ABSTRACT
The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.
ABSTRACT
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.
ABSTRACT
Phonon-induced dephasing processes that govern optical line widths, multiple exciton (ME) generation (MEG), and ME fission (MEF) in semiconductor quantum dots (QDs) are investigated by ab initio molecular dynamics simulation. Using Si QDs as an example, we propose that MEF occurs by phonon-induced dephasing and, for the first time, estimate its time scale to be 100 fs. In contrast, luminescence and MEG dephasing times are all sub-10 fs. Generally, dephasing is faster for higher-energy and higher-order excitons and increased temperatures. MEF is slow because it is facilitated only by low-frequency acoustic modes. Luminescence and MEG couple to both acoustic and optical modes of the QD, as well as ligand vibrations. The detailed atomistic simulation of the dephasing processes advances understanding of exciton dynamics in QDs and other nanoscale materials.
