Some explicit solutions to the non-linear diffusion equation

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Abstract
Mathematical solutions to the diffusion equation are considered for the case in which the diffusion coefficient varies as some power of the concentration, i.e. D=kCn. For the 'constant source' set of boundary conditions, explicit solutions can be found using a self-similar technique; for the 'infinite source' set of conditions, approximate solutions can be found. They agree very well with previously published calculations using relatively laborious numerical techniques. A procedure is described whereby the errors involved in the approximation can be determined. Diffusion coefficients of the form D=kCn are important in semiconductor diffusion. The diffusion of zinc in GaAs is taken as an example and theoretical profiles are plotted. Their agreement with experimentally determined profiles is discussed.