Effect of hydrostatic pressure, temperature, and doping on self-diffusion in germanium

Abstract

The tracer-diffusion coefficient for $^{71}\mathrm{Ge}$ has been measured in Ge single crystals as a function of pressure, temperature, and doping. Ion-beam sputtering was used for microsectioning. The activation volume in intrinsic Ge increases slightly with temperature from 0.24\ensuremath{\Omega} at 876 K to 0.41\ensuremath{\Omega} at 1086 K (\ensuremath{\Omega} is the atomic volume). The fairly small values of the activation volume show that the defect or defects which act as diffusion vehicles must be either strongly relaxed and/or spread out. Measurements of the doping dependence performed at 973 K show that the diffusivity increases with n doping and decreases with p doping. This supports the view that self-diffusion in Ge proceeds by a vacancy mechanism and that the vacancy acts as an acceptor. As a consequence the contribution of negatively charged vacancies, which is about 77% for intrinsic material, increases (decreases) with n doping (p doping). The measurements of the pressure dependence of the diffusivity in doped materials, also performed at 973 K, show that the activation volume is larger for pth volume for the neutral vacancy and 0.28\ensuremath{\Omega} for the negatively charged vacancy.