Vacancy properties in germanium probed by cobalt diffusion

Abstract

We assessed the equilibrium concentration (CVeq) and diffusivity (DV) of vacancies (V) in Ge as a function of temperature from a detailed analysis of the diffusion behavior of Co in electronic-grade Ge wafers. Diffusion experiments were performed with the radiotracer 57Co over the temperature range 650–900 °C using short-term isothermal lamp annealing and mechanical sectioning. The sensitivity of Co diffusion for the vacancy properties of the Ge host lattice relies on substantial evidence that Co migrates via the dissociative mechanism involving V-mediated interstitial-substitutional exchange. Co turned out to be a particularly interesting probe atom, as its diffusion behavior shows a crossover from a Co-interstitial-controlled mode at high temperatures to a V-controlled mode at lower temperatures. Also, the finding that the solubility of (substitutional) Co proved to be similar in magnitude to CVeq constitutes a crucial feature in the evaluation of the V-related data. Surprisingly, it was found that the deduced CVeq values exceed the literature data by one order of magnitude or more. Consistently, DV falls below existing estimates by roughly a factor of ten in order to reproduce the well-established Ge self-diffusivity due to the vacancy mechanism. Furthermore, our analysis yields a low value (∼0.5 eV) for the enthalpy of vacancy formation, which is at variance with the results from ab initio theoretical calculations.