Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures

Authors

  • Eman Ali Hussain department of Mathematics, Faculty of Science, Mustansiriyah University.
  • Jamil A. Al-Hawasy department of Mathematics, Faculty of Science, Mustansiriyah University.
  • Lamyaa Hussein Ali department of Mathematics, Faculty of Science, Mustansiriyah University.

DOI:

https://doi.org/10.23851/mjs.v30i2.150

Keywords:

nanoscale, Finite elements method, Ben Daniel-Duke boundary conditions, InAs⁄GaAs quantum rings

Abstract

This paper concerned with the solution of the nanoscale structures consisting of the   with an effective mass envelope function theory, the electronic states of the  quantum ring are studied.  In calculations, the effects due to the different effective masses of electrons in and out the rings are included. The energy levels of the electron are calculated in the different shapes of rings, i.e., that the inner radius of rings sensitively change the electronic states. The energy levels of the electron are not sensitively dependent on the outer radius for large rings. The structures of  quantum rings are studied by the one electronic band Hamiltonian effective mass approximation, the energy- and position-dependent on electron effective mass approximation, and the spin-dependent on the Ben Daniel-Duke boundary conditions. In the description of the Hamiltonian matrix elements, the Finite elements method with different base linear triangular element is adopted. The non-linear energy confinement problem is solved approximately by using the Finite elements method with  linear triangular element, to calculate the energy of the electron states for the   quantum ring.

References

Yiming Li, O. Voskoboynikov, C.P. Lee, S.M. Sze ''Computer simulation of electron energy levels for different shape InAs/GaAs semiconductor quantum dots'' Computer Physics Communications, Vol. 141, (2001), pp. 66-72. [Crossref]

Yiming Li, O. Voskoboynikov, C.P. Lee, S.M. Sze O. Tretyak ''Electron energy state spin-splitting in 3D cylindrical semiconductor quantum dots'' THE EUROPEAN PHYSICAL JOURNAL B, Vol. 28, No. 8 (2002), pp. 475-481. [

">Crossref]

G. Paasch, P. H. Nguyen and G. Gobsch ''Envelope Equation and Wave Function Matching for Narrow-Gap Semiconductors'' Physica Status Solidi (b), Vol. 162, No. 1 (1990), pp. 155-163. [Crossref]

D. L. Mathine, S. K. Myjak and G. N. Maracas ''A Computational Fourier Series Solutin of the BenDaniel-Duke Hamiltonian for Arbitrary Shaped Quantum Wells'' IEEE Journal of Quantum Electronics, Vol. 31, (1995), pp. 1216‑1222. [Crossref]

M. Willatzence, R. Melnik, C. Galeriu and L. C. Lew Yan Voon ''Finite Element Analysis of Nanowire Superlattice Structures'' Springer, Vol. 31, (2003), pp. 755‑763. [Crossref]

Yiming Li, ''An Iterative Method for Single and Vertically Stacked Semiconductor Quantum Dots Simulation'' Mathematical and Computer Modelling, Vol. 42, (2005), pp. 711‑718. [Crossref]

D. Sarkara, A. Deyasib ''Field Induced Tuning of DOS and Eigenstates in Double Quantum Well Structure having Gaussian Geometry'' American Scientific Publishers , Vol. 5, No. 1, (2016), pp. 138‑143.

Downloads

Published

2019-09-30

How to Cite

[1]
E. A. Hussain, J. A. Al-Hawasy, and L. H. Ali, “Finite Element Method Linear Triangular Element for Solving Nanoscale InAs⁄GaAs Quantum Ring Structures”, MJS, vol. 30, no. 2, pp. 19–26, Sep. 2019.

Issue

Section

Mathematics