TY - GEN A1 - Lang, Jens A1 - Merz, Wilhelm T1 - Two-Dimensional Adaptive Simulation of Dopant Diffusion in Silicon N2 - 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. T3 - ZIB-Report - 00-03 KW - Semiconductor devices KW - nonlinear reaction-drift-diffusion equations KW - mesh control KW - multilevel finite elements KW - Rosenbrock methods Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5716 ER - TY - THES A1 - Lang, Jens T1 - Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems. Theory, Algorithm, and Applications N2 - This monograph has been written to illustrate the interlocking of theory, algorithm, and application in developing solution techniques for complex PDE systems. A deep theoretical understanding is necessary to produce a powerful idea leading to a successful algorithm. Efficient and robust implementation is the key to make the algorithm perform satisfactorily. The extra insight obtained by solving real--life problems brings out the structure of the method more clearly and suggests often ways to improve the numerical algorithm. It is my intention to impart the beauty and complexity found in both the theoretical investigation of the adaptive algorithm proposed here, i.e., the coupling of Rosenbrock methods in time and multilevel finite elements in space, and its realization. I hope that this method will find many more interesting applications. T3 - ZIB-Report - SC-99-20 KW - Adaptive multilevel finite elements KW - Rosenbrock methods KW - a posteriori error estimates KW - Rothe method Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-4089 ER -