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

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 the way that one coordinate coincides with the growth direction, whereas the effects of a tilted external magnetic field are taken into account throught 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.