TY - JOUR

T1 - A second-order finite volume scheme for three dimensional truncated pyramidal quantum dot

AU - Wang, Weichung

AU - Hwang, Tsung Min

AU - Jang, Jia Chuan

N1 - Funding Information:
The authors are grateful to the anonymous referee for the precious comments and suggestions. This work is partially supported by the National Science Council and the National Center for Theoretical Sciences in Taiwan.

PY - 2006/3/1

Y1 - 2006/3/1

N2 - Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrödinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel-Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

AB - Three dimensional truncated pyramidal quantum dots are simulated numerically to compute the energy states and the wave functions. The simulation of the hetero-structures is realized by using a novel finite volume scheme to solve the Schrödinger equation. The simulation benefits greatly from the finite volume scheme in threefold. Firstly, the BenDaniel-Duke hetero-junction interface condition is ingeniously embedded into the scheme. Secondly, the scheme uses uniform meshes in discretization and leads to simple computer implementation. Thirdly, the scheme is efficient as it achieves second-order convergence rates over varied mesh sizes. The scheme has successfully computed all the confined energy states and visualized the corresponding wave functions. The results further predict the relation of the energy states and wave functions versus the height of the truncated pyramidal quantum dots.

KW - Energy levels

KW - Finite volume scheme

KW - Numerical simulations

KW - Schrödinger equation

KW - Second-order convergence

KW - Three dimensional truncated pyramidal quantum dot

KW - Wave functions

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U2 - 10.1016/j.cpc.2005.10.012

DO - 10.1016/j.cpc.2005.10.012

M3 - Article

AN - SCOPUS:31544453868

VL - 174

SP - 371

EP - 385

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

IS - 5

ER -