TY - JOUR
T1 - Accuracy of transfer matrix approaches for solving the effective mass schrödinger equation
AU - Jirauschek, Christian
N1 - Funding Information:
Manuscript received September 09, 2008; revised March 03, 2009. Current version published July 29, 2009. This work was supported by the Emmy Noether Program of the German Research Foundation (DFG) under Grant JI115/1-1. The author is with the Institute for Nanoelectronics, TU München, D-80333 München, Germany (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JQE.2009.2020998
PY - 2009
Y1 - 2009
N2 - The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrödinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position-dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrödinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.
AB - The accuracy of different transfer matrix approaches, widely used to solve the stationary effective mass Schrödinger equation for arbitrary one-dimensional potentials, is investigated analytically and numerically. Both the case of a constant and a position-dependent effective mass are considered. Comparisons with a finite difference method are also performed. Based on analytical model potentials as well as self-consistent Schrödinger-Poisson simulations of a heterostructure device, it is shown that a symmetrized transfer matrix approach yields a similar accuracy as the Airy function method at a significantly reduced numerical cost, moreover avoiding the numerical problems associated with Airy functions.
KW - Eigenvalues and eigenfunctions
KW - MOS devices
KW - Numerical analysis
KW - Quantum theory
KW - Quantum-effect semiconductor devices
KW - Quantum-well devices
KW - Semiconductor heterojunctions
KW - Tunneling
UR - http://www.scopus.com/inward/record.url?scp=68949194690&partnerID=8YFLogxK
U2 - 10.1109/JQE.2009.2020998
DO - 10.1109/JQE.2009.2020998
M3 - Article
AN - SCOPUS:68949194690
SN - 0018-9197
VL - 45
SP - 1059
EP - 1067
JO - IEEE Journal of Quantum Electronics
JF - IEEE Journal of Quantum Electronics
IS - 9
ER -