Tuning Electron-Phonon Interactions in Nanocrystals through Surface Termination

Intrinsically Slow Cooling of Hot Electrons in CdSe Nanocrystals Compared to CdS

The utilization of excited charge carriers in semiconductor nanocrystals (NCs) for optoelectronic technologies has been a long-standing goal in the field of nanoscience. Experimental efforts to extend the lifetime of excited carriers have therefore been a principal focus. To understand the limits of these lifetimes, in this work, we theoretically study the time scales of pure electron relaxation in negatively charged NCs composed of two prototypical materials: CdSe and CdS. We find that hot electrons in CdSe have lifetimes that are 5 to 6 orders of magnitude longer than in CdS when the relaxation is governed only by the intrinsic properties of the materials. Although these two materials are known to have somewhat different electronic structure, we elucidate how this enormous difference in lifetimes arises from relatively small quantitative differences in electronic energy gaps and phonon frequencies, as well as the crucial role of Fröhlich-type electron-phonon couplings.

Ligand Controls Excited Charge Carrier Dynamics in Metal-Rich CdSe Quantum Dots: Computational Insights

Small metal-rich semiconducting quantum dots (QDs) are promising for solid-state lighting and single-photon emission due to their highly tunable yet narrow emission line widths. Nonetheless, the anionic ligands commonly employed to passivate these QDs exert a substantial influence on the optoelectronic characteristics, primarily owing to strong electron-phonon interactions. In this work, we combine time-domain density functional theory and nonadiabatic molecular dynamics to investigate the excited charge carrier dynamics of Cd28Se17X22 QDs (X = HCOO-, OH-, Cl-, and SH-) at ambient conditions. These chemically distinct but regularly used molecular groups influence the dynamic surface-ligand interfacial interactions in Cd-rich QDs, drastically modifying their vibrational characteristics. The strong electron-phonon coupling leads to substantial transient variations at the band edge states. The strength of these interactions closely depends on the physicochemical characteristics of passivating ligands. Consequently, the ligands largely control the nonradiative recombination rates and emission characteristics in these QDs. Our simulations indicate that Cd28Se17(OH)22 has the fastest nonradiative recombination rate due to the strongest electron-phonon interactions. Conversely, QDs passivated with thiolate or chloride exhibit considerably longer carrier lifetimes and suppressed nonradiative processes. The ligand-controlled electron-phonon interactions further give rise to the broadest and narrowest intrinsic optical line widths for OH and Cl-passivated single QDs, respectively. Obtained computational insights lay the groundwork for designing appropriate passivating ligands on metal-rich QDs, making them suitable for a wide range of applications, from blue LEDs to quantum emitters.

Nonequilibrium Lattice Dynamics of Individual and Attached PbSe Quantum Dots under Photoexcitation

Quantum dot (QD) solids are emerging materials for many optoelectronic applications. To enhance interdot coupling and charge transport, surface ligands can be removed, allowing individual QDs to be attached along specific crystal orientations (termed "oriented attachment"). Optimizing the electronic and optical properties of QD solids demands a comprehensive understanding of the nanoscale energy flow in individual and attached QDs under photoexcitation. In this work, we employed ultrafast electron diffraction to directly measure how oriented attachment along ⟨100⟩ directions affects the nonequilibrium lattice dynamics of lead selenide QDs. The oriented attachment anisotropically alters the ultrafast energy relaxation along specific crystal axes. Along the ⟨100⟩ directions, both the lattice deformation and atomistic random motions are suppressed in comparison with those of individual QDs. Conversely, the effects are enhanced along the unattached ⟨111⟩ directions due to ligand removal. The oriented attachment switches the major lattice thermalization pathways from ⟨100⟩ to ⟨111⟩ directions.

Size Dependent Specific Heat Capacity of PbSe Nanocrystals

Specific heat capacity is one of the most fundamental thermodynamic properties of materials. In this work, we measured the specific heat capacity of PbSe nanocrystals with diameters ranging from 5 to 23 nm, and its value increases significantly from 0.2 to 0.6 J g-1 °C-1. We propose a mass assignment model to describe the specific heat capacity of nanocrystals, which divides it into four parts: electron, inner, surface, and ligand. By eliminating the contribution of ligand and electron specific heat capacity, the specific heat capacity of the inorganic core is linearly proportional to its surface-to-volume ratio, showing the size dependence. Based on this linear relationship, surface specific heat capacity accounts for 40-60% of the specific heat capacity of nanocrystals with size decreasing. It can be attributed to the uncoordinated surface atoms, which is evidenced by the appearance of extra surface phonons in Raman spectra and ab initio molecular dynamics (AIMD) simulations.

Surface Reconstructions in II-VI Quantum Dots

Although density functional theory (DFT) calculations have been crucial in our understanding of colloidal quantum dots (QDs), simulations are commonly carried out on QD models that are significantly smaller than those generally found experimentally. While smaller models allow for efficient study of local surface configurations, increasing the size of the QD model will increase the size or number of facets, which can in turn influence the energetics and characteristics of trap formation. Moreover, core-shell structures can only be studied with QD models that are large enough to accommodate the different layers with the correct thickness. Here, we use DFT calculations to study the electronic properties of QDs as a function of size, up to a diameter of ∼4.5 nm. We show that increasing the size of QD models traditionally used in DFT studies leads to a disappearance of the band gap and localization of the HOMO and LUMO levels on facet-specific regions of the QD surface. We attribute this to the lateral coupling of surface orbitals and the formation of surface bands. The introduction of surface vacancies and their a posteriori refilling with Z-type ligands leads to surface reconstructions that widen the band gap and delocalize both the HOMO and LUMO. These results show that the surface geometry of the facets plays a pivotal role in defining the electronic properties of the QD.

The smallest PbS nanocrystals pervasively show decreased brightness, linked to surface-mediated decay on the average particle

PbS semiconductor nanocrystals (NCs) have been heavily explored for infrared optoelectronics but can exhibit visible-wavelength quantum-confined optical gaps when sufficiently small (⌀ = 1.8-2.7 nm). However, small PbS NCs traditionally exhibited very broad ensemble absorption linewidths, attributed to poor size-heterogeneity. Here, harnessing recent synthetic advances, we report photophysical measurements on PbS ensembles that span this underexplored size range. We observe that the smallest PbS NCs pervasively exhibit lower brightness and anomalously accelerated photoluminescence decays-relative to the idealized photophysical models that successfully describe larger NCs. We find that effects of residual ensemble size-heterogeneity are insufficient to explain our observations, so we explore plausible processes that are intrinsic to individual nanocrystals. Notably, the anomalous decay kinetics unfold, surprisingly, over hundreds-of-nanosecond timescales. These are poorly matched to effects of direct carrier trapping or fine-structure thermalization but are consistent with non-radiative recombination linked to a dynamic surface. Thus, the progressive enhancement of anomalous decay in the smallest particles supports predictions that the surface plays an outsized role in exciton-phonon coupling. We corroborate this claim by showing that the anomalous decay is significantly remedied by the installation of a rigidifying shell. Intriguingly, our measurements show that the anomalous aspect of these kinetics is insensitive to temperature between T = 298 and 77 K, offering important experimental constraint on possible mechanisms involving structural fluctuations. Thus, our findings identify and map the anomalous photoluminescence kinetics that become pervasive in the smallest PbS NCs and call for targeted experiments and theory to disentangle their origin.

Design Rules for Obtaining Narrow Luminescence from Semiconductors Made in Solution

Solution-processed semiconductors are in demand for present and next-generation optoelectronic technologies ranging from displays to quantum light sources because of their scalability and ease of integration into devices with diverse form factors. One of the central requirements for semiconductors used in these applications is a narrow photoluminescence (PL) line width. Narrow emission line widths are needed to ensure both color and single-photon purity, raising the question of what design rules are needed to obtain narrow emission from semiconductors made in solution. In this review, we first examine the requirements for colloidal emitters for a variety of applications including light-emitting diodes, photodetectors, lasers, and quantum information science. Next, we will delve into the sources of spectral broadening, including "homogeneous" broadening from dynamical broadening mechanisms in single-particle spectra, heterogeneous broadening from static structural differences in ensemble spectra, and spectral diffusion. Then, we compare the current state of the art in terms of emission line width for a variety of colloidal materials including II-VI quantum dots (QDs) and nanoplatelets, III-V QDs, alloyed QDs, metal-halide perovskites including nanocrystals and 2D structures, doped nanocrystals, and, finally, as a point of comparison, organic molecules. We end with some conclusions and connections, including an outline of promising paths forward.

Simulations of nonradiative processes in semiconductor nanocrystals

The description of carrier dynamics in spatially confined semiconductor nanocrystals (NCs), which have enhanced electron-hole and exciton-phonon interactions, is a great challenge for modern computational science. These NCs typically contain thousands of atoms and tens of thousands of valence electrons with discrete spectra at low excitation energies, similar to atoms and molecules, that converge to the continuum bulk limit at higher energies. Computational methods developed for molecules are limited to very small nanoclusters, and methods for bulk systems with periodic boundary conditions are not suitable due to the lack of translational symmetry in NCs. This perspective focuses on our recent efforts in developing a unified atomistic model based on the semiempirical pseudopotential approach, which is parameterized by first-principle calculations and validated against experimental measurements, to describe two of the main nonradiative relaxation processes of quantum confined excitons: exciton cooling and Auger recombination. We focus on the description of both electron-hole and exciton-phonon interactions in our approach and discuss the role of size, shape, and interfacing on the electronic properties and dynamics for II-VI and III-V semiconductor NCs.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

In this work, we report a new methodology for nonadiabatic molecular dynamics calculations within the extended tight-binding (xTB) framework. We demonstrate the applicability of the developed approach to finite and periodic systems with thousands of atoms by modeling "hot" electron relaxation dynamics in silicon nanocrystals and electron-hole recombination in both a graphitic carbon nitride monolayer and a titanium-based metal-organic framework (MOF). This work reports the nonadiabatic dynamic simulations in the largest Si nanocrystals studied so far by the xTB framework, with diameters up to 3.5 nm. For silicon nanocrystals, we find a non-monotonic dependence of "hot" electron relaxation rates on the nanocrystal size, in agreement with available experimental reports. We rationalize this relationship by a combination of decreasing nonadiabatic couplings related to system size and the increase of available coherent transfer pathways in systems with higher densities of states. We emphasize the importance of proper treatment of coherences for obtaining such non-monotonic dependences. We characterize the electron-hole recombination dynamics in the graphitic carbon nitride monolayer and the Ti-containing MOF. We demonstrate the importance of spin-adaptation and proper sampling of surface hopping trajectories in modeling such processes. We also assess several trajectory surface hopping schemes and highlight their distinct qualitative behavior in modeling the excited-state dynamics in superexchange-like models depending on how they handle coherences between nearly parallel states.

Ultra-narrow room-temperature emission from single CsPbBr3 perovskite quantum dots

Semiconductor quantum dots have long been considered artificial atoms, but despite the overarching analogies in the strong energy-level quantization and the single-photon emission capability, their emission spectrum is far broader than typical atomic emission lines. Here, by using ab-initio molecular dynamics for simulating exciton-surface-phonon interactions in structurally dynamic CsPbBr₃ quantum dots, followed by single quantum dot optical spectroscopy, we demonstrate that emission line-broadening in these quantum dots is primarily governed by the coupling of excitons to low-energy surface phonons. Mild adjustments of the surface chemical composition allow for attaining much smaller emission linewidths of 35−65 meV (vs. initial values of 70–120 meV), which are on par with the best values known for structurally rigid, colloidal II-VI quantum dots (20−60 meV). Ultra-narrow emission at room-temperature is desired for conventional light-emitting devices and paramount for emerging quantum light sources.

Narrow emission is desired for light-emitting devices. Here, Kovalenko et al. demonstrate that the emission line-broadening in perovskite quantum dots is dominated by the coupling between excitons and surface phonon modes which can be controlled by minimal surface modifications.

Toward Bright Mid-Infrared Emitters: Thick-Shell n-Type HgSe/CdS Nanocrystals

A procedure is developed for the growth of thick, conformal CdS shells that preserve the optical properties of 5 nm HgSe cores. The n-doping of the HgSe/CdS core/shell particles is quantitatively tuned through a simple postsynthetic Cd treatment, while the doping is monitored via the intraband optical absorption at 5 μm wavelength. Photoluminescence lifetime and quantum yield measurements show that the CdS shell greatly increases the intraband emission intensity. This indicates that decoupling the excitation from the environment reduces the nonradiative recombination. We find that weakly n-type HgSe/CdS are the brightest solution-phase mid-infrared chromophores reported to date at room temperature, achieving intraband photoluminescence quantum yields of 2%. Such photoluminescence corresponds to intraband lifetimes in excess of 10 ns, raising important questions about the fundamental limits to achievable slow intraband relaxation in quantum dots.

Interplay of Surface and Interior Modes in Exciton-Phonon Coupling at the Nanoscale

Exciton-phonon coupling (EXPC) plays a key role in the optoelectronic properties of semiconductor nanocrystals (NCs), but a microscopic picture of EXPC is still lacking, particularly regarding the magnitude and scaling with NC size, the dependence on phonon frequency, and the role of the NC surface. The computational complexity associated with accurately describing excitons and phonons has limited previous theoretical studies of EXPC to small NCs, noninteracting electron-hole models, and/or a small number of phonon modes. Here, we develop an atomistic approach for describing EXPC in NCs of experimentally relevant sizes. We validate our approach by calculating the reorganization energies, a measure of EXPC, for CdSe and CdSe-CdS core-shell NCs, finding good agreement with experimental measurements. We demonstrate that exciton formation distorts the NC lattice primarily along the coordinates of low-frequency acoustic modes. Modes at the NC surface play a significant role in smaller NCs while interior modes dominate for larger systems.

The role of alkane chain in primary amine capped CdSe and CdS quantum dots from first-principles

In this study, we performab initiocalculations, using density functional theory, to provide more insights about the role of alkane chain in primary amine capped (CdSe)₃₃and (CdS)₃₃quantum dots (QDs). We passivate the QDs surfaces with seven primary amines of different carbon chain lengths starting from NH₃to hexylamine. The primary amine ligands induce a blue shift in the band gap of the ligated QDs, in agreement with experimental studies, but the alkane chain itself show negligible changes in the band gap. By increasing the chain length the binding energy between ligands and the QDs increases but its rate decreases due to the increase of steric hindrance between the ligands. The role of van der Waals forces in such behavior is found to be notable which is done by performing geometry optimization through adding and neglecting the dispersion correction effects for each system. The results of this study can provide helpful information for ligand selectivity in controlling the size and properties of the QDs using primary amines.

Facet-Oriented Coupling Enables Fast and Sensitive Colloidal Quantum Dot Photodetectors

Charge carrier transport in colloidal quantum dot (CQD) solids is strongly influenced by coupling among CQDs. The shape of as-synthesized CQDs results in random orientational relationships among facets in CQD solids, and this limits the CQD coupling strength and the resultant performance of optoelectronic devices. Here, colloidal-phase reconstruction of CQD surfaces, which improves facet alignment in CQD solids, is reported. This strategy enables control over CQD faceting and allows demonstration of enhanced coupling in CQD solids. The approach utilizes post-synthetic resurfacing and unites surface passivation and colloidal stability with a propensity for dots to couple via (100):(100) facets, enabling increased hole mobility. Experimentally, the CQD solids exhibit a 10× increase in measured hole mobility compared to control CQD solids, and enable photodiodes (PDs) exhibiting 70% external quantum efficiency (vs 45% for control devices) and specific detectivity, D* > 10¹²  Jones, each at 1550 nm. The photodetectors feature a 7 ns response time for a 0.01 mm² area-the fastest reported for solution-processed short-wavelength infrared PDs.

Multiple exciton generation in isolated and interacting silicon nanocrystals

An important challenge in the field of renewable energy is the development of novel nanostructured solar cell devices which implement low-dimensional materials to overcome the limits of traditional photovoltaic systems. For optimal energy conversion in photovoltaic devices, one important requirement is that the full energy of the solar spectrum is effectively used. In this context, the possibility of exploiting features and functionalities induced by the reduced dimensionality of the nanocrystalline phase, in particular by the quantum confinement of the electronic density, can lead to a better use of the carrier excess energy and thus to an increment of the thermodynamic conversion efficiency of the system. Carrier multiplication, i.e. the generation of multiple electron-hole pairs after absorption of one single high-energy photon (with energy at least twice the energy gap of the system), can be exploited to maximize cell performance, promoting a net reduction of loss mechanisms. Over the past fifteen years, carrier multiplication has been recorded in a large variety of semiconductor nanocrystals and other nanostructures. Owing to the role of silicon in solar cell applications, the mission of this review is to summarize the progress in this fascinating research field considering carrier multiplication in Si-based low-dimensional systems, in particular Si nanocrystals, both from the experimental and theoretical point of view, with special attention given to the results obtained by ab initio calculations.

Dynamic lattice distortions driven by surface trapping in semiconductor nanocrystals

Nonradiative processes limit optoelectronic functionality of nanocrystals and curb their device performance. Nevertheless, the dynamic structural origins of nonradiative relaxations in such materials are not understood. Here, femtosecond electron diffraction measurements corroborated by atomistic simulations uncover transient lattice deformations accompanying radiationless electronic processes in colloidal semiconductor nanocrystals. Investigation of the excitation energy dependence in a core/shell system shows that hot carriers created by a photon energy considerably larger than the bandgap induce structural distortions at nanocrystal surfaces on few picosecond timescales associated with the localization of trapped holes. On the other hand, carriers created by a photon energy close to the bandgap of the core in the same system result in transient lattice heating that occurs on a much longer 200 picosecond timescale, dominated by an Auger heating mechanism. Elucidation of the structural deformations associated with the surface trapping of hot holes provides atomic-scale insights into the mechanisms deteriorating optoelectronic performance and a pathway towards minimizing these losses in nanocrystal devices.

Charge trapping can lead to severe nonradiative losses in colloidal semiconductor nanocrystals (NCs). The authors report femtosecond electron diffraction measurements on photoexcited NCs to reveal atomic-scale insights into how localization of charges at trap sites induce surface deformations.

A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach

We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.

Manipulating Electronic Structure from the Bottom-Up: Colloidal Nanocrystal-Based Semiconductors

Semiconductors assembled from colloidal nanocrystals (NCs) are often described in the same terms as their single-crystalline counterparts with references to conduction and valence band edges, doping densities, and electronic defects; however, how and why semiconductor properties manifest in these bottom-up fabricated thin films can be fundamentally different. In this Perspective, we describe the factors that determine the electronic structure in colloidal NC-based semiconductors, and comment on approaches for measuring or calculating this electronic structure. Finally, we discuss future directions for these semiconductors and highlight their potential to bridge the divide between localized quantum effects and long-range transport in thin films.

Intersubband Relaxation in CdSe Colloidal Quantum Wells

The dynamics of intersubband relaxation are critical to quantum well technologies such as quantum cascade lasers and quantum well infrared photodetectors. Here, intersubband relaxation in CdSe colloidal quantum wells, or nanoplatelets, is studied via pump-push-probe transient spectroscopy. An initial interband pump pulse is followed by a secondary infrared push excitation, resonant with intersubband absorption, which promotes electrons from the first conduction band of the quantum well to the second conduction band. A probe pulse monitors subsequent electron cooling to the band edge of the quantum well. Using this technique, intersubband relaxation is studied as a function of critical variables such as colloidal quantum well size and thickness, surface ligand chemistry, temperature, and excitation pulse intensity. Larger quantum well sizes, judicious selection of surface ligand chemistry (e.g., thiolates), low temperatures, and elevated push pulse fluences slow intersubband relaxation. However, compared to resonant intraband relaxation in colloidal quantum dots (up to hundreds of picoseconds), intersubband relaxation in colloidal quantum wells is rapid (<1 ps) under all examined conditions. These experiments indicate that rapid relaxation is driven by both LO phonon and surface scattering. The short time scale of relaxation observed in these materials may hinder intersubband technologies such as mid-infrared detectors, although such rapid relaxation may prove valuable in optical switching.

A neutron scattering perspective on the structure, softness and dynamics of the ligand shell of PbS nanocrystals in solution

Small-angle neutron and X-ray scattering, neutron backscattering and neutron time-of-flight spectroscopy are applied to reveal the structure of the ligand shell, the temperature-dependent diffusion properties and the phonon spectrum of PbS nanocrystals functionalized with oleic acid in deuterated hexane. The nanocrystals decorated with oleic acid as well as the desorbed ligand molecules exhibit simple Brownian diffusion with a Stokes-Einstein temperature-dependence and inhibited freezing. Ligand molecules desorbed from the surface show strong spatial confinement. The phonon spectrum of oleic acid adsorbed to the nanocrystal surface exhibits hybrid modes with a predominant Pb-character. Low-energy surface modes of the NCs are prominent and indicate a large mechanical softness in solution. This work provides comprehensive insights into the ligand-particle interaction of colloidal nanocrystals in solution and highlights its effect on the diffusion and vibrational properties as well as their mechanical softness.

Size- and temperature-dependent photoluminescence spectra of strongly confined CsPbBr3 quantum dots

Lead-halide perovskite nanocrystals (NCs) are receiving much attention as a potential high-quality source of photons due to their superior luminescence properties in comparison to other semiconductor NCs. To date, research has focused mostly on NCs with little or no quantum confinement. Here, we measured the size- and temperature-dependent photoluminescence (PL) from strongly confined CsPbBr₃ quantum dots (QDs) with highly uniform size distributions, and examined the factors determining the evolution of the energy and linewidth of the PL with varying temperature and QD size. Compared to the extensively studied II-VI QDs, the spectral position of PL from CsPbBr₃ QDs shows an opposite dependence on temperature, with weaker dependence overall. On the other hand, the PL linewidth is much more sensitive to the temperature and size of the QDs compared to II-VI QDs, indicating much stronger coupling of excitons to the vibrational degrees of freedom both in the lattice and at the surface of the QDs.

Charge transport in semiconductors assembled from nanocrystal quantum dots

The potential of semiconductors assembled from nanocrystals has been demonstrated for a broad array of electronic and optoelectronic devices, including transistors, light emitting diodes, solar cells, photodetectors, thermoelectrics, and phase change memory cells. Despite the commercial success of nanocrystal quantum dots as optical absorbers and emitters, applications involving charge transport through nanocrystal semiconductors have eluded exploitation due to the inability to predictively control their electronic properties. Here, we perform large-scale, ab initio simulations to understand carrier transport, generation, and trapping in strongly confined nanocrystal quantum dot-based semiconductors from first principles. We use these findings to build a predictive model for charge transport in these materials, which we validate experimentally. Our insights provide a path for systematic engineering of these semiconductors, which in fact offer previously unexplored opportunities for tunability not achievable in other semiconductor systems.

Atomic Sulfur Passivation Improves the Photoelectrochemical Performance of ZnSe Nanorods

We introduced atomic sulfur passivation to tune the surface sites of heavy metal-free ZnSe nanorods, with a Zn²⁺-rich termination surface, which are initially capped with organic ligands and under-coordinated with Se. The S²⁻ ions from a sodium sulfide solution were used to partially substitute a 3-mercaptopropionic acid ligand, and to combine with under-coordinated Zn termination atoms to form a ZnS monolayer on the ZnSe surface. This treatment removed the surface traps from the ZnSe nanorods, and passivated defects formed during the previous ligand exchange process, without sacrificing the efficient hole transfer. As a result, without using any co-catalysts, the atomic sulfur passivation increased the photocurrent density of TiO₂/ZnSe photoanodes from 273 to 325 μA/cm². Notably, without using any sacrificial agents, the photocurrent density for sulfur-passivated TiO₂/ZnSe nanorod-based photoanodes remained at almost 100% of its initial value after 300 s of continuous operation, while for the post-deposited ZnS passivation layer, or those based on ZnSe/ZnS core–shell nanorods, it declined by 28% and 25%, respectively. This work highlights the advantages of the proper passivation of II-VI semiconductor nanocrystals as an efficient approach to tackle the efficient charge transfer and stability of photoelectrochemical cells based thereon.

Phonon-Mediated and Weakly Size-Dependent Electron and Hole Cooling in CsPbBr3 Nanocrystals Revealed by Atomistic Simulations and Ultrafast Spectroscopy

We combine state-of-the-art ultrafast photoluminescence and absorption spectroscopy and nonadiabatic molecular dynamics simulations to investigate charge-carrier cooling in CsPbBr3 nanocrystals over a very broad size regime, from 0.8 to 12 nm. Contrary to the prevailing notion that polaron formation slows down charge-carrier cooling in lead-halide perovskites, no suppression of carrier cooling is observed in CsPbBr3 nanocrystals except for a slow cooling (over ∼10 ps) of "warm" electrons in the vicinity (within ∼0.1 eV) of the conduction band edge. At higher excess energies, electrons and holes cool with similar rates, on the order of 1 eV ps-1 carrier-1, increasing weakly with size. Our ab initio simulations suggest that cooling proceeds via fast phonon-mediated intraband transitions driven by strong and size-dependent electron-phonon coupling. The presented experimental and computational methods yield the spectrum of involved phonons and may guide the development of devices utilizing hot charge carriers.

Hot Electron Cooling in Silicon Nanoclusters via Landau-Zener Nonadiabatic Molecular Dynamics: Size Dependence and Role of Surface Termination

We develop a new express methodology for modeling excited-state dynamics occurring in dense manifolds of electronic states in atomistic systems. The approach leverages a modified Landau-Zener formula, the neglect of a back-reaction approximation, and the highly efficient density functional tight-binding method. We study the hot electron dynamics in a series of H- and F-terminated silicon nanocrystals (NCs) containing up to several hundred atoms. We explain the slower electron cooling dynamics in F-terminated NCs by the larger energy gaps between the adjacent electronic states in these systems as well as their slower fluctuations. We conclude that both the mass and chemical identity of the surface termination groups equally influence the electron dynamics, on average. However, the mass effect becomes dominant for higher-energy excitations. We find that the electron decay dynamics in F-terminated NCs has a greater sensitivity to the mass of the surface ligands than do the H-terminated NCs and explain this observation by the details of the electron-phonon coupling in the systems. We find that in the H-terminated NCs, electronic transitions in the cooling process occur predominantly between the surface states, whereas in F-terminated Si NCs, both surface and NC core states are coupled to the nuclear vibrations. We find that electron energy relaxation is accelerated in larger NCs and attribute this effect to the higher densities of states and smaller energy gaps in these systems.

Modeling nonadiabatic dynamics in condensed matter materials: some recent advances and applications

This review focuses on recent developments in the field of nonadiabatic molecular dynamics (NA-MD), with particular attention given to condensed-matter systems. NA-MD simulations for small molecular systems can be performed using high-level electronic structure (ES) calculations, methods accounting for the quantization of nuclear motion, and using fewer approximations in the dynamical methodology itself. Modeling condensed-matter systems imposes many limitations on various aspects of NA-MD computations, requiring approximations at various levels of theory-from the ES, to the ways in which the coupling of electrons and nuclei are accounted for. Nonetheless, the approximate treatment of NA-MD in condensed-phase materials has gained a spin lately in many applied studies. A number of advancements of the methodology and computational tools have been undertaken, including general-purpose methods, as well as those tailored to nanoscale and condensed matter systems. This review summarizes such methodological and software developments, puts them into the broader context of existing approaches, and highlights some of the challenges that remain to be solved.

Evidence of Skewness and Sub-Gaussian Character in Temperature-Dependent Distributions of One Million Electronic Excitation Energies in PbS Quantum Dots

Obtaining statistical distributions by sampling a large number of conformations is vital for an accurate description of temperature-dependent properties of chemical systems. However, constructing distributions with 10⁵-10⁶ samples is computationally challenging because of the prohibitively high computational cost of performing first-principles quantum mechanical calculations. In this work, we present a new technique called the effective stochastic potential configuration interaction singles (ESP-CIS) method to obtain excitation energies. The ESP-CIS method uses random matrix theory for the construction of an effective stochastic representation of the Fock operator and combines it with the CIS method. Excited-state energies of PbS quantum dots (0.75-1.75 nm) at temperatures of 10-400 K were calculated using the ESP-CIS method. Results from a total of 27 million excitation energy calculations revealed the distributions to be sub-Gaussian in nature with negative skewness, which progressively became red-shifted with increasing temperature. This study demonstrates the efficacy of the ESP-CIS method as a general-purpose method for efficient excited-state calculations.

Causes and Solutions of Recombination in Perovskite Solar Cells

Organic-inorganic hybrid perovskite materials are receiving increasing attention and becoming star materials on account of their unique and intriguing optical and electrical properties, such as high molar extinction coefficient, wide absorption spectrum, low excitonic binding energy, ambipolar carrier transport property, long carrier diffusion length, and high defects tolerance. Although a high power conversion efficiency (PCE) of up to 22.7% is certified for perovskite solar cells (PSCs), it is still far from the theoretical Shockley-Queisser limit efficiency (30.5%). Obviously, trap-assisted nonradiative (also called Shockley-Read-Hall, SRH) recombination in perovskite films and interface recombination should be mainly responsible for the above efficiency distance. Here, recent research advancements in suppressing bulk SRH recombination and interface recombination are systematically investigated. For reducing SRH recombination in the films, engineering perovskite composition, additives, dimensionality, grain orientation, nonstoichiometric approach, precursor solution, and post-treatment are explored. The focus herein is on the recombination at perovskite/electron-transporting material and perovskite/hole-transporting material interfaces in normal or inverted PSCs. Strategies for suppressing bulk and interface recombination are described. Additionally, the effect of trap-assisted nonradiative recombination on hysteresis and stability of PSCs is discussed. Finally, possible solutions and reasonable prospects for suppressing recombination losses are presented.

PbS Nanocrystals Made with Excess PbCl2 Have an Intrinsic Shell that Reduces Their Stokes Shift

The use of excess PbCl₂ in the synthesis of PbS nanocrystals has become a convenient route to produce narrow-line-width infrared emitters. However, these materials have found limited adoption in optoelectronic devices-even compared to PbS nanocrystals prepared with lead oleate. Here, using both transmission electron microscopy and small-angle X-ray scattering, we show that excess PbCl₂ results in larger-diameter PbS nanocrystals for the same excitonic features, which is consistent with the formation of an intrinsic insulating shell. We observe further differences in excess-lead-chloride nanocrystals consistent with a shell, including lattice strain and smaller Stokes shifts for intermediate sizes (⌀: 4.8-6.8 nm) that match the passivation/rigidification predicted for a chloride-terminate surface. Our results clarify and rationalize the divergent properties of PbS nanocrystals prepared using different synthetic methodologies, give guidance for device implementation, and offer a new target for synthetic control.

Nanocrystal superlattices as phonon-engineered solids and acoustic metamaterials

Phonon engineering of solids enables the creation of materials with tailored heat-transfer properties, controlled elastic and acoustic vibration propagation, and custom phonon-electron and phonon-photon interactions. These can be leveraged for energy transport, harvesting, or isolation applications and in the creation of novel phonon-based devices, including photoacoustic systems and phonon-communication networks. Here we introduce nanocrystal superlattices as a platform for phonon engineering. Using a combination of inelastic neutron scattering and modeling, we characterize superlattice-phonons in assemblies of colloidal nanocrystals and demonstrate that they can be systematically engineered by tailoring the constituent nanocrystals, their surfaces, and the topology of superlattice. This highlights that phonon engineering can be effectively carried out within nanocrystal-based devices to enhance functionality, and that solution processed nanocrystal assemblies hold promise not only as engineered electronic and optical materials, but also as functional metamaterials with phonon energy and length scales that are unreachable by traditional architectures.

Carboxylate Anchors Act as Exciton Reporters in 1.3 nm Indium Phosphide Nanoclusters

Developing interfacial probes of ligand-nanocluster interactions is crucial for understanding and tailoring the optoelectronic properties of these emerging nanomaterials. Using transient IR spectroscopy, we demonstrate that ligand vibrational modes of oleate-capped 1.3 nm InP nanoclusters report on the photogenerated exciton. The exciton induces an intensity change in the asymmetric carboxylate stretching mode by 57% while generating no appreciable shift in frequency. Thus, the observed difference signal is attributed to an exciton-induced change in the dipole magnitude of the asymmetric carboxylate stretching mode. Additionally, the transient IR data reveal that the infrared dipole change is dependent on the geometry of the ligand bound to the nanocluster. The experimental results are interpreted using TDDFT calculations, which identify how the spatial dependence of an exciton-induced electron density shift affects the vibrational motion of the carboxylate anchors. More broadly, this work demonstrates transient IR spectroscopy as a useful method for characterizing ligand-nanocluster coupling interactions.

Effects of a Lead Chloride Shell on Lead Sulfide Quantum Dots

The size of a quantum-confined nanocrystal determines the energies of its excitonic transitions. Previous work has correlated the diameters of PbS nanocrystals to their excitonic absorption; however, we observe that PbS quantum dots synthesized in saturated dispersions of PbCl₂ can deviate from the previous 1S_h-1S_e energy vs diameter curve by 0.8 nm. In addition, their surface differs chemically from that of PbS quantum dots produced via other syntheses. We find that these nanocrystals are coated in a shell that is measurable in transmission electron micrographs and contains lead and chlorine, beyond the monatomic chlorine termination previously proposed. This finding has implications for understanding the growth mechanism of this reaction, the line width of these quantum dots' photoluminescence, and electronic transport within films of these nanocrystals. Such fundamental knowledge is critical to applications of PbS quantum dots such as single-photon sources, photodetectors, solar cells, light-emitting diodes, lasers, and biological labels.

Effect of Bond Dispersion on Raman Spectra Shift in II-VI Semiconductor Nanocrystals

To understand Raman spectra shifts of nanocrystals, the top-down phonon confinement approach and the bottom-up quantum chemical approach were developed. The former is suitable for large-sized nanocrystals, and the latter is suitable for clusters containing fewer atoms. Here, we find that a simpler chemical bond model based on the bond dispersion feature can demonstrate Raman spectra shift either in normal size II-VI semiconductor nanocrystals or in atomically precise clusters. According to the bond dispersion model, the Raman spectral line of the II-VI semiconductor nanocrystal (A^IIB^VI) is expressed as the sum of the Lorentz subpeaks of the A^{II( i)}B^{VI( j)} bonds with different coordinates i and j. The calculated Raman lines of CdSe, CdS, CdTe, ZnS, and ZnSe nanocrystals are in agreement with the measured Raman spectral lines. The origin of the red shift and asymmetric broadening of the peak position of nanocrystals may be revealed as well. Results provide insight into how different bonds contribute to different vibrational spectra.

In Situ Measurement and Control of the Fermi Level in Colloidal Nanocrystal Thin Films during Their Fabrication

In engineering a high-performance semiconductor device, understanding of the Fermi level position is critical. Here, we demonstrate that open-circuit potential (OCP) measurements can be used to quantify the Fermi level in nanocrystal thin films in situ during their solution-based fabrication. We use this method to study the influence of (1) a metal contact and (2) nanocrystal surface termination on the Fermi level of the nanocrystal film, and find that oxidization or reduction of the nanocrystals as well as surface terminations with dipoles can be used to tune the Fermi level over large energy ranges. Finally, to emphasize the compatibility of the technique with device fabrication, we show that we can use blends of ligands to design the Fermi level landscape in a nanocrystal film. Our work highlights that OCP measurements can be used to gain insight into existing device operation and direct further optimization of optoelectronic devices.

Non-adiabatic molecular dynamics with ΔSCF excited states

Accurate modelling of nonadiabatic transitions and electron-phonon interactions in extended systems is essential for understanding the charge and energy transfer in photovoltaic and photocatalytic materials. The extensive computational costs of the advanced excited state methods have stimulated the development of many approximations to study the nonadiabatic molecular dynamics (NA-MD) in solid-state and molecular materials. In this work, we present a novel ▵SCF-NA-MD methodology that aims to account for electron-hole interactions and electron-phonon back-reaction critical in modelling photoinduced nuclear dynamics. The excited states dynamics is described using the delta self-consistent field (▵SCF) technique within the density functional formalism and the trajectory surface hopping. The technique is implemented in the open-source Libra-X package freely available on the Internet (https://github.com/Quantum-Dynamics-Hub/Libra-X). This work illustrates the general utility of the developed ▵SCF-NA-MD methodology by characterizing the excited state energies and lifetimes, reorganization energies, photoisomerization quantum yields, and by providing the mechanistic details of reactive processes in a number of organic molecules.

A Simple Phase Correction Makes a Big Difference in Nonadiabatic Molecular Dynamics

The outcomes of nonadiabatic molecular dynamics (NA-MD) calculations are modulated by the parameters entering the time-dependent Schrödinger equation (TD-SE). The adiabatic states are commonly used as the basis in which the TD-SE is integrated. However, the phase inconsistencies of such states along the nuclear trajectories obtained in NA-MD simulations may render the wave function and other relevant properties ill-behaving, adversely affecting the dynamics. This work illustrates the consequence of adiabatic state phase inconsistencies in nonadiabatic Ehrenfest dynamics. A simple phase-correction approach is proposed and is demonstrated to alter the dynamics to make it consistent with the reference calculations done in the phase-consistent diabatic representation.

Quantum Dot Solar Cells: Small Beginnings Have Large Impacts

From a niche field over 30 years ago, quantum dots (QDs) have developed into viable materials for many commercial optoelectronic devices. We discuss the advancements in Pb-based QD solar cells (QDSCs) from a viewpoint of the pathways an excited state can take when relaxing back to the ground state. Systematically understanding the fundamental processes occurring in QDs has led to improvements in solar cell efficiency from ~3% to over 13% in 8 years. We compile data from ~200 articles reporting functioning QDSCs to give an overview of the current limitations in the technology. We find that the open circuit voltage limits the device efficiency and propose some strategies for overcoming this limitation.

The Many "Facets" of Halide Ions in the Chemistry of Colloidal Inorganic Nanocrystals

Over the years, scientists have identified various synthetic "handles" while developing wet chemical protocols for achieving a high level of shape and compositional complexity in colloidal nanomaterials. Halide ions have emerged as one such handle which serve as important surface active species that regulate nanocrystal (NC) growth and concomitant physicochemical properties. Halide ions affect the NC growth kinetics through several means, including selective binding on crystal facets, complexation with the precursors, and oxidative etching. On the other hand, their presence on the surfaces of semiconducting NCs stimulates interesting changes in the intrinsic electronic structure and interparticle communication in the NC solids eventually assembled from them. Then again, halide ions also induce optoelectronic tunability in NCs where they form part of the core, through sheer composition variation. In this review, we describe these roles of halide ions in the growth of nanostructures and the physical changes introduced by them and thereafter demonstrate the commonality of these effects across different classes of nanomaterials.

Measuring the Vibrational Density of States of Nanocrystal-Based Thin Films with Inelastic X-ray Scattering

Knowledge of the vibrational structure of a semiconductor is essential for explaining its optical and electronic properties and enabling optimized materials selection for optoelectronic devices. However, measurement of the vibrational density of states of nanomaterials is challenging. Here, using the example of colloidal nanocrystals (quantum dots), we show that the vibrational density of states of nanomaterials can be accurately and efficiently measured with inelastic X-ray scattering (IXS). Using IXS, we report the first experimental measurements of the vibrational density of states for lead sulfide nanocrystals with different halide-ion terminations and for CsPbBr₃ perovskite nanocrystals. IXS findings are supported with ab initio molecular dynamics simulations, which provide insight into the origin of the measured vibrational structure and the effect of nanocrystal surface. Our findings highlight the advantages of IXS compared to other methods for measuring the vibrational density of states of nanocrystals such as inelastic neutron scattering and Raman scattering.