Temperature and magnetic-field dependence of radiative decay in colloidal germanium quantum dots

We conduct spectroscopic and theoretical studies of photoluminescence (PL) from Ge quantum dots (QDs) fabricated via colloidal synthesis. The dynamics of late-time PL exhibit a pronounced dependence on temperature and applied magnetic field, which can be explained by radiative decay involving two closely spaced, slowly emitting exciton states. In 3.5 nm QDs, these states are separated by ∼1 meV and are characterized by ∼82 μs and ∼18 μs lifetimes. By using a four-band formalism, we calculate the fine structure of the indirect band-edge exciton arising from the electron-hole exchange interaction and the Coulomb interaction of the Γ-point hole with the anisotropic charge density of the L-point electron. The calculations suggest that the observed PL dynamics can be explained by phonon-assisted recombination of excitons thermally distributed between the lower-energy "dark" state with the momentum projection J = ± 2 and a higher energy "bright" state with J = ± 1. A fairly small difference between lifetimes of these states is due to their mixing induced by the exchange term unique to crystals with a highly symmetric cubic lattice such as Ge.