A three-dimensional model for artificial atoms and molecules: influence of substrate orientation and magnetic field dependence

Abstract

A full three-dimensional model for the calculation of the electronic structure of semiconductor quantum dots (QD) and molecules (QDM) grown on high index surfaces and/or in the presence of an external magnetic field is presented. The strain distribution of the dots is calculated using continuum elasticity and singe-particle states are extracted from the nonsymmetrized eight-band k·p theory. The model properly takes into account the effects of different substrate orientation by rotation of the coordinate system in such a way that one coordinate coincides with the growth direction, whereas the effects of a tilted external magnetic field are taken into account through the Zeeman effect and employing a gauge invariant scheme based on Wilson's formulation of lattice gauge theory. We point out the role of piezoelectricity for InAs/GaAs QDs grown on [11k], where k = 1,2,3,4,5,7,9 and for QDMs containing eight InAs/GaAs QDs grown on [11l], where l = 1,2,3. We predict the variation of the transition energies of the QDM as a function of substrate orientation and interdot distances in the molecule. We address the magnetic field direction dependent variation of the electronic properties of QD and QDM.