scattering mechanism has been modeled in Ge_1-<i>x</i>Sn<i>_x</i> alloys. Results indicate that scattering rate <i>R_ΓL</i> is about an order of magnitude higher than <i>R_LΓ</i>, while <i>R_ΓL</i> decreases with the increase of Sn composition and tends to saturate when Sn component is greater than 0.1. And <i>R_ΓL</i> is almost independent of the Sn component.<br>Thirdly, kinetic processes of carriers between <i>Γ</i>and <i>L</i> valleys have been proposed to analyze the electron transmission dynamics in Ge_1-<i>x</i>Sn<i>_x</i> alloys. Numerical results indicate that the electron population ratio for <i>Γ</i>-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 <i>Γ</i>-valley in indirect-Ge_1-<i>x</i>Sn<i>_x</i> alloys is independent of the injected electron concentration, while the electron population ratio for <i>Γ</i>-valley in direct-Ge_1-<i>x</i>Sn<i>_x</i> alloys is dependent of the injected electron concentration, and the lower the electron concentration, the greater the electron population ratio for <i>Γ</i>-valley.<br>Results open a new way to understanding the mechanisms of electron mobility, electrical transport, and photoelectric conversion in Ge_1-<i>x</i>Sn<i>_x</i> alloys, and can provide theoretical value for the design of Ge_1-<i>x</i>Sn<i>_x</i> alloys in the fields of microelectronics and optoelectronics.