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Nonlinear diffusion of impurities in semiconductors

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Abstract

We study the concentration-dependent diffusion of dopant impurities into semiconductors. In particular, we examine the two-dimensional diffusion in the vicinity of a mask. Numerical solutions are obtained for dopant diffusion with fixed-total-concentration and with constant-surface-concentration. For the fixed-total-concentration case, we also obtain approximate power series solutions. Our numerical and approximate results are compared with analytical and numerical results obtained by other investigators.

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References

  1. D. A. Antoniadis and R. W. Dutton,Models for computer simulation of complete IC fabrication process. IEEE Trans. Elec. Dev.26, 490–500 (1979).

    Google Scholar 

  2. G. I. Barenblatt,On some unsteady motions of a liquid or a gas in a porous medium. Prikl. Math. I. Mekh. (in Russian)16, 67–78 (1952).

    Google Scholar 

  3. J. Buckmaster,Viscous sheets advancing over dry beds. J. Fluid Mech.81, 735–756 (1977).

    Google Scholar 

  4. E. Doedel,AUTO 86 user manual. Caltech Applied Mathematics Report, 1988.

  5. I. W. Johnson, A. J. Wathen and M. J. Baines,Moving finite element methods for evolutionary problems. II. Applications. J. Comp. Phys.79, 270–297 (1988).

    Google Scholar 

  6. W. L. Kath and D. S. Cohen,Waiting-time behavior in a nonlinear diffusion equation. Studies Appl. Math.67, 79–105 (1982).

    Google Scholar 

  7. D. P. Kennedy and R. R. O'Brien,Analysis of the impurity atom distribution near the diffusion mask for planar p-n junction. IBM J. Res. Dev.9, 179–186 (1965).

    Google Scholar 

  8. J. R. King,Approximate solutions to a nonlinear diffusion equation. J. Eng. Math.22, 53–72 (1988).

    Google Scholar 

  9. E. W. Larsen and G. C. Pomraning,Asymptotic analysis of nonlinear Marshak waves. SIAM J. Appl. Math.39, 201–212 (1980).

    Google Scholar 

  10. A. Luque, J. Martin and G. L. Araújo,Zn diffusion in GaAs under constant As pressure. J. Electrochem. Soc.123, 249–254 (1976).

    Google Scholar 

  11. M. Muskat,The Flow of Homogeneous Fluids through Porous Media. McGraw-Hill, New York 1937.

    Google Scholar 

  12. D. W. Peaceman and H. H. Rachford,The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math.3, 28–41 (1955).

    Google Scholar 

  13. P. YA. Polubarinova-Kochina,Theory of Ground Water Movement, Princeton University Press, Princeton 1962.

    Google Scholar 

  14. K. A. Salsburg and H. H. Hansen,FEDSS—Finite element diffusion simulation system. IEEE Trans. Elec. Dev.30, 1004–1011 (1983).

    Google Scholar 

  15. S. M. Sze,Semiconductor Devices, Wiley, New York 1985.

    Google Scholar 

  16. A. B. Tayler, J. B. Ockendon and A. A. Lacey,‘Waiting-time’ solutions of a nonlinear diffusion equation. SIAM J. Appl. Math.42, 1252–1264 (1982).

    Google Scholar 

  17. D. D. Warner and C. L. Wilson,Two-dimensional concentration dependent diffusion. Bell Sys. Tech. J.59, 1–41 (1980).

    Google Scholar 

  18. L. R. Weisberg and J. Blanc,Diffusion with interstitial-substitutional equilibrium, Zinc in GaAs. Phys. Rev.131, 1548–1552 (1963).

    Google Scholar 

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Schwendeman, D.W. Nonlinear diffusion of impurities in semiconductors. Z. angew. Math. Phys. 41, 607–627 (1990). https://doi.org/10.1007/BF00946097

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  • DOI: https://doi.org/10.1007/BF00946097

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