Symmetric band structures and asymmetric ultrafast electron and hole relaxations in silicon and germanium quantum dots: time-domain ab initio simulation

State-of-the-art time domain density functional theory and non-adiabatic (NA) molecular dynamic simulations are used to study phonon-induced relaxation of photoexcited electrons and holes in Ge and Si quantum dots (QDs). The relaxation competes with productive processes and causes energy and voltage losses in QD solar cells. The ab initio calculations show that quantum confinement makes the electron and hole density of states (DOS) more symmetric in Si and Ge QDs compared to bulk. Surprisingly, in spite of the symmetric DOS, the electron and hole relaxations are quite asymmetric: the electrons decay faster than the holes. The asymmetry arises due to stronger NA coupling in the conduction band (CB) than in the valence band (VB). The stronger NA coupling of the electrons compared to the holes is rationalized by the larger contribution of the high-frequency Ge-H and Si-H surface passivating bonds to the CB relative to the VB. Linear relationships between the electron and hole relaxation rates and the CB and VB DOS are found in agreement with Fermi's golden rule. The faster relaxation of the electrons compared to the holes in the Ge and Si QDs is unexpected and is in contrast with the corresponding dynamics in the majority of binary QDs, such as CdSe. It suggests that Auger processes will transfer energy from holes to electrons rather than in the opposite direction as in CdSe, and that a larger fraction of the photoexcitation energy will be transferred to phonons coupled with electrons rather than holes. The difference in the phonon-induced electron and hole decay rates is larger in Ge than Si, indicating that the Auger processes should be particularly important in Ge QDs. The simulations provide direct evidence that the high-frequency ligand modes on the QD surface play a pivotal role in the electron-phonon relaxation dynamics of semiconductor QDs.