Pseudopotential study of electron-hole excitations in colloidal free-standing InAs quantum dots

Excitonic spectra are calculated for free-standing, surface passivated, InAs quantum dots using atomic pseudopotentials for the single-particle states and screened Coulomb interactions for the two-body terms. We present an analysis of the single particle states involved in each excitation in terms of their angular momenta and Bloch-wave parentage. We find that (i) in agreement with other pseudopotential studies of CdSe and InP quantum dots, but in contrast to $k\cdot p$ calculations, the dot wave functions exhibit strong odd-even angular momentum envelope function mixing (e.g., s with $p)$ and large valence-conduction coupling. (ii) While the pseudopotential approach produced very good agreement with experiment for free-standing, colloidal CdSe and InP dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted spectrum does not agree well with the measured (ensemble average over dot sizes) spectra. (1) Our calculated excitonic gap is larger than the photoluminescence measured one, and (2) while the spacing between the lowest excitons is reproduced, the spacings between higher excitons is not fit well. Discrepancy (1) could result from surface state emission. As for (2), agreement is improved when account is taken of the finite-size distribution in the experimental data. (iii) We find that the single-particle gap scales as $R^{-1.01}$ (not $R^{-2}),$ that the screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$ ${(R}^{-0.7}),$ and that the excitonic gap scales as $R^{-0.9}.$ These scaling laws are different from those expected from simple models.