NONLINEAR DIFFUSION IN CUBIC CRYSTALS

We have made a mathematical consideration of an important case of nonlinear diffusion of impurities for a three-dimensional cubic crystals case through a square window or point sources in the x y plane for more exact evaluation of technological parameters for the production of electronic devices or crystals properties modification. The well known nonlinear diffusion model with diffusion coefficients proportional to the concentration of impurities defining spreading of impurities with finite velocity was used. The solutions of the presented nonlinear diffusion equation determine profiles of impurities more exactly. The directions of diffusion can be included taking in the care crystals symmetry. For approximate analytical solving of the three-dimensional nonlinear diffusion equation we introduced similarity variables. The approximate analytical solution of the transformed equation was expressed by Taylor series using the expansion about the maximum penetration depths of the impurities in x y z axes including the square terms.