Numerical Solutions of Basic Equations for Kick-Out Mechanism of Diffusion

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Abstract
The basic equations for the kick-out mechanism of diffusion are a set of non-linear differential equations. These equations are solved numerically for the diffusion of gold in silicon at 1100°C for both in-diffusion and annealing, and analytical expressions for the solutions are given. It is found that the numerical solution for the interstitial gold atoms reaches the thermal equilibrium value most rapidly. The time at which the interstitial gold atoms reach their thermal equilibrium, and the time at which the interchange reactions between substitutional and interstitial gold atoms reach a local equilibrium are obtained from the analytical expressions of the numerical solutions.

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