Recent progress in photovoltaic and thermoelectric applications of coupled colloidal quantum dot solids: insights into charge transport fundamentals

Colloidal quantum dots (QDs) have emerged as transformative materials with diverse properties, holding tremendous promise for reshaping the landscape of photovoltaics and thermoelectrics. Emphasizing the pivotal role of surface ligands, ranging from extended hydrocarbon chains to intricate metal chalcogenide complexes, halides, and hybrid ligands, we underscore their influence on the electronic behavior of the assembly. The ability to tailor interdot coupling can have profound effects on charge transport, making colloidal QDs a focal point for research aimed at enhancing the efficiency and performance of energy conversion devices. This perspective provides insights into the multifaceted realm of QD solids, starting from fundamentals of charge transport through the coupled assemblies. We delve into recent breakthroughs, spotlighting champion devices across various architectures and elucidating the sequential advancements that have significantly elevated efficiency levels.


Introduction
The emergence of nanometer-sized low-dimensional systems has ushered in exciting avenues of exploration within condensed matter physics.When electrons and holes find themselves confined within regions of space smaller than their de Broglie wavelength due to potential barriers, it leads to pronounced quantization effects.Such confinement can manifest in various dimensions, giving rise to quantum wells, quantum wires, and quantum dots (QDs) corresponding to confinement in all three spatial dimensions [1].In the initial years of the 1980s, Aleksey Yekimov achieved a significant milestone by inducing size-dependent quantum effects in colored glass.The vibrant hues were attributed to nanoparticles of copper chloride, and Yekimov demonstrated that the alteration in particle size directly influenced the glass's color, underscoring the role of quantum effects in this phenomenon [2].Subsequently, a few years later, Louis Brus made history as the first scientist to confirm sizedependent quantum effects in particles suspended freely in a fluid, marking a crucial advancement in the understanding of quantum behaviors at the nanoscale [3].In a groundbreaking development in 1993, Moungi Bawendi revolutionized the chemical synthesis of quantum dots, leading to the creation of nearly flawless particles.This exceptional quality was imperative to enable their practical utilization in various applications [4].Over the past decade, colloidal QD semiconductors from diverse chemical groups, such as II-VI, II-IV, III-V, and IV-VI, have gained remarkable prominence due to their exceptional optical, electronic, and thermoelectric properties [5][6][7][8][9][10][11]. Notably, when dealing with semiconductors, it becomes crucial to consider the exciton Bohr radius, as its size dictates intriguing electronic behaviors within these dots, adding another layer of complexity to their versatile nature [12].Because a system of electrons confined in all three dimensions has discrete energy and charge states, just like atoms and molecules, quantum dots are also referred to as artificial atoms [13].
A colloidal QD consists of a core, typically semiconducting or metallic, with a diameter on the order of a few nanometers.This core is enveloped by an organic ligand that acts both to passivate the dot's surface and to isolate it from its external environment, as depicted in figure 1(a) [4,17].Additionally, these colloidal dots may feature a complementary shell of another material or incorporate various chemically, electrically, or optically active groups [18].Electron micrographs in figure 1((b)-(d)) offer visual representations of colloidal quantum dots.Long range ordering of assemblies, where observed, are evident from GISAXS maps (see figure 1(e)).To a very good approximation, a semiconducting dot can be described by a particle in a spherical box of radius R, with zero potential inside the box and infinite potential outside.The spectrum of quantized energy levels, E n,l obtained from solutions to the Schrodinger's equation as [1,19]: where m * is the effective mass of the particle, h is the Planck's constant.The nth zero of the 1st spherical Bessel function is represented by the coefficient β n,l .The quantum numbers n, 1 are the same as those used in atomic notation of states, so n = 0, l = 0 would be the 1S state.The estimated spacing between energy levels (1S and 1P) for a CdSe dot (m * = 0.13m e ) with a radius of 2 nm is approximately 1 eV, allowing quantization effects to be observed even at room temperature.In small quantum dots, the electrostatic repulsion (Coulomb interaction) between electrons becomes highly pronounced, and it can prevent additional electrons from entering the dot unless sufficient energy to overcome this repulsion [20].This energy, which stems from electrostatic interactions is referred to as the charging energy (U C ) representing the energy required to add or remove a single electron from the quantum dot.For a spherical dot, this is given by [20]: where e is the electronic charge, ò 0 is the vacuum permittivity, r is the radius of the dot and k is the dielectric constant of the dot.
Utilizing the tunability of semiconductor QDs has yielded remarkable success in optical and optoelectronic domains [5,[8][9][10][11][21][22][23], including the development of light-emitting devices [24,25], luminescent tags [26][27][28], and lasers [29].However, the practical realization of these applications often involves the utilization of assemblies or ensembles of quantum dots, rather than individual dots alone.This shift towards coupling quantum dots into structures like quantum dot solids [30] allows for the exploration of emergent electronic properties and synergistic effects that may not be achievable when considering isolated quantum dots .In this review, we explore the intricacies of colloidal quantum dot assemblies, focusing on how the interplay and coupling between individual dots mediated by the surface ligands impact their collective properties.We study the various competing energetic contributions and their role in the charge transport mechanism through the solid.Finally, we review how each of these aspects influences photovoltaic and thermoelectric device performance and efficiency, a crucial consideration for fully harnessing quantum dot assemblies in sustainable energy solutions and advanced net-zero technologies.[14]; Reprinted with permission from [14].Copyright ©2018 American Chemical Society;(c) Transmission electron micrograph (TEM) of PbSe QD cubes [15]; Reprinted with permission from [15].Copyright ©2012 American Chemical Society;(d) TEM and Fourier transform images of binary nanocrystal superlattice (BNSL) films self-assembled with 4.5 and 6.0nm PbSe NCs [16];(e) Corresponding GISAXS of BNSL films highlighting the long range ordering [16].Reprinted with permission from [16].Copyright ©2017 American Chemical Society.

Ligand engineering to control coupling in QD solids
QD assemblies behave as artificial solids, where each QD is equivalent to an artificial atom, and fundamental properties of solids such as bond lenghth, crystal structure, interatomic interaction etc can be tuned [31].The energy levels of each dot can be tuned by changing the size of the dot.The ligand and the resulting inter-dot interaction controls the bonding and structural arrangement.If the barriers between dots are sufficiently small, the quantum dot array is analogous to a covalently bonded solid [32], even though the coupling ligand itself is much more complex than a single bond.For ionic coupling, we need Coulomb interactions between neighboring dots.This has led to the evolution of binary superlattices of dissimilar quantum dots [33].The surface ligands therefore play a pivotal role not only in the synthesis of colloidal dots, but also in governing the structure and electronic properties of the QD assemblies, and therefore represent a critical aspect of QD engineering [34].Besides the discrete energy and charge states of individual dots, the properties of QD solids are dictated by two additional factors.Firstly, as charges need to navigate through the tunnel barriers formed by the ligands in order to move between dots, the associated energy scale is estimated as, β ∼ Γ, where β is the coupling energy, ÿ is the Planck's constant and Γ is the tunneling rate between neighboring dots, approximated by [1]: where m * is the effective mass of the charge carrier, ΔE and Δx are the height and width of the tunnel barrier respectively.When in a state of weak coupling, the electronic arrangement of an array can be characterized by distinct quantum-confined wave functions constrained to each particle.Conversely, in instances of robust coupling, wave functions emanating from neighboring dots can interact, resulting in states that extend over a fraction or the entire array.
The second and most important aspect is the role of disorder.Unlike identical atoms found in solids, every colloidal dot may have a different size, shape, and ligand coverage due to experimental factors.This diversity contributes to the presence of disorder energy within a quantum dot array.Given that the energies of occupied and unoccupied states in semiconductor quantum dots vary around 1/r 2 , the spread in site energies is directly linked to 2Δr/r.Another source of disorder may come from packing of dots in the solid, and both these sources play a significant role in determining the properties of the resulting solid [32].The interplay between the disorder energy (α), charging energy (E c ) and the energy associated with tunneling (β), in general determines electronic properties of the solid.In the absence of disorder, the electron and hole states of isolated QDs in solids with significant interdot distances are degenerate.However, as the dots become more closely coupled at shorter interdot distances, the electronic states within the solid may split into bands.However, most chemical synthesis routes produce QDs with a size standard deviation of around 3%-5%, which may in turn affect the QD's composition, charge, and surface passivation, further leading to non-uniformity in the energy levels of QD electronic states.The result is the emergence of intermediary trap states within the energy gap.Therefore, in a real QD solids, differences in the spacing and organization of neighboring QDs result in variations in the width and height of the barriers between them, further broadening the distribution of electronic states (see figure 2(a,  b)).Lower-energy states can function as dopants, while deeper band-tail and mid-gap states may serve to capture charge carriers and establish a pathway for rapid electron-hole recombination [52].Table 1 lists the most common types of ligands used for QDs with associated carrier mobilities for each type of assembly.One of the most straightforward routes to measure the carrier mobility of QD solids is through fabrication of QD based field-effect transistors (QD-FETs).While the behaviour of a conventional FET is modulated by varying the electric field in a semiconductor channel, the QD-FET consists of an active channel made of QDs.The most commonly employed class of surface ligands consists of molecules with a head group (e.g., thio-, amino-, carboxylic) exhibiting a strong affinity for the NC surface, complemented by an aliphatic tail that imparts steric stability to the colloidal solution in nonpolar solvents [21].These insulating ligands, while essential for colloidal stability, pose a significant challenge due to their role in hindering interdot carrier transport, typically resulting in poor carrier mobilities ∼10 −6 cm 2 [39].To address this limitation, a transition from long alkyl chains to short ligands like mercaptopropionic acid (MPA) and 1,2-ethanedithiol (EDT) became necessary [53,54].Ligand exchange, the process of replacing the original ligands with these shorter alternatives, can occur through two primary methods: solid-state and solution-phase [55].The solid-state exchange encompasses post-deposition treatments, which involve subjecting quantum dots to chemical precursors after dropcasting them onto a given substrate (see figure 2(c)), and solution-phase exchange, wherein new ligands in a solvent are utilized to replace the original ligands, and the resulting solution is then directly dropcast onto a substrate (see figure 2(d)).The process of solid exchange provides the means to regulate interparticle distance through a diverse array of ligand and quantum dot (QD) chemistries (see figure 2(e), (f)) , however, the loss of ligand volume during this exchange frequently leads to the creation of voids and cracks within the QD thin films.In the solution phase process, the ligand-exchanged QD dispersions, when deposited, yield dense, close-packed, and crack-free QD thin films, albeit generally lacking long-range order and exhibiting a glassy structure (see figure 2(g)), but facilitate large-area coating of uniform QD thin films with controlled thickness for integration in solution-deposited QD devices.
In a typical solid-state ligand exchange process, QDs with long alkyl ligands are deposited onto a substrate using techniques like spin-coating [56].Subsequently, a solution containing short organic ligands such as MPA or EDT is deposited onto the QD film.After a brief soaking period and subsequent removal of the solution by Possible ligand passivations for PbS QDs, along with energy shifts associated with each ligand [35].Reprinted with permission from [35].Copyright ©2014 American Chemical Society.(c) Schematic diagram depicting solid state ligand exchange and (d) solution phase ligand exchange.Reprinted with permission from [36].Copyright ©2016 Royal Society of Chemistry (e,f) TEM images of 6nm PbSe QD films before (e) and after (f) solid-state exchange of long-chain oleate for compact, thiocyanate ligands (scale bar is 20 nm) [37] (g) SEM image of solution-deposited, thiocyanate-exchanged 3.9 nm CdSe QD films, after annealing at 250 °C for 10 min(scale bar is 50 nm) [38].Reprinted with permission from [37].Copyright ©2014 American Chemical Society.Reprinted with permission from [38].Copyright ©2012 American Chemical Society a As the composition of MCC ligands can be the same as that of the CQDs, these can act as molecular solders giving negligible interdot spacing [51].
spin-coating, a solvent is cast onto the film to wash away both the exchanged ligands and excess new short ligands, leaving the QD surface passivated with the desired short ligands.Careful control of the QD concentration is essential to achieve film thicknesses typically in the range of tens of nanometers, making this method suitable for applications like solar cells where light harvesting efficiency is a key consideration.This strategy also allows for the utilization of bifunctional ligands in QD cross-linking, enhancing interparticle connectivity [57,58].Ligand exchanges with short hydrocarbon chain ligands have resulted in improvement in carrier mobilities up to 10 −2 cm 2 /Vs.Halide ligands have shown promise in reducing defect densities and improving surface passivation [44].Their atomic sizes allow for efficient carrier transport between QDs, and their strong binding to the QD surfaces enhances passivation.Compared to bromide and chloride ligands, iodides have been found to form stronger bonds to the QD surface atoms, reducing film defect density significantly [36].
FETs fabricated using PbS CQDs passivated with halide ligands show excellent mobility values, with electron mobilities increasing with the size of the halide ion (from 3.9 × 10 −4 cm 2 /Vs for fluoride-treated to 2.1 × 10 −2 cm 2 /Vs for iodide-treated).Fluoride being the smallest halide ion provides for the shortest interdot separation as compared to other halide ligands.However the decrement in the size of ligand is associated with inherent positional and thus energetic disorder which results in the least electron mobility.The hole mobility however shows negligible change between 1 × 10 −5 cm 2 /Vs and 10 −4 cm 2 /Vs.The slight increase in hole mobility from I to Cl suggests a coupling limited transport.For CQD solar cell fabrication purposes, PbS-F and PbS-Cl serve as p-type layers whereas PbS-Br and PbS-I serve as n-type layers [44,59,60].To further enhance ligand passivation in final QD solids, solution-phase halide ligand exchanges have been developed.By dissolving tetrabutylammonium iodide salts in oleylamine and mixing this solution with QDs in toluene, the passivation quality can be improved [36].This approach has led to reduced defect densities and higher carrier mobility in QD films, ultimately enhancing the performance of optoelectronic devices.Despite these advances in ligand exchange techniques, the field continues to evolve.For instance, hybrid materials that combine organic crosslinkers and inorganic passivants have gained prominence in recent years [61].This hybrid ligand passivation scheme involves a two-step process: solution-phase halide ligand exchange followed by a solid-state organic ligand exchange.Halide anions are introduced either in situ or during the late stages of synthesis, allowing for the passivation of sites that may be inaccessible to bulkier organic ligands.Small organic ligands like MPA and EDT are then employed in the solid state to replace the long organic ligands, further enhancing the film density and interdot distances.
Charge transport in tetrahedral InP QD-based thin-film assemblies was enhanced using a hybrid ligandexchange strategy combining solution-based exchange with S 2− and solid-state exchange with N 3− was undertaken [62].Furthermore, overlaying the QD assembly surface with thin, thermally evaporated Se layers caused an enhancement in the drain current and yielded an average electron mobility of 0.45 cm 2 V −1 s −1 , which accounts for almost 10 times the mobility of previously reported devices.This Se-modified InP QD assemblybased FET possessed lower trap-state densities, longer carrier lifetimes, and thus longer carrier diffusion length.More recently, the field has seen the emergence of molecular metal chalcogenide complexes (MCCs) as efficient ligand replacements [63].These MCCs, including Zintl ions and one-dimensional metal chalcogenide chains solvated by hydrazinium cations and/or neutral hydrazine molecules, provide a versatile platform for ligand exchange.They are particularly valuable for solution-processed semiconductor thin films and mesoporous frameworks [64].MCC ligands exhibit strong binding to the QD surfaces, effectively replacing the original organic ligands and enabling precise control over surface properties.The ease with which MCCs thermally decompose to metal chalcogenides not only reduces inter-dot spacing further, but also creates a layer of conductive 'glue' between the dots [5].As the composition of MCC ligands can be the same as that of the CQDs, these have been used as molecular solders to achieve mobilities as high as 200 cm 2 /Vs [49].
Ligands can provide an additional level of control over electronic properties [35].As measured by ultraviolet photoelectron spectroscopy (UPS) on PbS dots with different ligands, the band energies of colloidal dots can be changed by ligand exchange, resulting in energy level shifts of up to 0.9 eV (see figure 2(f)).Atomistic modelling also confirmed the trends in energy level position between different ligands, demonstrating that the observed shifts result from contributions from the ligand's dipole moment as well as the dipole-surface.Ligands also impact the structure of the resulting QD assembly, which is also influenced by other factors.Different coating techniques like spin-, spray-, dip coating [65], drop casting [66] and doctor blading [67] have been employed in literature for depositing QD solids for measurement and device integration [68,69].In general, superlattices with long range order form through self assembly guided by entropy and weak interparticle forces.The most basic method for creating arrays and superlattices is to dropcast a small volume of dots onto a substrate and then slowly evaporate the solvent from the dispersion with a narrow size distribution [70].The order is then determined by the rate of solvent evaporation and the inter-dot interaction, with slow evaporation and long ligands favouring long range order.Three specific scenarios emerge as a consequence of variations in solvent evaporation time and the sticking coefficient.Firstly, when the solvent evaporation time is brief and the sticking coefficient tends towards unity, it gives rise to the formation of disordered aggregates [71].Secondly, in cases where both parameters exhibit low values and the solvent evaporation transpires within seconds, the outcome is the generation of Bernal glasses [30].Thirdly, when the sticking coefficient remains low while the solvent evaporation prolongs into minutes or even hours, the outcome manifests as the creation of structured thin films known as superlattices or super crystals [17,72].

Charge transport through coupled quantum dot solids
In the majority of colloidal QD solids, disorder constitutes the predominant energy factor, leading to observed transport mechanisms involving hopping through localized electronic states akin to those witnessed in doped and disordered semiconductor systems [30].Each hopping mechanism can theoretically be discerned through the investigation of the temperature dependence of the conductance.In the cases where phonon-assisted hopping is directed towards nearest neighbor sites, the conductance exhibits an Arrhenius profile, where G is proportional to where ΔE is the activation energy, k B is the Boltzmann constant and T is the absolute temperature [75].At lower temperatures, hopping towards a dot that isn't the nearest neighbor may prove energetically more favorable.This signifies the realm of variable range hopping, marked by a temperature dependence in the form of G proportional to ( ) ~- [78].The outcomes, which were similar to findings on Au nanocrystals [79], were understood with adjustments to the ES variable-range hopping model by introducing an expression for nonresonant tunneling grounded in localized energy fluctuations.
For a given semiconductor QD, literature reflects a notable diversity in the transport properties of semiconducting quantum dots [30].However, on careful observation certain trends emerge by understanding variations in the dot size, surface ligand and passivation for the dots.Initial transport studies on colloidal dots with long native ligands, showed no steady-state dark current for electric fields up to 10 6 V/cm.Instead, a power law decay was observed as a function of time.This was attributed to the formation of an electron 'Coulomb glass' where long-range Coulomb interactions between charges residing on different dots significantly hamper the dynamics of injected electrons, resulting in the gradual decay of current with time [80].To increase the conductivity, the solids were annealed [73].As seen from transmission electron micrographs (see figure 3(a)), annealing results in a significant reduction of interdot spacing from 1.1 nm to 0.5 nm.Annealing also resulted in enhancement of dark current and photocurrent by several orders of magnitude, which was attributed to enhancement of interdot tunneling caused by the decreased separation between the dots and by chemical changes in their organic ligand (see figure 3(b)).The dark current can be fit to , where k is a constant,V 0 is the applied voltage and L is the gap between the electrodes.The current showed a very weak dependence on temperature within the range of 56 to 250 K, with the exponent V 0 being nearly temperatureindependent.This suggests that electron tunneling serves as the primary transport mechanism in annealed CdSe dot solids.
In another report on transport through CdSe QD solids, the charge transport behavior was effectively described using a nearest-neighbor-hopping mechanism, incorporating a size-dependent activation energy and a pre-exponential factor for mobility [74,81].At lower temperature the systems were found to show a transition to ES-VRH [77].An important difference was a chemical treatment involving 0.08 M NaOH in anhydrous methanol for 10 minutes to improve the conductivity of the QD solid.This treatment reduced the interparticle spacing to approximately 0.2 nm, much smaller than what was achieved through annealing.Notably, the transport properties exhibited significant and systematic variations based on the dot diameter.Key findings included a strong correlation between the device turn-on voltage and the size-dependent position of the lowest unoccupied electronic states of the dots.Moreover, electron mobility increased with larger dot diameters, reaching a substantial value of 0.6 cm 2 /Vs for films containing 5.1 nm dots.In the temperature range of 233 to 300 K, the mobilities of the system exhibited behavior consistent with Arrhenius-type kinetics (see figure 3 , where, μ 0 represents the pre-exponential factor, E a is the activation energy for charge transport, k B is the Boltzmann constant, and T is the temperature in Kelvin.The activation energy E a was proportional to the Coulombic charging energy of an individual dot.This was further confirmed by the linear variation of the activation energy with the inverse of the dot diameter (see figure 3(d)).
Choi et al [38] reported bandlike transport in solution-deposited thin films composed of CdSe QDs with room temperature field-effect electron mobilities of 27 cm 2 /(Vs)[see 3(e)].To achieve this, the long-chain organic ligands on the QD surface were replaced with ammonium thiocyanate, a noncorrosive and compact inorganic ligand capable of maintaining the colloidal dispersibility of the semiconductor QDs in a single step solution-based procedure.Temperature-dependent measurements revealed bandlike transport behavior, extending down to 220 K when using a SiO 2 as the gate insulator.This temperature range was further extended to 140 K by reducing the interface trap density with an Al 2 O 3 /SiO 2 gate insulator.In the lower temperature range (77 K < T < 220 K), carrier transport was influenced by shallow traps with a small activation energy of 7.5 meV.For devices employing an Al 2 O 3 /SiO 2 dielectric stack, the negative slope region extended from room temperature down to 140 K, with a lower activation energy of 6.2 meV (Region II)[see figure 3(f)].This observation highlighted the role of traps at the QD/dielectric interface in determining the transition between bandlike and thermally activated transport.Interestingly, the authors presented an effective inter-dot resistance of 55 kΩ, a value comparable to the conductance quantum.
A more direct comparison of the role of ligands in the charge transport mechanism was given by Ray et al [82] for PbS QDs where they investigated transport in weakly coupled arrays within the low-bias regime using an integrated charge sensor (see figure 4(a)).The use of an integrated sensor allowed the study of temperature and field dependence of resistance in nanopatterned oleic-acid and n-butylamine-capped PbS arrays, observing resistances reaching as high as 10 18 Ω.It was found that the conduction mechanism shifted from nearest neighbor hopping in oleic-acid-capped PbS dots to Mottʼs variable range hopping in n-butylamine capped PbS dots.A cartoon depicting the differences between nearest neighbor hopping and variable range hopping is depicted in figure 4(b).The transition was inferred experimentally from the temperature dependence of the conductance measuring using direct current as well as integrated charge sensor measurements.With the shorter butylamine ligands, the conductance could not be fit to Arrhenius form, but to Mott's variable range hopping described by For the native ligands, the conductance followed Arrhenius form with activation energies comparable to the disorder between the site energies (see figure 4(d)).The implications of the findings could be comprehended by considering alterations in either the strength of interdot coupling or adjustments in the density of trap states, with changes in the ligand.These outcomes further highlighted the significance of the capping ligand in governing the charge transport within the CQD assembly.Similar studies were performed by Oh et al [37] with PbSe QDs and more conducting ligands, to enable direct measurement of current.In comparison to the native oleic acid (OA)-capped PbSe dots, treatments with thiocyanate (SCN) and PbCl 2 produced distinct effects on the Pb:Se ratio.SCN treatment results in a slight decrease in the Pb:Se ratio, indicating a reduction in surface lead atoms as a consequence of lead oleate removal, Conductance as a function of inverse temperature for (c) n-butylamine (NBA)-capped and (d) oleic acid (OA)-capped PbS dots PbS dots.[83].Reprinted with permission from [83].Copyright ©2015 American Chemical Society.Ligand dependent charge transport in PbSe QD solids (e) Pb:Se ratios for (black) OA-capped, (blue) SCN-treated, and (green) SCN followed by PbCl 2 treated PbSe QD films, as measured using energy dispersive x-ray spectroscopy.Schematic of the SCN-treated PbSe NC surface before and after PbCl 2 treatment.(f) Temperature-dependent carrier mobility for 6nm PbSe QD FETs treated with tetrabutylammonium iodide (TBAI), thiocyanate (SCN), and SCN and PbCl 2 [37].Reprinted with permission from [37].Copyright ©2014 American Chemical Society.Temperature-dependent conductance measurements in different configurations of PbS quantum dot assemblies, ranging from (g) EDT-bridged, (h) epitaxially connected 2-terminal FETs and (i) epitaxially connected 4-terminal FETs demonstrating variations in electron conductivity [84] Copyright ©2023 Springer Nature.thereby exposing unpassivated selenium atoms (see figure 4(e)).Conversely, PbCl 2 treatment lead to a slight increase in the Pb:Se ratio, suggesting the binding of lead to surface selenium atoms generated during ligand exchange, effectively repairing the surface.Figure 4(f) shows the temperature dependence of the carrier mobility measured in a field-effect transistor.The temperature-dependent conductivity behavior was characterized by thermally activated nearest neighbor hopping (NNH) with the native ligands.However, when shorter ligands like TBAI or SCN were employed, the electron conductivity exhibited a substantially lower activation energy (E a ) of approximately 10 meV at low temperatures and appears nearly temperature-independent within the range of 200 to 300 K, indicative of a transition resembling a metal-insulator transition.The combination of SCN followed by PbCl 2 treatment lead to electron conductivity that gradually increased as temperature decreased from 300 to 200 K, signifying a transition toward bandlike transport.
Efforts have been directed towards achieving bulk-like carrier transport across minibands, which arise due to robust interparticle coupling, known as the Bloch regime.However, attaining this regime has been intricate due to experimental complexities tied to securing sufficient inter-dot coupling, maintaining low electronic trap densities, and minimizing energetic disorder.A breakthrough was recently achieved with the elimination of orientational disorder by precise control of facet orientation, leading to the creation of highly ordered quasitwo-dimensional epitaxially-connected quantum dot superlattices (QD-SL) resulted in intrinsically high mobility values exceeding 10 cm 2 /Vs, and the behavior remains temperature-independent [84].The significantly higher electron mobility observed in the epitaxially-connected QD-SL compared to the state-ofthe-art EDT-bridged QD assembly (see figure 4(g)-(i)), exceeding expectations by more than an order of magnitude, is noteworthy.Additionally, the epitaxially-connected QD-SLs exhibit a remarkable consistency in electron mobility across various QD diameters, in contrast to the conventional understanding that suggests a strong size-dependent decrease in electron mobility, as observed in the EDT-bridged QD assemblies.The observation of a finite zero-degree conductance, surpassing quantum conductance values, implied an early indication of delocalized (metallic) behavior.

Colloidal quantum dot optoelectronics
Two critical parameters which influence CQD photovoltaic device performance are carrier mobility and trap density.Enhancements in CQD solar cell performance stem from improvements in materials, such as CQD growth, surface management, electronic trap state removal,deposition methods, along with innovations in device architectures influenced by inorganic and organic optoelectronic fields, tailored to CQD films and materials.The crucial role of interactions between linkers and QDs in altering the physical and chemical properties of QD solids was recently investigated by Kirmani et al [23], by developing a mechanistic model of solid state exchange employing 3-mercaptopropionic acid (MPA) and 1,2-ethanedithiol (EDT) as the linkers .The model suggested that QD solids undergo a phase-transition-like transformation in properties once a critical number of linker molecules are introduced, leading to complete exchange of the QDs.Below this critical point, the solid remains unexchanged and performs poorly as a photovoltaic material.Applying this model, the authors succesfully fabricated solar cells, achieving an impressive device with a power conversion efficiency of 10.7 %.Defects in the band gap can act as recombination centers, reducing photocarrier populations and quasi-Fermi level splitting range under illumination, leading to lower open-circuit voltage in CQD solar cells [85,86].Defects often result from ligand loss during ligand exchange.Hybrid ligands decrease trap density compared to pure organic or inorganic ligands.Solution-phase iodide ligand processing reduces defect concentration as compared to untreated QDs.

Colloidal QD solar cells
Colloidal QD based solar cells can be designed using various architectures, including Schottky junction, depleted heterojunctions, bulk heterojunctions, and tandem cell configurations, each offering distinct advantages for harnessing solar energy (see table 2 for a summary of different architectures and their associated band diagrams).In the early stages of developing QD photovoltaic device, significant progress was achieved through the engineering of Schottky QD solar cells [87], where a thin QD film was electrically connected via ohmic contact using a transparent conductive oxide (TCO) on one side and a shallow work function metal on the other side, resulting in a built-in potential relative to the QD film.In the Schottky architecture, the QD films could act as both absorbers and as the charge transport medium, When incident light the active QD layer, photons having energy greater than the band gap of the corresponding QD material are absorbed and electron-hole pair is generated, and henceforth, charge separation takes place resulting in the generation of an open circuit voltage (V OC ).The metal layer is utilized as the electron extracting contact, where the photogenerated electrons result in current density due to electrons (J n,PV ), and photogenerated holes are extracted through the transparent conducting ITO contact,indicated by J p,PV .While the Schottky architecture presents advantages in terms of fabrication simplicity and limited interfaces, its absolute device performance has been constrained.This limitation arises from Fermi level pinning at the metal-QD interface, imposing an upper bound on the opencircuit voltage that falls well below the voltage anticipated solely based on the consideration of the QD band gap. Figure 5(a) shows PbS dots with 1,4-benzenedithiol ligands with their first excitonic peak at λ = 1100 nm, in this architecture.The current density-voltage behaviour is characteristic of a Schottky junction, and large improvements can be seen in the current density with iluumination.This architecture reached a solar power conversion efficiency of 5.2% for [88].
Developed as a solution to the limitations of Schottky solar cells, heterojunction architectures, specifically the depleted heterojunction design [89], utilize a highly doped n-type metal oxide in a p-n heterojunction with a p-type QD film.This facilitates photogeneration in close proximity to the junction region, overcoming the drawbacks associated with the Schottky design.A wide-band-gap semiconductor, typically TiO 2 or ZnO, forms the n-doped junction layer, and the p-type QD films are deposited on top, creating a structure illuminated through the transparent substrate and the wide-band-gap semiconductor.Depletion widths in the p-n junction device depend on the relative free carrier densities, and drift currents generated by the electric field drive carriers in the QD film.Increasing the interfacial area between CQD films and metal oxides in the depleted bulk heterojunction solar cells provides improved carrier collection and increased photocurrent generation due to reduction in the distance that the photogenerated minority charge carriers need to travel to reach the electrodes.concentration was varied and PCE of 7.55% was achieved with a doping concentration of 3.6 * 10 19 cm −3 [90].
However, this approach had limitations related to the thickness of the current-contributing QD layer and partial absorption of near-infrared light [91].Depleted bulk heterojunctions (DBH) addressed the limitations of Schottky cell by using a nanoporous architecture to extend photon interaction length while maintaining a short exit route for electrons [92].Nanopillars, nanowires, or larger nanoparticles of the electron acceptor material are typically used as a platform for depositing QDs.With precise control of the growth orientation of ZnO nanowires, promoting capillary attractive interactions between the nanowires and PbS QDs have resulted in denser packing and increased infiltration of the QDs, pushing PCEs closer to the 10 % mark [93].
Tandem solar cells depict charge separation as a combination of two depleted heterojunction solar cells separated by a graded recombination layer (GRL), indicated by step potentials in the band diagram.With solar energy absorption, depending on the band gap of the individual active materials of the two heterojunction solar cells, electron hole pairs are generated at different rates.Active photon absorption in both the QD layers causes generation of two different open circuit voltages, indicated by (V OC1 ) and (V OC2 ).These generated carriers traverse to the oppositely charged carrier laden transport layers similar to that of an individual heterojunction solar cell.The GRL ensures that the photogenerated holes from the front cell and the photogenerated electrons from the back cell recombine with high efficiency and minimum loss of electrical potential.This combined layer provides a progression of work function from the hole accepting electrode in one cell to electron accepting electrode in another cell thus facilitating effective charge acceptance (both electrons and holes) and subsequent recombination processes.The electron and hole recombination currents in the GRL are represented by J nR and J pR respectively.The active materials in the QD layers of each of the heterojunction cells in a Tandem cell are appropriately chosen (based on their individual band gaps) such that a major part of the solar spectrum can be utilized which in turn helps achieve a better power conversion efficiency.Proof-of-principle tandem solar cells, utilizing PbS colloidal quantum dots, demonstrated voltage addition with two distinct recombination layer strategies (see figure 5(c) [94].
Perovskite QD based solar cells have attracted tremendous attention lately due to their excellent defect tolerant ability, enhanced QD coupling, suppressed recombination rate of carriers, high absorption coefficient, spectral bandwidth and long photocarrier lifetime.Among the different CsPbX 3 QD based solar cells, due to the smallest band gap possessed by CsPbI 3 , these are considered to be the best materials for solar cell devices.Unlike bulk CsPbI 3 which are quite unstable in ambient conditions, nanocrystalline CsPbI 3 is relatively more stable due to their inherent surface strain [95].Tuning the active layer thicknesses in tandem solar cells with Cs 0.25 FA 0.75 PbI 3 and CsPbI 3 as the active layers a PCE as high as 15.52% [96]could be achieved.The first stable CsPbI 3 QD based solar cells were demonstrated where they proposed removal of long chain ligands in a magic' non polar solvent methyl acetate (MeOAc) and these solar cells showed a promising photo conversion efficiency (PCE) of 10.77% [105].Treating the perovskite QD surface with MeOAc saturated with a variety of halide salts (AX) and treating the QD film with FAI which helped reach an QDSC of 13.43% [106,107].Using short chain secondary amines, successful oleate and oleylammonium ligand removal in CsPbI 3 QDs resulted in a 15% PCE [108].On addition of guanidinium (GA + ) [a larger organic cation as compared to Cs + ], onto CsPbI 3 QD surfaces through ligand exchange route, an enhanced PCE of 15.21% could be obtained [109].The addition of a heterojunction hybrid layer at the interface between the QD and hole transport layer, a PCE of 14% could be achieved [110].Tuning the A-site cation allows entropic stabilization of perovskite QD structure and band gap modulation [111].Because of slightly narrower band gap of FAPbI 3 as compared to the already investigated CsPbI 3 , Xue et al constructed the first FAPbI 3 QD based solar cells having a PCE of about 8.38% [112] and on treating these CQDs with MeOAc/FAI the PCE increased to about 9.01% [113].Zhao et al constructed heterojunction solar cells using varied stoichiometric ratios of Cs 1−x FA x PbI 3 CQD layers which resulted in improved photo conversion efficiency of 15.74% [96].Wang et al fabricated solar cells using Cs 0.5 FA 0.5 PbI 3 QDs and managed to achieve an efficiency of 16.6% [114].The first flexible PQD solar cells on PET substrates achieving an efficiency of 12.3% have been reported by Yuan et al which are capable of withstanding higher mechanical endurance as compared to thin film perovskite solar cells [115].While perovskite quantum dots (QDs) have demonstrated high power conversion efficiencies (PCEs), their operational lifetime and moisture stability have posed challenges.To address these limitations, researchers have explored the use of inorganic metal oxides as barrier layers to prevent moisture and oxygen from infiltrating the QD layers, as well as the effectiveness of silica coatings in protecting perovskite QDs from atmospheric damage [116,117].

Colloidal QD based thermoelectric devices
The efficiency of thermoelectric materials is assessed through the dimensionless figure-of-merit (ZT), which depends on the electrical conductivity (σ), Seebeck coefficient (S), temperature (T) and thermal conductivity (κ) as: Enhancing thermoelectric efficiency presents challenges due to the interdependence of these parameters, as described by the Wiedemann-Franz law, where heat transport is linked to charge carrier diffusion.Increasing the charge carrier concentration boosts electrical conductivity but reduces the Seebeck coefficient.Metallic systems have high carrier concentration and electrical conductivity but also high thermal conductivity and low Seebeck coefficients, making them unsuitable for thermoelectric applications.The Seebeck coefficient in electronic materials is associated with the density of states (DOS), and therefore various strategies have been explored, including nanostructuring the material's shape, size, and surface properties to enhance the DOS [118].In bulk systems, the DOS scales with energy as E 1/2 , but in low-dimensional nanoscale materials like quantum dots (QDs), the quantum confinement effect leads to sharp, quantized DOS.The Seebeck coefficient in such systems is determined by the Boltzmann transport equation and is linked to the offset between the Fermi level and the transport energy level, such as the conduction band or the highest occupied molecular orbital (HOMO) level for p-type materials, as S ∝ (E F − E c ), where E F is the Fermi energy and E c is the energy of the conduction band minima [119] (see figure 6(a)).Quantum dots exhibit size-dependent optical properties, resulting in increased energy offsets between the Fermi and transport energy levels, ultimately leading to higher Seebeck coefficients [120].
In bulk semiconductors, the phonon mean-free path can often exceed the carrier mean-free path.For typical semiconductors like PbTe and PbSe, the phonon mean free path ranges from 0.1 to 10 nm [121].Interestingly, when these bulk semiconductors are engineered into nanostructures with crystal domains in the 5-10nm range, phonon scattering becomes significant due to the comparable size of the crystalline domain and the phonon mean-free path (see 6(a)).If the QD solids can be coupled so that the carrier-mean free path is considerably longer than the size of individual QDs, this could lead to a regime where thermal conductivity effects could become decoupled from electrical conductivity effects [122].These unique characteristics make QDs promising candidates for next-generation thermoelectric applications.
Primarily, PbS, PbTe and HgTe QDs have shown promising thermoelectric activity which could be further modulated with ligands (see figure 6(b), (c)).P-type thermoelectric activity has been demonstrated in PbTe QD layers functionalized with EDA and ammonium thiocyanate (NH 4 SCN) ligands.Due to improved necking between adjacent QDs EDA ligands show a higher figure merit of 0.26, as compared to 0.013 for PbTe (NH 4 SCN) [123].It is to be noted that both of these ZT values are higher as compared to bulk PbTe [124].EDA passivated PbS-PbTe heterojunctions show a ZT of 0.3 [?] due to energy filtering effect.Iodide capping ligands have been found to result in n-type thermoelectric characteristics [125].Surface passivation of PbTe thin films with PbI 2 resulted in an increased figure of merit of 2 * 10 −3 and on introducing caesium carbonate (Cs 2 CO 3 ) as an n-type molecular dopant,the CQD films show a Seebeck coefficient which ranges from −160 to −240 μV K −1 and achieve an improved power factor of 1.5 μW m −1 K −2 (i.e. 3 times higher) at temperatures below 360 K [126].With the introduction of PbI 2 to the PbX films, pronounced phonon scattering occurs due to increased interfacial density of PbI 2 /PbX heterostructures, eventually reducing the thermal conductivity to 0.25Wm −1 K −1 .
HgX (X = Te,Se) have shown that these materials generally exhibit a high Seebeck co-efficient (>±500μVK −1 ) and figure of merit (almost approaching unity near RT) [127].HgX CQDs can be used as p-type (HgTe) as well as n-type (HgSe) materials for thermoelectric device applications.For both the p-type as well as n-type CQD materials, an increase in the electrical conductivity occurs with the increment in QD sizes [127].This can be attributed to the lesser number of interfaces and thus lesser interface related scattering hindrances.HgTe CQD based films have shown an increase in the Seebeck co-efficient with the decrease in QD sizes.For example,a 9.3 nm sized dot has a S of 1220 μV K −1 and a 3.7 nm dot has been found to have an increased S of 1890 μV K −1 .The maximum ZT attained by these p-type films is 0.092 whereas for n-type HgSe dot based films, the maximum achievable ZT at RT has been found to be 0.68 [128].For majority of these HgX dots, the thermal conductivity varies as 0.17-0.29 Wm −1 K −1 [127,128].
Different capping ligands and extent of surface passivation are capable of altering the electronic transport across QDs and thus their thermoelectric properties.PbS QD films exhibit p-type thermoelectric properties on surface passivation with 1,2-ethanedithiols (EDT) ligands [129].An electrical conductivity of 1.1 Scm −1 Seebeck coefficient of 500 μVK −1 , power factor of 27.5 μWm −1 K −2 and a thermal conductivity of 0.6 Wm −1 K −1 leading to an overall figure of merit of 0.02 has been reported for PbS (EDT).Iodide-capped lead sulfide (PbS) QDs on the other hand act as efficient n-type thermoelectric materials.Through the utilization of different iodide salts with specific counterions, such as isobutylammonium iodide (IBAI), formamidinium iodide (FI), and methylammonium iodide (MAI), it was found that MAI stands out as the most effective choice for native ligand removal, promoting superior charge transport, and demonstrating optimum doping characteristics.This leads to exceptional n-type thermoelectric properties, featuring a remarkable power factor of up to 24 μW m −1 K −2 [130].Seebeck coefficients and power factors of MAI and EDT passivated PbS QDs devices have been represented in figure 7(a)-(d).Using PbS dots with different capping ligands as n-and p-type materials, an eight paired p-n thermoelectric generator (TEG) was designed (see figure 7(e)).The p-n TEG generated an impressive output thermal voltage of up to 0.25 V with a 50 K temperature gradient using eight p-n pairs, and a remarkable electrical power density of up to 63μW/cm 2 under the same temperature gradient [130](see figure 7(f)-(g)).These results underscore the promising prospects of QD systems for future thermoelectric applications, with further enhancements anticipated through doping and hybrid approaches to improve electrical conductivity.

Outlook
Tailoring the shape, size, and composition of quantum dots (QDs) and efficiently assembling and passivating these nanostructures have ushered in a new era of strongly coupled QD assemblies with superior optical and electronic properties, surpassing those of their bulk counterparts.These advancements, combined with the costeffectiveness, large-scale solution processing capabilities, and spectral tunability inherent to colloidal quantum dots (CQDs), have propelled their widespread adoption across diverse technological applications.CQDs have found their niche in quantum light-emitting diodes (LEDs), QD-based solar cells, photodetectors, and thermoelectric devices, contributing significantly to the pursuit of sustainable energy solutions [131,132].
Nonetheless, when it comes to assembling CQDs into high-performance solid-state devices, formidable challenges emerge.Energetic and positional disorders during assembly processes can compromise device efficiency.While utilizing long chain, bulky ligands for passivating QD surfaces render CQD solids highly insulating due to minimal wave function overlap of neighboring QDs, complete removal of surface ligands has proven to be difficult, resulting in dangling bonds on the surface as well as trap states.The use of shorter ligands, dot cross-linking with bi-functional ligands, inorganic ligands such as soluble molecular metal chalcogenide complexes (MCCs) can also be used to replace the original long chain organic ligands and result in significant improvements in charge transport and device performance.
In conclusion, the advancements in coupled colloidal quantum dot (CQD) solids hold immense promise for revolutionizing charge transport in a wide range of optoelectronic and thermoelectric applications.The precision engineering of CQD materials, along with innovative strategies for assembly and passivation, has paved the way for superior optoelectronic performance, making them highly attractive for solar cells and photovoltaic devices.Additionally, the exploration of emerging physical mechanisms like hot carrier collection and multiple exciton generation (MEG) opens up exciting avenues for further enhancing the efficiency of CQDbased photovoltaics, aligning with the quest for sustainable energy solutions.

Figure 2 .
Figure 2. (a) Schematic depicting how coupling between individual dots determine the electronic properties of resulting QD solids (b)Possible ligand passivations for PbS QDs, along with energy shifts associated with each ligand[35].Reprinted with permission from[35].Copyright ©2014 American Chemical Society.(c) Schematic diagram depicting solid state ligand exchange and (d) solution phase ligand exchange.Reprinted with permission from[36].Copyright ©2016 Royal Society of Chemistry (e,f) TEM images of 6nm PbSe QD films before (e) and after (f) solid-state exchange of long-chain oleate for compact, thiocyanate ligands (scale bar is 20 nm)[37] (g) SEM image of solution-deposited, thiocyanate-exchanged 3.9 nm CdSe QD films, after annealing at 250 °C for 10 min(scale bar is 50 nm)[38].Reprinted with permission from[37].Copyright ©2014 American Chemical Society.Reprinted with permission from[38].Copyright ©2012 American Chemical Society

Figure 3 .
Figure 3. Charge transport mechanisms for CdSe dots (a) TEM images showing TOPO capped dots with diameter ∼6 nm under different conditions: as-deposited, after annealing in forming gas at 350 °C, and after annealing at 430 °C [73].(b) Current-voltage characteristics at 77 K in the dark (top) and under green LED illumination (bottom), labeled I-III for distinct annealing conditions.Inset shows current transient, indicating a well-described behavior of I(t) ∼78t −0.13 pA, for a specific voltage step after annealing at 110°C [73].Reprinted with permission from [73].Copyright ©2002 AIP Publishing.(c) Charge transport in NaOH treated CdSe dots of different sizes, with temperature dependence of the mobility showing simply activated Arrhenius behaviour.(d) Size dependence of the activation energy showing scaling with dot size and d which represents sum of dot size and interdot spacing [74].Reprinted with permission from [74].Copyright ©2010 American Chemical Society (e) Transfer characteristics of CdSe QD transistors.Inset shows output characteristics of the CdSe QD transistor;(f) Temperature-dependent mobility of devices with SiO 2 and Al 2 O 3 /SiO 2 gate insulators; Reprinted with permission from [38].Copyright ©2012 American Chemical Society.

Figure 5 (
b) shows a cross-sectional SEM image of n + -ZnO/PbS heterojunction QD solar cell.The n-type doping

Figure 5 .
Figure 5. (a) Absorption spectrum and photovoltaic device structure (inset) for a high-performing PbS QD Schottky solar cell, along with current-voltage characteristics in the dark and under illumination [88].Reprinted with permission from [88].Copyright ©2013 Royal Society of Chemistry.(b) Cross-sectional SEM image of depleted heterojunction solar cell with a boron-doped ZnO layer as a transparent electrode and the associated J-V characteristics [90].Copyright ©2015 Advanced Materials.(c) Illustration of an optimized tandem cell with PbS QD band gaps, alongside the corresponding J-V characteristic and control single-junction devices.The tandem cell exhibits a V oc equal to the sum of the V oc values of the subcells [54].Copyright ©2011 Advanced Materials.

Figure 6 .
Figure 6.Factors affecting thermoelectric properties of QD solids (a) Scaling of Seebeck coefficient (S) with QD size and phonon scattering associated with quantum confinement.(b) Reported thermoelectric figure of merit, ZT and (c) Seebeck co-efficient for different QDs with surface ligands.

Table 1 .
Different types of coupling ligands used to form QD solids and the associated field effect mobilities.

Table 2 .
[97]oconversion efficiencies of different solar cell architectures and their limitations.Schematic of architecture and band diagrams reprinted with permission from[97].
[104]: Sensitivity to defects, trap states and interfaces 15.74 [103],16.07[104]Features:Extension of absorption range, combination of cells to ensure more efficient carrier transport.Limitations: Complexities in fabrication, Bulkier and heavier.