Analytical Diffusion Profiles Under Various Boundary Conditions

Abstract

We can obtain analytical models for impurity diffusion profiles in some specific cases, although it is difficult to solve this in general. We first show various analytical models assuming constant diffusion coefficients, and then present the models with variable diffusion coefficients. We further display analytical models for two-dimensional diffusion profiles, and profiles for multi-layers.

Keywords: Diffusion coefficient, diffusion length, diffusion equation, differential equation, initial condition, boundary condition, Fourier transformation, Laplace transformation, Gaussian profile, surface, third order moment, forth order moment, Gamma function, Beta function, analytical model.