Effect of dot size on exciton binding energy and electron-hole recombination probability in CdSe quantum dots

Exciton binding energy and electron-hole recombination probability are presented as the two important metrics for investigating effect of dot size on electron-hole interaction in CdSe quantum dots. Direct computation of electron-hole recombination probability is challenging because it requires an accurate mathematical description of electron-hole wavefunction in the neighborhood of the electron-hole coalescence point. In this work, we address this challenge by solving the electron-hole Schrodinger equation using the electron-hole explicitly correlated Hartree-Fock (eh-XCHF) method. The calculations were performed for a series of CdSe clusters ranging from $\mathrm{Cd}_{20}\mathrm{Se}_{19}$ to $\mathrm{Cd}_{74608}\mathrm{Se}_{74837}$ that correspond to dot diameter range of 1-20 nm. The calculated exciton binding energies and electron-hole recombination probabilities were found to decrease with increasing dot size. Both of these quantities were found to scale as $D_\mathrm{dot}^{-n}$ with respect to the dot diameter D. One of the key insights from this study is that the electron-hole recombination probability decreases at a much faster rate than the exciton binding energy as a function of dot size. It was found that an increase in the dot size by a factor of 16.1, resulted in a decrease in the exciton binding energy and electron-hole recombination probability by a factor of 14.4 and $5.5\times10^{6}$, respectively.