Monte Carlo study of the statistics of electron capture by shallow donors in silicon at low temperatures

A statistical study of electron capture by shallow donors in silicon without an electric field as a function of temperature and impurity concentration is presented. The Monte Carlo calculations (based on the cascade capture theory) of the times spent by carriers in the conduction band before falling into impurity centers (i.e., the capture times) show evidence of nonexponential capture kinetics behavior. This work has allowed us to interpret the slow time decay of the distributions of capture times as the capture time actually measured in experiments. We have achieved very good agreement between the capture cross sections calculated by our Monte Carlo simulation with the experimental ones and with a previous analytical model that provides asymptotic behaviors of the thermal capture cross section.