We analyzed a diffusion model based on the assumption that the sufficient condition for the mass flux at point x + L to be different from zero is a nonzero value of the impurity gradient and of impurity concentration at point x. In our model, the length of the jump of diffusing particles from one equilibrium position to another has a defined value L. By describing variation of impurity concentration with time when the frequency of the jumps depends on coordinates and L, the nonlinear diffusion equation was derived. We found that the diffusion coefficient in this nonlinear equation is directly proportional to the concentration of impurities, as it had been proposed in earliest papers. The derived nonlinear diffusion equation was solved numerically for the case of spherical symmetry.

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We will discu8s the properties of the nonlinear equation in the nonisothermical case. In our previous papers the diffusion coefficient directly proportional to the concentration of the impurities was proposed and it was exactly defined. Now the nonlinear diffusion equation is solved for the temperature and for the diffusion coefficient depending on time in a special way.The temperature function T(t) has the singularity at the free chosen time moment t0. The obtained analytical solutions define the diffusion profiles for increasing temperatures and in the case of excited systems when the vacancies and the impurity's atoms are not in the thermal equilibrinm with lattice. Considering the connection between temperature function and the population of excited states for atoms surrounding vacancies the possibility of the superdiffusion is shown.

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We considered and solved the nonlinear diffusion equation formerly. The more complicated but more useful task of many-staged diffusion is solved in this paper. The obtained solution satisfies the initial distribution of the impurities and can be generalized for many-staged diffusion. Using these solutions we can take into account all the stages of a planary transistor formation.