Abstract
The problem of computing the electrostatic potential in a one dimensional multilayer semiconductor device with quantized electrons density is analysed using results of monotone operator theory and perturbation calculus. An error estimate is proved for the discretization with Lagrange finite elements of degree one. A practical implementation of the method, using a quasi-Newton algorithm is presented together with some numerical results.
Zusammenfassung
Das Problem der Berechnung des elektrostatischen Potentials in eindimensionalen Mehrschichtstrukturen mit quantifizierter Elektronenladung wird unter Zuhilfenahme der Theorie monotoner Operatoren und von Störungstheorie untersucht. Eine Fehlerabschätzung wird gegeben für den Fall einer Diskretisierung mit Lagrange-finiten Elementen erster Ordnung. Eine praktische Implementierung dieser Methode bei Verwendung eines quasi-Newton Algorithmus sowie numerische Resultate werden gezeigt.
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Caussignac, P., Zimmermann, B. & Ferro, R. Finite element approximation of electrostatic potential in one dimensional multilayer structures with quantized electronic charge. Computing 45, 251–264 (1990). https://doi.org/10.1007/BF02250636
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DOI: https://doi.org/10.1007/BF02250636