Direct Pseudopotential Calculation of Exciton Coulomb and Exchange Energies in Semiconductor Quantum Dots

The effects of electron-hole interaction on the exciton energy of semiconductor quantum dots are calculated using pseudopotential wave functions. A comparison with the widely used, but never tested, effective-mass approximation (EMA) shows that the electron-hole Coulomb energy is significantly ( $\sim 40\%$) overestimated by the EMA, and that the scaling with the dot size $R$ is sublinear in $1/R$. The exchange splitting is much smaller than the Coulomb energy, and in the case of CdSe quantum dots shows significant deviations from the ${1/R}^3$ scaling predicted by the EMA.