Exchange effects on electron scattering through a quantum dot embedded in a two-dimensional semiconductor structure

Abstract

We have developed a theoretical method to study the scattering processes of an incident electron through an $N$-electron quantum dot (QD) embedded in a two-dimensional (2D) semiconductor. The generalized Lippmann-Schwinger equations including the electron-electron interaction in this system are solved for the continuum electron by using the method of continued fractions (MCF) combined with a 2D partial wave expansion technique. The method is applied to a one-electron QD case. Scattering cross sections are obtained for both the singlet and triplet couplings between the incident electron and the QD electron during the scattering. The total elastic scattering cross sections as well as the spin-flip scattering cross sections resulting from the exchange potential are presented. Furthermore, inelastic scattering processes are also studied using a multichannel formalism of the MCF.