Study of Effect of Shape, Size and Symmetry on Electronic States of Some Three-dimensional Structures in Mesoscopic Size Regime

Rajesh Kumar; S.N. Singh

Abstract

This study presents theoretical study of effect of size and symmetry of different shaped three-dimensional GaAs structures in mesoscopic size regime. The effective mass Schrӧdinger equation is used in various shapes and its solution are modified as a function of volume and aspect ratio of structures. The calculated energy eigenvalues for square prism, equilateral prism, regular tetrahedral, cylindrical and spherical are comparatively analyzed to observe the effect of shape, size and symmetry on it. The result shows that energy eigenvalues decreases with increase in order of symmetry and volume. However, the energy eigenvalue doesn’t vary monotonically with aspect ratio of structures. It decreases first rapidly and then increases with increase in aspect ratio of structures. Degeneracy of first excited state of different structures was found to depend upon both their order of symmetry and aspect ratio. Keywords: Confinement, aspect ratio, elements of symmetry, effective mass Schrödinger equationCite this ArticleRajesh Kumar, S.N. Singh. Study of Effect of Shape, Size and Symmetry on Electronic States of Some Three-dimensional Structures in Mesoscopic Size Regime. Research & Reviews: Journal of Physics. 2019; 8(1): 23–33p.