Impact ionization of excitons in Ge and Si

A charged free carrier in an applied electric field may pick up enough energy from the field to allow it to impact ionize an excition. For this to occur, the carrier must have an energy greater than the exciton binding energy. At low temperatures ($T\lesssim 10°$K in Ge and $T\lesssim 30°$K in Si) and modest electric fields ($E\sim 2$ V/cm in pure Ge and $E\sim 20$ V/cm in pure Si), the energy of a significant number of carriers exceed this threshold energy. Once this happens, the impact-ionization process can change the relative concentration of excitons and free carriers; the equilibrium law of mass action is no longer satisfied. Calculations of exciton concentration (for fixed carrier concentration) as a function of temperature and applied-field strength show that a sudden drop in exciton concentration occurs when electric fields exceed a temperature-dependent critical field.