Geometrical-confinement effects on excitons in quantum disks

Excitons confined to flat semiconductor quantum dots with elliptical cross section are considered as we study geometrical effects on exciton binding energy, electron-hole separation, and the resulting linear optical properties. We use numerical matrix diagonalization techniques with appropriately large and optimized basis sets in an effective-mass Hamiltonian approach. The linear optical susceptibilities of GaAs and InAs dots for several different size ratios are discussed and compared to experimental photoluminescence spectra obtained on GaAs/AlGaAs and InAs/GaAs quantum dots. For quantum dots with several nm in size, there is a strong blue shift of the luminescence due to geometrical confinement effects. Also, transition peaks are split and shifted towards higher energy, in comparison with dots with circular cross sections.