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 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 the electron-hole wave function 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 Cd ₂₀Se₁₉ to Cd₇₄₆₀₈Se₇₄₈₃₇ that correspond to dot diameter range 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 _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 12.9 and 4.55 × 10⁵, respectively.