Analysis of Charge Transport: A Mathematical Study of Semiconductor DevicesSpringer Berlin Heidelberg, 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. |
المحتوى
Introduction 12355 | 1 |
Development of DriftDiffusion Models | 9 |
Microscopic to Macroscopic | 27 |
حقوق النشر | |
5 من الأقسام الأخرى غير ظاهرة
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
applied approximation theory assumed Assumption 5.3 Boltzmann Boltzmann transport equation boundary conditions boundary values bounded calculus carrier Chap chapter computed constant convergence convex convex set decoupling defined definition denotes derived differential domain drift-diffusion model Einstein relations electric field electron employed equivalent estimate exp(u exp(w exponential finite element fixed point map flux follows Galerkin Galerkin approximation given Gummel map H¹ norm hold Hölder's inequality hydrodynamic model hypothesis inf-sup integral iteration J.W. Jerome k₁ L2 norm lagging left hand side Lemma Lipschitz continuous maximum principles mobility Newton Newton's method nonlinear numerical fixed point obtain operator Picard iterates pointwise Poisson equation proof properties quantum quantum hydrodynamic quasi-Fermi levels relations result right hand side satisfies semiconductor device sequence simulation solution space steady-state subsection test function Theorem tion variables variational inequality VWƒ yields zero