Hostname: page-component-6bb9c88b65-wr9vw Total loading time: 0 Render date: 2025-07-20T11:54:55.521Z Has data issue: false hasContentIssue false
  • English
  • Français

Surface-concentration-dependent nonlinear diffusion

Published online by Cambridge University Press:  16 July 2009

J. R. King
J. R. King
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss a nonlinear diffusion equation in which the diffusivity has a non-local dependence on the surface concentration. Exact results are obtained for some special cases by means of similarity methods and non-local transformations. We indicate some of the implications the analysis has for more general cases.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 1 , March 1992 , pp. 1 - 20
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aczél, J. 1966 Lectures on Functional Equations and their Applications. Academic Press, New York.Google Scholar
Akhatov, I. Sh., Gazizov, R. K. & Ibragimov, N. Kh. 1988 Bäcklund transformations and nonlocal symmetries. Sov. Math. Dokl. 36, 393–395.Google Scholar
Anderson, D. & Jeppson, K. J. 1985 Evaluation of diffusion coefficients from nonlinear impurity profiles. J. Electrochem. Soc. 132, 1409–1412.CrossRefGoogle Scholar
Barenblatt, G. I. 1952 On some unsteady motions of a liquid or a gas in a porous medium. Prikl. Mat. i. Mekh. 16, 67–78.Google Scholar
Bluman, G. W. & Cole, J. D. 1974 Similarity Methods for Differential Equations. Springer-Verlag, Heidelberg.CrossRefGoogle Scholar
Bluman, G. W., Reid, G. J. & Kumei, S. 1988 New classes of symmetries for partial differential equations. J. Math. Phys. 29, 806–811.CrossRefGoogle Scholar
Cannon, J. R. & Yin, H.-M. 1989 A class of non-linear non-classical parabolic equations. J. Diff. Equations. 79, 266–288.CrossRefGoogle Scholar
Fair, R. B. & Tsai, J. C. C. 1975 The diffusion of ion-implanted arsenic in silicon. J. Electrochem. Soc. 122, 1689–1696.CrossRefGoogle Scholar
Fair, R. B. & Tsai, J. C. C. 1977 A quantitative model for the diffusion of phosphorus in silicon and the emitter dip effect. J. Electrochem. Soc. 124, 1107–1118.CrossRefGoogle Scholar
Ghezzo, M. 1972 Diffusion from a thin layer into a semi-infinite medium with concentration dependent diffusion coefficient. J. Electrocheni. Soc. 119, 977–979.CrossRefGoogle Scholar
King, J. R. 1989 Exact solutions to some nonlinear diffusion equations. Quart. J. Mech. Appl. Math. 42, 537–552.CrossRefGoogle Scholar
King, J. R. 1990 Phosphorus diffusion in silicon. Euro. J. Appl. Math. 1, 151–175.CrossRefGoogle Scholar
King, J. R. 1991 Asymptotic analysis of an impurity-defect pair diffusion model. To appear in Quart. J. Mech. Appl. Math.CrossRefGoogle Scholar
Konstantinov, A. O. 1988 Mechanism of boron diffusion in silicon carbide. Sov. Phys. Semicond. 22, 102–104.Google Scholar
Morehead, F. F. & Lever, R. F. 1986 A new model of tail diffusion of phosphorus and boron in silicon. Mat. Res. Soc. Symp. Proc. 52, 49–56.CrossRefGoogle Scholar
Ovsiannikov, L. V. 1959 Group relations of the equation of nonlinear conductivity. Dokl. Akad. Nauk SSSR 125, 492–495.Google Scholar
Philip, J. R. 1960 General method for exact solution of the concentration-dependent diffusion equation. Aust. J. Phys. 13, 1–12.CrossRefGoogle Scholar
Stolwijk, N. A. 1990 On diffusion by the dissociative mechanism in the case of a finite foreign-atom source. Phys. Stat. Sol. (b) 157, 107–115.CrossRefGoogle Scholar
Tuck, B. 1974 Introduction to Diffusion in Semiconductors. Peter Peregrinus, Hitchin.Google Scholar