Diffusion of Dopant in Crystalline Silicon: An Asymptotic Analysis

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Abstract
An existing model of the diffusion of dopant in crystalline silicon is presented. The model is used in predicting semiconductor device properties. For small concentrations of dopant, the diffusion is linear. However, at large concentrations, enhanced diffusion occurs. This may be modelled by a concentration-dependent diffusion coefficient that is approximately constant at small concentrations but increases linearly at higher concentrations. The initial distribution of implanted dopant is confined to a small region of the crystal, and has a high peak concentration. This initial distribution develops into a high-concentration region with advancing steep fronts and decaying tail regions. In the enhanced region, the dominant balance is given by the filtration equation, and the tail regions are dominated by quasi-steady convection—diffusion. These two regions are analysed and matched together, using singular perturbation theory.

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