Simulation of spontaneous emission spectrum of degenerate Ge under large injection level

Abstract

Germanium (Ge) is considered as a promising material for silicon (Si) based light source. Based on tensile strain and n-type heavy doping approaches, the light emitting efficiency of Ge can be improved. Nevertheless, due to the difficulty in introducing large tensile strain into Ge, the photoluminescence or electroluminescence of Ge is demonstrated under degenerated states currently. Traditional spontaneous emission (SE) theory deduced from Boltzmann approximation is inapplicable for this case. To accurately analyze the SE properties of Ge, the influences of strain, temperature and doping on quasi-Fermi level and subsequent SE spectrum of degenerated Ge are theoretically investigated based on Fermi-Dirac distribution model. Owing to large density of states (DOS) in heavy hole (hh) the valance band (VB) and L valley, it is found that compressive strain has a negligible effect on the quasi-Fermi level under carrier concentration of 1019-1020 cm-3, while tensile strain is of benefit to the improvement of carrier occupation levels, leading to dramatic increases of both peak and integrated intensities of SE spectra. Although the peak intensity of SE from -hh transition is larger than that from -1h transition regardless of strain levels in Ge, the integrated intensities of SE from -hh and -1h transitions are almost equal. With the increase of sample temperature, the carriers acquire lager kinetic energy, resulting in more dispersive distribution of electrons (holes) in valley (VB). However, more electrons (holes) are induced into conduction (valence) band at the same time. And according to Varshini's law the energy difference between and L valleys is reduced at higher temperature. Thus, both the peak and integrated intensities of the SE spectra become larger at higher temperature. It is impressive that n-type doping can greatly enhance the SE intensity compared with p-type doping irrespective of strain levels in Ge, demonstrating the significance of n-type doping in the enhancement of Ge SE. Furthermore, it is found that m factors, which can be extracted from linear fitting of log L-log n curves, diminish at heavier doping concentration. Under tensile strain condition, the variation of m factors for Ge SE with the sample temperature becomes less sensitive, implying that the tensile strain can effectively enhance the temperature stability of Ge SE. These results provide a significant guidance for analyzing the SE properties of degenerated Ge and other degenerated semiconductors.