Understanding how junction resistances impact the conduction mechanism in nano-networks.

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.

New Theoretical Model to Describe Carrier Multiplication in Semiconductors: Explanation of Disparate Efficiency in MoTe2 versus PbS and PbSe.

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.

Developments and Challenges Involving Triplet Transfer across Organic/Inorganic Heterojunctions for Singlet Fission and Photon Upconversion.

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.

Stacking-Order-Dependent Excitonic Properties Reveal Interlayer Interactions in Bulk ReS2.

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.

Single-particle properties of topological Wannier excitons in bismuth chalcogenide nanosheets.

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.

Effects of Pump Photon Energy on Generation and Ultrafast Relaxation of Excitons and Charge Carriers in CdSe Nanoplatelets.

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.

Electronic Coupling of Highly Ordered Perovskite Nanocrystals in Supercrystals.

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.

Effects of the Structure and Temperature on the Nature of Excitons in the Mo0.6W0.4S2 Alloy.

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.

Photon Recycling in CsPbBr3 All-Inorganic Perovskite Nanocrystals.

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.

Generating Triplets in Organic Semiconductor Tetracene upon Photoexcitation of Transition Metal Dichalcogenide ReS2.

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.

Probing Excitons in Ultrathin PbS Nanoplatelets with Enhanced Near-Infrared Emission.

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.

Change in Tetracene Polymorphism Facilitates Triplet Transfer in Singlet Fission-Sensitized Silicon Solar Cells.

Singlet fission in tetracene generates two triplet excitons per absorbed photon. If these triplet excitons can be effectively transferred into silicon (Si), then additional photocurrent can be generated from photons above the bandgap of Si. This could alleviate the thermalization loss and increase the efficiency of conventional Si solar cells. Here, we show that a change in the polymorphism of tetracene deposited on Si due to air exposure facilitates triplet transfer from tetracene into Si. Magnetic field-dependent photocurrent measurements confirm that triplet excitons contribute to the photocurrent. The decay of tetracene delayed photoluminescence was used to determine a transfer efficiency of ∼36% into Si. Our study suggests that control over the morphology of tetracene during the deposition will be of great importance to boost the triplet transfer yield further.

Efficient Carrier Multiplication in Low Band Gap Mixed Sn/Pb Halide Perovskites.

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.

Engineering the Band Alignment in QD Heterojunction Films via Ligand Exchange.

Colloidal quantum dots (QDs) allow great flexibility in the design of optoelectronic devices, thanks to their size-dependent optical and electronic properties and the possibility to fabricate thin films with solution-based processing. In particular, in QD-based heterojunctions, the band gap of both components can be controlled by varying the size of the QDs. However, control over the band alignment between the two materials is required to tune the dynamics of carrier transfer across a heterostructure. We demonstrate that ligand exchange strategies can be used to control the band alignment of PbSe and CdSe QDs in a mixed QD solid, shifting it from a type-I to a type-II alignment. The change in alignment is observed in both spectroelectrochemical and transient absorption measurements, leading to a change in the energy of the conduction band edges in the two materials and in the direction of electron transfer upon photoexcitation. Our work demonstrates the possibility to tune the band offset of QD heterostructures via control of the chemical species passivating the QD surface, allowing full control over the energetics of the heterostructure without requiring changes in the QD composition.

Photoexcitation of PbS nanosheets leads to highly mobile charge carriers and stable excitons.

Solution-processable two-dimensional (2D) semiconductors with chemically tunable thickness and associated tunable band gaps are highly promising materials for ultrathin optoelectronics. Here, the properties of free charge carriers and excitons in 2D PbS nanosheets of different thickness are investigated by means of optical pump-terahertz probe spectroscopy. By analyzing the frequency-dependent THz response, a large quantum yield of excitons is found. The scattering time of free charge carriers increases with nanosheet thickness, which is ascribed to reduced effects of surface defects and ligands in thicker nanosheets. The data discussed provide values for the DC mobility in the range 550-1000 cm2 V-1 s-1 for PbS nanosheets with thicknesses ranging from 4 to 16 nm. Results underpin the suitability of colloidal 2D PbS nanosheets for optoelectronic applications.

Size-dependent exciton substructure in CdSe nanoplatelets and its relation to photoluminescence dynamics.

CdSe nanoplatelets can be synthesized with different lateral sizes; very small nanoplatelets have almost quantum dot like features (almost discrete exciton states), while very large ones are expected to have properties of colloidal quantum wells (exciton continuum). However, nanoplatelets can be in an intermediate confinement regime with a rich substructure of excitons, which is neither quantum dot like nor an ideal 2D exciton. In this manuscript, we discuss the experimental transition energies and relaxation dynamics of exciton states in CdSe platelets with varying lateral dimensions and compare them with a microscopic theoretical model including exciton-phonon scattering. The model takes special care of the interplay of confinement and Coulomb coupling in the intermediate regime showing strong changes with respect to simple weak or strong confinement models by solving the full four dimensional lateral factorization free exciton wavefunction. Depending on the platelet size broad resonances previously attributed to just ground and excited states are actually composed of a rich substructure of several exciton states in their temporal dynamics. We show that these factorization free exciton states can explain the spectral features observed in photoluminescence experiments. Furthermore we demonstrate that the interplay of exciton bright and dark states provides principle insights into the overall temporal relaxation dynamics, and allows tuning of the exciton cooling via lateral platelet size. Our results and theoretical approach are directly relevant for understanding e.g. the size tuneability of lasing, excitonic cooling dynamics or light harvesting applications in these and similar 2D systems of finite lateral size.

Room-Temperature Electron Transport in Self-Assembled Sheets of PbSe Nanocrystals with a Honeycomb Nanogeometry.

It has been shown recently that atomically coherent superstructures of a nanocrystal monolayer in thickness can be prepared by self-assembly of monodisperse PbSe nanocrystals, followed by oriented attachment. Superstructures with a honeycomb nanogeometry are of special interest, as theory has shown that they are regular 2-D semiconductors, but with the highest valence and lowest conduction bands being Dirac-type, that is, with a linear energy-momentum relation around the K-points in the zone. Experimental validation will require cryogenic measurements on single sheets of these nanocrystal monolayer superstructures. Here, we show that we can incorporate these fragile superstructures into a transistor device with electrolyte gating, control the electron density, and measure the electron transport characteristics at room temperature. The electron mobility is 1.5 ± 0.5 cm2 V-1 s-1, similar to the mobility observed with terahertz spectroscopy on freestanding superstructures. The terahertz spectroscopic data point to pronounced carrier scattering on crystallographic imperfections in the superstructure, explaining the limited mobility.

Spectroscopic Evidence for the Contribution of Holes to the Bleach of Cd-Chalcogenide Quantum Dots.

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.

Charge Mobility and Recombination Mechanisms in Tellurium van der Waals Solid.

Trigonal tellurium is a small band gap elemental semiconductor consisting of van der Waals bound one-dimensional helical chains of tellurium atoms. We study the temperature dependence of the charge carrier mobility and recombination pathways in bulk tellurium. Electrons and holes are generated by irradiation of the sample with 3 MeV electrons and detected by time-resolved microwave conductivity measurements. A theoretical model is used to explain the experimental observations for different charge densities and temperatures. Our analysis reveals a high room temperature mobility of 190 ± 20 cm2 V-1 s-1. The mobility is thermally deactivated, suggesting a band-like transport mechanism. According to our analysis, the charges predominantly recombine via radiative recombination with a radiative yield close to 98%, even at room temperature. The remaining charges recombine by either trap-assisted (Shockley-Read-Hall) recombination or undergo trapping to deep traps. The high mobility, near-unity radiative yield, and possibility of large-scale production of atomic wires by liquid exfoliation make Te of high potential for next-generation nanoelectronic and optoelectronic applications, including far-infrared detectors and lasers.

Model To Determine a Distinct Rate Constant for Carrier Multiplication from Experiments.

Carrier multiplication (CM) is the process in which multiple electron-hole pairs are created upon absorption of a single photon in a semiconductor. CM by an initially hot charge carrier occurs in competition with cooling by phonon emission, with the respective rates determining the CM efficiency. Up until now, CM rates have only been calculated theoretically. We show for the first time how to extract a distinct CM rate constant from experimental data of the relaxation time of hot charge carriers and the yield of CM. We illustrate this method for PbSe quantum dots. Additionally, we provide a simplified method using an estimated energy loss rate to estimate the CM rate constant just above the onset of CM, when detailed experimental data of the relaxation time is missing.