Modeling the Charge State of Monatomic Hydrogen and Other Defects with Arbitrary Concentrations in Crystalline Silicon

Abstract

A rigorous physical-mathematical model for predicting the charge states of both mono- and multivalent defects with arbitrary concentrations in Si in both thermal equilibrium and non-equilibrium steady-state conditions is presented. The model avoids the assumption that the defect concentration is much lower than the doping level, which is common in previous approaches. It is shown that the general occupancy ratio given by α = (kn1 + p)/(kn + p1) is still valid under these more general conditions. However, more caution needs to be taken when calculating the equilibrium and excess carrier densities in the presence of larger defect concentrations, because of: a) the non-negligible contribution to n0 and p0 from defect ionisation, and b) unequal Δn and Δp caused by the change in the occupied states at the defect level from equilibrium to non-equilibrium. Modeled examples of monatomic H and interstitial Fe in Si are shown and the effects of defect concentration, temperature, and carrier injection are discussed.