Analysis of Charge Transport: A Mathematical Study of Semiconductor Devices
U.S. Government Printing Office, 1996 - 167 من الصفحات
This book addresses the mathematical aspects of semiconductor modeling, with particular attention focused on the drift-diffusion model. The aim is to provide a rigorous basis for those models which are actually employed in practice, and to analyze the approximation properties of discretization procedures. The book is intended for applied and computational mathematicians, and for mathematically literate engineers, who wish to gain an understanding of the mathematical framework that is pertinent to device modeling. The latter audience will welcome the introduction of hydrodynamic and energy transport models in Chap. 3. Solutions of the nonlinear steady-state systems are analyzed as the fixed points of a mapping T, or better, a family of such mappings, distinguished by system decoupling. Significant attention is paid to questions related to the mathematical properties of this mapping, termed the Gummel map. Compu tational aspects of this fixed point mapping for analysis of discretizations are discussed as well. We present a novel nonlinear approximation theory, termed the Kras nosel'skii operator calculus, which we develop in Chap. 6 as an appropriate extension of the Babuska-Aziz inf-sup linear saddle point theory. It is shown in Chap. 5 how this applies to the semiconductor model. We also present in Chap. 4 a thorough study of various realizations of the Gummel map, which includes non-uniformly elliptic systems and variational inequalities. In Chap.
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Development of DriftDiffusion Models
Numerical Fixed Point Approximation in Banach Space
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analysis applied approximation argument assumed Assumption Banach space boundary conditions bounded carrier Chap chapter choice closed complete components computed consider constant continuity convergence convex corresponding defined definition denotes dependent derived described determined developed device differential dimension discretization discussed domain drift-diffusion electric electron employed energy equation equivalent estimate existence fact field final finite element fixed point fixed point map follows formulation function given gradient hand side hold hypothesis inequality integral introduced involving iteration lagging Lemma linear Lipschitz maximum principles method mobility Newton norm Note numerical obtain operator particular pointwise positive potential present problem proof properties range relations Remark respectively result satisfies scale semiconductor sequence similar simulation solution space specified subsection subsystem Suppose Theorem theory tion transport unique units values variables variational weak yields zero
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