Title: Determining bound states in a semiconductor device with contacts using a nonlinear eigenvalue solver
Authors: Vandenberghe, William ×
Fischetti, Massimo V
Van Beeumen, Roel #
Meerbergen, Karl
Michiels, Wim #
Effenberger, Cedric #
Issue Date: 23-Jul-2014
Series Title: Journal of Computational Electronics vol:13 issue:3 pages:753-762
Abstract: We present a nonlinear eigenvalue solver enabling the calculation of bound solutions of the Schrödinger equation in a system with contacts. We discuss how the imposition of contacts leads to a nonlinear eigenvalue problem and discuss the numerics for a one- and two-dimensional potential. We reformulate the problem so that the eigenvalue problem can be efficiently solved by the recently proposal rational Krylov method for nonlinear eigenvalue problems, known as NLEIGS. In order to improve the convergence of the method, we propose a holomorphic extension such that we can easily deal with the branch points introduced by a square root. We use our method to determine the bound states of the one-dimensional Pöschl–Teller potential, a two-dimensional potential describing a particle in a canyon and the multi-band Hamiltonian of a topological insulator.
ISSN: 1569-8025
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
Associated Section of ESAT - INSYS, Integrated Systems
× corresponding author
# (joint) last author

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