Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T09:13:05.410Z Has data issue: false hasContentIssue false

Phosphorus diffusion in silicon

Published online by Cambridge University Press:  16 July 2009

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

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
Copyright
Copyright © Cambridge University Press 1990

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.)

References

Anderson, D. & Lisak, M. 1980 Approximate solutions of some nonlinear diffusion equations. Phys. Rev. A 22, 27612768.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, 6778 (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, 373378.CrossRefGoogle Scholar
Fair, R. B. 1978 Analysis of phosphorus-diffused layers in silicon. J. Electrochem. Soc. 125, 323327.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, 11071118.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, 3741.Google Scholar
Grundy, R. E. & Mclaughlin, R. 1982 Large-time solution of a nonlinear diffusion equation. Proc. R. Soc. Lond. A 381, 395406.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, 14381453.CrossRefGoogle Scholar
Hu, S. M., Fahey, P. & Dutton, R. W. 1983 On models of hosphorus diffusion in silicon. J. Appl. Phys. 54, 69126922.CrossRefGoogle Scholar
Jeppson, K. O. & Anderson, D. 1986 Analytical model for phosphorus diffusion in silicon. J. Electrochem. Soc. 133, 397400.CrossRefGoogle Scholar
King, J. R. 1988 Approximate solutions to a nonlinear diffusion equation. J. Eng. Math. 22, 5372.CrossRefGoogle Scholar
King, J. R. & Please, C. P. 1986 Diffusion of dopant in crystalline silicon: An asymptotic analysis. IMA J. Appl. Math. 37, 185197.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. 304342. Martinus Nijhoff.CrossRefGoogle Scholar
Lau, F. & GöSele, U. 1986 Two-dimensional phosphorus diffusion for soft drains in silicon MOS transistors. Appl. Phys. A 40, 101107.CrossRefGoogle Scholar
Rosen, G. 1979 Nonlinear heat conduction in solid H2. Phys. Rev. B 19, 23982399.CrossRefGoogle Scholar
Tan, T. Y. 1984 Intrinsic point defects and diffusion processes in silicon. Mat. Res. Soc. Symp. Proc. 31, 127141.CrossRefGoogle Scholar
Yoshida, M., Arai, E., Nakamura, H. & Terunuma, Y. 1974 Excess vacancy generation mechanism at phosphorus diffusion into silicon. J. Appl. Phys. 45, 14981506.CrossRefGoogle Scholar