Isotope effect for self-diffusion in Ge

Although diffusion processes in elemental semiconductors have been extensively studied for nearly two decades, considerable controversy still exists over basic aspects of the diffusion process. In Ge, the vacancy mechanism is considered largely compatible with both experiment and theory but direct, experimental evidence indicating the single vacancy as the mechanism of self-diffusion at high temperature has not been previously offered. A radiotracer diffusion measurement can, in principle, identify the mechanism of self-diffusion via the isotope effect. This measurement was performed by simultaneously diffusing the isotopes ${}_{}{}^{77}{}_{}{}^{}\mathrm{Ge}$ and ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ge}$ into single crystal, intrinsic Ge at temperatures of 900 and 925°C. In each of four runs the relative diffusivities of the two isotopes were measured from which four values of $f\Delta K$ ranging from 0.25 to 0.31 could be determined. The results are consistent with a single vacancy mechanism for which the correlation factor $f$ is 0.5, placing $\Delta K$ in the range 0.5 to 0.6.