Plane wave methodology for single quantum dot electronic structure calculations

Abstract

The development of the plane wave methodology for the calculation of the electronic structure of single quantum dots within the framework of multiband envelope function theory was presented. The methodology developed enables one to use a small embedding box, sufficient to eliminate electronic coupling, without introducing the artificial interaction with periodically replicated array of quantum dots caused by periodic boundary conditions. The appropriate formulas for Fourier transforms of strain tensor components on the embedding box that eliminate the strain field of the neighboring dots were derived. The expressions that enable the evaluation of Coulomb integrals in inverse space without the introduction of artificial electrostatic interactions with surrounding dots were presented. It was also shown how symmetry can be exploited to further reduce the computational effort in the case of quantum dots of symmetric shape. Numerical results illustrating the application of the methods to the calculation of single-particle states, as well as the configuration interaction calculation of exciton, biexciton, and negative trion states in InAs∕GaAs quantum dots were given.