Broadband Cooling Spectra of Hot Electrons and Holes in PbSe Quantum Dots

Abstract

Understanding cooling of hot charge carriers in semiconductor quantum dots (QDs) is of fundamental interest and useful to enhance the performance of QDs in photovoltaics. We study electron and hole cooling dynamics in PbSe QDs up to high energies where carrier multiplication occurs. We characterize distinct cooling steps of hot electrons and holes and build up a broadband cooling spectrum for both charge carriers. Cooling of electrons is slower than of holes. At energies near the band gap we find cooling times between successive electronic energy levels in the order of 0.5 ps. We argue that here the large spacing between successive electronic energy levels requires cooling to occur by energy transfer to vibrational modes of ligand molecules or phonon modes associated with the QD surface. At high excess energy the energy loss rate of electrons is 1–5 eV/ps and exceeds 8 eV/ps for holes. Here charge carrier cooling can be understood in terms of emission of LO phonons with a higher density-of-states in the valence band than the conduction band. The complete mapping of the broadband cooling spectrum for both charge carriers in PbSe QDs is a big step toward understanding and controlling the cooling of hot charge carriers in colloidal QDs.

Efficient Steplike Carrier Multiplication in Percolative Networks of Epitaxially Connected PbSe Nanocrystals

“…This agrees with charge cooling times less than 2 ps reported for PbSe NCs before. 24 , 25 On a longer time scale on the order of 100 ps, the charges decay by trapping or recombination, as discussed before. 23 …”

Multiscale in modelling and validation for solar photovoltaics

“…Another objective is to calculate carrier mobilities including electron-phonon interactions, e.g. in PbTe, and other materials [64].…”

Carrier Multiplication Mechanisms and Competing Processes in Colloidal Semiconductor Nanostructures

“…The individual cooling rates of electrons and holes in PbSe QDs have been determined by Spoor et al [ 53 , 54 ] (see Figure 5 ) where the separation of hole and electron transitions was facilitated by using a dye (methylene blue) to extract photogenerated electrons and so identify which transitions in TA spectra arise from either type of carrier relaxation. The work was further extended to higher excited state relaxations away from the band edge [ 54 ]. Near the band gap, the electron and hole cooling rates were 0.54 eV/ps and 2.75 eV/ps respectively whilst for the highest excited states the rates increased to 1.52 eV/ps and 6.8 eV/ps.…”

“…The near band edge dissimilarity in cooling rates does lend support to Zunger et al’s [ 55 ] modelling of PbSe QDs which shows differing valence and conduction band DOS (with the valence band DOS being greater than for the conduction band) in contrast to the case for the bulk material. Spoor et al [ 54 ] attributed only the cooling at very high excess energies for either carrier to be due to bulk-like LO phonon emission but at lower energies resolved several separate cooling steps (in cooling rates) which were each explained as involving phonon or surface ligand vibrational modes in view of the larger separations in energy levels nearer the band edge ( Figure 5 ).…”

“…Midgett et al [ 81 ] inferred a size dependent hot carrier cooling rate in addition to a size dependent CM rate in their studies on PbS, PbSe and PbS x Se 1− x alloy QDs which they suggested may be tied to variations in stoichiometry with size, imperfect surfaces or changes in ligand coupling modifying the competing cooling channels. Spoor et al [ 54 ] also note the potential impact of the choice of ligands and exciton-molecular vibration coupling on the cooling rate in their detailed study of the hole and electron cooling spectrum in PbSe QDs (see Figure 5 ). Near the band edge in particular, a cooling mechanism via coupling of both electrons and holes to surface ligand vibrations or to surface phonon modes of the QD itself is a necessary conclusion.…”