Effect of lateral electric field on the transition energies of neutral and charged excitons inIn0.5Ga0.5As/GaAsquantum dots

Abstract

We have calculated the transition energies of neutral and charged excitons in ${\mathrm{In}}_{0.5}\mathrm{Ga}{\phantom{\rule{0.16em}{0ex}}}_{0.5}\mathrm{As}$/GaAs quantum dots (QDs) under a lateral electric field up to 40 kV/cm. First, the single-particle electron and hole states under the lateral field are calculated using the 8-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ theory. The linear and quadratic piezoelectricity is included. Next, the transition energies are calculated from the electron-hole, electron-electron, and hole-hole Coulomb energies. For a QD with 15-nm base length under a lateral electric field along the $[100]$ direction, the transition energy of the positively charged exciton exhibits a blueshift with increasing field up to 28 kV/cm, followed by a redshift under higher field. In contrast, those of the neutral and negatively charged excitons exhibit only redshifts accompanied by a crossing of the two exciton levels. The calculated result for the positively charged exciton reproduces the unconventional ``M''-shaped exciton energy shift observed in our experiment by Nakaoka et al. [Appl. Phys. Lett. 99, 181109 (2011)]. The origin of the blueshift calculated for the positively charged exciton is the enhanced hole density in the QD base corner due to the modification of the piezoelectric potential by the lateral electric field, which causes an increase in the hole-hole Coulomb energy. We found that the amount of the blueshift increases with the QD size. In order to understand the effect of the lateral field direction, we calculate the transition energies under a lateral electric field of 20 kV/cm along the $[1\overline{1}0],[100]$, and $[110]$ directions. For the positively charged exciton, the transition energy exhibits a redshift for the $[1\overline{1}0]$ direction, and blueshifts of different amounts for the $[100]$ and $[110]$ directions, indicating that the effects of the lateral field are not equivalent for the $[1\overline{1}0]$ and $[110]$ directions. It is demonstrated that the direction dependence of the transition energy reflects the symmetry of the confinement potential in the QDs due to piezoelectricity.