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Two-Dimensional Adaptive Simulation of Dopant Diffusion in Silicon

Please always quote using this URN: urn:nbn:de:0297-zib-5716
  • One important step in the fabrication of silicon-based integrated circuits is the creation of semiconducting areas by diffusion of dopant impurities into silicon. Complex models have been developed to investigate the redistribution of dopants and point defects. In general, numerical analysis of the resulting PDEs is the central tool to assess the modelling process. We present an adaptive approach which is able to judge the quality of the numerical approximation and which provides an automatic mesh improvement. Using linearly implicit methods in time and multilevel finite elements in space, we are able to integrate efficiently the arising reaction-drift-diffusion equations with high accuracy. Two different diffusion processes of practical interest are simulated.

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Author:Jens Lang, Wilhelm Merz
Document Type:ZIB-Report
Tag:Rosenbrock methods; Semiconductor devices; mesh control; multilevel finite elements; nonlinear reaction-drift-diffusion equations
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Cxx Probabilistic methods, simulation and stochastic differential equations (For theoretical aspects, see 68U20 and 60H35) / 65C20 Models, numerical methods [See also 68U20]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2000/02/22
Series (Serial Number):ZIB-Report (00-03)
Published in:Appeared in: Computing and Visualization in Science 3 (2001) 169-176
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