Local-density-derived semiempirical pseudopotentials

Coupled 2D quantum dot films for next generation solar cells: electronic structure and anomalous light absorption behaviour

There is an increasing interest into the fabrication of high-dimensionality colloidal quantum dot (CQD) arrays, with long-range periodicity and reduced inter-dot distances. The synthesis of such super-solids, where the dots play the role of conventional atoms in a crystal, is, however, still challenging. This work focuses on understanding the physics of those systems and finding applications for them in solar cells of two different architectures: the hot carrier solar cell and the intermediate band solar cell. We combine the accuracy of the atomistic semiempirical pseudopotential method, at the single-dot level, with the versatility of the tight-binding formalism, for the array calculations, to investigate the electronic structure and optical absorption of individual and stacked 2D InX (X = P, As, Sb) CQD arrays (films), and their dependence on the dot material, the number of layers and the interlayer distance. Our results support the hypothesis of a universal behaviour of absorption in 2D materials, already found in graphene and InAs nanomembranes, where the optical absorption in the region 0.5-1.2 eV is nearly independent of the photon energy and equal to a universal quantum of absorption AQ = πafs = 0.02293 (where afs is the fine structure constant). However, our findings contradict the assumption that the absorbance of n layers is simply nAQ. Indeed, according to our results this conclusion only holds for uncoupled stacked layers, whereas the presence of inter-layer coupling degrades the absorption properties, leading to A(n) < nA(1), questioning the wisdom of the efforts of achieving 3D super-solids if the aim is to improve optical absorption. Additionally, we propose a simplified model that accurately describes the intermediate band structure, useful for device simulations.

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.

Reductive pathways in molten inorganic salts enable colloidal synthesis of III-V semiconductor nanocrystals

Colloidal quantum dots, with their size-tunable optoelectronic properties and scalable synthesis, enable applications in which inexpensive high-performance semiconductors are needed. Synthesis science breakthroughs have been key to the realization of quantum dot technologies, but important group III-group V semiconductors, including colloidal gallium arsenide (GaAs), still cannot be synthesized with existing approaches. The high-temperature molten salt colloidal synthesis introduced in this work enables the preparation of previously intractable colloidal materials. We directly nucleated and grew colloidal quantum dots in molten inorganic salts by harnessing molten salt redox chemistry and using surfactant additives for nanocrystal shape control. Synthesis temperatures above 425°C are critical for realizing photoluminescent GaAs quantum dots, which emphasizes the importance of high temperatures enabled by molten salt solvents. We generalize the methodology and demonstrate nearly a dozen III-V solid-solution nanocrystal compositions that have not been previously reported.

Layered Hydride LiH4 with a Pressure-Insensitive Superconductivity

For hydride superconductors, each significant advance is built upon the discovery of novel H-based structural units, which in turn push the understanding of the superconducting mechanism to new heights. Based on first-principles calculations, we propose a metastable LiH4 with a wavy H layer composed of the edge-sharing pea-like H18 rings at high pressures. Unexpectedly, it exhibits pressure-insensitive superconductivity manifested by an extremely small pressure coefficient (dTc/dP) of 0.04 K/GPa. This feature is attributed to the slightly weakened electron-phonon coupling with pressure, caused by the reduced charge transfer from Li atoms to wavy H layers, significantly suppressing the substantial increase in the contribution of phonons to Tc. Its superconductivity originates from the strong coupling between the H 1s electrons and the high-frequency phonons associated with the H layer. Our study extends the list of H-based structural units and enhances the in-depth understanding of pressure-related superconductivity.

Theory of Photoluminescence Spectral Line Shapes of Semiconductor Nanocrystals

Single-molecule photoluminescence (PL) spectroscopy of semiconductor nanocrystals (NCs) reveals the nature of exciton-phonon interactions in NCs. Understanding the homogeneous spectral line shapes and their temperature dependence remains an open problem. Here, we develop an atomistic model to describe the PL spectrum of NCs, accounting for excitonic effects, phonon dispersion relations, and exciton-phonon couplings. We validate our model using single-NC measurements on CdSe/CdS NCs from T = 4 to 290 K, and we find that the slightly asymmetric main peak at low temperatures is comprised of a narrow zero-phonon line (ZPL) and acoustic phonon sidebands. Furthermore, we identify the specific phonon modes that give rise to the optical phonon sidebands. At temperatures above 200 K, the spectral line width shows a stronger dependence upon the temperature, which we demonstrate to be correlated with higher order exciton-phonon couplings. We also identify the line width dependence upon reorganization energy, NC core sizes, and shell thicknesses.

Composition-Defined Optical Properties and the Direct-to-Indirect Transition in Core-Shell In1-xGaxP/ZnS Colloidal Quantum Dots

Semiconductors are commonly divided into materials with direct or indirect band gaps based on the relative positions of the top of the valence band and the bottom of the conduction band in crystal momentum (k) space. It has, however, been debated if k is a useful quantum number to describe the band structure in quantum-confined nanocrystalline systems, which blur the distinction between direct and indirect gap semiconductors. In bulk III-V semiconductor alloys like In_1-xGa_xP, the band structure can be tuned continuously from the direct- to indirect-gap by changing the value of x. The effect of strong quantum confinement on the direct-to-indirect transition in this system has yet to be established because high-quality colloidal nanocrystal samples have remained inaccessible. Herein, we report one of the first systematic studies of ternary III-V nanocrystals by utilizing an optimized molten-salt In-to-Ga cation exchange protocol to yield bright In_1-xGa_xP/ZnS core-shell particles with photoluminescence quantum yields exceeding 80%. We performed two-dimensional solid-state NMR studies to assess the alloy homogeneity and the extent of surface oxidation in In_1-xGa_xP cores. The radiative decay lifetime for In_1-xGa_xP/ZnS monotonically increases with higher gallium content. Transient absorption studies on In_1-xGa_xP/ZnS nanocrystals demonstrate signatures of direct- and indirect-like behavior based on the presence or absence, respectively, of excitonic bleach features. Atomistic electronic structure calculations based on the semi-empirical pseudopotential model are used to calculate absorption spectra and radiative lifetimes and evaluate band-edge degeneracy; the resulting calculated electronic properties are consistent with experimental observations. By studying photoluminescence characteristics at elevated temperatures, we demonstrate that a reduced lattice mismatch at the III-V/II-VI core-shell interface can enhance the thermal stability of emission. These insights establish cation exchange in molten inorganic salts as a viable synthetic route to nontoxic, high-quality In_1-xGa_xP/ZnS QD emitters with desirable optoelectronic properties.

Optical Absorption in N-Dimensional Colloidal Quantum Dot Arrays: Influence of Stoichiometry and Applications in Intermediate Band Solar Cells

We present a theoretical atomistic study of the optical properties of non-toxic InX (X = P, As, Sb) colloidal quantum dot arrays for application in photovoltaics. We focus on the electronic structure and optical absorption and on their dependence on array dimensionality and surface stoichiometry motivated by the rapid development of experimental techniques to achieve high periodicity and colloidal quantum dot characteristics. The homogeneous response of colloidal quantum dot arrays to different light polarizations is also investigated. Our results shed light on the optical behaviour of these novel multi-dimensional nanomaterials and identify some of them as ideal building blocks for intermediate band solar cells.

Indirect to Direct Band Gap Transformation by Surface Engineering in Semiconductor Nanostructures

Indirect band gap semiconductor materials are routinely exploited in photonics, optoelectronics, and energy harvesting. However, their optical conversion efficiency is low, due to their poor optical properties, and a wide range of strategies, generally involving doping or alloying, has been explored to increase it, often, however, at the cost of changing their material properties and their band gap energy, which, in essence, amounts to changing them into different materials altogether. A key challenge is therefore to identify effective strategies to substantially enhance optical transitions at the band gap in these materials without sacrificing their intrinsic nature. Here, we show that this is indeed possible and that GaP can be transformed into a direct gap material by simple nanostructuring and surface engineering, while fully preserving its "identity". We then distill the main ingredients of this procedure into a general recipe applicable to any indirect material and test it on AlAs, obtaining an increase of over 4 orders of magnitude in both emission intensity and radiative rates.

Decoupling Radiative and Auger Processes in Semiconductor Nanocrystals by Shape Engineering

One of the most challenging aspects of semiconductor nanotechnology is the presence of extremely efficient nonradiative decay pathways (known as Auger processes) that hinder any attempt at creating population inversion and obtaining gain in nanocrystals. What is even more frustrating is that, in most cases, the strategies adopted to slow down Auger in these nanostructures also lead to a comparable increase in the radiative recombination times, so that there is no overall improvement from the point of view of their applicability as emissive media. Here we present a comprehensive theoretical characterization of CdTe tetrapods and show that in these versatile nanostructures it is possible to achieve a complete decoupling between radiative and Auger processes, where the latter can be strongly suppressed compared to spherical structures, by careful shape engineering, without affecting the efficiency of radiative recombination.

Inverse-designed semiconductor nanocatalysts for targeted CO2 reduction in water

The most commonly used photocatalyst for CO₂ reduction is TiO₂. However, this semiconductor material is far from being ideally suited for this purpose, owing to its inefficient energy harvesting (it absorbs in the UV), low reduction rates (it exhibits short carrier lifetimes), and lack of selectivity with respect to competing reactions (such as the nearly isoenergetic and kinetically more favourable water reduction). In this work we compile a wish-list of properties for the ideal photocatalyst (including high reaction selectivity, availability of multiple redox equivalents at one time, large contact area for CO₂ adsorption with independently tunable band gap, and availability of electrons and holes at different locations on the surface for the two redox reactions to take place), and, using the principles of inverse design, we engineer a semiconductor nanostructure that not only meets all the necessary fundamental criteria to act as a catalyst for CO₂ reduction, but also exhibits all the wish-list properties, as confirmed by our state-of-the-art atomistic semi-empirical pseudopotential modelling. The result is a potentially game-changing material.

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.

Tuning the Radiative Lifetime in InP Colloidal Quantum Dots by Controlling the Surface Stoichiometry

InP nanocrystals exhibit a low photoluminescence quantum yield. As in the case of CdS, this is commonly attributed to their poor surface quality and difficult passivation, which give rise to trap states and negatively affect emission. Hence, the strategies adopted to improve their quantum yield have focused on the growth of shells, to improve passivation and get rid of the surface states. Here, we employ state-of-the-art atomistic semiempirical pseudopotential modeling to isolate the effect of surface stoichiometry from features due to the presence of surface trap states and show that, even with an atomistically perfect surface and an ideal passivation, InP nanostructures may still exhibit very long radiative lifetimes (on the order of tens of microseconds), broad and weak emission, and large Stokes' shifts. Furthermore, we find that all these quantities can be varied by orders of magnitude, by simply manipulating the surface composition, and, in particular, the number of surface P atoms. As a consequence it should be possible to substantially increase the quantum yield in these nanostructures by controlling their surface stoichiometry.

Coherent Exciton Dynamics in Ensembles of Size-Dispersed CdSe Quantum Dot Dimers Probed via Ultrafast Spectroscopy: A Quantum Computational Study

Interdot coherent excitonic dynamics in nanometric colloidal CdSe quantum dots (QD) dimers lead to interdot charge migration and energy transfer. We show by electronic quantum dynamical simulations that the interdot coherent response to ultrashort fs laser pulses can be characterized by pump-probe transient absorption spectroscopy in spite of the inevitable inherent size dispersion of colloidal QDs. The latter, leading to a broadening of the excitonic bands, induce accidental resonances that actually increase the efficiency of the interdot coupling. The optical electronic response is computed by solving the time-dependent Schrodinger equation including the interaction with the oscillating electric field of the pulses for an ensemble of dimers that differ by their size. The excitonic Hamiltonian of each dimer is parameterized by the QD size and interdot distance, using an effective mass approximation. Local and charge transfer excitons are included in the dimer basis set. By tailoring the QD size, the excitonic bands can be tuned to overlap and thus favor interdot coupling. Computed pump-probe transient absorption maps averaged over the ensemble show that the coherence of excitons in QD dimers that lead to interdot charge migration can survive size disorder and could be observed in fs pump-probe, four-wave mixing, or covariance spectroscopy.

Charge Dynamics in Quantum-Dot-Acceptor Complexes in the Presence of Confining and Deconfining Ligands

Nanocrystal surface functionalization is becoming widespread for applications exploiting fast charge extraction or ultrasensitive redox reactions. A variety of molecular acceptors are being linked to the dot surface via a new generation of organic ligands, ranging from neutral linkers to charge delocalizers. Understanding how core states interact with these molecular orbitals, localized outside the dot, is paramount for optimizing the design of efficient nanocrystal-acceptor conjugates. Here we look at two examples of this interaction: charge transfer to a molecular acceptor linked through either an exciton-delocalizing ligand or a more conventional localizing molecule. We find that such transfer can be described in terms of an Auger-mediated process whose rates can be tuned within a window of a few orders of magnitude (for the same dot-ligand-acceptor conjugate) by a suitable choice of the dispersion solvent and nanocrystal's dielectric environment. This result provides clear guidelines for charge extraction rate engineering in nanocrystal-based devices.

QuantumATK: an integrated platform of electronic and atomic-scale modelling tools

QuantumATK is an integrated set of atomic-scale modelling tools developed since 2003 by professional software engineers in collaboration with academic researchers. While different aspects and individual modules of the platform have been previously presented, the purpose of this paper is to give a general overview of the platform. The QuantumATK simulation engines enable electronic-structure calculations using density functional theory or tight-binding model Hamiltonians, and also offers bonded or reactive empirical force fields in many different parametrizations. Density functional theory is implemented using either a plane-wave basis or expansion of electronic states in a linear combination of atomic orbitals. The platform includes a long list of advanced modules, including Green's-function methods for electron transport simulations and surface calculations, first-principles electron-phonon and electron-photon couplings, simulation of atomic-scale heat transport, ion dynamics, spintronics, optical properties of materials, static polarization, and more. Seamless integration of the different simulation engines into a common platform allows for easy combination of different simulation methods into complex workflows. Besides giving a general overview and presenting a number of implementation details not previously published, we also present four different application examples. These are calculations of the phonon-limited mobility of Cu, Ag and Au, electron transport in a gated 2D device, multi-model simulation of lithium ion drift through a battery cathode in an external electric field, and electronic-structure calculations of the composition-dependent band gap of SiGe alloys.

Resilient Pathways to Atomic Attachment of Quantum Dot Dimers and Artificial Solids from Faceted CdSe Quantum Dot Building Blocks

The goal of this work is to identify favored pathways for preparation of defect-resilient attached wurtzite CdX (X = S, Se, Te) nanocrystals. We seek guidelines for oriented attachment of faceted nanocrystals that are most likely to yield pairs of nanocrystals with either few or no electronic defects or electronic defects that are in and of themselves desirable and stable. Using a combination of in situ high-resolution transmission electron microscopy (HRTEM) and electronic structure calculations, we evaluate the relative merits of atomic attachment of wurtzite CdSe nanocrystals on the {11̅00} or {112̅0} family of facets. Pairwise attachment on either facet can lead to perfect interfaces, provided the nanocrystal facets are perfectly flat and the angles between the nanocrystals can adjust during the assembly. Considering defective attachment, we observe for {11̅00} facet attachment that only one type of edge dislocation forms, creating deep hole traps. For {112̅0} facet attachment, we observe that four distinct types of extended defects form, some of which lead to deep hole traps whereas others only to shallow hole traps. HRTEM movies of the dislocation dynamics show that dislocations at {11̅00} interfaces can be removed, albeit slowly. Whereas only some extended defects at {112̅0} interfaces could be removed, others were trapped at the interface. Based on these insights, we identify the most resilient pathways to atomic attachment of pairs of wurtzite CdX nanocrystals and consider how these insights can translate to the creation of electronically useful materials from quantum dots with other crystal structures.

Theoretical Characterization of GaSb Colloidal Quantum Dots and Their Application to Photocatalytic CO2 Reduction with Water

With a large exciton Bohr radius and a high hole mobility in the bulk, GaSb is an important semiconductor material for technological applications. Here, we present a theoretical investigation into the evolution of some of its most fundamental characteristics at the nanoscale. GaSb emerges as a widely tunable, potentially disruptive new colloidal material with huge potential for application in a wide range of fields.

A bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles

We describe a bulk adjusted linear combination of atomic orbitals (BA-LCAO) approach for nanoparticles. In this method, we apply a many-body scaling function (in similar manner as in the environment-modified total energy based tight-binding method) to the DFT-derived diatomic AO interaction potentials (like in the conventional orbital-based density-functional tight binding approach) strictly according to atomic valences acquired naturally in a bulk structure. This modification, (a) facilitates all atom orbital-based electronic structure calculations of charge carrier dynamics in nanoscale structures with a molecular acceptor, and (b) allows to closely match high-level density functional calculation data (previously adjusted to the available experimental findings) for bulk structures. To advance practical application of the BA-LCAO approach we parameterize the Hamiltonian of wurtzite CdSe by fitting its band structure to a high-level DFT reference, corrected for experimentally measured band edges. Here, unlike in conventional DFTB approach, we: (1) use hydrogen-like AOs for the basis as exact atomic eigenfunctions, while orbital energies of which are taken from experimentally measured ionization potentials, and (2) parameterize the many-body scaling functions rather than the atomic wavefunctions. Development of this approach and parameters is guided by our goals to devise a method capable of simultaneously treating the problems of (i) interfacial electron/hole transfer between finite, variable size nanoparticles and electron scavenging molecules, and (ii) high-energy electronic transitions (Auger transitions) that mediate multi-exciton decay in quantum dots. Electronic structure results are described for CdSe quantum dots of various sizes. © 2018 Wiley Periodicals, Inc.

Quasi-Direct Optical Transitions in Silicon Nanocrystals with Intensity Exceeding the Bulk

Comparison of the measured absolute absorption cross section on a per Si atom basis of plasma-synthesized Si nanocrystals (NCs) with the absorption of bulk crystalline Si shows that while near the band edge the NC absorption is weaker than the bulk, yet above ∼ 2.2 eV the NC absorbs up to 5 times more than the bulk. Using atomistic screened pseudopotential calculations we show that this enhancement arises from interface-induced scattering that enhances the quasi-direct, zero-phonon transitions by mixing direct Γ-like wave function character into the indirect X-like conduction band states, as well as from space confinement that broadens the distribution of wave functions in k-space. The absorption enhancement factor increases exponentially with decreasing NC size and is correlated with the exponentially increasing direct Γ-like wave function character mixed into the NC conduction states. This observation and its theoretical understanding could lead to engineering of Si and other indirect band gap NC materials for optical and optoelectronic applications.

Exciton Dynamics in InSb Colloidal Quantum Dots

Extraordinarily fast biexciton decay times and unexpectedly large optical gaps are two striking features observed in InSb colloidal quantum dots that have remained so far unexplained. The former, should its origin be identified as an Auger recombination process, would have important implications regarding carrier multiplication efficiency, suggesting these nanostructures as potentially ideal active materials in photovoltaic devices. The latter could offer new insights into the factors that influence the electronic structure and consequently the optical properties of systems with reduced dimensionality and provide additional means to fine-tune them. Using the state-of-the-art atomistic semiempirical pseudopotential method we unveil the surprising origins of these features and show that a comprehensive explanation for these properties requires delving deep into the atomistic detail of these nanostructures and is, therefore, outside the reach of less sophisticated, albeit more popular, theoretical approaches.

Calculation of the specific heat of optimally K-doped BaFe₂As₂

The calculated specific heat of optimally K-doped BaFe2As2 in density functional theory is about five times smaller than that found in the experiment. We report that by adjusting the potential on the iron atom to be slightly more repulsive for electrons improves the calculated heat capacity as well as the electronic band structure of Ba0.6K0.4Fe2As2. In addition, structural and magnetic properties are moved in the direction of experimental values. Applying the same correction to the antiferromagnetic state, we find that the electron-phonon coupling is strongly enhanced.

Origins of photoluminescence decay kinetics in CdTe colloidal quantum dots

Recent experimental studies have identified at least two nonradiative components in the fluorescence decay of solutions of CdTe colloidal quantum dots (CQDs). The lifetimes reported by different groups, however, differed by orders of magnitude, raising the question of whether different types of traps were at play in the different samples and experimental conditions and even whether different types of charge carriers were involved in the different trapping processes. Considering that the use of these nanomaterials in biology, optoelectronics, photonics, and photovoltaics is becoming widespread, such a gap in our understanding of carrier dynamics in these systems needs addressing. This is what we do here. Using the state-of-the-art atomistic semiempirical pseudopotential method, we calculate trapping times and nonradiative population decay curves for different CQD sizes considering up to 268 surface traps. We show that the seemingly discrepant experimental results are consistent with the trapping of the hole at unsaturated Te bonds on the dot surface in the presence of different dielectric environments. In particular, the observed increase in the trapping times following air exposure is attributed to the formation of an oxide shell on the dot surface, which increases the dielectric constant of the dot environment. Two types of traps are identified, depending on whether the unsaturated bond is single (type I) or part of a pair of dangling bonds on the same Te atom (type II). The energy landscape relative to transitions to these traps is found to be markedly different in the two cases. As a consequence, the trapping times associated with the different types of traps exhibit a strikingly contrasting sensitivity to variations in the dot environment. Based on these characteristics, we predict the presence of a sub-nanosecond component in all photoluminescence decay curves of CdTe CQDs in the size range considered here if both trap types are present. The absence of such a component is attributed to the suppression of type I traps.

Envelope function method for electrons in slowly-varying inhomogeneously deformed crystals

We develop a new envelope-function formalism to describe electrons in slowly-varying inhomogeneously strained semiconductor crystals. A coordinate transformation is used to map a deformed crystal back to a geometrically undeformed structure with deformed crystal potential. The single-particle Schrödinger equation is solved in the undeformed coordinates using envelope function expansion, wherein electronic wavefunctions are written in terms of strain-parametrized Bloch functions modulated by slowly varying envelope functions. Adopting a local approximation of the electronic structure, the unknown crystal potential in the Schrödinger equation can be replaced by the strain-parametrized Bloch functions and the associated strain-parametrized energy eigenvalues, which can be constructed from unit-cell level ab initio or semi-empirical calculations of homogeneously deformed crystals at a chosen crystal momentum. The Schrödinger equation is then transformed into a coupled differential equation for the envelope functions and solved as a generalized matrix eigenvector problem. As the envelope functions are slowly varying, a coarse spatial or Fourier grid can be used to represent the envelope functions, enabling the method to treat relatively large systems. We demonstrate the effectiveness of this method using a one-dimensional model, where we show that the method can achieve high accuracy in the calculation of energy eigenstates with relatively low cost compared to direct diagonalization of the Hamiltonian. We further derive envelope function equations that allow the method to be used empirically, in which case certain parameters in the envelope function equations will be fitted to experimental data.

Genetic design of enhanced valley splitting towards a spin qubit in silicon

The long spin coherence time and microelectronics compatibility of Si makes it an attractive material for realizing solid-state qubits. Unfortunately, the orbital (valley) degeneracy of the conduction band of bulk Si makes it difficult to isolate individual two-level spin-1/2 states, limiting their development. This degeneracy is lifted within Si quantum wells clad between Ge-Si alloy barrier layers, but the magnitude of the valley splittings achieved so far is small--of the order of 1 meV or less--degrading the fidelity of information stored within such a qubit. Here we combine an atomistic pseudopotential theory with a genetic search algorithm to optimize the structure of layered-Ge/Si-clad Si quantum wells to improve this splitting. We identify an optimal sequence of multiple Ge/Si barrier layers that more effectively isolates the electron ground state of a Si quantum well and increases the valley splitting by an order of magnitude, to ~9 meV.

Universal trapping mechanism in semiconductor nanocrystals

Size tunability of the optical properties and inexpensive synthesis make semiconductor nanocrystals one of the most promising and versatile building blocks for many modern applications such as lasers, single-electron transistors, solar cells, and biological labels. The performance of these nanocrystal-based devices is however compromised by efficient trapping of the charge carriers. This process exhibits different features depending on the nanocrystal material, surface termination, size, and trap location, leading to the assumption that different mechanisms are at play in each situation. Here we revolutionize this fragmented picture and provide a unified interpretation of trapping dynamics in semiconductor nanocrystals by identifying the origins of this so far elusive detrimental process. Our findings pave the way for a general suppression strategy, applicable to any system, which can lead to a simultaneous efficiency enhancement in all nanocrystal-based technologies.

Multiexciton Generation in IV-VI Nanocrystals: The Role of Carrier Effective Mass, Band Mixing, and Phonon Emission

We study the role of the effective mass, band mixing, and phonon emission on multiexciton generation in IV-VI nanocrystals. A four-band k · p effective mass model, which allows for an independent variation of these parameters, is adopted to describe the electronic structure of the nanocrystals. Multiexciton generation efficiencies are calculated using a Green's function formalism, providing results that are numerically similar to impact excitation. We find that multiexciton generation efficiencies are maximized when the effective mass of the electron and hole are small and similar. Contact with recent experimental results for multiexciton generation in PbS and PbSe is made.

The birth of a type-II nanostructure: carrier localization and optical properties of isoelectronically doped CdSe:Te nanocrystals

CdTe/CdSe core/shell nanocrystals are the prototypical example of type-II nanoheterostructures, in which the electron and the hole wave functions are localized in different parts of the nanostructure. As the thickness of the CdSe shell increases above a few monolayers, the spectroscopic properties of such nanocrystals change dramatically, reflecting the underlying type-I → type-II transition. For example, the exciton Stokes shift and radiative lifetime increase, while the decreasing biexciton binding energy changes sign from positive to negative. Recent experimental results for CdSe nanocrystals isoelectronically doped with a few Te substitutional impurities, however, have revealed a very different dependence of the optical and electronic properties on the nanocrystal size. Here we use atomistic calculations based on the pseudopotential method for single-particle excitations and the configuration-interaction approach for many-particle excitations to investigate carrier localization and electronic properties of CdTe/CdSe nanocrystals as the size of the CdTe core decreases from a few nm (characteristic of core/shell CdTe/CdSe nanocrystals) to the single impurity limit. We find that the unusual spectroscopic properties of isoelectronically doped CdSe:Te nanocrystals can be rationalized in terms of the change in the localization volume of the electron and hole wave functions as the size of the nanocrystal increases. The size dependence of the exciton Stokes shift, exciton radiative lifetime, and biexciton binding energy reflects the extent of carrier localization around the Te impurities.

Genetic-algorithm discovery of a direct-gap and optically allowed superstructure from indirect-gap Si and Ge semiconductors

Combining two indirect-gap materials-with different electronic and optical gaps-to create a direct gap material represents an ongoing theoretical challenge with potentially rewarding practical implications, such as optoelectronics integration on a single wafer. We provide an unexpected solution to this classic problem, by spatially melding two indirect-gap materials (Si and Ge) into one strongly dipole-allowed direct-gap material. We leverage a combination of genetic algorithms with a pseudopotential Hamiltonian to search through the astronomic number of variants of Si(n)/Ge(m)/…/Si(p)/Ge(q) superstructures grown on (001) Si(1-x)Ge(x). The search reveals a robust configurational motif-SiGe(2)Si(2)Ge(2)SiGe(n) on (001) Si(x)Ge(1-x) substrate (x≤0.4) presenting a direct and dipole-allowed gap resulting from an enhanced Γ-X coupling at the band edges.

Photoinduced surface trapping and the observed carrier multiplication yields in static CdSe nanocrystal samples

Photocharging has been suggested recently as the explanation for the spread of carrier multiplication yields reported by different groups. If this hypothesis can be plausible in the case of PbSe, it is inconsistent with the reported experimental data relative to CdSe nanocrystals and cannot therefore explain the large discrepancies found in that material system between static and stirred samples. An alternative explanation, photoinduced surface trapping, is suggested here, based on the results of atomistic semiempirical pseudopotential calculations of the Auger recombination rates in a number of excitonic configurations including a variety of surface traps, which show that the photoinduced surface trapping of the hole, which leaves the core negatively charged (but the nanocrystal neutral overall), can lead to recombination rates that are indistinguishable from those of a conventional biexciton with four core-delocalized carriers and therefore result in exaggerated CM yields in static samples. In contrast, the recombination rate of a charged exciton is found to be at least a factor of 2.3 smaller than that of the biexciton and therefore easily distinguishable from it experimentally. Although increased trapping at surface states was dismissed as unlikely for PbSe nanocrystals, in the case of CdSe, this hypothesis is further supported by much experimental evidence including recent spectroscopic measurements on CdSe nanostructures, single-nanocrystal photoionization studies on CdSe core/shell nanocrystals, and state-resolved transient absorption studies of biexcitonic states, all showing increased probability of surface trapping for highly excited states. These results suggest that multicarrier processes could be mediated by different mechanisms in CdSe and PbSe nanocrystals.

Novel Computational Methods for Nanostructure Electronic Structure Calculations

Experimentally relevant nanocrystals often contain a few thousands to hundreds of thousands of atoms. Yet, to understand their electronic structures, surface and impurity effects, atomic relaxations, interior electric fields, carrier dynamics, and transports, it is often necessary to carry out atomistic simulations. Owing to the advance of recent algorithm developments and improved supercomputer powers, it is now possible to calculate such nanocrystals based on ab initio methods. In this review, we discuss the numerical algorithms (the plane-wave pseudopotential method and the real-space finite-difference method) used in conventional density-functional-theory calculations, which enable the simulations of systems up to one or two thousand atoms. We also introduce methods designed specifically for nanostructure calculations. These methods [the charge-patching method (CPM) and the linear scaling three-dimensional fragment method (LS3DF)] can be used to calculate systems with hundreds of thousands of atoms. Whereas CPM is an approximation with ab initio quality, the LS3DF method is an O(N) method with essentially the same results as the direct methods. The computational aspects of the algorithms, especially for their parallelization scalability, are also emphasized in the review.

Direct and inverse auger processes in InAs nanocrystals: can the decay signature of a trion be mistaken for carrier multiplication?

A complete and detailed theoretical investigation of the main processes involved in the controversial detection and quantification of carrier multiplication (CM) is presented, providing a coherent and comprehensive picture of excited state relaxation in InAs nanocrystals (NCs). The observed rise and decay times of the 1S transient bleach are reproduced, in the framework of the Auger model, using an atomistic semiempirical pseudopotential method, achieving excellent agreement with experiment. The CM time constants for small core-only and core/shell nanocrystals are obtained as a function of the excitation energy, assuming an impact-ionization-like process. The resulting lifetimes at energies close to the observed CM onset are consistent with the upper limits deduced experimentally from PbSe and CdSe samples. Most interestingly, as the Auger recombination lifetimes calculated for charged excitons are found to be of a similar order of magnitude to those computed for biexcitons, both species are expected to exhibit the fast decay component in NC population dynamics so far attributed exclusively to the presence of biexcitons and therefore identified as the signature of CM occurrence in high-energy low-pump-fluence spectroscopic studies. However, the ratio between trions and biexcitons time constants is found to be larger than the typical experimental accuracy. It is therefore concluded that, in InAs NCs, it should be experimentally possible to discriminate between the two species and that the origin of the observed discrepancies in CM yields is unlikely to lay in the presence of charged excitons.

Beyond Förster resonance energy transfer in biological and nanoscale systems

After photoexcitation, energy absorbed by a molecule can be transferred efficiently over a distance of up to several tens of angstroms to another molecule by the process of resonance energy transfer, RET (also commonly known as electronic energy transfer, EET). Examples of where RET is observed include natural and artificial antennae for the capture and energy conversion of light, amplification of fluorescence-based sensors, optimization of organic light-emitting diodes, and the measurement of structure in biological systems (FRET). Forster theory has proven to be very successful at estimating the rate of RET in many donor-acceptor systems, but it has also been of interest to discover when this theory does not work. By identifying these cases, researchers have been able to obtain, sometimes surprising, insights into excited-state dynamics in complex systems. In this article, we consider various ways that electronic energy transfer is promoted by mechanisms beyond those explicitly considered in Forster RET theory. First, we recount the important situations when the electronic coupling is not accurately calculated by the dipole-dipole approximation. Second, we examine the related problem of how to describe solvent screening when the dipole approximation fails. Third, there are situations where we need to be careful about the separability of electronic coupling and spectral overlap factors. For example, when the donors and/or acceptors are molecular aggregates rather than individual molecules, then RET occurs between molecular exciton states and we must invoke generalized Forster theory (GFT). In even more complicated cases, involving the intermediate regime of electronic energy transfer, we should consider carefully nonequilibrium processes and coherences and how bath modes can be shared. Lastly, we discuss how information is obscured by various forms of energetic disorder in ensemble measurements and we outline how single molecule experiments continue to be important in these instances.

Direct-bandgap InAs quantum-dots have long-range electron-hole exchange whereas indirect gap Si dots have short-range exchange

Excitons in quantum dots manifest a lower-energy spin-forbidden "dark" state below a spin-allowed "bright" state; this splitting originates from electron-hole (e-h) exchange interactions, which are strongly enhanced by quantum confinement. The e-h exchange interaction may have both a short-range and a long-range component. Calculating numerically the e-h exchange energies from atomistic pseudopotential wave functions, we show here that in direct-gap quantum dots (such as InAs) the e-h exchange interaction is dominated by the long-range component, whereas in indirect-gap quantum dots (such as Si) only the short-range component survives. As a result, the exciton dark/bright splitting scales as 1/R(2) in InAs dots and 1/R(3) in Si dots, where R is the quantum-dot radius.

Electronic excitations in nanostructures: an empirical pseudopotential based approach

Physics at the nanoscale has emerged as a field where discoveries of fundamental physical effects lead to a greater understanding of the solid state. Additionally, the field is believed to have a large potential for technological applications, which has driven a high pace of experimental achievements in fabrication and characterization. From the side of theoretical modeling-so successful in solid state physics in general, since the emergence of density functional theory-we must acknowledge a weak connection to state of the art experimental achievements in the realm of nanostructures. The cause for this partial disconnect resides in the difficulty of the matter, nanostructures being small in size but large in the number of atoms constituting them, and the relevant observables being accessible only through proper treatment of excitations. The large number of atoms and the need for excited state properties makes this a challenging task for theory and modeling. In this contribution we will outline the framework, based on empirical pseudopotentials and configuration interaction, to obtain quantitative predictions of the excited state properties of semiconductor nanostructures using their experimental sizes, compositions and shapes. The methodology can be used to describe colloidal nanostructures of a few hundred atoms all the way to epitaxial structures requiring millions of atoms. The aim is to fill the gap existing between ab initio approaches and continuum descriptions. Based on the pseudopotential idea and the developments of empirical pseudopotentials for bulk materials in the early 1960s, the method has evolved into a powerful tool where the pseudopotential construction has lost some of its empirical character and is now based on modern density functional theory. We will present the construction of these potentials and the way the ensuing wavefunctions are used in a subsequent configuration interaction treatment of the excitation. We will illustrate the available capabilities by recent applications of the methodology to unveil new effects in the optics of nanostructures, quantum entanglement and wavefunction imaging.

Carrier multiplication in semiconductor nanocrystals: theoretical screening of candidate materials based on band-structure effects

Direct carrier multiplication (DCM) occurs when a highly excited electron-hole pair decays by transferring its excess energy to the electrons rather than to the lattice, possibly exciting additional electron-hole pairs. Atomistic electronic structure calculations have shown that DCM can be induced by electron-hole Coulomb interactions, in an impact-ionization-like process whose rate is proportional to the density of biexciton states rho XX. Here we introduce a DCM "figure of merit" R2(E) which is proportional to the ratio between the biexciton density of states rhoXX and the single-exciton density of states rhoX, restricted to single-exciton and biexciton states that are coupled by Coulomb interactions. Using R2(E), we consider GaAs, InAs, InP, GaSb, InSb, CdSe, Ge, Si, and PbSe nanocrystals of different sizes. Although DCM can be affected by both quantum-confinement effects (reflecting the underly electronic structure of the confined dot-interior states) and surface effects, here we are interested to isolate the former. To this end the nanocrystal energy levels are obtained from the corresponding bulk band structure via the truncated crystal approximation. We find that PbSe, Si, GaAs, CdSe, and InP nanocrystals have larger DCM figure of merit than the other nanocrystals. Our calculations suggest that high DCM efficiency requires high degeneracy of the corresponding bulk band-edge states. Interestingly, by considering band structure effects we find that as the dot size increases the DCM critical energy E0 (the energy at which R2(E) becomes >or=1) is reduced, suggesting improved DCM. However, whether the normalized E0/epsilong increases or decreases as the dot size increases depends on dot material.

A pseudopotential method for investigating the surface roughness effect in ultrathin body transistors

An atomistic method based on the diffraction pseudopotential model is established, for investigating the surface roughness (SR) effect in ultrathin body double-gate metal-oxide-semiconductor field effect transistors. The scattering of electrons due to atoms and vacancies responsible for roughness results from a three-dimensional effective field, and its planar components provide essentially roughness scattering, while a vertical effective field is the source of scattering in the method developed in which roughness is treated as a semiclassical barrier fluctuation. The present model involves a stronger effect on mobility than the previously developed one and results in an excellent fit, as regards mobility, to the reported experimental data. The extracted SR parameter also matches the observed value.

Anomalous photoluminescence in CdSe quantum-dot solids at high pressure due to nonuniform stress

The application of static high pressure provides a means to precisely control and investigate many fundamental and unique properties of nanoparticles. CdSe is a model quantum-dot system, the behavior of which under high pressure has been extensively studied; however, the effect of nonuniform stresses on this system has not been fully appreciated. Photoluminescence data obtained from CdSe quantum-dot solids in different stress environments varying from purely uniform to highly nonuniform are presented. Small deviations from a uniform stress distribution profoundly affect the electronic properties of this system. In nonuniform stress environments, a pronounced flattening of the photoluminescence enegy is observed above 3 GPa. The observations are validated with theoretical calculations obtained using an all-atom semiempirical pseudopotential technique. This effect must be considered when investigating other potentially pressure-mediated phenomena.

Multiexciton absorption and multiple exciton generation in CdSe quantum dots

Efficient multiple-exciton generation (MEG) in semiconductor quantum dots has been recently reported. The MEG efficiency has so far been evaluated assuming that the change (bleaching) of the absorption spectrum due to MEG is linearly proportional to the number of excitons N(X). Here, we critically examine this assumption using atomistic pseudopotential calculations for colloidal CdSe nanocrystals. We find that the bleaching of the first absorption peak depends nonlinearly on N(X), due to carrier-carrier interactions. This nonlinearity mandates an upper bound of 1.5 to the value of the normalized bleaching that can be attributed to MEG, significantly smaller than the limit of 2.0 predicted by the linear scaling assumption. Thus, measured values of the normalized bleaching in excess of 1.5 cannot be due entirely to MEG, but must originate in part from other mechanisms.

The peculiar electronic structure of PbSe quantum dots

PbSe is a pseudo-II-VI material distinguished from ordinary II-VI's (e.g., CdSe, ZnSe) by having both its valence band maximum (VBM) and its conduction band minimum (CBM) located at the fourfold-degenerate L-point in the Brillouin zone. It turns out that this feature dramatically affects the properties of the nanosystem. We have calculated the electronic and optical properties of PbSe quantum dots using an atomistic pseudopotential method, finding that the electronic structure is different from that of ordinary II-VI's and, at the same time, is more subtle than what k.p or tight-binding calculations have suggested previously for PbSe. We find the following in PbSe dots: (i) The intraband (valence-to-valence and conduction-to-conduction) as well as interband (valence-to-conduction) excitations involve the massively split L-manifold states. (ii) In contrast to previous suggestions that the spacings between valence band levels will equal those between conduction band levels (because the corresponding effective-masses me approximately mh are similar), we find a densely spaced hole manifold and much sparser electron manifold. This finding reflects the existence of a few valence band maxima in bulk PbSe within approximately 500 meV. This result reverses previous expectations of slow hole cooling in PbSe dots. (iii) The calculated optical absorption spectrum reproduces the measured absorption peak that had previously been attributed to the forbidden 1Sh --> 1Pe or 1Ph --> 1Se transitions on the basis of k.p calculations. However, we find that this transition corresponds to an allowed 1Ph --> 1Pe excitation arising mainly from bulk states near the L valleys on the Gamma-L lines of the Brillouin zone. We discuss this reinterpretation of numerous experimental results.

Theory of excitonic spectra and entanglement engineering in dot molecules

We present results of correlated pseudopotential calculations of an exciton in a pair of vertically stacked InGaAs/GaAs dots. Competing effects of strain, geometry, and band mixing lead to many unexpected features missing in contemporary models. The first four excitonic states are all optically active at small interdot separation, due to the broken symmetry of the single-particle states. We quantify the degree of entanglement of the exciton wave functions and show its sensitivity to interdot separation. We suggest ways to spectroscopically identify and maximize the entanglement of exciton states.

Pseudopotential theory of Auger processes in CdSe quantum dots

Auger rates are calculated for CdSe colloidal quantum dots using atomistic empirical pseudopotential wave functions. We predict the dependence of Auger electron cooling on size, on correlation effects (included via configuration interaction), and on the presence of a spectator exciton. Auger multiexciton recombination rates are predicted for biexcitons as well as for triexcitons. The results agree quantitatively with recent measurements and offer new predictions.