Doping dependence of self-diffusion in germanium and the charge states of vacancies

Self-diffusion in boron-doped germanium has been studied at temperatures between 526 and 749 degrees C with secondary ion mass spectrometry. Self-diffusion under acceptor doping is retarded compared to intrinsic conditions. This demonstrates the contribution of charged vacancies in self-diffusion. Taking into account the dominance of doubly negatively charged vacancies under donor doping, the doping dependence of self-diffusion is best described with an inverse level ordering for singly and doubly negatively charged vacancies for all doping conditions. The level ordering explains the dominance of doubly charged vacancies under donor doping and their decreasing contribution with increasing acceptor doping until neutral vacancies mediate self-diffusion.