Electron and hole wave functions in self-assembled quantum rings

Abstract

We use a plane-wave technique to study the electron and hole wave functions in self-assembled InGaAs quantum rings, investigating the influence on the electron-hole overlap of variations in the ring shape and composition profiles, and including the effects of built-in strain and the piezoelectric potential. Lateral variation of the ground-state electron and hole wave functions in a perfect ringlike structure is observed as a consequence of the piezoelectric potential, which has minima and maxima on the (110) and $(11\ifmmode\bar\else\textasciimacron\fi{}0)$ planes passing through the center of the ring. We find for rings with reflection symmetry in the vertical direction that although the average electron and hole positions are equal, there is a significant vertical separation of the electron and hole peak probability densities in the (110) and $(11\ifmmode\bar\else\textasciimacron\fi{}0)$ planes. A net vertical separation of the electron and hole may occur either through the piezoelectric potential when the (110) and $(11\ifmmode\bar\else\textasciimacron\fi{}0)$ planes are no longer equivalent, or through strain effects when there is a shape or composition asymmetry in the [001] direction. Comparison of the theoretical predictions with experimental data confirm the presence of a large asymmetry in the ring profile both in the vertical direction, where the ring is deduced to be volcanolike, and also in the growth plane, where the rings are elongated along the $[11\ifmmode\bar\else\textasciimacron\fi{}0]$ direction.