Limits of the ratios of tracer diffusivities for diffusion by vacancy pairs: application to compound semiconductors

In this paper, the vacancy-pair diffusion mechanism in cubic materials is revisited with emphasis on the limits of the ratio of the tracer diffusion coefficients to demonstrate the operation of this mechanism. The vacancy-pair mechanism puts very strict upper and lower bounds on this ratio. Extensive high precision Monte Carlo simulation is used to calculate tracer correlation factor, ratios of tracer diffusivities, and percolation effects (in mixed compounds). The three major cubic lattices-NaCl, CsCl, and zinc blende structures-are analyzed, and correct limits for the ratio of the tracer diffusivities are found to be 5.6, 11.2, and 2.6, respectively. For the case of the CsCl structure correlation factors are redetermined using the matrix method to obtain good agreement with the Monte Carlo results. Self-diffusion in the compound semiconductors PbSe (NaC1 structure) InSb, GaSb, CdTe, and HgCdTe (zinc blende structure) is reanalyzed. It is shown that the vacancy-pair mechanism is unlikely to contribute to self-diffusion in CdTe and HgCdTe but it remains a valid possibility for self-diffusion in PbSe, InSb, and GaSb.