Open Access

ARTICLE

Modeling of the Electronic Properties of Vertical Quantum Dots by the Finite Element Method

by Philippe Matagne¹, Jean-Pierre Leburton², Jacques Destine, Guy Cantraine³

1 Philippe Matagne is PHD student in Electrical Engineering at the Mon-tefiore Institute, University of Liège, Belgium, and visitor at the Beck-man Institute for Advanced Science & Technology, University of Illinoisat Urbana-Champaign.
2 Jean-Pierre Leburton is Professor in the de partment of Electrical & Computer Engineering at the University of Illinois at Urbana-Champaign and at the Beckman Institute for Advanced Science & Technology.
3 Jacques Destiné and Guy Cantraine are Professors in the department of Electrical & Computer Engineering at the Montefiore Institute, University of Liège, Belgium.

Computer Modeling in Engineering & Sciences 2000, 1(1), 1-10. https://doi.org/10.3970/cmes.2000.001.001

Abstract

We investigate the quantum mechanical properties and single-electron charging effects in vertical semiconductor quantum dots by solving the Schrödinger and Poisson (SP) equations, self-consistently. We use the finite element method (FEM), specifically the Bubnov-Galerkin technique to discretize the SP equations. Owing to the cylindrical symmetry of the structure, the mesh is generated from hexahedral volume elements. The fine details of the electron spectrum and wavefunctions in the quantum dot are obtained as a function of macroscopic parameters such as the gate voltage, device geometry and doping level. The simulations provide comprehensive data for the analysis of the experimental data of Tarucha, Austing, Honda, van der Hage, and Kouwenhoven (1996).

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