Solutions modeling of nonlinear equation of diffusion for three dimensions case

Abstract

We have made a practical consideration of an important case of nonlinear diffusion of impurities in a three-dimensional case through square window in the x, y plane for the production of electronic devices and evaluation of its parameters. The nonlinear diffusion coefficients for diffusion in x, y, z directions are proportional to the concentration of impurities. The three-dimensional nonlinear diffusion equation was transformed using similarity variables. The approximate analytical solution of the transformed equation expressed by Taylor series approximate expansion for three similarity variables about the maximum impurities penetration points in x, y, z axes including the square terms.

Keywords

• nonlinear diffusion equation
• approximate analytical solution
• similarity variables