In(Ga)As/GaAs quantum dots grown on a (111) surface as ideal sources of entangled photon pairs

Abstract

Self-organized In(Ga)As/GaAs quantum dots (QDs) grown on (111) substrate are proposed as ideal sources for the generation of entangled photon pairs. Due to the threefold rotational symmetry of the (111) surface, QDs with ${C}_{3v}$ symmetry or higher are expected to develop during growth. In contrast to QDs on (001)-oriented substrates, the symmetry of the confinement potential of (111) QDs is not lowered by piezoelectric effects. As a result the excitonic bright splitting vanishes and the $\text{biexciton}\ensuremath{\rightarrow}\text{exciton}\ensuremath{\rightarrow}0$ recombination cascade can be used for the generation of entangled photons. We evaluate the spectroscopic separability of excitonic and biexcitonic emissions as a function of QD size, shape, and composition using the configuration-interaction model in conjunction with eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ theory. The piezoelectric field in (111) QDs predominantly aligns along the growth direction and gives rise to vertical charge separation. First- and second-order piezoelectric fields are oriented in opposite directions. The In/Ga ratio inside the QD determines the leading contribution and can be employed to balance both terms in order to achieve a field-free situation with maximal electron-hole overlap. The biexciton binding energy depends on the net piezoelectric potential drop across the QD vertical extension and becomes maximal if the first- and second-order fields outweigh each other within the QD interior.