Abstract
The diffusion is the result of Brownian movement and occurs with a finite velocity. We presented the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. Analytical solutions, showing that the maximum displacements of diffusing particles are proportional to the square root of diffusion time like for Brownian movement, was obtained. For small concentrations of impurities, nonlinear diffusion equation transforms to linear.
Highlights
This paper is stimulated by author’s scientific investigations about period of thirty years
In late 1982 author proposed nonlinear diffusion equation with diffusion coefficient directly proportional to the impurities concentration. This equation corresponds to the diffusion process which can occur with a finite velocity
The nonlinear diffusion equation was solved for temperature and for the diffusion coefficient depending on time in a special way
Summary
This paper is stimulated by author’s scientific investigations about period of thirty years. In late 1982 author proposed nonlinear diffusion equation with diffusion coefficient directly proportional to the impurities concentration. This equation corresponds to the diffusion process which can occur with a finite velocity. The obtained analytical solutions describe the diffusion in the case of excited systems when the vacancies and the impurity atoms are not in thermal equilibrium with the lattice. Diffusion coefficients for that excited vacancies are about 104 times large than diffusion coefficients of vacancies obtained by thermal heating. These excited vacancies we used for fast introducing Boron and Phosphorus at room temperature in crystal silicon. Eq (2) coincides with phenomenological Fick’s first law published in 1855
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