Propagation of Structural Disorder in Epitaxially Connected Quantum Dot Solids from Atomic to Micron Scale

Ligand Interactions and Nanoparticle Shapes Guide the Pathways toward Interfacial Self-Assembly

Non-equilibrium molecular dynamics simulations are used to probe the driving forces behind the formation of highly ordered, epitaxially connected superlattices of polyhedral-shaped nanoparticles (NPs) at fluid-fluid interfaces. By explicitly modeling coarse-grained ligands that cap the NP surface, it is shown that differences in NP shapes and time-dependent facet-specific ligand densities give rise to drastically different transformation mechanisms. Our results indicate that the extent of screening of the inter-particle interactions by the surrounding solvation environment has a significant impact on reversibility and ultimately the coherence of the final two-dimensional superlattice obtained. For the particle shapes examined, a hexagonal pre-assembly and a square superlattice final assembly (upon preferential ligand desorption from {100} facets) were prevalent; however, cuboctahedral NPs formed intermediate epitaxially bonded branched clusters, which eventually grew and rearranged into a square lattice; in contrast, truncated octahedral NPs exhibited an abrupt rhombic-to-square transition driven by the clustering of their numerous {111}-ligands that favored the stacking of linear NP rods. To track the incipient order in the system, we also outline a set of novel order parameters that measure the local orientation alignment between nearest-neighbor pairs. The simulation protocols advanced in this work could pave the way forward for exploration of the vast phase space associated with the interfacial self-assembly of NPs.

Trade-offs between Translational and Orientational Order in 2D Superlattices of Polygonal Nanocrystals with Differing Edge Count

The goal of this work is to identify factors which modulate structural order in 2D self-assembled superlattices of polygon-shaped colloidal nanocrystals. Using combined experimental and simulation techniques, we quantify order in superlattices of hexagonal prism-shaped CdSe/CdS nanocrystals and cube-shaped CsPbBr₃ nanocrystals. Superlattices derived from cube-shaped nanocrystals display less translational order compared to hexagonal prism-shaped nanocrystals both experimentally and in simulations. This effect can be attributed to geometric considerations inherent to the combined rotational and translational symmetries of different polygonal shapes and their superlattices. Cubes form a simple cubic lattice where nanocrystals can slide without steric overlap, whereas hexagonal prisms interlock, preventing translation. Regarding orientational order, cube assemblies display a narrower orientation distribution. Intuitively, hexagonal prisms are a more "spherical" shape compared to cubes. The results presented here outline a conceptual framework for identifying superlattice structures which favor translationally and orientationally ordered self-assembled superlattices.

Emergent properties in supercrystals of atomically precise nanoclusters and colloidal nanocrystals

We provide a comprehensive account of the optical, electrical and mechanical properties that result from the self-assembly of colloidal nanocrystals or atomically precise nanoclusters into crystalline arrays with long-range order....

Thermodynamically Stable Colloidal Solids: Interfacial Thermodynamics from the Particle Size Distribution

True thermodynamic stability of a solid colloidal dispersion is generally unexpected, so much that thorough experimental validation of proposed stable systems remains incomplete. Such dispersions are under investigated and would be of interest due to their long-term stability and insensitivity to preparation pathway. We apply classical nucleation theory (CNT) to such colloidal systems, providing a relationship which links the size-dependent interfacial free energy density of the particles to their size distribution, and use this expression in the fitting of previously reported size distributions for putatively thermodynamically stable nanoparticles. Experimental data from a gold-thiol system exhibiting inverse coarsening or "digestive ripening" can be well-described in terms of a power-law dependence of the interfacial free energy γ on radius based on capacitive charging of the nanoparticles, going asr - 3 , as suggested by prior authors. Data from magnetite nanoparticles in highly basic solutions also can be well-fit using the CNT relation, but with γ going asr - 2 . Slightly better fits are possible if the power of the radius is non-integral, but we stress that more complex models of γ will require richer data sets to avoid the problem of overfitting. Some parameters of the fits are still robustly at odds with earlier models that implicitly assumed absolute thermodynamic stability: first, the extrapolated free energy density of the flat surface in these systems is small and positive, rather than strongly negative; second, the shape of the distributions indicates the solution phase to be supersaturated in monomer relative to the bulk, and thus that these two systems may only be metastable. For future work, we derive expressions for the important statistical thermodynamic and chemical parameters of the interface energy in terms of 1) the surfactant concentration, 2) the temperature dependence, and 3) the concentrations of particles in the tail of the distribution.

The mesoscale order of nacreous pearls

A pearl's distinguished beauty and toughness are attributable to the periodic stacking of aragonite tablets known as nacre. Nacre has naturally occurring mesoscale periodicity that remarkably arises in the absence of discrete translational symmetry. Gleaning the inspiring biomineral design of a pearl requires quantifying its structural coherence and understanding the stochastic processes that influence formation. By characterizing the entire structure of pearls (∼3 mm) in a cross-section at high resolution, we show that nacre has medium-range mesoscale periodicity. Self-correcting growth mechanisms actively remedy disorder and topological defects of the tablets and act as a countervailing process to long-range disorder. Nacre has a correlation length of roughly 16 tablets (∼5.5 µm) despite persistent fluctuations and topological defects. For longer distances (>25 tablets , ∼8.5 µm), the frequency spectrum of nacre tablets follows [Formula: see text] behavior, suggesting that growth is coupled to external stochastic processes-a universality found across disparate natural phenomena, which now includes pearls.

Enhanced Carrier Transport in Strongly Coupled, Epitaxially Fused CdSe Nanocrystal Solids

Strongly coupled, epitaxially fused colloidal nanocrystal (NC) solids are promising solution-processable semiconductors to realize optoelectronic devices with high carrier mobilities. Here, we demonstrate sequential, solid-state cation exchange reactions to transform epitaxially connected PbSe NC thin films into Cu₂Se nanostructured thin-film intermediates and then successfully to achieve zinc-blende, CdSe NC solids with wide epitaxial necking along {100} facets. Transient photoconductivity measurements probe carrier transport at nanometer length scales and show a photoconductance of 0.28(1) cm² V^-1 s^-1, the highest among CdSe NC solids reported. Atomic-layer deposition of a thin Al₂O₃ layer infiltrates and protects the structure from fusing into a polycrystalline thin film during annealing and further improves the photoconductance to 1.71(5) cm² V^-1 s^-1 and the diffusion length to 760 nm. We fabricate field-effect transistors to study carrier transport at micron length scales and realize high electron mobilities of 35(3) cm² V^-1 s^-1 with on-off ratios of 10⁶ after doping.

Hierarchical carrier transport simulator for defected nanoparticle solids

The efficiency of nanoparticle (NP) solar cells has grown impressively in recent years, exceeding 16%. However, the carrier mobility in NP solar cells, and in other optoelectronic applications remains low, thus critically limiting their performance. Therefore, carrier transport in NP solids needs to be better understood to further improve the overall efficiency of NP solar cell technology. However, it is technically challenging to simulate experimental scale samples, as physical processes from atomic to mesoscopic scales all crucially impact transport. To rise to this challenge, here we report the development of TRIDENS: the Transport in Defected Nanoparticle Solids Simulator, that adds three more hierarchical layers to our previously developed HINTS code for nanoparticle solar cells. In TRIDENS, we first introduced planar defects, such as twin planes and grain boundaries into individual NP SLs superlattices (SLs) that comprised the order of 10³ NPs. Then we used HINTS to simulate the transport across tens of thousands of defected NP SLs, and constructed the distribution of the NP SL mobilities with planar defects. Second, the defected NP SLs were assembled into a resistor network with more than 10⁴ NP SLs, thus representing about 10⁷ individual NPs. Finally, the TRIDENS results were analyzed by finite size scaling to explore whether the percolation transition, separating the phase where the low mobility defected NP SLs percolate, from the phase where the high mobility undefected NP SLs percolate drives a low-mobility-to-highmobility transport crossover that can be extrapolated to genuinely macroscopic length scales. For the theoretical description, we adapted the Efros-Shklovskii bimodal mobility distribution percolation model. We demonstrated that the ES bimodal theory’s two-variable scaling function is an effective tool to quantitatively characterize this low-mobility-to-high-mobility transport crossover.

Application of Dislocation Theory to Minimize Defects in Artificial Solids Built with Nanocrystal Building Blocks

ConspectusOriented atomic attachment of colloidal inorganic nanocrystals represents a powerful synthetic method for preparing complex inorganic superstructures. Examples include fusion of nanocrystals into dimer and superlattice structures. If the attachment were perfect throughout, then the resulting materials would have single crystal-like alignment of the individual nanocrystals' atomic lattices. While individual colloidal nanocrystals typically are free of many defects, there are a multitude of pathways that can generate defects upon nanocrystal attachment. These attachment generated defects are typically undesirable, and thus developing strategies to favor defect-free attachment or heal defective interfaces are essential. There may also be some cases where attachment-derived defects are desirable. In this Account, we summarize our current understanding of how these defects arise, in order to offer guidance to those who are designing nanocrystal derived solids.The small size of inorganic nanocrystals means short diffusion lengths to the surface, which favor the formation of nanocrystal building blocks with pristine atomic structures. Upon attachment, however, there are numerous pathways that can lead to atomic scale defects, and bulk crystal dislocation theory provides an invaluable guide to understanding these phenomena. As an example, an atomic step edge can be incorporated into the interface leading to an extra half-plane of atoms, known as an edge dislocation. These dislocations can be well described by the Burgers vector description of dislocations, which geometrically identifies planes in which a dislocation can move. Our in situ measurements have verified that bulk dislocation theory predictions for 1D defects hold true at few-nanometer length scales in PbTe and CdSe nanocrystal interfaces. Ultimately, the applicability of dislocation theory to nanocrystal attachment enables the predictive design of attachment to prevent or facilitate healing of defects upon nanocrystal attachment. We applied similar logic to understand formation of planar (2D) defects such as stacking faults upon nanocrystal attachment. Again concepts from bulk crystal defect crystallography can identify attachment pathways that can prevent or deterministically form planar defects upon nanocrystal attachment. The concepts we discuss work well for identifying favorable attachment geometries for nanocrystal pairs; however it is currently unclear how to translate these ideas to near-simultaneous multiparticle attachment. Geometric frustration, which prevents nanocrystal rotation, and yet-to-be considered defect generation pathways unique to multiparticle attachment complicate defect-free superlattice attachment. New imaging methods now allow for the direct observation of local attachment trajectories and may enable improved understanding of such multiparticle phenomena. With further refinement, a unified framework for understanding and ultimately eliminating structural defects in fused nanocrystal superstructures may well be achievable in coming years.

Colloidal Synthesis Path to 2D Crystalline Quantum Dot Superlattices

By combining colloidal nanocrystal synthesis, self-assembly, and solution phase epitaxial growth techniques, we developed a general method for preparing single dot thick atomically attached quantum dot (QD) superlattices with high-quality translational and crystallographic orientational order along with state-of-the-art uniformity in the attachment thickness. The procedure begins with colloidal synthesis of hexagonal prism shaped core/shell QDs (e.g., CdSe/CdS), followed by liquid subphase self-assembly and immobilization of superlattices on a substrate. Solution phase epitaxial growth of additional semiconductor material fills in the voids between the particles, resulting in a QD-in-matrix structure. The photoluminescence emission spectra of the QD-in-matrix structure retains characteristic 0D electronic confinement. Importantly, annealing of the resulting structures removes inhomogeneities in the QD-QD inorganic bridges, which our atomistic electronic structure calculations demonstrate would otherwise lead to Anderson-type localization. The piecewise nature of this procedure allows one to independently tune the size and material of the QD core, shell, QD-QD distance, and the matrix material. These four choices can be tuned to control many properties (degree of quantum confinement, quantum coupling, band alignments, etc.) depending on the specific applications. Finally, cation exchange reactions can be performed on the final QD-in-matrix, as demonstrated herein with a CdSe/CdS to HgSe/HgS conversion.

Mapping Defect Relaxation in Quantum Dot Solids upon In Situ Heating

Epitaxially connected quantum dot solids have emerged as an interesting class of quantum confined materials with the potential for highly tunable electronic structures. Realization of the predicted emergent electronic properties has remained elusive due in part to defective interdot epitaxial connections. Thermal annealing has shown potential to eliminate such defects, but a direct understanding of this mechanism hinges on determining the nature of defects in the connections and how they respond to heating. Here, we use in situ heating in the scanning transmission electron microscope to probe the effect of heating on distinct defect types. We apply a real space, local strain mapping technique, which allows us to identify tensile and shear strain in the atomic lattice, highlighting tensile, shear, and bending defects in interdot connections. We also track the out-of-plane orientation of individual QDs and infer the prevalence of out-of-plane twisting and bending defects as a function of annealing. We find that tensile and shear defects are fully relaxed upon mild thermal annealing, while bending defects persist. Additionally, out-of-plane orientation tracking reveals an increase in correctly oriented QDs, pointing to a relaxation of either twisting defects or out-of-plane bending defects. While bending defects remain, highlighting the need for further study of orientational ordering during the preattachment phase of superlattice formation, these atomic-scale insights show that annealing can effectively eliminate tensile and shear defects, a promising step toward delocalization of charge carriers and tunable electronic properties.

An Implicit-Solvent Model for the Interfacial Configuration of Colloidal Nanoparticles and Application to the Self-Assembly of Truncated Cubes

This study outlines the development of an implicit-solvent model that reproduces the behavior of colloidal nanoparticles at a fluid-fluid interface. The center point of this formulation is the generalized quaternion-based orientational constraint (QOCO) method. The model captures three major energetic characteristics that define the nanoparticle configuration-position (orthogonal to the interfacial plane), orientation, and inter-nanoparticle interaction. The framework encodes physically relevant parameters that provide an intuitive means to simulate a broad spectrum of interfacial conditions. Results show that for a wide range of shapes, our model is able to replicate the behavior of an isolated nanoparticle at an explicit fluid-fluid interface, both qualitatively and often nearly quantitatively. Furthermore, the family of truncated cubes is used as a test bed to analyze the effect of changes in the degree of truncation on the potential-of-mean-force landscape. Finally, our results for the self-assembly of an array of cuboctahedra provide corroboration to the experimentally observed honeycomb and square lattices.

Unravelling three-dimensional adsorption geometries of PbSe nanocrystal monolayers at a liquid-air interface

The adsorption, self-organization and oriented attachment of PbSe nanocrystals (NCs) at liquid-air interfaces has led to remarkable nanocrystal superlattices with atomic order and a superimposed nanoscale geometry. Earlier studies examined the NC self-organization at the suspension/air interface with time-resolved in-situ X-ray scattering. Upon continuous evaporation of the solvent, the NC interfacial layer will finally contact the (ethylene glycol) liquid substrate on which the suspension was casted. In order to obtain structural information on the NC organization at this stage of the process, we examined the ethylene glycol/NC interface in detail for PbSe NCs of different sizes, combining in-situ grazing-incidence small-and-wide-angle X-ray scattering (GISAXS/GIWAXS), X-ray reflectivity (XRR) and analytical calculations of the adsorption geometry of these NCs. Here, we observe in-situ three characteristic adsorption geometries varying with the NC size. Based on the experimental evidence and simulations, we reveal fully three-dimensional arrangements of PbSe nanocrystals at the ethylene glycol-air interface with and without the presence of rest amounts of toluene.

Collective topo-epitaxy in the self-assembly of a 3D quantum dot superlattice

Epitaxially fused colloidal quantum dot (QD) superlattices (epi-SLs) may enable a new class of semiconductors that combine the size-tunable photophysics of QDs with bulk-like electronic performance, but progress is hindered by a poor understanding of epi-SL formation and surface chemistry. Here we use X-ray scattering and correlative electron imaging and diffraction of individual SL grains to determine the formation mechanism of three-dimensional PbSe QD epi-SL films. We show that the epi-SL forms from a rhombohedrally distorted body centred cubic parent SL via a phase transition in which the QDs translate with minimal rotation (~10°) and epitaxially fuse across their {100} facets in three dimensions. This collective epitaxial transformation is atomically topotactic across the 10³-10⁵ QDs in each SL grain. Infilling the epi-SLs with alumina by atomic layer deposition greatly changes their electrical properties without affecting the superlattice structure. Our work establishes the formation mechanism of three-dimensional QD epi-SLs and illustrates the critical importance of surface chemistry to charge transport in these materials.

Orientational Disorder in Epitaxially Connected Quantum Dot Solids

Periodic arrays of strongly coupled colloidal quantum dots (QDs) may enable unprecedented control of electronic band structure through manipulation of QD size, shape, composition, spacing, and assembly geometry. This includes the possibilities of precisely engineered bandgaps and charge carrier mobilities, as well as remarkable behaviors such as metal-insulator transitions, massless carriers, and topological states. However, experimental realization of these theoretically predicted electronic structures is presently limited by structural disorder. Here, we use aberration-corrected scanning transmission electron microscopy to precisely quantify the orientational disorder of epitaxially connected QD films. In spite of coherent atomic connectivity between nearest neighbor QDs, we find misalignment persists with a standard deviation of 1.9°, resulting in significant bending strain localized to the adjoining necks. We observe and quantify a range of out-of-plane particle orientations over thousands of QDs and correlate the in-plane and out-of-plane misalignments, finding QDs misoriented out-of-plane display a statistically greater misalignment with respect to their in-plane neighbors as well. Using the bond orientational order metric ψ₄, we characterize the 4-fold symmetry and introduce a quantification of the local superlattice (SL) orientation. This enables direct comparison between local orientational order in the SL and atomic lattice (AL). We find significantly larger variations in the SL orientation and a statistically robust but locally highly variable correlation between the orientations of the two differently scaled lattices. Distinct AL and SL behaviors are observed about a grain boundary, with a sharp boundary in the AL orientations, but a more smooth transition in the SL, facilitated by lattice deformation between the neighboring grains. Coupling between the AL and SL is a fundamental driver of film growth, and these results suggest nontrivial underlying mechanics, implying that simplified models of epitaxial attachment may be insufficient to understand QD growth and disorder when oriented attachment and superlattice growth occur in concert.

Revealing Structure and Crystallographic Orientation of Soft Epitaxial Assembly of Nanocrystals by Grazing Incidence X-ray Scattering

We study the structural coherence of a self-assembled overlayer of PbS nanocrystal (NC) superlattice onto an underlying PbS NC monolayer, which acts as a template. We explore the effect of the templating layer on the structure of the overlayer asemblies by varying interfacial strain and determine the impact of new ligands on their superlattice structure. The overlayers and templates are analyzed by grazing-incidence X-ray scattering and microscopy. We find that differences in the lattice parameters of 7.7% between the two layers are tolerated in terms of a "soft epitaxial" assembly into the body-centered tetragonal superstucture and lead to structural registry within the overlayer. Conversely, at the interface, a lattice mismatch of 24.4% is too large for soft epitaxy and invokes a change in the superlattice. Upon ligand treatment, the overlayer superlattices transform their orientation axis and the NCs orient preferentially. These results provide new insights into mitigating defects in layered, heterostructured NC assemblies.

Triangular nanoperforation and band engineering of InGaAs quantum wells: a lithographic route toward Dirac cones in III-V semiconductors

The design of two-dimensional periodic structures at the nanoscale has renewed attention for band structure engineering. Here, we investigate the nanoperforation of InGaAs quantum wells epitaxially grown on InP substrates using high-resolution e-beam lithography and highly plasma based dry etching. We report on the fabrication of a honeycomb structure with an effective lattice constant down to 23 nm by realising triangular antidot lattice with an ultimate periodicity of 40 nm in a 10 nm thick InGaAs quantum well on a p-type InP. The quality of the honeycomb structures is discussed in detail, and calculations show the possibility to measure Dirac physics in these type of samples. Based on the statistical analysis of the fluctuations in pore size and periodicity, calculations of the band structure are performed to assess the robustness of the Dirac cones with respect to distortions of the honeycomb lattice.

Mono- and Multilayer Silicene-Type Honeycomb Lattices by Oriented Attachment of PbSe Nanocrystals: Synthesis, Structural Characterization, and Analysis of the Disorder

Nanocrystal (NC) solids are commonly prepared from nonpolar organic NC suspensions. In many cases, the capping on the NC surface is preserved and forms a barrier between the NCs. More recently, superstructures with crystalline connections between the NCs, implying the removal of the capping, have been reported, too. Here, we present large-scale uniform superstructures of attached PbSe NCs with a silicene-type honeycomb geometry, resulting from solvent evaporation under nearly reversible conditions. We also prepared multilayered silicene honeycomb structures by using larger amounts of PbSe NCs. We show that the two-dimensional silicene superstructures can be seen as a crystallographic slice from a 3-D simple cubic structure. We describe the disorder in the silicene lattices in terms of the nanocrystals position and their atomic alignment. The silicene honeycomb sheets are large enough to be used in transistors and optoelectronic devices.

Interfacial Self-Assembly and Oriented Attachment in the Family of PbX (X = S, Se, Te) Nanocrystals

The realization of materials with new optoelectronic properties draws much scientific attention toward the field of nanocrystal superstructures. Low-dimensional superstructures created by interfacial assembly and oriented attachment of PbSe nanocrystals are a striking example because theory showed that PbSe sheets with a honeycomb geometry possess non-trivial flat bands and Dirac cones in the valence and conduction bands. Here, we report on the formation of one-dimensional linear and zigzag structures and two-dimensional (2D) square and honeycomb structures for the entire lead chalcogenide family: PbX (X = S, Se, Te). We observe that PbTe, with a lower bulk melting temperature and enthalpy of formation than those of PbSe, shows a higher nanocrystal surface reactivity, such that the surface must be passivated and the reaction conditions moderated to obtain reasonably ordered superstructures. The present findings constitute a step forward in the realization of a larger family of atomically coherent 2D superstructures with variable IV-VI and II-VI compositions and with electronic properties dictated by the nanogeometry.

Dynamics and Removal Pathway of Edge Dislocations in Imperfectly Attached PbTe Nanocrystal Pairs: Toward Design Rules for Oriented Attachment

Using in situ high-resolution TEM, we study the structure and dynamics of well-defined edge dislocations in imperfectly attached PbTe nanocrystals. We identify that attachment of PbTe nanocrystals on both {100} and {110} facets gives rise to b = a/2⟨110⟩ edge dislocations. Based on the Burgers vector of individual dislocations, we can identify the glide plane of the dislocations. We observe that defects in particles attached on {100} facets have glide planes that quickly intersect the surface, and HRTEM movies show that the defects follow the glide plane to the surface. For {110} attached particles, the glide plane is collinear with the attachment direction, which does not provide an easy path for the dislocation to reach the surface. Indeed, HRTEM movies of dislocations for {110} attached particles show that defect removal is much slower. Further, we observe conversion from pure edge dislocations in imperfectly attached particles to dislocations with mixed edge and screw character, which has important implications for crystal growth. Finally, we observe that dislocations initially closer to the surface have a higher speed of removal, consistent with the strong dislocation free surface attractive force. Our results provide important design rules for defect-free attachment of preformed nanocrystals into epitaxial assemblies.

Emergent Electronic and Dielectric Properties of Interacting Nanoparticles at Finite Temperature

Lead chalcogenide nanoparticle solids have been successfully integrated into certified solar cells and represent promising platforms for the design of novel photoabsorbers for photoelectrochemical cells. While much attention has been drawn to improving efficiency and device performance through altering the character of the individual nanoparticles, the role of interactions between nanoparticles is not yet well-understood. Using first-principles molecular dynamics and electronic structure calculations, we investigated the combined effect of temperature and interaction on functionalized lead chalcogenide nanoparticles (NPs). Here, we show that at finite temperature, interacting NPs are dynamical dipolar systems, with the average values of dipole moments and polarizabilities substantially increased with respect to those of the isolated building blocks. In addition, we show that the interacting NPs exhibit slightly smaller fundamental gaps that decrease as a function of temperature and that the radiative lifetimes of both the isolated NPs and the solids are greatly reduced at finite temperature compared to T = 0. Finally, we present a critical discussion of various results reported in the literature for the values of dipole moments of nanoparticles.

Colloidal nanocrystals as LEGO® bricks for building electronic band structure models

Semiconductor nanocrystals can be seen as LEGO® bricks for synthesizing new 2D materials and for engineering band structures.

Metal-Insulator Transition in Nanoparticle Solids: Insights from Kinetic Monte Carlo Simulations

Progress has been rapid in increasing the efficiency of energy conversion in nanoparticles. However, extraction of the photo-generated charge carriers remains challenging. Encouragingly, the charge mobility has been improved recently by driving nanoparticle (NP) films across the metal-insulator transition (MIT). To simulate MIT in NP films, we developed a hierarchical Kinetic Monte Carlo transport model. Electrons transfer between neighboring NPs via activated hopping when the NP energies differ by more than an overlap energy, but transfer by a non-activated quantum delocalization, if the NP energies are closer than the overlap energy. As the overlap energy increases, emerging percolating clusters support a metallic transport across the entire film. We simulated the evolution of the temperature-dependent electron mobility. We analyzed our data in terms of two candidate models of the MIT: (a) as a Quantum Critical Transition, signaled by an effective gap going to zero; and (b) as a Quantum Percolation Transition, where a sample-spanning metallic percolation path is formed as the fraction of the hopping bonds in the transport paths is going to zero. We found that the Quantum Percolation Transition theory provides a better description of the MIT. We also observed an anomalously low gap region next to the MIT. We discuss the relevance of our results in the light of recent experimental measurements.

Formation of Epitaxially Connected Quantum Dot Solids: Nucleation and Coherent Phase Transition

The formation of epitaxially connected quantum dot solids involves a complex interplay of interfacial assembly, surface chemistry, and irreversible-directed attachment. We describe the basic mechanism in the context of a coherent phase transition with distinct nucleation and propagation steps. The proposed mechanism explains how defects in the preassembled structure influence nucleation and how basic geometric relationships govern the transformation from hexagonal assemblies of isolated dots to interconnected solids with square symmetry. We anticipate that new mechanistic insights will guide future advances in the formation of high-fidelity quantum dot solids with enhanced grain size, interconnectivity, and control over polymorph structures.