Title
On improving accuracy of finite-element solutions of the effective-mass Schrodinger equation for interdiffused quantum wells and quantum wires On improving accuracy of finite-element solutions of the effective-mass Schrodinger equation for interdiffused quantum wells and quantum wires
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Wallingford ,
Subject
Physics
Source (journal)
Communications in theoretical physics. - Wallingford
Volume/pages
65(2016) :1 , p. 105-113
ISSN
0253-6102
ISI
000372333900018
Carrier
E
Target language
English (eng)
Affiliation
University of Antwerp
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.
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