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Recently, many high-throughput calculation materials databases have been constructed and found wide applications. However, a database is only useful if its content is reliable and sufficiently accurate. It is thus of paramount importance to gauge the reliabilities and accuracies of these databases. Although many properties have been predicted accurately in these databases, electronic band gap is well known to be underestimated by traditional density functional theory (DFT) calculations under local density approximation (LDA), which becomes a challenging problem for materials database building. Here, we introduce MaterialGo ( http://www.pkusam.com/data-base.html ), a new database calculating the band structures of crystals using both Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. Comparing different PBE databases, it is found that their band gaps are consistent when no U parameter is used for transition metal d-state or heavy element f-state to correct their self-interaction error, but rather different when PBE+ U are used, mostly because of the different values of U used in different database. HSE calculations under standard parameters will give larger band gaps that are closer to experiment. Based on the high-throughput HSE calculations over 10000 crystal structures, we might have a better understanding of the relationship between crystal structures and electronic structures, which will help us to further explore material genome science and engineering.

Non-adiabatic chemical reaction refers to the electronic excitation during reactions. This effect cannot be modeled by the ground-state Born–Oppenheimer molecular dynamics (BO-MD), where the electronic structure is at the ground state for every step of ions’ movement. Although the non-adiabatic effect has been explored extensively in gas phase reactions, its role in electrochemical reactions, such as water splitting and CO2 reduction, in electrolyte has been rarely explored. On the other hand, electrochemical reactions usually involve electron transport; thus, a non-adiabatic process can naturally play a significant role. In this work, using one-step CO2 reduction as an example, we investigated the role of the non-adiabatic effect in the reaction. The reaction barriers were computed by adiabatic BO-MD and non-adiabatic real-time time dependent density functional theory (rt-TDDFT). We found that by including the non-adiabatic effect, rt-TDDFT could increase the reaction barrier up to 6% compared to the BO-MD calculated barrier when the solvent model is used to represent water. Simulations were carried out using explicit water molecules around the reaction site under different overpotentials, and similar non-adiabatic effects were found.

Author(s): Liu, YY; Liu, F; Wang, R; Luo, JW; Jiang, X; Huang, R; Li, SS; Wang, LW | Abstract: The complexity of charge trapping in semiconductor devices, such as high-κ MOSFETs, is increasing as the devices themselves become more complicated. To facilitate research into such charge-trapping issues, here we propose an optimized simulation framework that is composed of density-functional theory (DFT) for electronic structure calculation and Marcus theory for the calculation of charge-trapping rates. The DFT simulations are either carried out or corrected by using the Heyd-Scuseria-Ernzerhof hybrid functional. Using this framework, the hole-trapping characteristics along multiple paths in Si/SiO2/HfO2 stacks are investigated, and the relative importance of each path is revealed by calculating its exact hole-trapping rate. Besides the study on crystalline stacks, we also create an amorphous stack, which is more realistic compared with experiments and real devices, to reveal more active trapping centers and to study the statistical feature of charge trapping induced by structural disorder. In addition, to seek effective measures for relieving these charge-trapping problems, the effects of hydrogen and fluorine passivations are discussed, and physical insights for improving the performance of high-κ MOSFETs are provided.

Theoretical study of the electronic structures of protein is a fundamental challenge in computational biochemistry due to the large size of the systems. The electronic structure of a protein is important for some of the important protein functionalities, such as photosynthesis. In this study, we explored the charge-patching method to calculate the electronic structure of polypeptides. This method generates the charge densities of the systems by patching the charge motifs calculated from small prototype systems. The method was tested on a range of polypeptides, including the glycine polypeptide in 27-ribbon, α-helix, 310-helix, and β-strand structures. After the charge density profiles of these systems were obtained, the electronic structures of these glycine polypeptides were further calculated based on density functional theory (DFT) using a folded-spectrum method. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) were analyzed and compared with conventional direct DFT calculations. The charge-patching method results were found to be in good agreement with the directed DFT results.

LS3DF, namely linear scaling three-dimensional fragment method, is an efficient linear scaling ab initio total energy electronic structure calculation code based on a divide-and-conquer strategy. In this paper, we present our GPU implementation of the LS3DF code. Our test results show that the GPU code can calculate systems with about ten thousand atoms fully self-consistently in the order of 10 min using thousands of computing nodes. This makes the electronic structure calculations of 10,000-atom nanosystems routine work. This speed is 4.5–6 times faster than the CPU calculations using the same number of nodes on the Titan machine in the Oak Ridge leadership computing facility (OLCF). Such speedup is achieved by (a) carefully re-designing of the computationally heavy kernels; (b) redesign of the communication pattern for heterogeneous supercomputers .

The formation energies and charge-transition levels of intrinsic point defects in lead halide perovskite CsPbBr3 are studied from first-principles calculations. It is shown that the formation energy of dominant defect under Br-rich growth condition is much lower than that under moderate or Br-poor conditions. Thus avoiding the Br-rich condition can help to reduce the defect concentration. Interestingly, CsPbBr3 is found to be highly defect-tolerant in terms of its electronic structure. Most of the intrinsic defects induce shallow transition levels. Only a few defects with high formation energies can create deep transition levels. Therefore, CsPbBr3 can maintain its good electronic quality despite the presence of defects. Such defect tolerance feature can be attributed to the lacking of bonding-antibonding interaction between the conduction bands and valence bands.

The crystalline-Si/amorphous-SiO2 (c-Si/a-SiO2) interface is an important system used in many applications, ranging from transistors to solar cells. The transition region of the c-Si/a-SiO2 interface plays a critical role in determining the band alignment between the two regions. However, the question of how this interface band offset is affected by the transition region thickness and its local atomic arrangement is yet to be fully investigated. Here, by controlling the parameters of the classical Monte Carlo bond switching algorithm, we have generated the atomic structures of the interfaces with various thicknesses, as well as containing Si at different oxidation states. A hybrid functional method, as shown by our calculations to reproduce the GW and experimental results for bulk Si and SiO2, was used to calculate the electronic structure of the heterojunction. This allowed us to study the correlation between the interface band characterization and its atomic structures. We found that although the systems with different thicknesses showed quite different atomic structures near the transition region, the calculated band offset tended to be the same, unaffected by the details of the interfacial structure. Our band offset calculation agrees well with the experimental measurements. This robustness of the interfacial electronic structure to its interfacial atomic details could be another reason for the success of the c-Si/a-SiO2 interface in Si-based electronic applications. Nevertheless, when a reactive force field is used to generate the a-SiO2 and c-Si/a-SiO2 interfaces, the band offset significantly deviates from the experimental values by about 1 eV.

Many experiments have indicated that a large polaron may be formed in hybrid perovskites, and its existence is proposed to screen the carrier–carrier and carrier–defect scattering, thus contributing to the long lifetime of the carriers. However, a detailed theoretical study of the large polaron and its effect on carrier transport at the atomic level is still lacking. In particular, how strong is the large polaron binding energy? How does its effect compare with the effect of dynamic disorder caused by the A-site molecular rotation? And how does the inorganic sublattice vibration impact the motion of the large polaron? All of these questions are largely unanswered. In this work, using CH3NH3PbI3 as an example, we implement a tight-binding model fitted from density-functional theory to describe the electron large polaron ground state and to understand the large polaron formation and transport at its strong-coupling limit. We find that the formation energy of the large polaron is around −12 meV for the case without dynamic disorder, and −55 meV by including dynamic disorder. By performing the explicit time-dependent wavefunction evolution of the polaron state, together with the rotations of CH3NH3+ and vibrations of the PbI3− sublattice, we studied the diffusion constant and mobility of the large polaron state driven by the dynamic disorder and the sublattice vibration. Two effects of the inorganic sublattice vibrations are found: on one hand, the vibration of the sublattice provides an additional driving force for carrier mobility; on the other hand, the large polaron polarization further localizes the electron, reducing its mobility. Overall, the effect of the large polaron is to slow down the electron mobility by roughly a factor of two. We believe that both dynamic disorder due to rotation of the organic molecule, and large polaron effects induced by the polarization and vibration of the inorganic sublattice, play important roles for the electronic structure and carrier dynamics of the system.

Artificial solids composed of semiconductor quantum dots (QDs) are being developed for large-area electronic and optoelectronic applications, but these materials often have defect-induced in-gap states (IGS) of unknown chemical origin. Here we performed scanning probe based spectroscopic analysis and density functional theory calculations to determine the nature of such states and their electronic structure. We found that IGS near the valence band occur frequently in the QDs except when treated with reducing agents. Calculations on various possible defects and chemical spectroscopy revealed that molecular oxygen is most likely at the origin of these IGS. We expect this impurity-induced deep IGS to be a common occurrence in ionic semiconductors, where the intrinsic vacancy defects either do not produce IGS or produce shallow states near band edges. Ionic QDs with surface passivation to block impurity adsorption are thus ideal for high-efficiency optoelectronic device applications.

ZnSn_(1-x)Ge_xN_2 direct bandgap semiconductor alloys, with a crystal structure and electronic structure similar to InGaN, are earth-abundant alternatives for efficient, high-quality optoelectronic devices and solar energy conversion. The bandgap is tunable almost monotonically from 2 eV (ZnSnN_2) to 3.1 eV (ZnGeN_2) by control of the Sn/Ge ratio.

The Si:WO3 heterostructure is expected to have suitable band alignment for the Z-scheme water splitting, but the heterostructure interfaces have been scarcely studied. In this work, a series of interfaces between the WO3 (100) and Si (001) surfaces, which have a small lattice-mismatch, are studied using ab initio calculations. When there is no atom diffusion across the interface, a Si–O bonded interface with Si dimers is the most stable. Analysis of the electronic structure shows that the interfacial Si and O atoms are fully saturated, leading to a clean interface without localized gap states. O diffusion from WO3 into Si is found to be thermodynamically possible, but it does not affect the full bond saturation of the interfacial atoms. A type-II band alignment exists between Si and WO3, with the WO3 conduction band about 0.5 eV higher than the Si valence band, which is not influenced by O diffusion. A band diagram is plotted for the Si:WO3 heterostructure to evaluate its photocatalytic capability, and the influence of the small Schottky barrier and the interface amorphous layer is discussed.

We present large-scale calculations of electronic structure of strongly disordered conjugated polymers. The calculations have been performed using the density functional theory based charge patching method for the construction of single-particle Hamiltonian and the overlapping fragments method for the efficient diagonalization of that Hamiltonian. We find that the hole states are localized due to the fluctuations of the electrostatic potential and not by the breaks in the conjugation of the polymer chain. The tail of the density of hole states exhibits an exponentially decaying behavior. The main features of the electronic structure of the system can be described by an one-dimensional nearest neighbor tight-binding model with a correlated Gaussian distribution of on-site energies and constant off-site coupling elements.

Enforcing a straight-line condition of the total energy upon removal/addition of fractional electrons on eigen states has been successfully applied to atoms and molecules for calculating ionization potentials and electron affinities, but fails for solids due to the extended nature of the eigen orbitals. Here we have extended the straight-line condition to the removal/addition of fractional electrons on Wannier functions constructed within the occupied/unoccupied subspaces. It removes the self-interaction energies of those Wannier functions, and yields accurate band gaps for solids compared to experiments. It does not have any adjustable parameters and the computational cost is at the DFT level. This method can also work for molecules, providing eigen energies in good agreement with experimental ionization potentials and electron affinities. Our approach can be viewed as an alternative approach of the standard LDA+U procedure.

We report detailed ab initio calculations of poly(3-hexylthiophene) (P3HT) on top of a ZnO (1010) surface. We studied different absorption sites and orientations. We found that the P3HT chain prefers to lay along the dimer row direction of the ZnO surface. We also found strong coupling between the P3HT molecule and the ZnO substrate in the conduction band states, while minimum coupling in the valence band states.

The size-dependent electronic structure of CdTe quantum wires is determined by density functional theory using the local density approximation with band-corrected pseudopotential method. The results of the calculations are then used to assign the size-dependent absorption spectrum of colloidal CdTe quantum wires synthesized by the solution-liquid-solid mechanism. Quantitative agreement between experiment and theory is achieved. The absorption features comprise transitions involving the highest 25-30 valence-band states and lowest 15 conduction-band states. Individual transitions are not resolved; rather, the absorption features consist of clusters of transitions that are determined by the conduction-band energy-level spacings. The sequence, character, and spacing of the conduction-band states are strikingly consistent with the predictions of the simple effective-mass-approximation, particle-in-a-cylinder model. The model is used to calculate the size dependence of the electron effective mass in CdTe quantum wires.

We theoretically study the energy transfer between semiconductor nanocrystal dots and rods of CdSe using a semiempirical pseudopotential method (SEPM) description of the electronic structure of the...

The band edge states determine optical and electronic properties of semiconductor nano-structures which can be computed from an interior eigenproblem. We study the reliability and performance of state-of-the-art iterative eigensolvers on large quantum dots and wires, focusing on variants of preconditioned CG, Lanczos, and Davidson methods. One Davidson variant, the GD+k (Olsen) method, is identified to be as reliable as the commonly used preconditioned CG while consistently being between two and three times faster.

We describe a systematic and efficient method of determining pseudo-atom positions and potentials for use in nanostructure calculations based on bulk empirical pseudopotentials (EPMs). Given a bulk EPM for binary semiconductor X, we produce parameters for pseudo-atoms necessary to passivate a nanostructure of X in preparation for quantum mechanical electronic structure calculations. These passivants are based on the quality of the wave functions of a set of small test structures that include the passivants. Our method is based on the global optimization method DIRECT. It enables and/or streamlines surface passivation for empirical pseudopotential calculations.

We present a new technique to accelerate the convergence of the folded spectrum method in empirical pseudopotential band edge state calculations for colloidal quantum dots. We use bulk band states of the materials constituent of the quantum dot to construct initial vectors and a preconditioner. We apply these to accelerate the convergence of the folded spectrum method for the interior states at the top of the valence and the bottom of the conduction band. For large CdSe quantum dots, the number of iteration steps until convergence decreases by about a factor of 4 compared to previous calculations.

Type II core-shell nanowires based on III-V and II-VI semiconductors are designed to provide the highly desirable but not readily available feature--efficient charge separation--and concurrently address the different material challenges specific for a few key renewable energy applications: including hydrogen generation via photoelectrochemical water splitting, dye-sensitized solar cells, and conventional solar cells. They also open up new avenues for studying novel physics and material sciences in reduced dimensionality of very unusual quasi-one-dimensional systems. A first-principles density function theory within the local density approximation (LDA) is used for the electronic structure calculation and a valence-force-field method for the structural relaxation, and empirical corrections to the LDA errors are applied.

We propose a systematic approach that can empirically correct three major errors typically found in a density functional theory (DFT) calculation within the local density approximation (LDA) simultaneously for a set of common cation binary semiconductors, such as III-V compounds, (Ga or In)$X$ with $X=\mathrm{N},\mathrm{P},\mathrm{As},\mathrm{Sb},$ and II-VI compounds, (Zn or Cd)$X$, with $X=\mathrm{O},\mathrm{S},\mathrm{Se},\mathrm{Te}$. By correcting (1) the binary band gaps at high-symmetry points $\mathrm{\ensuremath{\Gamma}}, L, X$, (2) the separation of $p$-and $d$-orbital-derived valence bands, and (3) conduction band effective masses to experimental values and doing so simultaneously for common cation binaries, the resulting DFT-LDA-based quasi-first-principles method can be used to predict the electronic structure of complex materials involving multiple binaries with comparable accuracy but much less computational cost than a GW level theory. This approach provides an efficient way to evaluate the electronic structures and other material properties of complex systems, much needed for material discovery and design.

Charge hopping and percolation in quantum dot (QD) solids has been widely studied, but the microscopic nature of the percolation process is not understood or determined. Here we present the first imaging of the charge percolation pathways in two-dimensional PbS QD arrays using Kelvin probe force microscopy (KPFM). We show that under dark conditions electrons percolate via in-gap states (IGS) instead of the conduction band, while holes percolate via valence band states. This novel transport behavior is explained by the electronic structure and energy level alignment of the individual QDs, which was measured by scanning tunneling spectroscopy (STS). Chemical treatments with hydrazine can remove the IGS, resulting in an intrinsic defect-free semiconductor, as revealed by STS and surface potential spectroscopy. The control over IGS can guide the design of novel electronic devices with impurity conduction, and photodiodes with controlled doping.

The past ~10 years have witnessed revolutionary breakthroughs both in synthesis of quantum dots (leading to nearly monodispersed, defect-free nanostructures) and in characterization of such systems, revealing ultra narrow spectroscopic lines of

Dimensionality is an important factor to govern the electronic structures of semiconductor nanocrystals. The quantum confinement energies in one-dimensional quantum wires and zero-dimensional quantum dots are quite different. Using large-scale first-principles calculations, we systematically study the electronic structures of semiconductor (including group IV, III-V, and II-VI) surface-passivated quantum wires and dots. The band-gap energies of quantum wires and dots have the same scaling with diameter for a given material. The ratio of band-gap-increases between quantum wires and dots is material-dependent, and slightly deviates from 0.586 predicted by effective-mass approximation. Highly linear polarization of photoluminescence in quantum wires is found. The degree of polarization decreases with the increasing temperature and size.

In this work, the oxygen vacancy in WO 3 has been studied by an ab initio pseudopotential method within the local density approximation (LDA). It is shown that with the charge state change of the vacancy, a strong lattice relaxation, swing from one to the other side of the un-relaxed position, is found for the nearest W ions, accompanied by large changes in the electronic structure of the vacancy. It is found that an oxygen vacancy in WO 3 gives rise to three types of defect states: a donor-like state near the fundamental band gap, derived from the top valence bands, a hyper-deep resonant state in the valence band and a high-lying resonant state in the conduction band, derived from the oxygen 2s bonding and anti-bonding band, respectively. The existence of the donor-like defect state offers a possible explanation for the dependence of the conductivity and the mid-gap absorption on the O deficiency.

The electronic structures of zinc blende InP quantum rods are calculated using an atomistic pseudopotential method. The quantum rods in ref [001] and [111] growth directions are studied. We found dramatic differences in the valence bands between the wurtzite CdSe, zinc blende InP [111], and InP [001] quantum rods. We also found an unexpected Γ-X coupling in the conduction bands of the [111] direction quantum wires. Our calculated results await experimental confirmations.

The dependence of electronic states on the length and diameter of CdSe quantum rods is investigated using semiempirical pseudopotential calculations. Energy levels cross as the aspect ratio increases due to their different dependence on length. The crossover between the highest occupied levels leads to a transition from plane-polarized to linearly polarized light emission at aspect ratio ca. 1.3. Further increasing aspect ratio results in levels with similar symmetry converging and forming “bands”. This calculation demonstrates the transition of electronic structure from zero-dimensional quantum dots to one-dimensional quantum wires.

Colloidal quantum rods of cadmium selenide (CdSe) exhibit linearly polarized emission. Empirical pseudopotential calculations predict that slightly elongated CdSe nanocrystals have polarized emission along the long axis, unlike spherical dots, which emit plane-polarized light. Single-molecule luminescence spectroscopy measurements on CdSe quantum rods with an aspect ratio between 1 and 30 confirm a sharp transition from nonpolarized to purely linearly polarized emission at an aspect ratio of 2. Linearly polarized luminescent chromophores are highly desirable in a variety of applications.

We present a parallel implementation of the previously developed folded spectrum method for empirical pseudopotential electronic structure calculations. With the parallel implementation we can calculate a small number of electronic states for systems of up to one million atoms. A plane-wave basis is used to expand the wavefunctions in the same way as is commonly used in ab initio calculations, but the potential is a fixed external potential generated using atomistic empirical pseudopotentials. Two techniques allow the calculation to scale to million atom systems. First, the previously developed folded spectrum method allows us to calculate directly a few electronic states of interest around the gap. This makes the scaling of the calculation O(N) for an N atom system and a fixed number of electronic states. Second, we have now developed an efficient parallel implementation of the algorithm that scales up to hundreds of processors, giving us the memory and computer power to simulate one million atoms. The program's performance is demonstrated for many large semiconductor nanostructure systems.

This paper describes two recent innovations related to the restarted Lanczos method for eigenvalue problems, namely the thick-restart technique and dynamic restarting schemes. Previous restarted versions of the Lanczos method use considerably more iterations than the non-restarted versions, largely because too much information is discarded during restarting. The thick-restart technique provides a mechanism to preserve a large portion of the existing basis and dynamic restarting schemes decide exactly how many vectors to save. Combining these two new techniques we are able to implement an efficient eigenvalue problem solver. This paper will demonstrate its effectiveness on one particular class of problems for which this method is well suited: linear eigenvalue problems generated from non-selfconsistent electronic structure calculations.

The electronic structure of abrupt $(\mathrm{InAs}{)}_{n}/(\mathrm{GaSb}{)}_{n}$ superlattices is calculated using a plane wave pseudopotential method and the more approximate eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method. The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters are extracted from the pseudopotential band structures of the zinc-blende constituents near the $\ensuremath{\Gamma}$ point. We find, in general, good agreement between pseudopotential results and $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ results, except as follows. (1) The eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ significantly underestimates the electron confinement energies for $nl~20.$ (2) While the pseudopotential calculation exhibits (a) a zone center electron-heavy hole coupling manifested by band anticrossing at $n=28,$ and (b) a light hole--heavy hole coupling and anticrossing around $n=13,$ these features are absent in the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model. (3) As $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ misses atomistic features, it does not distinguish the ${C}_{2v}$ symmetry of a superlattice with no-common-atom such as InAs/GaSb from the ${D}_{2d}$ symmetry of a superlattice that has a common atom, e.g., InAs/GaAs. Consequently, $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ lacks the strong in-plane polarization anisotropy of the interband transition evident in the pseudopotential calculation. Since the pseudopotential band gap is larger than the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ values, and most experimental band gaps are even smaller than the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ band gap, we conclude that to understand the experimental results one must consider physical mechanisms beyond what is included here (e.g., interdiffusing, rough interfaces, and internal electric fields), rather than readjust the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ parameters.

Lateral composition modulation (CM) is a periodic, position-dependent variation in alloy composition occurring in the substrate plane, perpendicular to the growth direction. It can be induced by growing size-mismatched short-period AC/BC superlattices (SL). Here we study the electronic structure induced by such lateral composition modulation in GaAs/InAs, GaP/InP, and AlP/GaP, in search of optical properties relative to the corresponding random alloys. We investigate in detail the properties of (a) pure CM without any SL, (b) pure SL without any CM, and (c) the combined CM+SL system. The systems are modeled by constructing a large supercell where the cation sublattice sites are randomly occupied in the lateral (vertical) direction according to the composition variation induced by CM (SL). The atomic structure and strain induced by CM and SL are explicitly taken into account using an {ital atomistic} force field. This approach is found to be crucial for an accurate description of the microscopic strain in CM+SL systems. The electronic structure is solved using specially constructed empirical pseudopotentials and plane-wave expansion of the wave functions. We find that (i) CM in GaAs/InAs and GaP/InP systems induces type-I band alignment (electrons and holes localized in the same spatial region), while CM in AlP/GaPmore » is shown as an example exhibiting type-II band alignment. (ii) CM and SL both induce significant contributions (which add up nearly linearly) to band-gap redshift with respect to random alloy. CM in GaP/InP is found to induce larger band-gap redshifts than in GaAs/InAs due to larger band offsets in the former system. (iii) The symmetry of electronic states at the valence band maximum is sensitively affected by CM: the lowest energy optical transitions exhibit strong polarization where transitions polarized perpendicular to the CM are favored, while transitions polarized parallel to the CM are surpressed by being shifted to higher energy. These observations, as well as the magnitude of the predicted band-gap redshift, agree with available experimental data, and suggest that control of composition modulation during growth might be used to tailor band gaps, carrier localization, and transition polarizations relative to random alloys. {copyright} {ital 1999} {ital The American Physical Society}« less

The conditions under which the band gaps of free standing and embedded semiconductor quantum dots are direct or indirect are discussed. Semiconductor quantum dots are classified into three categories; (i) free standing dots, (ii) dots embedded in a direct gap matrix, and (iii) dots embedded in an indirect gap matrix. For each category, qualitative predictions are first discussed, followed by the results of both recent experiments and state of the art pseudopotential calculations. We show that: Free standing dots of InP, InAs, and CdSe will remain direct for all sizes, while dots made of GaAs and InSb will turn indirect below a critical size. Dots embedded within a direct gap matrix material will either stay direct (InAs/GaAs at zero pressure) or will become indirect at a critical size (InSb/InP). Dots embedded within an indirect gap matrix material will exhibit a transition to indirect gap for sufficiently small dots (GaAs/AlAs and InP/GaP quantum well) or will be always indirect (InP/GaP dots, InAs/GaAs above 43 k bar pressure and GeSi/Si dots).

We present an approach to calculate the excitonic fine-structure splittings due to electron-hole short-range exchange interactions using the local-density approximation pseudopotential method, and apply it to bulk semiconductors CdSe, InP, GaAs, and InAs. Comparing with previous theoretical results, the current calculated splittings agree well with experiments. Furthermore, we provide an approximate relationship between the short-range exchange splitting and the exciton Bohr radius, which can be used to estimate the exchange splitting for other materials. The current calculation indicates that a commonly used formula for exchange splitting in quantum dot is not valid. Finally, we find a very large pressure dependence of the exchange splitting: a factor of 4.5 increase as the lattice constant changes by 3.5%. This increase is mainly due to the decrease of the Bohr radius via the change of electron effective mass.

We calculate the electronic structures of pyramidal quantum dots with supercells containing 250 000 atoms, using spin-orbit-coupled, nonlocal, empirical pseudopotentials. We compare the results with previous theoretical calculations. Our calculation circumvents the approximations underlying the conventional effective-mass approach: we describe the potential, the strain and the wave functions using atomistic rather than continuum models. The potential is given by a superposition of screened atomic pseudopotentials, the strain is obtained from minimizing the atomistic strain energy, and the wave function is expanded using a plane-wave basis set. We find the following. (1) The conduction bands are formed essentially from single envelope functions, so they can be classified according to the nodal structure as $s, p,$ and d. However, due to strong multiband coupling, most notably light hole with heavy hole, the valence states cannot be classified in the language of single-band envelope functions. In fact, the hole states have no nodal planes. (2) There is a strong anisotropy in the polarization of the lowest valence state to conduction state optical transition. This is in contrast to the eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model, which finds essentially zero anisotropy. (3) There are at least four bound electron states for a 113-\AA{}-based quantum dot. This number of bound states is larger than that found in eight band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculations. (4) Since our atomistic description retains the correct ${C}_{2v}$ symmetry of a square-based pyramid made of zinc-blende solids, we find that the otherwise degenerate p states are split by about 25 meV. This splitting is underestimated in the eight-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculation.

Despite the lack of translational symmetry in random substitutional alloys, their description in terms of single Bloch states has been used in most phenomenological models and spectroscopic practices. We present a new way of analyzing the alloy electronic structures based on a {open_quotes}majority representation{close_quotes} phenomenon of the reciprocal space spectrum P({bold k}) of the wave function. This analysis provides a quantitative answer to the questions: When can an alloy state be classified according to the crystal Bloch state symmetry, and under what circumstances are the conventional theoretical alloy models applicable. {copyright} {ital 1998} {ital The American Physical Society}

Using a pseudopotential plane-wave approach, we have calculated the electronic structure of strained InAs pyramidal quantum dots embedded in a GaAs matrix, for a few height $(h)$-to-base$(b)$ ratios, corresponding to different facet orientations ${101}$, ${113},$ and ${105}$. We find that the dot shape (not just size) has a significant effect on its electronic structure. In particular, while the binding energies of the ground electron and hole states increase with the pyramid volumes ${(b}^{2}h)$, the splitting of the $p\ensuremath{-}$like conduction states increases with facet orientation $(h/b),$ and the $p\ensuremath{-}$to-$s$ splitting of the conduction states decreases as the base size $(b)$ increases. We also find that there are up to six bound electron states (12 counting the spin), and that all degeneracies other than spin, are removed. This is in accord with the conclusion of electron-addition capacitance data, but in contrast with simple k\ensuremath{\cdot}p calculations, which predict only a single electron level.

The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ method has become the ``standard model'' for describing the electronic structure of nanometer-size quantum dots. In this paper we perform parallel $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ $(6\ifmmode\times\else\texttimes\fi{}6$ and $8\ifmmode\times\else\texttimes\fi{}8)$ and direct-diagonalization pseudopotential studies on spherical quantum dots of an ionic material---CdSe, and a covalent material---InP. By using an equivalent input in both approaches, i.e., starting from a given atomic pseudopotential and deriving from it the Luttinger parameters in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ calculation, we investigate the effect of the different underlying wave-function representations used in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ and in the more exact pseudopotential direct diagonalization. We find that (i) the $6\ifmmode\times\else\texttimes\fi{}6\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ envelope function has a distinct (odd or even) parity, while atomistic wave function is parity-mixed. The $6\ifmmode\times\else\texttimes\fi{}6\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ approach produces an incorrect order of the highest valence states for both InP and CdSe dots: the $p$-like level is above the $s$-like level. (ii) It fails to reveal that the second conduction state in small InP dots is folded from the $L$ point in the Brillouin zone. Instead, all states in $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ are described as \ensuremath{\Gamma}-like. (iii) The $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ overestimates the confinement energies of both valence states and conduction states. A wave-function projection analysis shows that the principal reasons for these $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ errors in dots are (a) use of restricted basis set, and (b) incorrect bulk dispersion relation. Error (a) can be reduced only by increasing the number of basis functions. Error (b) can be reduced by altering the $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ implementation so as to bend upwards the second lowest bulk band, and to couple the conduction band into the $s$-like dot valence state. Our direct diagonalization approach provides an accurate and practical replacement to the standard model in that it is rather general, and can be performed simply on a standard workstation.

It is well known that in a sequence of flat, type-I (GaAs){sub m}/(AlAs){sub n}/(GaAs){sub p}/(AlAs){sub q}{center_dot}{center_dot}{center_dot} multiple quantum wells (MQWs), the wave functions of both the valence-band maximum and the conduction-band minimum are localized on the widest well. Thus, electron-hole charge separation is not possible. On the other hand, for short-period superlattices (type II), the electron and hole are localized on different materials (electron on AlAs and hole on GaAs) and different band-structure valleys (hole at {Gamma} and electron at X). Using a plane-wave pseudopotential direct-diagonalization approach, we predict that electron-hole charge separation on different layers of the {ital same} material (GaAs) and {ital same} valley ({Gamma}) is possible in {ital curved} (but not in flat) {ital geometries}. This is predicted for a set of concentric, nested cylinders of GaAs and AlAs. Since the flat multiple-quantum-well structure and the nested cylindrical structure with the same layer thicknesses have the same band offset diagram, the difference in behavior is not due to the potential. Rather, it reflects different interband coupling and kinetic energy confinement induced by the {ital curvature}, present in the nested-cylinder geometry but absent in the MQW. This identifies a geometric degree of freedom (curvature) that can be usedmore » to tailor electronic properties of nanostructures. {copyright} {ital 1997} {ital The American Physical Society}« less

Coupling between different \ensuremath{\Gamma}, $X,$ and $L$ band-structure valleys is responsible for (a) level anticrossing in superlattices as a function of period, pressure, and electric field and for (b) ``optical bowing'' of band gaps in random alloys. We investigate the symmetry, magnitude, and size scaling of intervalley coupling in semiconductor superlattices and alloys by direct supercell calculations, performed with screened pseudopotentials and a plane-wave basis, considering up to ${10}^{6}$ atoms/supercell. Projecting the calculated electronic wave functions ${\ensuremath{\psi}}_{i}$ of alloys or superlattices onto the bulk states of the constituent zinc-blende materials shows that ${\ensuremath{\psi}}_{i}$ contain a ``majority representation'' from one or more zinc-blende states \ensuremath{\gamma}. The intervalley coupling $E(i,j)$ between the alloy states ${\ensuremath{\psi}}_{i}$ and ${\ensuremath{\psi}}_{j}$ then includes a term $2F(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})V(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ due to the ``majority representations'' \ensuremath{\gamma} and ${\ensuremath{\gamma}}^{\ensuremath{'}}$ of ${\ensuremath{\psi}}_{i}$ and ${\ensuremath{\psi}}_{j},$ respectively, plus residual terms due to the minority representations. We find the following: (i) In alloys, the orbital overlap function $F(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ is large, since the wave functions are extended. The intervalley coupling element $V(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ exhibits simple selection rules: being zero for $({\ensuremath{\Gamma}}_{1c}{,X}_{1c}),$ $({\ensuremath{\Gamma}}_{1c}{,L}_{3c}),$ ${(X}_{1c}^{x}{,X}_{1c}^{y}),$ etc. (``weak coupling''), and nonzero for $({\ensuremath{\Gamma}}_{1c}{,X}_{3c}),$ $({\ensuremath{\Gamma}}_{1c}{,L}_{1c}),$ ${(L}_{3c}{,X}_{1c}),$ etc. (``strong coupling''). This explains why the $\overline{\ensuremath{\Gamma}}$-like conduction band of mixed-cation alloys contains zinc-blende ${\ensuremath{\Gamma}}_{1c}$ and ${L}_{1c}$ character, but not ${X}_{1c}.$ In the case of strong coupling, $E(i,j)$ scales as $1/\sqrt{\ensuremath{\Omega}},$ where \ensuremath{\Omega} is the volume, while in the weak-coupling case the entire coupling originates from the ``minority representation,'' and is 20--100 times smaller. The minority representation, however, contributes to the bowing of the band gap vs composition. (ii) In superlattices, although the above selection rule for $V(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ still exists, the magnitude of the intervalley coupling is governed by the overlap function $F(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}}).$ For simple superlattices, $F(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ is small, since the wave functions are localized in particular segments (``weak coupling''). Consequently, the ``majority representation'' contributes 5--100 times less than in the analogous case of alloys. Furthermore, $E(i,j)$ scales as ${1/n}^{3},$ where $n$ is the superlattice period.

We have developed a ``linear combination of bulk bands'' method that permits atomistic, pseudopotential electronic structure calculations for $\ensuremath{\sim}{10}^{6}$ atom nanostructures. Application to $(\mathrm{GaAs}{)}_{n}/(\mathrm{AlAs}{)}_{n}$ (001) superlattices (SL's) reveals even-odd oscillations in the $\ensuremath{\gamma}\ensuremath{-}X$ coupling magnitude ${V}_{\ensuremath{\gamma}X}(n)$, which vanishes for $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{odd}$, even for abrupt and segregated SL's, respectively. Surprisingly, in contrast with recent expectations, 0D quantum dots are found here to have a smaller $\ensuremath{\gamma}\ensuremath{-}X$ coupling than equivalent 2D SL's. Our analysis shows that for large quantum dots this is largely due to the existence of level repulsion from many $X$ states.

With increasing demands on hardware in quantum chemistry calculations, modern Graphical Processing Units (GPUs) have great potential meeting the resources of high performance computing. In this paper we investigate the possibility to accelerate the planewave pseudopotential code PEtot on CUDA architecture. In particular, we execute two most time consuming steps, i.e., the nonlocal projections and FFT transformations on GPU with careful implementations to reduce the data exchanges between the CPU and the GPU. Our experience for the molecule with as many as 512 atoms is also shown.

The electronic structure of quantum wells, wires, and dots is conventionally described by the envelope-function eight-band k\ensuremath{\cdot}p method (the ``standard k\ensuremath{\cdot}p model'') whereby coupling with bands other than the highest valence and lowest conduction bands is neglected. There is now accumulated evidence that coupling with other bands and a correct description of far-from-\ensuremath{\Gamma} bulk states is crucial for quantitative modeling of nanostructure. While multiband generalization of the k\ensuremath{\cdot}p exists for bulk solids, such approaches for nanostructures are rare. Starting with a pseudopotential plane-wave representation, we develop an efficient method for electronic-structure calculations of nanostructures in which (i) multiband coupling is included throughout the Brillouin zone and (ii) the underlying bulk band structure is described correctly even for far-from-\ensuremath{\Gamma} states. A previously neglected interband overlap matrix now appears in the k\ensuremath{\cdot}p formalism, permitting correct intervalley couplings. The method can be applied either using self-consistent potentials taken from ab initio calculations on prototype small systems or from the empirical pseudopotential method. Application to both short- and long-period (GaAs${)}_{\mathit{p}}$/(AlAs${)}_{\mathit{p}}$ superlattices (SL) recovers (i) the bending down (``deconfinement'') of the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}(\ensuremath{\Gamma}) energy level of (001) SL at small periods p; (ii) the type-II--type-I crossover at p\ensuremath{\approxeq}8 SL, and (iii) the even-odd oscillation of the energies of the R\ifmmode\bar\else\textasciimacron\fi{}/X\ifmmode\bar\else\textasciimacron\fi{}(L) state of (001) SL and \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}(L) state of (111) SL. Introducing a few justified approximations, this method can be used to calculate the eigenstates of physical interest for large nanostructures. Application to spherical GaAs quantum dots embedded in an AlAs barrier (with \ensuremath{\sim}250 000 atoms) shows a type-II--type-I crossover for a dot diameter of 70 \AA{}, with an almost zero \ensuremath{\Gamma}-X repulsion at the crossing point. Such a calculation takes less than 30 min on an IBM/6000 workstation model 590. \textcopyright{} 1996 The American Physical Society.

A plane-wave semiempirical pseudopotential method with nonlocal potentials and spin-orbit coupling is used to calculate the electronic structure of surface-passivated wurtzite CdSe quantum dots with up to 1000 atoms. The calculated optical absorption spectrum reproduces the features of the experimental results and the exciton energies agree to within \ensuremath{\sim}0.1 eV over a range of dot sizes. The correct form of Coulomb interaction energy with size-dependent dielectric constant is found to be essential for such good agreement. \textcopyright{} 1996 The American Physical Society.

The electronic states of core/shell CdSe/CdS and CdSe/CdTe heterostructure quantum dots are studied by large-scale first-principles calculations. According to their natural band-offset alignments CdSe/CdS is a type-I heterostructure and CdSe/CdTe is a type-II heterostructure. We found that, the electron state changes very little, but the hole wave function in CdSe/CdS quantum dots has been localized within the core, while the hole wave function in CdSe/CdTe quantum dots is localized within the shell. The hole state in CdSe/CdTe quantum dots has drastically different characteristics as in CdSe and CdSe/CdS quantum dots. The band alignment, strain effect, and quantum confinement are all important to determine the electronic structures of these systems.

We study the effects of a few types of atomic disorder on the electronic and optical properties of AlAs/GaAs (001) and (111) superlattices: (i) atomic intermixing across the interfaces; (ii) replacing a single monolayer in a superlattice by one containing the opposite atomic type (isoelectronic δ doping); and (iii) random layer‐thickness fluctuations in superlattices (SL). Type (i) is an example of lateral disorder, while types (ii) and (iii) are examples of vertical disorder. Using three‐dimensional empirical pseudopotential theory and a plane‐wave basis, we calculate the band gaps, electronic wave functions, and optical matrix elements for systems containing up to 2000 atoms in the computational unit cell. Spin‐orbit interactions are omitted. Computationally much less costly effective‐mass calculations are used to evaluate the density of states and eigenstates away from the band edges in vertically disordered SLs. Our main findings are: (i) Chemical intermixing across the interface can significantly shi...

A new method using a small fixed number (much less than the total number of electrons in the system) of orbitals to calculate the electronic structure of an arbitrarily large system is presented. For crystals, this method reduces to a conventional Brillouin zone k-point integration method with the total number of states of all the k-points equal to the number of orbitals used in this method. If one uses a fixed number of orbitals the total computational time is linear in the size of the system. The method is applied to two test systems using a plane wave basis and the results are compared with conventional methods.

Quantum mechanical pseudopotential calculations of the absorption spectra and static dielectric constant ${\ensuremath{\epsilon}}_{s}$ of Si quantum dots with \ensuremath{\sim}100-1300 atoms are presented. The predicted ${\ensuremath{\epsilon}}_{s}$ is found to be significantly reduced relative to the bulk value, but is considerably larger than the value deduced from currently available model calculations. A convenient parametrization of ${\ensuremath{\epsilon}}_{s}$ vs size $R$ is provided. We find that for quantum dots with $Rl20$ \AA{} the electron-hole pair is confined by the physical dimension of the dot, not by the Coulomb attraction.