Showing papers by "Alex Zunger published in 2009"
TL;DR: In this article, a scaling of the Madelung-like screened first-order correction term is proposed to correct the formation energy of charged defects in semiconductors, by potential alignment.
Abstract: The theoretical description of defects and impurities in semiconductors is largely based on density functional theory (DFT) employing supercell models. The literature discussion of uncertainties that limit the predictivity of this approach has focused mostly on two issues: (1) finite-size effects, in particular for charged defects; (2) the band-gap problem in local or semi-local DFT approximations. We here describe how finite-size effects (1) in the formation energy of charged defects can be accurately corrected in a simple way, i.e. by potential alignment in conjunction with a scaling of the Madelung-like screened first order correction term. The factor involved with this scaling depends only on the dielectric constant and the shape of the supercell, and quite accurately accounts for the full third order correction according to Makov and Payne. We further discuss in some detail the background and justification for this correction method, and also address the effect of the ionic screening on the magnitude of the image charge energy. In regard to (2) the band-gap problem, we discuss the merits of non-local external potentials that are added to the DFT Hamiltonian and allow for an empirical band-gap correction without significantly increasing the computational demand over that of standard DFT calculations. In combination with LDA + U, these potentials are further instrumental for the prediction of polaronic defects with localized holes in anion-p orbitals, such as the metal-site acceptors in wide-gap oxide semiconductors.
317 citations
TL;DR: In this article, a generalized Koopmans condition was proposed to remove the de-localization bias of the Hartree-Fock (HF) and local density (LD) models.
Abstract: Acceptor-bound holes in oxides often localize asymmetrically at one out of several equivalent oxygen ligands. Whereas Hartree-Fock (HF) theory overly favors such symmetry-broken polaronic hole localization in oxides, standard local-density (LD) calculations suffer from spurious delocalization among several oxygen sites. These opposite biases originate from the opposite curvatures of the energy as a function of the fractional occupation number $n$, i.e., ${d}^{2}E/d{n}^{2}l0$ in HF and ${d}^{2}E/d{n}^{2}g0$ in LD. We recover the correct linear behavior, ${d}^{2}E/d{n}^{2}=0$, that removes the (de)localization bias by formulating a generalized Koopmans condition. The correct description of oxygen hole localization reveals that the cation-site nominal single acceptors in ZnO, ${\text{In}}_{2}{\text{O}}_{3}$, and ${\text{SnO}}_{2}$ can bind multiple holes.
298 citations
TL;DR: In this article, the authors employ a band-structure-corrected theory, and present simultaneously the chemical trends for electronic properties, carrier doping, and magnetism along the series of transition-metal impurities in the representative wide-gap oxide hosts.
Abstract: $3d$ transition impurities in wide-gap oxides may function as donor/acceptor defects to modify carrier concentrations, and as magnetic elements to induce collective magnetism. Previous first-principles calculations have been crippled by the LDA error, where the occupation of the $3d$-induced levels is incorrect due to spurious charge spilling into the misrepresented host conduction band, and have only considered magnetism and carrier doping separately. We employ a band-structure-corrected theory, and present simultaneously the chemical trends for electronic properties, carrier doping, and magnetism along the series of $3{d}^{1}--3{d}^{8}$ transition-metal impurities in the representative wide-gap oxide hosts ${\text{In}}_{2}{\text{O}}_{3}$ and ZnO. We find that most $3d$ impurities in ${\text{In}}_{2}{\text{O}}_{3}$ are amphoteric, whereas in ZnO, the early $3d$'s (Sc, Ti, and V) are shallow donors, and only the late $3d$'s (Co and Ni) have acceptor transitions. Long-range ferromagnetic interactions emerge due to partial filling of $3d$ resonances inside the conduction band and, in general, require electron doping from additional sources.
97 citations
TL;DR: It is demonstrated that the partial band occupation and the metallic band-structure character as predicted by local density calculations for II-VI materials containing cation vacancies is removed when the correct energy splitting between occupied and unoccupied p orbitals is recovered.
Abstract: Electronic correlation effects, usually associated with open d or f shells, have so far been considered in p orbitals only sporadically for the localized 2p states of first-row elements. We demonstrate that the partial band occupation and the metallic band-structure character as predicted by local density calculations for II-VI materials containing cation vacancies is removed when the correct energy splitting between occupied and unoccupied p orbitals is recovered. This transition into a Mott-insulating phase dramatically changes the structural, electronic and magnetic properties along the entire series (ZnO, ZnS, ZnSe, and ZnTe), and impedes ferromagnetism. Thus, important correlation effects due to open p shells exist not only for first-row (2p) elements, but also for much heavier anions like Te (5p).
87 citations
TL;DR: In this article, the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots using femtosecond spectroscopy and atomistic many-body pseudopotential calculations was reported.
Abstract: We report on the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots using femtosecond spectroscopy and atomistic many-body pseudopotential calculations. Time-resolved spectroscopy shows that optical transitions between excitonic and biexcitonic states are distinct for absorptive and emissive transitions, leading to a larger Stokes shift for the biexciton than for the single exciton. The calculations explain the experimental results by showing that there is a previously unobserved electronic substructure to the band-edge biexciton which yields two distinct families of transitions.
84 citations
TL;DR: Trimarchi et al. as discussed by the authors extended the fixed-composition global space-group optimization (GSGO) approach to predict all the minimum energy lattice types throughout the composition range.
Abstract: Whereas the Daltonian atom-to-atom ratios in ordinary molecules are well understood via the traditional theory of valence, the naturally occurring stoichiometries in intermetallic compounds ${A}_{p}{B}_{q}$, as revealed by phase-diagram compilations, are often surprising. Even equal-valence elements $A$ and $B$ give rise to unequal $(p,q)$ stoichiometries, e.g., the 1:2, 2:1, and 3:1 ratios in ${\text{Al}}_{p}{\text{Sc}}_{q}$. Moreover, sometimes different stoichiometries are associated with different lattice types and hence rather different physical properties. Here, we extend the fixed-composition global space-group optimization (GSGO) approach used to predict, via density-functional calculations, fixed-composition lattice types [G. Trimarchi and A. Zunger, J. Phys.: Condens. Matter 20, 295212 (2008)] to identify simultaneously all the minimum-energy lattice types throughout the composition range. Starting from randomly selected lattice vectors, atomic positions and stoichiometries, we construct the $T=0$ ``convex hull'' of energy vs composition. Rather than repeat a set of GSGO searches over a fixed list of stoichiometries, we minimize the distance to the convex hull. This approach is far more efficient than the former one as a single evolutionary search sequence simultaneously identifies the lowest-energy structures at each composition and among these it selects those that are ground states. For Al-Sc we correctly identify the stable stoichiometries and relative structure types: ${\text{AlSc}}_{2}\text{-B}{8}_{2}$, AlSc-B2, and ${\text{Al}}_{2}\text{Sc-C}15$ in the ${N}_{at}=6$ periodic cells, and ${\text{Al}}_{2}{\text{Sc}}_{6}\text{-D}{0}_{19}$, AlSc-B2, and ${\text{Al}}_{3}\text{Sc-L}{1}_{0}$ in the ${N}_{at}=8$ periodic cells. This extended evolutionary GSGO algorithm represents a step toward a fully ab initio materials synthesis, where compounds are predicted starting from sole knowledge of the chemical species of the constituents.
53 citations
TL;DR: In this article, the stability of bimetallics at low $T was evaluated based on density-functional theory and first-principles cluster expansions that are filtered against structural and magnetic bistabilities.
Abstract: While the binary $\text{Fe-}X$ $(X=\text{Ni},\text{Pd},\text{Pt})$ alloys are among the most widely applied bimetallics, open questions remain regarding whether and which of their compounds are stable at low $T$. Based on density-functional theory and first-principles cluster expansions that are ``filtered'' against structural and magnetic bistabilities, we assess all three systems. We (i) review the stability of the known phases; (ii) predict phases unstable with respect to bcc-fcc mixtures but stable if restricted to fcc; and, (iii) remarkably, predict previously unknown stable phases. This pinpoints where more definitive low-$T$ experiments should find new stable compounds.
49 citations
TL;DR: In this article, the structure-spectra relationship in semiconductor quantum dots QDs is investigated by subjecting the same QD sample to single-dot spectroscopy and cross-sectional scanning tunneling microscopy XSTM structural measurements.
Abstract: Structure-spectra relationship in semiconductor quantum dots QDs is investigated by subjecting the same QD sample to single-dot spectroscopy and cross-sectional scanning tunneling microscopy XSTM structural measurements. We find that the conventional approach of using XSTM structure as input to calculate the spectra produces some notable conflicts with the measured spectra. We demonstrate a theoretical “inverse approach” which deciphers structural information from the measured spectra and finds structural models that agree with both XSTM and spectroscopy data. This effectively “closes the loop” between structure and spectroscopy in QDs.
42 citations
TL;DR: In this paper, the effect of atomic-scale alloy randomness on the fine structure-splitting (FSS) of the multiexciton observed via the polarization anisotropy of its components was examined.
Abstract: Alloy systems such as Ga{sub 1-x}In{sub x}As consist of different random assignments {sigma} of the Ga and In atoms onto the cation sublattice; each configuration {sigma} having, in principle, distinct physical properties. In infinitely large bulk samples different {sigma}'s get self-averaged. However, in finite quantum dots (QDs) ({le} 10{sup 5} atoms), self-averaging of such configuration {sigma} may not be complete, so single-dot spectroscopy might observe atomic-scale alloy randomness effects. We examine theoretically the effect of such atomic-scale alloy randomness on the fine structure-splitting (FSS) of the multiexciton observed via the polarization anisotropy of its components. We find that (i) The FSS of the neutral monoexciton {chi}{sup 0} changes by more than a factor of 7 with {sigma}. Thus, dots provide clear evidence for the effect of the atomic-scale alloy randomness on the optical properties. (ii) For multiexcitons, the effect of alloy randomness can be so large that the polarization of given emission lines in samples that differ only in random realizations can be dramatically different, so it cannot be said that given transitions have fixed polarization. (iii) Polarization is affected both by atomic-scale randomness and by possible geometric elongation of the QD in one direction. Because of different random realizations,more » even 50% QD base elongation in [100] direction gives the same polarization as in a geometrically symmetric dot. Thus, measured polarization cannot be used to determine QD elongation.« less
42 citations
TL;DR: In this article, the authors discuss general potential pitfalls that are often encountered in energy minimization of crystal structure determination via some form of energy minimisation via global space-group optimization.
Abstract: In many theoretical studies of the properties of solids, the first and often crucial step entails the determination of the crystal structure via some form of energy minimization Here we discuss general potential pitfalls that are often encountered in such calculations We do so in the context of the classic zinc-blende crystal structure that underlines all octet semiconductors and was more recently invoked to explain nonoctet half-metallic magnets such as CrAs, as well as noble-metal nitrides such as PtN, PdN, and NiN These pitfalls are related to the way in which mechanical instabilities of assumed structures are identified, discarded, and replaced Using a more general global space-group optimization (GSGO) approach uncovers different and more complex structures that have much lower energies and do not have mechanical instabilities
38 citations
TL;DR: It is found that the largest spin splitting in the lowest conduction band and upper valence band (VB1) occurs surprisingly along the (210) direction, not the (110)direction, and that the splitting of the VB1 is comparable to that of the next two valence bands VB2 and VB3.
Abstract: The spin-orbit interaction---a fundamental electroweak force---is equivalent to an effective magnetic field intrinsic to crystals, leading to band spin splitting for certain $k$ points in sufficiently low-symmetry structures. This (Dresselhaus) splitting has usually been calculated at restricted regions in the Brillouin zone via small wave vector approximations (e.g., $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$), potentially missing the ``big picture.'' We provide a full-zone description of the Dresselhaus splitting in zinc blende semiconductors by using pseudopotentials, empirically corrected to rectify local density approximation errors by fitting $GW$ results. In contrast to what was previous thought, we find that the largest spin splitting in the lowest conduction band and upper valence band (VB1) occurs surprisingly along the (210) direction, not the (110) direction, and that the splitting of the VB1 is comparable to that of the next two valence bands VB2 and VB3.
Journal Article•
TL;DR: In this article, the authors provided a full-zone description of the Dresselhaus splitting in zinc blende semiconductors by using pseudopotentials, empirically corrected to rectify local density approximation errors by fitting $GW$ results.
Abstract: The spin-orbit interaction---a fundamental electroweak force---is equivalent to an effective magnetic field intrinsic to crystals, leading to band spin splitting for certain $k$ points in sufficiently low-symmetry structures. This (Dresselhaus) splitting has usually been calculated at restricted regions in the Brillouin zone via small wave vector approximations (e.g., $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$), potentially missing the ``big picture.'' We provide a full-zone description of the Dresselhaus splitting in zinc blende semiconductors by using pseudopotentials, empirically corrected to rectify local density approximation errors by fitting $GW$ results. In contrast to what was previous thought, we find that the largest spin splitting in the lowest conduction band and upper valence band (VB1) occurs surprisingly along the (210) direction, not the (110) direction, and that the splitting of the VB1 is comparable to that of the next two valence bands VB2 and VB3.
Journal Article•
TL;DR: In this paper, a unique structural anomaly of pure MnN, in which local density calculations fail to predict the experimentally observed distorted rocksalt as the ground-state structure, is resolved under the GGA+U$ and B3LYP formalisms.
Abstract: Pure MnN and (Ga,Mn)N alloys are investigated using the ab initio generalized gradient approximation $+U$ $(\\text{GGA}+U)$ or the hybrid-exchange density-functional (B3LYP) methods. These methods are found to predict dramatically different electronic structure, magnetic behavior, and relative stabilities compared to previous density-functional theory (DFT) calculations. A unique structural anomaly of MnN, in which local-density calculations fail to predict the experimentally observed distorted rocksalt as the ground-state structure, is resolved under the $\\text{GGA}+U$ and B3LYP formalisms. The magnetic configurations of MnN are studied and the results suggest the magnetic state of zinc-blende MnN might be complex. Epitaxial calculations are used to show that the epitaxial zinc-blende MnN can be stabilized on an InGaN substrate. The structural stability of (Ga,Mn)N alloys was examined and a crossover from the zinc-blende-stable alloy to the rocksalt-stable alloy at an Mn concentration of $\\ensuremath{\\sim}65%$ was found. The tendency for zinc-blende (Ga,Mn)N alloys to phase separate is described by an asymmetric spinodal phase diagram calculated from a mixed-basis cluster expansion. This predicts that precipitates will consist of Mn concentrations of $\\ensuremath{\\sim}5$ and $\\ensuremath{\\sim}50%$ at typical experimental growth temperatures. Thus, pure antiferromagnetic MnN, previously thought to suppress the Curie temperature, will not be formed. The Curie temperature for the $50%$ phase is calculated to be ${T}_{C}=354\\text{ }\\text{K}$, indicating the possibility of high-temperature ferromagnetism in zinc-blende (Ga,Mn)N alloys due to precipitates.
TL;DR: In this article, the authors distinguish between strain-free and strain-induced localized states (SILSs) appearing in strained systems, whereas in strain free systems the dot resonances in the continuum are the usual virtual bound states (VBSs), and show that the local barrier created around the dot by these potential wings suppresses the 0D-2D hybridization of the electron states.
Abstract: Quantum dots (QDs) embedded in a matrix exhibit a coexistence of ``zero-dimensional'' (0D) bound electron and hole states on the dot with ``three-dimensional'' (3D) continuum states of the surrounding matrix. In epitaxial QDs one encounters also ``two-dimensional'' (2D) states of a quantum well-like supporting structure (wetting layer). This coexistence of 0D, 2D, and 3D states leads to interesting electronic consequences explored here using multiband atomistic pseudopotential calculations. We distinguish strained dots (InAs in GaAs) and strain-free dots (InAs in GaSb) finding crucial differences: in the former case ``potential wings'' appear in the electron confining potential in the vicinity of the dot. This results in the appearance of localized electronic states that lie above the threshold of the 3D continuum. Such resonances are ``strain-induced localized states'' (SILSs) appearing in strained systems, whereas in strain-free systems the dot resonances in the continuum are the usual ``virtual bound states'' (VBSs). The SILSs were found to occur regardless of the thickness of the wetting layer and even in interdiffused dots, provided that the interdiffusion length is small compared to the QD size. Thus, the SILSs are well isolated from the environment by the protective potential wings, whereas the VBSs are strongly interacting. These features are seen in our calculated intraband as well as interband absorption spectra. Furthermore, we show that the local barrier created around the dot by these potential wings suppresses the 0D-2D (dot-wetting layer) hybridization of the electron states. Consequently, in contrast to findings of simple model calculations of envelope function, 0D-to-2D ``crossed transitions'' (bound hole-to-wetting layer electron) are practically absent because of their spatially indirect character. On the other hand, since no such barrier exists in the hole confining potential, a strong 0D-2D hybridization is present for the hole states. We show this to be the source for the strong 2D-to-0D crossed transitions determined experimentally.
TL;DR: In this paper, the authors discuss the existence of two types of resonant states within this continuum in self-assembled dots: (i) virtual bound states, which characterize square wells even without strain and (ii) strain-induced localized states.
Abstract: Quantum dot-based infrared detectors often involve transitions from confined states of the dot to states above the minimum of the conduction band continuum of the matrix We discuss the existence of two types of resonant states within this continuum in self-assembled dots: (i) virtual bound states, which characterize square wells even without strain and (ii) strain-induced localized states The latter emerge due to the appearance of “potential wings” near the dot, related to the curvature of the dots While states (i) do couple to the continuum, states (ii) are sheltered by the wings, giving rise to sharp absorption peaks
TL;DR: In this paper, a detailed theoretical study of the internal electronic structure of various multiexcitons was performed, where the number of holes and number of electrons in the self-assembled semiconductor quantum dots (QDs).
Abstract: We perform a detailed theoretical study of the characteristic internal electronic structure of various multiexcitons $({N}_{h},{N}_{e})$, where ${N}_{h}$ is number of holes and ${N}_{e}$ is the number of electrons in the self-assembled semiconductor quantum dots (QDs). For each of the leading $({N}_{h},{N}_{e})$ excitonic complexes we start from the single-particle configuration (e.g., a specific occupation pattern of $S$ and $P$ electron and hole levels by a few carriers) and then show the many-particle multiplet levels for the initial state of emission $({N}_{h},{N}_{e})$ and the final state of emission $({N}_{h}\ensuremath{-}1,\text{ }{N}_{e}\ensuremath{-}1)$. We denote which states are dark and which are bright; the order and multiplicity, the leading single-particle character of each multiplet state, and the fine-structure splittings. These are of general utility. We also show explicit numerical values for distances between various transitions for four specific QDs. Here the presented information is important and potentially useful for a few reasons: (i) the information serves as a guide for spectroscopic interpretation; (ii) the information reveals non-Aufbau cases, where the dot does not have Aufbau occupation of carriers' levels; (iii) the information shows which transitions are sensitive to random-alloy fluctuations (if the dot is alloyed) and importance of this effect. We show that because of such alloy information, distances between peaks cannot be used to gauge structural information.
TL;DR: In this paper, the second one-photon absorption peak originates from dipole-allowed P{sub h}-P{sub e} transitions and not from a dipole forbidden S-sub h-P-sub e transition.
Abstract: PbSe nanocrystals represent the paradigm nanoscale system exhibiting carrier multiplication upon light absorption, yet their absorption spectrum is poorly understood. Two very different interpretations of the absorption peaks have been proposed: is the second absorption peak a dipole-forbidden S{sub h}-P{sub e} or P{sub h}-S{sub e} transition or a dipole-allowed P{sub h}-P{sub e} transition? A recent two-photon photoluminescence-excitation experiment favored the first interpretation, raising the question of why a dipole-forbidden transition would be strongly absorptive. Here we report atomistic pseudopotential calculations of the one-photon and two-photon absorption spectra of PbSe nanocrystals, showing unequivocally that, contrary to previous interpretations by other authors, the second one-photon absorption peak originates from dipole-allowed P{sub h}-P{sub e} transitions.
TL;DR: In this article, a numerical atomistic approach was used to calculate the exchange integrals as a function of the e?h range of interaction S, revealing the internal structure of the integrals.
Abstract: The electron?hole (e?h) exchange interaction leads to the splitting of the exciton into a pair of bright and a pair of dark states. This bright?dark?or singlet?triplet?exciton splitting was historically calculated as the sum of a long-range (LR) and a short-range (SR) component. Using a numerical atomistic approach, we are able to calculate the exchange integrals as a function of the e?h range of interaction S, revealing the 'internal' structure of the integrals. We apply this procedure to thickness-fluctuation GaAs/AlGaAs quantum dots (QDs), self-assembled InAs/GaAs QDs and colloidal InAs QDs. We find a heterogeneous situation, where the SR component contributes ~10, ~20?30 and ~20?50% to the total e?h exchange splitting, which is in the range of 10, 100 and 10?000 ?eV, for the three types of QDs, respectively. The balance between SR and LR is found to depend critically on the size, shape and type of structure. For all types of QDs we find, surprisingly, a range of interaction, close to the physical dimension of the structures, contributing to a reduction of the integral's magnitude. These results highlight the complexity of the exchange interaction, warning against simplified models, and establish the basic features of the nature and origin of dark?bright excitonic splitting in QDs.
TL;DR: In this article, the authors propose the Spectral Barcoding (SBC) method that deciphers structural motifs of quantum dots by using such motifs as input to an artificial-intelligence learning system.
Abstract: Self-assembled semiconductor quantum dots (QDs) show in high-resolution single-dot spectra a multitude of sharp lines, resembling a barcode, due to various neutral and charged exciton complexes. Here we propose the 'spectral barcoding' method that deciphers structural motifs of dots by using such barcode as input to an artificial-intelligence learning system. Thus, we invert the common practice of deducing spectra from structure by deducing structure from spectra. This approach (i) lays the foundation for building a much needed structure-spectra understanding for large nanostructures and (ii) can guide future design of desired optical features of QDs by controlling during growth only those structural motifs that decide given optical features.
TL;DR: A general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions, which can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves.
Abstract: Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)2/(GaN)2 (at x = 0.50) and (InN)4/(GaN)1 (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.
TL;DR: In this paper, the authors used atomistic pseudopotential calculations to identify the origin of such non-monotonic behavior in a transition of the lowest conduction-band wave function from λ-like to X-like as the nanocrystal radius decreases below 19-angstrom.
Abstract: The dark/bright exciton splitting {Delta}{sub x} in semiconductor nanocrystals is usually caused by electron-hole exchange interactions. Since the electron-hole wave-function overlap is enhanced by quantum confinement, it is generally assumed that {Delta}{sub x} increases monotonically as the quantum-dot size decreases. Using atomistic pseudopotential calculations, we show that in GaAs nanocrystals {Delta}{sub x} scales nonmonotonically with the nanocrystal size. By analyzing the nanocrystal wave functions in terms of contributions from different k points in the bulk Brillouin zone, we identify the origin of such nonmonotonic behavior in a transition of the lowest conduction-band wave function from {lambda} like to X like as the nanocrystal radius decreases below 19{angstrom}. The nonmonotonicity arises because the long-range component of the electron-hole exchange interaction all but vanishes when the electron wave function becomes X like. We also show that the direct/indirect transition induced in GaAs nanocrystals by external pressure results in a sudden reduction in {Delta}{sub x}.
TL;DR: It is shown 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-gapquantum dots ( such as Si) only the short- range component survives.
Abstract: 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/R2 in InAs dots and 1/R3 in Si dots, where R is the quantum-dot radius.
TL;DR: In this paper, the authors combine a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms.
Abstract: This novel approach combines a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms. The basis set consists of the exact numerical atomic valence orbitals, augmented by charge transfer states, virtual atomic states, and single analytic Slater orbitals for increased variational flexibility. The initial potential is a non-muffin-tin overlapping atomic potential including nongradient local density exchange and correlation terms. Full self-consistency is obtained by a procedure that combines an iterative scheme within the superposition model with a self-consistent optimization of the Fourier components of the nonspherical charge density terms. Ground-state properties such as structure factors and cohesive energy are computed. The results for diamond show very good agreement with experiment. Comparison of the results with the Hartree–Fock calculation is discussed.
TL;DR: In this paper, the formation enthalpies of isovalent, isostructural rocksalt alloys are analyzed by breaking down the formation process in a Born-Haber-like cycle into volume and cell-shape deformation, chemical exchange, and cell internal relaxation using first-principles density functional theory calculations in the generalized gradient approximation.
Abstract: The formation enthalpies of isovalent, isostructural rocksalt alloys, $(A,B)$, where $X=\text{O}$ such as (Ca,Mg)O, are typically unfavorable (positive) for both ordered and random phases. Simple replacement of the single-atom anion, $X$, by a larger anionic group, such as ${\text{CO}}_{3}$ or ${\text{SO}}_{4}$, is able to induce a favorable (negative) formation enthalpy, leading to the formation of the ordered alternate monolayer, ${({\text{CaCO}}_{3})}_{1}/{({\text{MgCO}}_{3})}_{1}$, dolomite structure. The underlying cause of this behavior is analyzed by breaking down the formation process in a Born-Haber-like cycle into volume and cell-shape deformation, chemical exchange, and cell-internal relaxation using first-principles density-functional theory calculations in the generalized gradient approximation. It is found that when the anion is a group $({\text{CO}}_{3})$, rather than a single atom (O), the energy gained from the internal relaxation overcomes the energy required to compensate the volume mismatch. This explains the general experimental trends of phase separation in isovalent, isostructural alloys without internal-anion structure, compared to ordering tendencies when the anionic group removes internal strain. The importance of obtaining structural ideality in the design of stable solid solutions is highlighted.
TL;DR: In this article, a design principle for stable alloys was proposed to explore phases unsuspected to order by the common paradigm of strain instability, where the large components have the ability to raise (lower) their coordination number (CN) within the mixed phase.
Abstract: Large atomic size mismatch between compounds discourages their binding into a common lattice because of the ensuing cost in strain energy. This central paradigm in the theory of isovalent alloys long used to disqualify alloys with highly mismatched components from technological use is clearly broken by the occurrence of stable spontaneous long-range order in mixtures of alkali halides with as much as 40% size mismatch (e.g., LiF-CsF). Our theoretical analysis of these failures uncovered a different design principle for stable alloys: very large atomic size mismatch can lead to spontaneous ordering if the large (small) components have the ability to raise (lower) their coordination number (CN) within the mixed phase. This heuristic design principle has led us to explore via first-principles structure search a few very largely mismatched binary systems whose components have a propensity for CN disproportionation. We find ordered structures for BeO-BaO (37% size mismatch) and BeO-SrO (30%), and ordering in LiCl-KCl (20%), whereas BN-InN (33%) is found to lower its positive formation enthalpy by ∼60% when CN disproportionation is allowed. This new design principle could be used to explore phases unsuspected to order by the common paradigm of strain instability. © 2009 The American Physical Society.
TL;DR: The question of whether the Oxidation Number carries a predictive physical meaning in its own right beyond being an unquestionably convenient label was revisited recently [1, this article, where the authors showed that the ON does not lead to understanding of the person.
Abstract: The Oxidation Number (ON) of an atom within a molecule or solid is a well defined quantity in chemistry (assuming a consistent set of rules are followed), with a long and distinguished history of usefulness. The question revisited recently [1–3] is whether it carries a predictive physical meaning in its own right beyond being an unquestionably convenient label. For example, whereas the color of compounds physically reflects the relative energetic positions of occupied vs. unoccupied, dipolecoupled energy levels, can the color be explained [4] by the oxidation state of the central ion? Can the different colors of various Mn compounds be predicted or explained in terms of their oxidation numbers [e.g. pink Mn(II) vs. black Mn(IV) vs. purple Mn(VII)], or does such understanding entail knowledge of the occupancy of the hybridized d bands, a knowledge not provided by the ON (but possibly labeled by it, once such understanding is independently acquired)? Also, the photoemission core shifts of an atom within a molecule (e.g. relative to a reference of the atom in its elemental form) physically represent the balance of all electrostatic charges in the system as felt by that atomic site. Can this balance be predicted or explained [1] by the oxidation number of the ion, or is the latter only a convenient short-hand notation (often assigned ex post facto) for an otherwise possibly nontrivial electronic structure? In other words, the central question here is whether the Oxidation Number is predictive, in its own right, or does it act functionally as a Social Security Number that conveniently labels a person, but by itself (e.g., without additional access to financial, medical, or educational records, or psychoanalysis) does not lead to understanding of the person.
TL;DR: In this paper, a nonperturbative, correlated approach was used to show when such simple rules work and when they fail, thereby establishing a basis for the appropriate use of such rules.
Abstract: A simple model---the single-configuration perturbation theory---has traditionally been used to explain the main features of the multiexcitonic spectra of quantum dots, where an electron and a hole recombine in the presence of other ${N}_{e}\ensuremath{-}1$ electrons and ${N}_{h}\ensuremath{-}1$ holes. The model predicts the $({N}_{h},{N}_{e})$ values for which such spectra consist of a single line or multiple lines and whether singlet lines of different $({N}_{h},{N}_{e})$ values are energetically aligned. Here we use a nonperturbative, correlated approach that shows when such simple rules work and when they fail, thereby establishing a basis for the appropriate use of such rules.
TL;DR: In this paper, the authors used the tools of self-consistent band theory and ab-initio total energy calculations for solids to analyze the band gap anomalies in ternary chalcopyrites and pseudobinary alloys.
Abstract: Using the tools of self-consistent band theory and ab-initio total energy calculations for solids we analyze the band gap anomalies in ternary chalcopyrites (e.g., CuGaS2) and pseudobinary alloys (e.g., InxGa1–x, P) and predict hitherto unknown new ternary crystals (e.g., MgGeAs2) as well as the existence of ordered stable crystals of binary alloys (e.g., GaAIS2, InGaP2).
TL;DR: In this paper, a spontaneous rotation of the stablest chalcopyrite film axis from perpendicular to parallel to the (001) substrate was predicted. But the rotation was not observed on GaN and CaO substrates.
Abstract: Coherently strained In0.5Ga0.5N on GaN and CaO substrates are theoretically predicted to show stable ordering in the chalcopyrite structure, as is Ga2AsSb on GaAs and InP substrates. Depending on the substrate and the film concentration, we predict a spontaneous rotation of the stablest chalcopyrite film axis from perpendicular to parallel to the (001) substrate.