Energy-band structure of CdTe and Si: a sp(s)k.p model

The energy bands of the direct-band-gap semiconductor (CdTe) as well as the indirect-band-gap semiconductor (Si), throughout the entire Brillouin zone, have been obtained by diagonalizing a 24×24 k.p Hamiltonian referred to basis states at We extend the sp³s^∗ basis functions by the inclusion of orbitals. We find that the sp³‘d’(s^∗)²k.p model is fairly sufficient to describe the electronic structure of these systems over a wide energy range, obviating the use of any d orbitals. Finally, the comparison with available theoretical results shows that the present model reproduces known results for bulk CdTe and Si, that is, their band structure, including s and p valence bands and the lowest two conduction bands.     

An improved particle correction procedure for the particle level set method

The particle level set method [D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 183 (2002) 83–116.] can substantially improve the mass conservation property of the level set method by using Lagrangian marker particles to correct the level set function in the under-resolved regions. In this study, the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed, and an improved particle correction procedure is developed based on a new interface reconstruction scheme. Moreover, the zero level set is “anchored” as the level set functions are reinitialized; hence the additional particle correction after the level set reinitialization is avoided. With this new scheme, a well-defined zero level set can be obtained and the disturbances to the interface are significantly reduced. Consequently, the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary. To demonstrate the accuracy and robustness of the proposed method, two extreme particle reseeding strategies, one without reseeding and the other with reseeding every time step, are applied in several benchmark advection tests and the results are compared with each other. Three interfacial flow cases, a 2D surface tension driven oscillating droplet, a 2D gas bubble rising in a quiescent liquid, and a 3D drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications.     

Theoretical study on the composition dependence of Ga8−nAsn (n=0-8) clusters

Using full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method, we have investigated the dependence of GaAs clusters with eight atoms on composition. It is found that the ground state structures for Ga-rich and As-rich clusters are cube structures. As the ratio between gallium atoms and arsenic atoms is close to one, structural distortion become increasingly severe, or even the clusters adopt other geometrical configurations as their ground state structures. The energy gap E_g between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO), and the vertical electron affinity show a certain degree of even/odd alternation with cluster composition. Among nine Ga_8−nAs_n (n=0-8) clusters, only a few of clusters have different energy orders between the ionic and neutral isomers with large binding energy. Some ionic structures would change into other configurations due to severe structural distortion.     

Analytic and numeric Green’s functions for a two-dimensional electron gas in an orthogonal magnetic field

We have derived closed analytic expressions for the Green’s function of an electron in a two-dimensional electron gas threaded by a uniform perpendicular magnetic field, also in the presence of a uniform electric field and of a parabolic spatial confinement. A workable and powerful numerical procedure for the calculation of the Green’s functions for a large infinitely extended quantum wire is considered exploiting a lattice model for the wire, the tight-binding representation for the corresponding matrix Green’s function, and the Peierls phase factor in the Hamiltonian hopping matrix element to account for the magnetic field. The numerical evaluation of the Green’s function has been performed by means of the decimation-renormalization method, and quite satisfactorily compared with the analytic results worked out in this paper. As an example of the versatility of the numerical and analytic tools here presented, the peculiar semilocal character of the magnetic Green’s function is studied in detail because of its basic importance in determining magneto-transport properties in mesoscopic systems.     

Principal energy band gaps of the quaternary alloy AlxGa1−xSbyAs1−y

The correlated function expansion (CFE) interpolation procedure was presented to efficiently estimate principal energy band gaps and lattice constants of the quaternary alloy Al_xGa_1−xSb_yAs_1−y over the entire composition variable space. The lattice matching conditions between x and y for the alloy Al_xGa_1−xSb_yAs_1−y substrated to InAs and GaSb were obtained by optimizing the alloy lattice constant to that of the substrates. The corresponding principal band gaps (E(Γ), E(L), and E(X)) were also calculated along the lattice matching condition on each substrate (InAs and GaSb).     

Theoretical investigation of the conduction and valence band offsets of GaAs1−x Nx/GaAs1−yNy heterointerfaces

Theoretical investigations of the conduction band offset (CBO) and valence band offset (VBO) of the relaxed and pseudo-morphically strained GaAs_1−xN_x/GaAs_1−yN_y heterointerfaces at various nitrogen concentrations (x and y) within the range 0-0.05 and along the [0 0 1] direction are performed by means of the model-solid theory combined with the empirical pseudopotential method under the virtual crystal approximation that takes into account the effects of the compositional disorder. It has been found that for y < x, the CBO and VBO have negative and positive signs, respectively, whereas the reverse is seen when y > x. The band gap of the GaAs_1−xN_x over layer falls completely inside the band gap of the substrate GaAs_1−yN_y and thus the alignment is of type I (straddling) for y < x. When y > x, the alignment remains of type I but in this case it is the band gap of the substrate GaAs_1−yN_y which is fully inside the band gap of the GaAs_1−xN_x over layer. Besides the CBO, the VBO and the relaxed/strained band gap of two particular cases: GaAs_1−xN_x/GaAs and GaAs_1−xN_x/GaAs_0.98N_0.02 heterointerfaces have been determined.     

A simple GUI for modeling the optical properties of single metal nanoparticles

We present a graphical user interface, based on the modified long-wavelength approximation, to compute the optical properties of single metal nanoparticles of ellipsoidal geometry (spheres, rods, and disks). The user-friendly interface allows one to readily gauge the accuracy of results obtained using the modified long-wavelength approximation. For spherical particles, up to 10-nm diameter, we confirm that our approach yields an exact correspondence with Mie theory, and gives an approximation error of less than 15% for gold (silver) particles with diameters approaching 40 nm (26 nm). Results are shown to be sensitive to the source data for the optical constants for a given material. The modular nature of the simulation platform provides a quick and intuitive guide for optical characterization experiments.     

Polarization selection rules for the allowed optical transitions in europium-terbium double activated calcium tungstate phosphor

The paper is devoted to the problem of the optical anisotropy of the rare-earth ions occupying low-symmetry positions in crystals. The crystal field multiplets arising from LSJ terms of Eu³⁺ and Tb³⁺ ions in the crystal field of calcium tungstate scheelite (CaWO₄) are analyzed (S₄ point symmetry). The selection rules, in particular, polarization rules for the allowed electric dipole optical transitions in the electronic shells of the Eu³⁺ and Tb³⁺ in CaWO₄ host lattice are discussed. Special attention is paid to the study of the angular (polarization) dependence of the two-photon absorption that seems to be an effective tool for the understanding of the complicated optical pattern. The peculiarities of the anisotropy of the two-photon absorption prove to be specific for each allowed dipole transition in S₄ symmetry center.     

Optimization with extremal dynamics for the traveling salesman problem

By mapping the optimization problems to physical systems, the paper presents a general-purpose stochastic optimization method with extremal dynamics. It is built up with the traveling salesman problem (TSP) being a typical NP-complete problem. As self-organized critical processes of extremal dynamics, the optimization dynamics successively updates the states of those cities with high energy. Consequently, a near-optimal solution can be quickly obtained through the optimization processes combining the two phases of greedy searching and fluctuated explorations (ergodic walk near the phase transition). The computational results demonstrate that the proposed optimization method may provide much better performance than other optimization techniques developed from statistical physics, such as simulated annealing (SA). Since the proposed fundamental solution is based on the principles and micromechanisms of computational systems, it can provide systematic viewpoints and effective computational methods on a wide spectrum of combinatorial and physical optimization problems.     

An approximate block Newton method for coupled iterations of nonlinear solvers: Theory and conjugate heat transfer applications

A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss–Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.     

Dependence of electronic properties on nitrogen concentration in GaAs1−xNx dilute alloys

Based on the pseudopotential scheme, the effect of nitrogen concentration on electronic properties of zinc-blende GaAs_1−xN_x alloys has been investigated for small amounts of N. The agreement between our calculated electronic band parameters and the available experimental data is generally reasonable. In agreement with recent experiment, we find that the incorporation of a few percent of N in the material of interest reduces substantially the fundamental band-gap energy and narrows the full valence band width. The electron and heavy hole effective masses are found to decrease rapidly when adding a concentration of nitrogen less than 0.005 in GaAs. This may increase the mobility of electrons and heavy holes providing new opportunities regarding the transport properties. The information derived from the present study shows that GaAs_1−xN_x (0?x?0.05) properties may have an important optoelectronic applications in infrared and mid-infrared spectral regions.     

First-principles study on the metallic antiferromagnet Co[PhPO3]·H2O

The electronic structure and the magnetic properties of transition metal phosphonate Co(PhPO₃)·H₂O have been studied by first-principles within the density-functional theory (DFT) and the full potential linearized augmented plane wave (FP-LAPW) method. The total energy, the total magnetic moment, the atomic spin magnetic moments and the density of states(DOS) of Co(PhPO₃)·H₂O were all calculated. The calculations reveal that the title compound is a metallic antiferromagnet and has a metallic ferromagnetic metastable state, which are in good agreement with the experiment. The spin magnetic moment of Co(PhPO₃)·H₂O is about 4.93 _μB${\mu }_{\mathrm{B}}$ per molecule, and it is mainly assembled at the cobalt atom, at the same time, with a little contribution from the P, O1, O2, O3.     

Doping in silicon nanocrystals: An ab initio study of the structural, electronic and optical properties

There are experimental evidences that doping control at the nanoscale can significantly modify the optical properties with respect to the pure systems. This is the case of silicon nanocrystals (Si-nc), for which it has been shown that the photoluminescence (PL) peak can be tuned also below the bulk Si band gap by properly controlling the impurities, for example by boron (B) and phosphorus (P) codoping. In this work, we report on an ab initio study of impurity states in Si-nc. We consider B and P substitutional impurities for Si-nc with a diameter up to 2.2 nm. Formation energies (FEs), electronic, optical and structural properties have been determined as a function of the cluster dimension. For both B-doped and P-doped Si-nc the FE increases on decreasing the dimension, showing that the substitutional doping gets progressively more difficult for the smaller nanocrystals. Moreover, subsurface impurity positions result to be the most stable ones. The codoping reduces the FE strongly favoring this process with respect to the simple n-doping or p-doping. Such an effect can be attributed to charge compensation between the donor and the acceptor atoms. Moreover, smaller structural deformations, with respect to n-doped and p-doped cases, localized only around the impurity sites are observed. The band gap and the optical threshold are largely reduced with respect to the undoped Si-nc showing the possibility of an impurity-based engineering of the Si-nc PL properties.     

Structural phase transition of boron nitride compound

The full-potential band-structure scheme based on the linear combination of overlapping nonorthogonal local-orbital (FPLO) is used. The crystal potential and density are represented as a lattice sum of local overlapping nonspherical contributions. The energetic transitions of BN of zinc-blende and wurtzite structures are calculated using the band structure scheme. The energy gap at ambient pressure is found to be indirect for the two structures. The structural properties of two structures of BN are (obtained from the total energy calculations) and the total density of states are calculated. The phase transition parameter of BN is investigated. The ionicity character of BN has been calculated to test the validity of our recent models. The results are in reasonable agreement with experimental and other theoretical results.     

Semi-spectral Chebyshev method in quantum mechanics

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. The purpose of this work is first to provide the necessary tools and subsequently examine the efficiency of this method in quantum mechanical applications. Restricting our interest to time-independent two-body problems, we obtained the continuous and discrete spectrum solutions of the underlying Schrödinger or Lippmann-Schwinger equations in both, the coordinate and momentum space. In all of the numerically studied examples we had no difficulty in achieving the machine accuracy and the semi-spectral method showed exponential convergence combined with excellent numerical stability.     

The electronic structure and the ferromagnetic intermolecular interactions in the crystal of TEMPO radicals

Based on the generalized gradient approximation, full potential linearized augmented plane wave (FP-LAPW) calculations have been performed to study the electronic band structure and the intermolecular ferromagnetic (FM) interactions for the two TEMPO radicals 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1) and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2). The total and the partial density of states and the atomic spin magnetic moments are calculated and discussed. The calculation revealed that the two TEMPO radicals have the intermolecular FM interactions, and the spontaneous magnetic moment is 1.0 μ_B per molecule of each crystal, which is in good agreement with the experimental value. It is found that the unpaired electrons in these compounds are localized in a molecular orbital constituted primarily of π* (NO) orbital, and the main contribution of the spin magnetic moment comes from the NO-free radical. The origin of FM is also studied in detail.     

The electronic structure and the ferromagnetic properties of the organic radical 4-methacryloyloxy-2,2,6,6-tetramethyl-1-piperidinyloxyl (MOTMP)

The ab initio method of the full potential linearized augmented-plane-wave has been used to study the electronic band structure and the ferromagnetic (FM) properties of the organic radical MOTMP. The total and the partial density of states and the atomic spin magnetic moments are calculated. The calculation revealed that MOTMP has a stable ferromagnetic ground state and the spin magnetic moment is 1.0 μ_B per molecule, which is in good agreement with the experimental value. It is found that the unpaired electrons in this compound are localized in a molecular orbital constituted primarily of π*(NO) orbital and the main contribution of the spin magnetic moment comes from the NO free radical. It is also found that there exists ferromagnetic intermolecular interaction in the compound.     

Sylvester theorem and the multichannel transfer matrix method for arbitrary transverse potential profile inside a wave guide

Based on the Sylvester and Frobenius theorems, we drastically enhance the feasibility of the transfer-matrix approach to deal with problems involving a large number of propagating and interfering modes, which require the solution of coupled differential equations and the evaluation of functions of matrix variables. We report closed formulas for the spectral decomposition of this type of functions. As specific example, besides the calculation of simple and well-known 1D one channel transfer matrices, we derive the multi-channel transfer matrix for an electron gas in the presence of a transverse electric field.