Nonlinear Diffusion Equation with Diffusion Coefficient Directly Proportional to Concentration of Impurities

• Authors: A. Janavičius , A. Poškus
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

66.30.-h

Discipline

• 66.30.-h: Diffusion in solids(for surface and interface diffusion, see 68.35.Fx)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2005
• Volume: 107
• Issue: 3
• Pages: 519-524

Dates

published

2005-03

received

2004-10-27

Contributors

author

A. Janavičius

• Department of Physics and Mathematics, Šiauliai University, Višinskio 25, Šiauliai, 76351, Lithuania

author

A. Poškus

• Faculty of Physics, Vilnius University, Saulėtekio 9, 10222 Vilnius, Lithuania

References

• 1. A.J. Janavicius, V. Stukaite, D.J. Zanevicius, Electron Techn. Ser. 2: Semiconductor Dev., 160, 27, 1983 (in Russian)
• 2. A.J. Janavicius, Random Processes and Transfer Phenomena, Siauliai university, Siauliai 2002, p. 85 (in Lithuanian)
• 3. A.J. Janavicius, Phys. Lett. A, 224, 159, 1997
• 4. A.J. Janavicius, G. Luza, D. Jurgaitis, Acta Phys. Pol. A, 105, 475, 2004
• 5. B.-F. Apostol, Phys. Lett. A, 235, 363, 1997
• 6. M.E. Gliksman, Diffusion in Solids, Wiley, New York 2000, p. 472
• 7. W.-S. Wang, Y.-H. Lo, IEEE Trans. Electron Dev., ED-30, 1828, 1983
• 8. Laboratory Guide of Physics, Ed. L.L. Goldin, Nauka, Moscow 1983, p. 704 (in Russian)
• 9. N.K. Madsen, R.F. Sincovec, Trans. Math. Software, 5, 326, 1979

Identifiers

DOI

10.12693/APhysPolA.107.519