Publication
Title
On improving accuracy of finite-element solutions of the effective-mass Schrodinger equation for interdiffused quantum wells and quantum wires
Author
Abstract
We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrodinger equation. The accuracy of the solution is explored as it varies with the range of the numerical domain. The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires. Also, the model of a linear harmonic oscillator is considered for comparison reasons. It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range, which is thus considered to be optimal. This range is found to depend on the number of mesh nodes N approximately as alpha(0) log(e)(alpha 1) (alpha N-2), where the values of the constants alpha(0), alpha(1), and alpha(2) are determined by fitting the numerical data. And the optimal range is found to be a weak function of the diffusion length. Moreover, it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrodinger equation.
Language
English
Source (journal)
Communications in theoretical physics. - Wallingford
Publication
Wallingford : 2016
ISSN
0253-6102 [online]
1572-9494 [print]
Volume/pages
65:1(2016), p. 105-113
ISI
000372333900018
Full text (publishers version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 10.05.2016
Last edited 19.03.2017
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