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.
