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Phosphorus diffusion in silicon

Published online by Cambridge University Press:  16 July 2009

J. R. King
J. R. King
Affiliation:
Department of Theoretical Mathematics, University of Nottingham, Nottingham, NG7 2RD, UK
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Abstract

Phosphorus diffusion in silicon shows a number of anomalous effects, and we apply asymptotic methods to a model problem which includes most of these. Both constant surface concentration problems and the diffusion of implanted dopant are considered. An unusual feature of the model is the non-local dependence of the tail diffusivity on the peak concentration.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 2 , June 1990 , pp. 151 - 175
Copyright
Copyright © Cambridge University Press 1990

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References

Anderson, D. & Lisak, M. 1980 Approximate solutions of some nonlinear diffusion equations. Phys. Rev. A 22, 2761–2768.CrossRefGoogle Scholar
Barenblate, G. I. 1952 On some unsteady motions of a liquid or a gas in a porous medium. Priki. Mat. i Mekh. 16, 67–78 (in Russian).Google Scholar
Cerofolini, C. F., Polignano, M. L., Picco, P., Finetti, M., Solmi, S. & Gallorini, M. 1982 Phosphorus diffusion into silicon from chemically vapour-deposited phosphosilicate glass. Thin Solid Films 87, 373–378.CrossRefGoogle Scholar
Fair, R. B. 1978 Analysis of phosphorus-diffused layers in silicon. J. Electrochem. Soc. 125, 323–327.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
Finetti, M., Masetti, G., Negrini, P. & Solmi, S. 1980 Predeposition through a polysilicon layer as a tool to reduce anomalies in phosphorus profiles and the push-out effect in n–p–n transistors. IEE Proc. 127 Pt I, 37–41.Google Scholar
Grundy, R. E. & Mclaughlin, R. 1982 Large-time solution of a nonlinear diffusion equation. Proc. R. Soc. Lond. A 381, 395–406.Google Scholar
Ho, C. P., Plummer, J. D., Hansen, S. E. & Dutton, R. W. 1983 VLSI process modeling SUPREM III. IEEE Trans. Electron. Dev. ED-30, 1438–1453.CrossRefGoogle Scholar
Hu, S. M., Fahey, P. & Dutton, R. W. 1983 On models of hosphorus diffusion in silicon. J. Appl. Phys. 54, 6912–6922.CrossRefGoogle Scholar
Jeppson, K. O. & Anderson, D. 1986 Analytical model for phosphorus diffusion in silicon. J. Electrochem. Soc. 133, 397–400.CrossRefGoogle Scholar
King, J. R. 1988 Approximate solutions to a nonlinear diffusion equation. J. Eng. Math. 22, 53–72.CrossRefGoogle Scholar
King, J. R. & Please, C. P. 1986 Diffusion of dopant in crystalline silicon: An asymptotic analysis. IMA J. Appl. Math. 37, 185–197.CrossRefGoogle Scholar
Kump, M. & Dutton, R. W. 1983 Two-dimensional process simulation SUPRA. In Process and Device Simulation for MOS–VLSI circuits (ed. Antognetti, P., Antoniadis, D. A., Dutton, R. W. & Oldham, W. G.), pp. 304–342. Martinus Nijhoff.CrossRefGoogle Scholar
Lau, F. & GöSele, U. 1986 Two-dimensional phosphorus diffusion for soft drains in silicon MOS transistors. Appl. Phys. A 40, 101–107.CrossRefGoogle Scholar
Rosen, G. 1979 Nonlinear heat conduction in solid H2. Phys. Rev. B 19, 2398–2399.CrossRefGoogle Scholar
Tan, T. Y. 1984 Intrinsic point defects and diffusion processes in silicon. Mat. Res. Soc. Symp. Proc. 31, 127–141.CrossRefGoogle Scholar
Yoshida, M., Arai, E., Nakamura, H. & Terunuma, Y. 1974 Excess vacancy generation mechanism at phosphorus diffusion into silicon. J. Appl. Phys. 45, 1498–1506.CrossRefGoogle Scholar