Theoretical Study of Electron–Phonon Relaxation in PbSe and CdSe Quantum Dots: Evidence for Phonon Memory

Abstract

Wehavecombinedanalyticaltheorywithabinitio nonadiabatic molecular dynamics to study the phonon-induced relaxation of photoexcited charge carriers in PbSe and CdSe semiconductorquantumdots(QDs).Densityfunctionaltheory calculations show dense distributions of electronic levels near the energy gap, attributed to the reconstruction and lack of absolute symmetry of the QD surface. Most of these states are optically dark, but they do couple to phonons and facilitate charge carrier relaxation. The time-domain simulations show a complex, nonexponential relaxation, in agreement with the observed non-Lorenzian spectral line shapes. The relaxation accelerates athigherphotoexcitationenergiesduetobothahigherdensityofcarrierstatesandalargernonadiabaticelectronphononcoupling. Overtime,carrier relaxation changes fromGaussian toexponential. TheGaussian componentislargerinsmallerdots;this maybea manifestation of the phonon bottleneck effect. Since Markovian rate models give exponential decay, we suggest that the more complex form of the carrier relaxation, observed in our simulations, can be attributed to phonon memory. The analytic theory developed within the framework of quantized Hamilton dynamics rationalizes this observation. It shows that a detailed description of the phonon modes is more important than a model for the electronic states.