SUMMARY A procedure is described for estimating various parameters governing the diffusion of impurities in semiconductors; these parameters are required for a number of explicit numerical models of non-linear diffusion in III-V crystals. The method is based on an analytical solution of the continuum equivalent of a discrete numerical model due to Zahari and Tuck and provides a systematic procedure for analysing experimental data to yield predictions for the coefficient of diffusion of the impurity, the coefficient of self-diffusion of the host material, the bulk equilibrium vacancy concentration and, under conditions of 'dissociation' pressure, the surface vacancy concentration. Application of the procedure to two sets of independent experimental data provided reasonably consistent values of the parameters.
A discrete model which describes the influence of stress on interstitial diffusive processes in a simple cubic crystal is developed and analyzed. The model consists of two parts: (i) elasticity equations governing the evolution of the displacements, and hence the stresses in the crystal, and (ii) an equation governing interstitial diffusion through the crystal. In a continuum limit, it is found that the displacements satisfy the usual partial differential equations for a simple cubic crystal. Two-dimensional equilibrium solutions to the discrete elasticity equations are constructed analytically, by introducing a discrete Airy stress function and calculating polynomial solutions to the fourth-order difference equation this function satisfies. Numerical solutions are also constructed, and all of the solutions obtained are used in the study of diffused profiles, the results largely being in conformity with intuitive expectations. The specific model problems that are investigated are intended to allow classes of qualitative behaviour of stress-effected diffusion to be catalogued.
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