Finite element analysis of coupled electronic states in quantum dot nanostructures

Nanostructures, created by confinement of the motion of an electron from all three dimensions and known as quantum dots (QDs), provide materials scientists with a wide range of potential applications. These structures are produced today with advances of QD growth technology, and computational tools are fundamental in providing a better understanding of such structures. In this paper QD nanostructures are analysed with due account for coupling effects between electronic states in the dot and the wetting layer regions. The analysis, performed on the basis of the finite element methodology and Arnoldi iterations, demonstrates that the effect of coupling may be essential. The numerical procedure applied here is more efficient compared to the QR algorithm typically used in the context of modelling low-dimensional nanostructures. We report results of computational experiments for cylindrical and truncated conical QDs and compare them with the earlier results obtained for fully conical QD nanostructures.