Analysis of Charge Transport: A Mathematical Study of Semiconductor DevicesSpringer Science & Business Media, 06/12/2012 - 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. |
المحتوى
1 | |
Computational Foundations | 23 |
Microscopic to Macroscopic | 27 |
5 | 87 |
97 | 121 |
Numerical Fixed Point Approximation in Banach Space | 125 |
Construction of the Discrete Approximation Sequence | 143 |
155 | |
162 | |
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عبارات ومصطلحات مألوفة
applied approximation theory assumed Banach Banach space Boltzmann transport equation boundary conditions boundary values bounded carrier Chap chapter components computed constant continuously embedded convergence convex convex set current continuity decoupling defined definition denotes device differential discretization discussed domain drift-diffusion model electric field electron employed energy estimate existence exp(u exp(w finite element fixed point map flux follows formulation Galerkin Galerkin approximation given Gummel map Hilbert space hold Hölder's inequality hypothesis integral inverse k₁ Krasnosel'skii L2 norm lagging left hand side Lemma Lipschitz continuous maximum principles mobility Newton iterates Newton's method nonlinear numerical fixed point obtain operator calculus piecewise linear pointwise Poisson equation problem proof properties R-quadratic relations result right hand side satisfies semiconductor sequence solution space steady-state subsection subspace Suppose Theorem tion topologies Uj+1 variables variational inequality VWƒ yields zero