Impurity-Correlation Factors for Diffusion in Diamond-Structure Crystals

The correlation equations for impurity diffusion in the diamond structure have much in common with the equations for self-diffusion in pure face-centered-cubic and diamond structures. Comparison of these equations allows the four-frequency expression for the impurity-correlation factor in the diamond structure to be calculated to the same precision as the correlation factor for self-diffusion in a pure face-centered-cubic structure. This precision is an order of magnitude better than that for any previous calculation of this impurity-correlation factor. The calculation also illustrates an effect that choice of diffusion direction can have on the form of the correlation-factor equations. In these calculations, a generalized method is developed of calculating impurity-correlation factors in terms of effective-vacancy-return probabilities $U_q$, including contributions from vacancies which move far away from the impurity before effectively returning to their original site. Connections between various calculational techniques are discussed. The accurate values obtained here are compared with previous calculations done by a variety of other methods. This allows an evaluation of the problems arising in various standard calculational techniques.