We present a theoretical model to compute the efficiency of the generation of two or more electron-hole pairs in a semiconductor by the absorption of one photon via the process of carrier multiplication (CM). The photogeneration quantum yield of electron-hole pairs is calculated from the number of possible CM decay pathways of the electron and the hole. We apply our model to investigate the underlying cause of the high efficiency of CM in bulk 2H-MoTe₂, as compared to bulk PbS and PbSe. Electronic band structures were calculated with density functional theory, from which the number of possible CM decay pathways was calculated for all initial electron and hole states that can be produced at a given photon energy. The variation of the number of CM pathways with photon energy reflects the dependence of experimental CM quantum yields on the photon energy and material composition. We quantitatively reproduce experimental CM quantum yields for MoTe₂, PbS, and PbSe from the calculated number of CM pathways and one adjustable fit parameter. This parameter is related to the ratio of Coulomb coupling matrix elements and the cooling rate of the electrons and holes. Large variations of this fit parameter result in small changes in the modeled quantum yield for MoTe₂, which confirms that its high CM efficiency can be mainly attributed to its extraordinary large number of CM pathways. The methodology of this work can be applied to analyze or predict the CM efficiency of other materials.

Rhenium disulfide, a member of the transition metal dichalcogenide family of semiconducting materials, is unique among 2D van der Waals materials due to its anisotropy and, albeit weak, interlayer interactions, confining excitons within single atomic layers and leading to monolayer-like excitonic properties even in bulk crystals. While recent work has established the existence of two stacking modes in bulk, AA and AB_, the influence of the different interlayer coupling on the excitonic properties has been poorly explored. Here, we use polarization-dependent optical measurements to elucidate the nature of excitons in AA and AB-stacked rhenium disulfide to obtain insight into the effect of interlayer interactions. We combine polarization-dependent Raman with low-temperature photoluminescence and reflection spectroscopy to show that, while the similar polarization dependence of both stacking orders indicates similar excitonic alignments within the crystal planes, differences in peak width, position, and degree of anisotropy reveal a different degree of interlayer coupling. DFT calculations confirm the very similar band structure of the two stacking orders while revealing a change of the spin-split states at the top of the valence band to possibly underlie their different exciton binding energies. These results suggest that the excitonic properties are largely determined by in-plane interactions, however, strongly modified by the interlayer coupling. These modifications are stronger than those in other 2D semiconductors, making ReS₂ an excellent platform for investigating stacking as a tuning parameter for 2D materials. Furthermore, the optical anisotropy makes this material an interesting candidate for polarization-sensitive applications such as photodetectors and polarimetry.

Mobilities and lifetimes of photogenerated charge carriers are core properties of photovoltaic materials and can both be characterized by contactless terahertz or microwave measurements. Here, the expertise from fifteen laboratories is combined to quantitatively model the current-voltage characteristics of a solar cell from such measurements. To this end, the impact of measurement conditions, alternate interpretations, and experimental inter-laboratory variations are discussed using a (Cs,FA,MA)Pb(I,Br)₃ halide perovskite thin-film as a case study. At 1 sun equivalent excitation, neither transport nor recombination is significantly affected by exciton formation or trapping. Terahertz, microwave, and photoluminescence transients for the neat material yield consistent effective lifetimes implying a resistance-free JV-curve with a potential power conversion efficiency of 24.6 %. For grainsizes above ≈20 nm, intra-grain charge transport is characterized by terahertz sum mobilities of ≈32 cm² V⁻¹ s⁻¹. Drift-diffusion simulations indicate that these intra-grain mobilities can slightly reduce the fill factor of perovskite solar cells to 0.82, in accordance with the best-realized devices in the literature. Beyond perovskites, this work can guide a highly predictive characterization of any emerging semiconductor for photovoltaic or photoelectrochemical energy conversion. A best practice for the interpretation of terahertz and microwave measurements on photovoltaic materials is presented.

Photon recycling, the iterative process of re-Absorption and re-emission of photons in an absorbing medium, can play an important role in the power-conversion efficiency of photovoltaic cells. To date, several studies have proposed that this process may occur in bulk or thin films of inorganic lead-halide perovskites, but conclusive proof of the occurrence and magnitude of this effect is missing. Here, we provide clear evidence and quantitative estimation of photon recycling in CsPbBr3 nanocrystal suspensions by combining measurements of steady-state and time-resolved photoluminescence (PL) and PL quantum yield with simulations of photon diffusion through the suspension. The steady-state PL shows clear spectral modifications including red shifts and quantum yield decrease, while the time-resolved measurements show prolonged PL decay and rise times. These effects grow as the nanocrystal concentration and distance traveled through the suspension increase. Monte Carlo simulations of photons diffusing through the medium and exhibiting absorption and re-emission account quantitatively for the observed trends and show that up to five re-emission cycles are involved. We thus identify 4 quantifiable measures, PL red shift, PL QY, PL decay time, and PL rise time that together all point toward repeated, energy-directed radiative transfer between nanocrystals. These results highlight the importance of photon recycling for both optical properties and photovoltaic applications of inorganic perovskite nanocrystals.

Assembled perovskite nanocrystals (NCs), known as supercrystals (SCs), can have many exotic optical and electronic properties different from the individual NCs due to energy transfer and electronic coupling in the dense superstructures. We investigate the optical properties and ultrafast carrier dynamics of highly ordered SCs and the dispersed NCs by absorption, photoluminescence (PL), and femtosecond transient absorption (TA) spectroscopy to determine the influence of the assembly on the excitonic properties. Next to a red shift of absorption and PL peak with respect to the individual NCs, we identify signatures of the collective band-like states in the SCs. A smaller Stokes shift, decreased biexciton binding energy, and increased carrier cooling rates support the formation of delocalized states as a result of the coupling between the individual NC states. These results open perspectives for assembled perovskite NCs for application in optoelectronic devices, with design opportunities exceeding the level of NCs and bulk materials.

Solution-processed AgBiS₂ nanocrystal films are a promising material for nontoxic, earth-abundant solar cells. While solar cells with good device efficiency are demonstrated, so far, hardly anything is known about charge generation, transport, and recombination processes in these films. Here, a photoinduced time-resolved microwave conductivity study on AgBiS₂ nanocrystal films is presented. By modeling the experimental data with density-dependent recombination processes, the product of the temperature-dependent electron and hole quantum yield and mobility, and the electron and hole recombination kinetics are determined.

In transient absorption (TA) measurements on Cd-chalcogenide quantum dots (QDs), the presence of a band-edge (BE) bleach signal is commonly attributed entirely to conduction-band electrons in the 1S(e) state, neglecting contributions from BE holes. While this has been the accepted view for more than 20 years, and has often been used to distinguish electron and hole kinetics, the reason for the absence of a hole contribution to the BE-bleach has remained unclear. Here, we show with three independent experiments that holes do in fact have a significant impact on the BE-bleach of well-passivated Cd-chalcogenide QD samples. Transient absorption experiments on high photoluminescence quantum yield CdSe/CdS/ZnS core-shell-shell QDs clearly show an increase of the band-edge bleach as holes cool down to the band edge. The relative contribution of electron-to-hole bleach is 2:1, as predicted by theory. The same measurements on core-only CdSe QDs with a lower quantum yield do not show a contribution of holes to the band-edge bleach. We assign the lack of hole bleach to the presence of ultrafast hole trapping in samples with insufficient passivation of the QD surface. In addition, we show measurements of optical gain in core-shell-shell QD solutions, providing clear evidence of a significant hole contribution to the BE transient absorption signal. Finally, we present spectroelectrochemical measurements on CdTe QDs films, showing the presence of a BE-bleach for both electron and hole injections. The presence of a contribution of holes to the bleach in passivated Cd-chalcogenides QDs bears important implications for quantitative studies on optical gain as well as for TA determinations of carrier dynamics.

Carrier multiplication (CM) is a process in which a single photon excites two or more electrons. CM is of interest to enhance the efficiency of a solar cell. Until now, CM in thin films and solar cells of semiconductor nanocrystals (NCs) has been found at photon energies well above the minimum required energy of twice the band gap. The high threshold of CM strongly limits the benefits for solar cell applications. We show that CM is more efficient in a percolative network of directly connected PbSe NCs. The CM threshold is at twice the band gap and increases in a steplike fashion with photon energy. A lower CM efficiency is found for a solid of weaker coupled NCs. This demonstrates that the coupling between NCs strongly affects the CM efficiency. According to device simulations, the measured CM efficiency would significantly enhance the power conversion efficiency of a solar cell.

Carrier multiplication is a process in which one absorbed photon excites two or more electrons. This is of great promise to increase the efficiency of photovoltaic devices. Until now, the factors that determine the onset energy of carrier multiplication have not been convincingly explained. We show experimentally that the onset of carrier multiplication in lead chalcogenide quantum confined and bulk crystals is due to asymmetric optical transitions. In such transitions most of the photon energy in excess of the band gap is given to either the hole or the electron. The results are confirmed and explained by theoretical tight-binding calculations of the competition between impact ionization and carrier cooling. These results are a large step forward in understanding carrier multiplication and allow for a screening of materials with an onset of carrier multiplication close to twice the band gap energy. Such materials are of great interest for development of highly efficient photovoltaic devices.

An optical switch with two distinct resonances is formed by combining PbS nanocrystals and the conductive polymer poly[sodium 2-(2-ethynyl-4-methoxyphenoxy)acetate] (PAE) into a hybrid thin film. Infrared excitation of the nanocrystals invokes charge transfer and consecutive polaron formation in the PAE, which activates the switch for excited-state absorption at visible frequencies. The optical modulation of the photocurrent response of the switch exhibits highly wavelength-selective ON/OFF ratios. Transient absorption spectroscopy shows that the polaron formation is correlated with the excited state of the nanocrystals, opening up new perspectives for photonic data processing. Such correlated activated absorption can be exploited to enhance the sensitivity for one optical signal by a second light source of different frequency as part of an optical amplifier or a device with AND logic.

Self-assembled nanocrystal solids show promise as a versatile platform for novel optoelectronic materials. Superlattices composed of a single layer of lead-chalcogenide and cadmium-chalcogenide nanocrystals with epitaxial connections between the nanocrystals, present outstanding questions to the community regarding their predicted band structure and electronic transport properties. However, the as-prepared materials are intrinsic semiconductors; to occupy the bands in a controlled way, chemical doping or external gating is required. Here, we show that square superlattices of PbSe nanocrystals can be incorporated as a nanocrystal monolayer in a transistor setup with an electrolyte gate. The electron (and hole) density can be controlled by the gate potential, up to 8 electrons per nanocrystal site. The electron mobility at room temperature is 18 cm²/(V s). Our work forms a first step in the investigation of the band structure and electronic transport properties of two-dimensional nanocrystal superlattices with controlled geometry, chemical composition, and carrier density.

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.

We present a study of the application potential of CdSe nanoplatelets (NPLs), a model system for colloidal 2D materials, as field-controlled emitters. We demonstrate that their emission can be changed by 28% upon application of electrical fields up to 175 kV/cm, a very high modulation depth for field-controlled nanoemitters. From our experimental results we estimate the exciton binding energy in 5.5 monolayer CdSe nanoplatelets to be E_B = 170 meV; hence CdSe NPLs exhibit highly robust excitons which are stable even at room temperature. This opens up the possibility to tune the emission and recombination dynamics efficiently by external fields. Our analysis further allows a quantitative discrimination of spectral changes of the emission energy and changes in PL intensity related to broadening of the emission line width as well as changes in the intrinsic radiative rates which are directly connected to the measured changes in the PL decay dynamics. With the developed field-dependent population model treating all occurring field-dependent effects in a global analysis, we are able to quantify, e.g., the ground state exciton transition dipole moment (3.0 × 10^-29 Cm) and its polarizability, which determine the radiative rate, as well as the (static) exciton polarizability (8.6 × 10^-8 eV cm²/kV²), all in good agreement with theory. Our results show that an efficient field control over the exciton recombination dynamics, emission line width, and emission energy in these nanoparticles is feasible and opens up application potential as field-controlled emitters.