  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.
