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

Abstract

We have combined analytical theory with ab initio nonadiabatic molecular dynamics to study the phonon-induced relaxation of photoexcited charge carriers in PbSe and CdSe semiconductor quantum dots (QDs). Density functional theory 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 at higher photoexcitation energies due to both a higher density of carrier states and a larger nonadiabatic electron–phonon coupling. Over time, carrier relaxation changes from Gaussian to exponential. The Gaussian component is larger in smaller dots; this may be a 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.