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Boundary and Initial Conditions of Approximate Diffusion Equation for Gold in Silicon

In the basic partial differential equations for diffusion of gold in dissociative and kick-out mechanisms, substitutional gold, interstitial gold, vacancies and self-interstitials are taken into consideration. It takes a long time to solve these equations numerically. It is therefore convenient to solve the approximate partial differential equation for substitutional gold, which is obtained after the reactions between these four elements have reached their local equilibrium states and the interstitial gold has reached its thermal equilibrium state, under suitable boundary and initial conditions. In the in-diffusion process, the conditions of the approximate equation are different from those of the basic equations. In the annealing process, the conditions are the same for the basic and the approximate equations.