Non-Radiative Electron-Hole Recombination in Silicon Clusters: Ab Initio Non-Adiabatic Molecular Dynamics

Silicon clusters hold exciting potential for optoelectronic and solar energy applications by yielding strong and tunable visible absorption and luminescence. Nonradiative relaxation of excitons induced by electron-phonon interactions is detrimental to these applications. We combine nonadiabatic molecular dynamics (NAMD) with time-domain density functional theory to study electron-hole recombination in Si-n clusters (n = 5-10, 15). The recombination is much faster in clusters than in bulk Si due to enhanced electron-phonon coupling and transition from indirect to direct bandgap. By applying quantum-classical NAMD, we investigated the importance of the decoherence correction in determining the nonradiative lifetime. The recombination rates decrease by an order of magnitude due to decoherence, bringing the calculations in close agreement with experiment. We interpreted the results of the atomistic simulations analytically using Fermi's golden rule, rationalizing the dependence of the relaxation rate on the electron-phonon coupling and temperature. The electron-hole recombination time is roughly independent of the size of these small clusters, with Si-5 and Si-7 exhibiting longer lifetimes due to enhanced stability to thermal fluctuations.