Lattice scattering in n-type Ge-on-Si based on the unique dual-valley transitions

Silicon-based light emitting materials and devices with high efficiency are inarguably the most challenging elements in silicon (Si) photonics. Band-gap engineering approaches, including tensile strain and n-type doping, utilized for tuning germanium (Ge) to an optical gain medium have the potential for realizing monolithic optoelectronic integrated circuit. While previous experimental research has greatly contributed to optical gain and lasing of Ge direct-gap, many efforts were made to reduce lasing threshold, including the understanding of high efficiency luminescence mechanism with tensile strain and n-type doping in Ge. This paper focuses on the theoretical analysis of lattice scattering in n-type Ge-on-Si material based on its unique dual-valley transition for further improving the efficiency luminescence of Ge direct-gap laser. Lattice scattering of carriers, including inter-valley and intra-valley scattering, influence the electron distribution between the direct valley and indirect L valleys in the conduction of n-type Ge-on-Si material. This behavior can be described by theoretical model of quantum mechanics such as perturbation theory. In this paper, the lattice scatterings of intra-valley scattering in valley and L valleys, and of inter-valley scattering between the direct valley and L valleys in the n-type Ge-on-Si materials are exhibited based on its unique dual-valley transition by perturbation theory. The calculated average scattering times for phonon scattering in the cases of valley and L valleys, and for inter-valley optical phonon scattering between valley and L valleys are in agreement with experimental results, which are of significance for understanding the lattice scattering mechanism in the n-type Ge-on-Si material. The numerical calculations show that the disadvantaged inter-valley scattering of electrons from the direct valley to indirect L valleys reduces the electrons dwelling in the direct valley slightly with n-type doping concentration, while the strong inter-valley scattering from the indirect L valleys to indirect valleys increases electrons dwelling in the direct valley with n-type doping concentration. The competition between the two factors leads to an increasing electrons dwelling in the direct valley with n-type doping in a range from 1017 cm-3 to 1019 cm-3. That the electrons in the indirect L valleys are transited into the direct valley by absorbing inter-valley optical phonon modes is one of the effective ways to enhance the efficiency luminescence of Ge direct-gap laser. The results indicate that a low-threshold Ge-on-Si laser can be further improved by engineering the inter-valley scattering for enhancing the electrons dwelling in the valley.