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.

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Networks of nanowires, nanotubes, and nanosheets are important for many applications in printed electronics. However, the network conductivity and mobility are usually limited by the resistance between the particles, often referred to as the junction resistance. Minimising the junction resistance has proven to be challenging, partly because it is difficult to measure. Here, we develop a simple model for electrical conduction in networks of 1D or 2D nanomaterials that allows us to extract junction and nanoparticle resistances from particle-size-dependent DC network resistivity data. We find junction resistances in porous networks to scale with nanoparticle resistivity and vary from 5 Ω for silver nanosheets to 24 GΩ for WS2 nanosheets. Moreover, our model allows junction and nanoparticle resistances to be obtained simultaneously from AC impedance spectra of semiconducting nanosheet networks. Through our model, we use the impedance data to directly link the high mobility of aligned networks of electrochemically exfoliated MoS2 nanosheets (≈ 7 cm2 V−1 s−1) to low junction resistances of ∼2.3 MΩ. Temperature-dependent impedance measurements also allow us to comprehensively investigate transport mechanisms within the network and quantitatively differentiate intra-nanosheet phonon-limited bandlike transport from inter-nanosheet hopping.@en

Photo-conductive antennas (PCAs) are the workhorse of time-domain THz sensing and imaging. In this work, we employ a rigorous Norton equivalent circuit model to identify and estimate the substrate-related parasitic effects, that might limit the THz emission, to better design future PCAs.

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Heterostructures (HSs) based on two-dimensional transition metal dichalcogenides (TMDCs) are highly intriguing materials because of the layers’ pronounced excitonic properties and their nontrivial contributions to the HS. These HSs exhibit unique properties that are not observed in either of the constituent components in isolation. Interlayer excitons (IEs), which are electron-hole pairs separated across the HSs, play a central role in determining these HS properties and are of interest both fundamentally and for device applications. In recent years, a major focus has been on understanding and designing HSs composed of two or more TMDC materials. Less attention has been paid to HSs composed of one TMDC layer and a layer of perovskite material. A central challenge in the understanding of HS properties is that basic measurements such as optical spectroscopic analysis can be misinterpreted due to the complexity of the charge transfer dynamics. Addressing these aspects, this review presents an overview of the most common and insightful optical spectroscopic techniques used to study TMDC/TMDC and TMDC/halide perovskite HSs. Emphasis is placed on the interpretation of these measurements in terms of charge transfer and the formation of IEs. Recent advances have started to uncover highly interesting phenomena, and with improved understanding these HSs offer great potential for device applications such as photodetectors and miniaturized optics.

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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.

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We analyze the topology, dispersion, and optical selection rules of bulk Wannier excitons in nanosheets of Bi₂Se₃, a topological insulator in the family of the bismuth chalcogenides. Our main finding is that excitons also inherit the topology of the electronic bands, quantified by the skyrmion winding numbers of the constituent electron and hole pseudospins as a function of the total exciton momentum. The excitonic bands are found to be strongly indirect due to the band inversion of the underlying single-particle model. At zero total momentum, we predict that the s-wave and d-wave states of two exciton families are selectively bright under left- or right-circularly polarized light. We furthermore show that every s-wave exciton state consists of a quartet with a degenerate and quadratically dispersing nonchiral doublet, and a chiral doublet with one linearly dispersing mode as in transition metal dichalcogenides. Finally, we discuss the potential existence of topological edge states of chiral excitons arising from the bulk-boundary correspondence.

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In this Perspective, we provide an overview of recent advances in harvesting triplets for photovoltaic and photon upconversion applications from two angles. In singlet fission-sensitized solar cells, the triplets are harvested through a low band gap semiconductor such as Si. Recent literature has shown how a thin interlayer or orientation of the singlet fission molecule can successfully lead to triplet transfer. On the other hand, the integration of transition metal dichalcogenides (TMDCs) with suitable organic molecules has shown triplet-triplet annihilation upconversion (TTA-UC) of near-infrared photons. We consider the theoretical aspect of the triplet transfer process between a TMDC and organic semiconductors. We discuss possible bottlenecks that can limit the harvesting of energy from triplets and perspectives to overcome these.

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We studied the initial nature and relaxation of photoexcited electronic states in CdSe nanoplatelets (NPLs). Ultrafast transient optical absorption (TA) measurements were combined with the theoretical analysis of the formation and decay of excitons, biexcitons, free charge carriers, and trions. In the latter, photons and excitons were treated as bosons and free charge carriers as fermions. The initial quantum yields of heavy-hole (HH) excitons, light-hole (LH) excitons, and charge carriers vary strongly with photon energy, while thermal relaxation occurs always within 1 ps. After that, the population of LH excitons is negligible due to relaxation to HH excitons or decay into free electrons and holes. Up to the highest average number of about four absorbed photons per NPL in our experiments, we found no signatures of the presence of biexcitons or larger complexes. Biexcitons were only observed due to the interaction of a probe-generated exciton with an exciton produced previously by the pump pulse. For higher pump photon energies, the initial presence of more free charge carriers leads to formation of trions by probe photons. On increasing the number of absorbed pump photons in an NPL, the yield of excitons becomes higher as compared to free charge carriers, since electron-hole recombination becomes more likely. In addition to a TA absorption feature at energy below the HH exciton peak, we also observed a TA signal at the high-energy side of this peak, which we attribute to formation of LH-HH biexcitons or trions consisting of a charge and LH exciton.

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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.

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We studied the dynamics of transfer of photoexcited electronic states in a bilayer of the two-dimensional transition metal dichalcogenide ReS2 and tetracene, with the aim to produce triplets in the latter. This material combination was used as the band gap of ReS2 (1.5 eV) is slightly larger than the triplet energy of tetracene (1.25 eV). Using time-resolved optical absorption spectroscopy, transfer of photoexcited states from ReS2 to triplet states in tetracene was found to occur within 5 ps with an efficiency near 38%. This result opens up new possibilities for heterostructure design of two-dimensional materials with suitable organics to produce long-lived triplets. Triplets are of interest as sensitizers in a wide variety of applications including optoelectronics, photovoltaics, photocatalysis, and photon upconversion.

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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.

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Few-layered transition-metal dichalcogenides (TMDs) are increasingly popular materials for optoelectronics and catalysis. Among the various types of TMDs available today, rhenium chalcogenides (ReX2) stand out due to their remarkable electronic structure, such as the occurrence of anisotropic excitons and potential direct band gap behavior throughout multilayered stacks. In this paper, we have analyzed the nature and dynamics of charge carriers in highly crystalline liquid-phase exfoliated ReS2, using a unique combination of optical pump-THz probe and broad-band transient absorption spectroscopy. Two distinct time regimes are identified, both of which are dominated by unbound charge carriers despite the high exciton binding energy. In the first time regime, the unbound charge carriers cause an increase and a broadening of the exciton absorption band. In the second time regime, a peculiar narrowing of the excitonic absorption profile is observed, which we assign to the presence of built-in fields and/or charged defects. Our results pave the way to analyze spectrally complex transient absorption measurements on layered TMD materials and indicate the potential for ReS2 to produce mobile free charge carriers, a feat relevant for photovoltaic applications.

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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.

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In conventional solar cell semiconductor materials (predominantlySi)photons with energy higher than the band gap initially generate hot electrons and holes, which subsequently cool down to the band edge by phonon emission. Due to the latter process,the energy of the charge carriers in excess of the band gap is lost as heat and does not contribute to the conversion of solar to electrical power. If the excess energy is more than the band gap itcan in principle be utilized through a process known as carrier multiplication (CM) in which a single absorbed photon generates two (or more) pairs of electrons and holes. Thus, through CM the photon energy abovetwice the band gap enhancesthe photocurrentofa solar cell. In this review, we discuss recent progress in CM research in terms of fundamental understanding, emergenceof new materials for efficient CM, and CM based solar cell applications. Based on our current understanding, the CM threshold can get close to the minimal value of twice the band gap in materials where a photon induces an asymmetric electronic transition from a deeper valence band or to a higher conduction band. In addition,the material must have a low exciton binding energy and high charge carrier mobility, so that photoexcitation leads directly to the formation of free charges that can readily be extracted at external electrodes of a photovoltaic device. Percolative networks of coupled PbSe quantum dots, Sn/Pb based halide perovskites,and transition metal dichalcogenides such as MoTe2fulfill these requirements to a large extent. These findings pointtowards promising prospects for further development of new materials for highly efficient photovoltaics. @en

We studied the nature of excitons in the transition metal dichalcogenide alloy Mo0.6W0.4S2 compared to pure MoS2 and WS2 grown by atomic layer deposition (ALD). For this, optical absorption/transmission spectroscopy and time-dependent density functional theory (TDDFT) were used. The effects of temperature on A and B exciton peak energies and line widths in optical transmission spectra were compared between the alloy and pure MoS2 and WS2. On increasing the temperature from 25 to 293 K, the energy of the A and B exciton peaks decreases, while their line width increases due to exciton-phonon interactions. The exciton-phonon interactions in the alloy are closer to those for MoS2 than those for WS2. This suggests that exciton wave functions in the alloy have a larger amplitude on Mo atoms than that on W atoms. The experimental absorption spectra could be reproduced by TDDFT calculations. Interestingly, for the alloy, the Mo and W atoms had to be distributed over all layers. Conversely, we could not reproduce the experimental alloy spectrum by calculations on a structure with alternating layers, in which every other layer contains only Mo atoms and the layers in between also contain W atoms. For the latter atomic arrangement, the TDDFT calculations yielded an additional optical absorption peak that could be due to excitons with some charge transfer character. From these results, we conclude that ALD yields an alloy in which Mo and W atoms are distributed uniformly among all layers.

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Colloidal PbS nanoplatelets (NPLs) are highly interesting materials for near-infrared optoelectronic applications. We use ultrafast transient optical absorption spectroscopy to study the characteristics and dynamics of photoexcited excitons in ultrathin PbS NPLs with a cubic crystal structure. NPLs are synthesized at near room temperature from lead oleate and thiourea precursors; they show an optical absorption onset at 680 nm (1.8 eV) and photoluminescence at 720 nm (1.7 eV). By postsynthetically treating PbS NPLs with CdCl2, their photoluminescence quantum yield is strongly enhanced from 1.4% to 19.4%. The surface treatment leads to an increased lead to sulfur ratio in the structures and associated reduced nonradiative recombination. Additionally, exciton-phonon interactions in pristine and CdCl2 treated NPLs at frequencies of 1.96 and 2.04 THz are apparent from coherent oscillations in the transient absorption spectra. This study is an important step forward in unraveling and controlling the optical properties of IV-VI semiconductor NPLs.

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Carrier multiplication (CM) generates multiple electron-hole pairs in a semiconductor from a single absorbed photon with energy exceeding twice the band gap. Thus, CM provides a promising way to circumvent the Shockley-Queisser limit of solar cells. The ideal material for CM should have significant overlap with the solar spectrum and should be able to fully utilize the excess energy above the band gap for additional charge carrier generation. We report efficient CM in mixed Sn/Pb halide perovskites (band gap of 1.28 eV) with onset just above twice the band gap. The CM rate outcompetes the carrier cooling process leading to efficient CM with a quantum yield of 2 for photoexcitation at 2.8 times the band gap. Such efficient CM characteristics add to the many advantageous properties of mixed Sn/Pb metal halide perovskites for photovoltaic applications.

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To improve the stability and carrier mobility of quantum dot (QD) optoelectronic devices, encapsulation or pore infilling processes are advantageous. Atomic layer deposition (ALD) is an ideal technique to infill and overcoat QD films, as it provides excellent control over film growth at the sub-nanometer scale and results in conformal coatings with mild processing conditions. Different thicknesses of crystalline ZnO films deposited on InP QD films are studied with spectrophotometry and time-resolved microwave conductivity measurements. High carrier mobilities of 4 cm² (V s)⁻¹ and charge separation between the QDs and ZnO are observed. Furthermore, the results confirm that the stability of QD thin films is strongly improved when the inorganic ALD coating is applied. Finally, proof-of-concept photovoltaic devices of InP QD films are demonstrated with an ALD-grown ZnO electron extraction layer.

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We examine the impact of quantum confinement on the interaction potential between two charges in two-dimensional semiconductor nanosheets in solution. The resulting effective potential depends on two length scales, namely, the thickness d and an emergent length scale d∗ϵd/ϵsol, where ϵ is the permittivity of the nanosheet and ϵsol is the permittivity of the solvent. In particular, quantum confinement, and not electrostatics, is responsible for the logarithmic behavior of the effective potential for separations smaller than d, instead of the one-over-distance bulk Coulomb interaction. Finally, we corroborate that the exciton binding energy also depends on the two-dimensional Bohr radius a0 in addition to the length scales d and d∗ and analyze the consequences of this dependence.

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We present the phase diagram of free charges (electrons and holes), excitons, and biexcitons in highly excited CdSe nanoplatelets that predicts a crossover to a biexciton-dominated region at easily attainable low temperatures or high photoexcitation densities. Our findings extend previous work describing only free charges and excitons by introducing biexcitons into the equation of state, while keeping the exciton and biexciton binding energies constant in view of the relatively low density of free charges in this material. Our predictions are experimentally testable in the near future and offer the prospect of creating a quantum degenerate, and possibly even superfluid, biexciton gas. Furthermore, we also provide simple expressions giving analytical insight into the regimes of photoexcitation densities and temperatures in which excitons and biexcitons dominate the response of the nanoplatelets.

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