Assessment of carrier-multiplication efficiency in bulk PbSe and PbS

Abstract

One of the important factors limiting solar-cell efficiency is that incident photons generate one electron-hole pair, irrespective of the photon energy. Any excess photon energy is lost as heat. The possible generation of multiple charge carriers per photon (carrier multiplication) is therefore of great interest for future solar cells 1 . Carrier multiplication is known to occur in bulk semiconductors, but has been thought to be enhanced significantly in nanocrystalline materials such as quantum dots, owing to their discrete energy levels and enhanced Coulomb interactions 1-3 . Contrary to this expectation, we demonstrate here that, for a given photon energy, carrier multiplication occurs more efficiently in bulk PbS and PbSe than in quantum dots of the same materials. Measured carriermultiplication efficiencies in bulk materials are reproduced quantitatively using tight-binding calculations, which indicate that the reduced carrier-multiplication efficiency in quantum dots can be ascribed to the reduced density of states in these structures.Carrier multiplication is the process in which the absorption of a single, high-energy photon results in the generation of two or more electron-hole pairs. The excess energy of the initially excited electron is used to excite a second electron over the bandgap, rather than being converted into heat through sequential phonon emission. Carrier multiplication is important for the operation for high-speed electronic devices 4 , but is especially relevant for solar cells 1 , because relaxation of hot carriers through phonon emission is a common loss mechanism in bulk semiconductor solar cells. In this context, semiconductor quantum dots are promising building blocks for future solar cells 1 . In addition to the size-tunability of the quantum-dot optical properties, the carrier-multiplication efficiency in quantum dots was reported to be much higher than in bulk materials, where the process is generally referred to as impact ionization. It has been argued that carrier multiplication is more efficient in nanostructured semiconductors owing to quantum-confinement effects causing (1) a slowing of the phonon-mediated relaxation channel 1 and (2) enhanced Coulomb interactions 2 , resulting from forced overlap between wavefunctions and reduced dielectric screening at the quantum-dot surface 3 . In recent years, several femtosecond spectroscopy studies have revealed highly efficient carrier multiplication in PbSe and PbS (refs 2, 5-9) (refs 18, 19) quantum dots. In initial studies, carrier-multiplication efficiencies may have been overestimated owing to several experimental complications, including too high excitation fluences (generating multiple carriers by sequential absorption of multiple photons), lack of stirring of quantum-dot suspensions (causing photo-induced charging) and sample-to-sample variability 19 . Furthermore, recent tight-binding calculations 20 suggest carrier multiplication in quantum dots is not only not enhanced relative to bulk, but is actually lower. Answering the...

Carrier dynamics in semiconductors studied with time-resolved terahertz spectroscopy

“…This ability of THz spectroscopy to independently determine both scattering rates and plasma frequencies has proven particularly useful in recent work that assessed the efficiency of impact ionization processes in the low-band gap semiconductors PbS and PbSe (Pijpers et al, 2009). Impact ionization refers to a mechanism in which a photon possessing an energy of several times the band gap is able to convert its excess energy into the generation of more than one electron-hole pair.…”

Four-wave-mixing imaging and carrier dynamics of PbS colloidal quantum dots

“…After earlier reports of quantum efficiencies up to 700%, 15,17,18 recent measurements showed that no enhancement of the CM efficiency is observed in CQDs relatively to the bulk value. 16,19,20 This discrepancy has been attributed 16 to photoinduced charging of the CQDs giving rise to fast recombination dynamics similar to that of multiexcitons after CM.…”

Numerical Study of Carrier Multiplication Pathways in Photoexcited Nanocrystal and Bulk Forms of PbSe

“…The controversy possibly rise from experimental inaccuracy [8], sample-to-sample variation in surface properties [10], and contribution from extraneous effects, e.g., photocharging [11,12]. Comparison to the bulk PbS and PbSe spectroscopic measurements shows that bulk QE exceeds validated QE in NCs if compared on the scale of absolute energy [13]. These issues call for the reassessment of the quantum confinement role in the CM dynamics [7].…”

“…To account for degeneracy of the exciton (biexciton) states associated with four equivalent Lvalleys, the exciton (biexciton) population is multiplied by factor 4 (16). Introducing energy independent effective electron-phonon coupling in the high DOS region, the intraband cooling rates are obtained by fitting the total relaxation time, τ ph , to reproduce the experimentally observed values in the range 0.5 < τ ph < 5.0 ps [13,19]. The Monte Carlo sampling is used to handle ensemble of NCs with 5% size distribution.…”

“…3) as II rate (Fig 2(b)) and never exceeds the bulk values. For comparison, the experimental data for PbSe NCs [11] and the bulk [13] are also shown in the plot. Solid lines in Fig.…”