Self-consistent electronic structure and optical selection rules for tetrahedral quantum dots

Abstract

Recently, Fukui et al. (22nd conference on solid state devices and materials, 1990, Japan) have employed a controlled faceting technique in metal organic chemical vapor deposition (MOCVD) crystal growth to construct tetrahedral quantum dots without resorting to ion-implantation or chemical-etching techniques. We investigate the electronic structure of these dots, in the two-dimensional flat triangular approximation, with Hartree and exchange-correlation interactions between electrons taken into account. We compute the self-consistent electronic structure of a triangular dot in a density functional formalism, taking into account finite barrier height and treating exchange and correlation in the local density approximation. We present the results of eigenvalues and density profiles as a function of charge number N, dot size, and (perpendicular)magnetic field strength. We show that the three-fold symmetry of the dot implies a form of the Bloch theorem that separates the eigenfunctions into ‘zones’. This allows us further to derive selection rules for long-wavelength electromageetic waves polarized arbitrarily within the plane of the dot. These selection rules are independent of self-consistent effects.