A variational free-energy functional approach to the Schr\"{o}dinger-Poisson theory

ORAL

Abstract

In the numerical simulation of model electronic device systems, where electrons are typically under confinement, a key obstacle is the need to iteratively solve the coupled Schr\"{o}dinger-Poisson equation in order to obtain the electronic potential. We show that it is possible to bypass this obstacle by adopting a variational approach and obtaining the solution of the SP equation by minimizing a functional. We construct the required functional and establish some of its properties. We apply this formulation to the case of narrow channel quantum wells where the local density approximation yields accurate results.

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Authors

  • Francisco J. Solis

    • School of Mathematical and Natural Sciences. Arizona State University

  • Vikram Jadhao

    • Department of Physics and Astronomy, Johns Hopkins University
    • Johns Hopkins University

  • Kaushik Mitra

    • None

  • Monica Olvera de la Cruz

    • Northwestern University
    • Northwestern Univ
    • Department of Materials Science and Engineering, Northwestern University
    • Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States
    • Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208
    • Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA