Abstract
At very high concentrations phosphorus diffusion in silicon exhibits marked nonlinearities. The hierarchy of physical models that attempt to explain this anomalous diffusion are reviewed. An eight-species kinetic model is derived that yields a quasilinear, partly-dissipative system of reaction-diffusion partial differential equations. The numerical method of lines is used to solve the system for a simplified five-species model in three dimensions. The linear system in the Newton iteration is solved using several matrix-free methods. In all cases the dimension of the Krylov subspace must be quite large to insure convergence. This suggests that preconditioning will be more important for efficiency than choice of an accelerator.
This work was supported in part by NSF Grant DMS- 9024712
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© 1994 Springer-Verlag New York, Inc.
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Richardson, W.B. (1994). A Reaction-Diffusion System Modeling Phosphorus Diffusion. In: Coughran, W.M., Cole, J., Llyod, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 58. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8407-6_5
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DOI: https://doi.org/10.1007/978-1-4613-8407-6_5
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