Bond Orbital Approximation Research Articles

Effect of tensile strain on the electronic structure of Ge: A first-principles calculation

Taking the change of L-point conduction band valley degeneracy under strain into consideration, we investigate the effect of biaxially tensile strain (parallel to the (001), (110), and (111) planes) and uniaxially tensile strain (along the [001], [110], and [111] directions) on the electronic structure of Ge using density functional theory calculations. Our calculation shows that biaxial tension parallel to (001) is the most efficient way to transform Ge into a direct bandgap material among all tensile strains considered. [111]-tension is the best choice among all uniaxial approaches for an indirect- to direct-bandgap transition of Ge. The calculation results, which are further elaborated by bond-orbital approximation, provide a useful guidance on the optical applications of Ge through strain engineering.

Hückel transformation theory of ground state HF

In the elementary Hückel theory of ground state HF at its simplest valence level the two unknown parameters ∣ α p − α h ∣ and ∣ β∣ can be determined in terms of experimental bond dissociation energy and electric dipole moment. If some sp hybridization is admitted on F in a bond orbital approximation, optimization of the resulting Hückel energy against the hybridization parameter ω using 1-term SCF/STOs shows that little hybridization ( ω ≈ 8°) gives a 3% increase in the bond energy parameter ∣ β∣ and a 14% reduction in the value of the formal charges ∣ δ∣ on the interacting atoms.

Modeling of CdTe(1 1 1)B/Si(0 0 1) interfaces

Abstract A detailed numerical examination is performed of a model of the CdTe(1 1 1)B/Si(0 0 1) interface previously proposed by Sporken et al. Total energies of supercells simulating several interface atomic configurations are calculated employing the extended bond orbital approximation and approximated moments methods. Results suggest that the most stable interfaces are formed when the Si substrate contains single monolayer steps. This is consistent with the observation that small substrate miscut angles produce the highest-quality epilayers.

Elastic properties of semiconductors using universal tight-binding parameters.

Minimal-basis tight-binding theory, using free-atom term values and nearest-neighbor universal 1/${\mathit{d}}^{2}$ coupling, and an A/${\mathit{d}}^{3}$+B/${\mathit{d}}^{12}$ repulsion, is used to calculate elastic properties without further approximations. Specifically, the shear constants (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 and ${\mathit{c}}_{44}$ and the Kleinman internal-displacement parameter are calculated for diamond-structure and zinc-blende-structure semiconductors. Most are within 30% or so of experiment. Spin-orbit coupling is added and found not to make significant corrections. Addition of a Louie peripheral excited state considerably improves the conduction bands but has little effect upon the elastic properties. The transverse charge and the piezoelectric charge are calculated with the additional assumption that the only important charge transfers are between nearest neighbors. These charges are not in such good accord with experiment. Comparison with the predictions of the bond-orbital approximation to tight-binding theory for (${\mathit{c}}_{11}$-${\mathit{c}}_{12}$)/2 and the transverse charge suggests that the errors in that approximation are comparable to those of the tight-binding theory itself, small for the elastic constant but sizable for the transverse charge.

Exceptional solid-state properties of organic 2:1 donor–acceptor metals with integral charge transfer

The material properties of low-dimensional 2:1 donor (D)–acceptor (A) salts with integral mutual charge transfer (CT) are exceptional in the class of the synthetic metals. The electronic charge fluctuations in the majority component of D+2A− and A−2D+ compounds are of extremal character in the presence of strong electronic correlations. In the minority component the fluctuations are extensively suppressed. The corresponding solids are one-chain conductors. The charge fluctuations are investigated by a simple analytic model formulated on the basis of the local approach for the many-particle problem and the bond-orbital approximation for the independent-particle wave function. The Fermi surfaces of the D+2A− and A+2D− CT salts are effectively flat also for smaller anisotropy ratios. Structural phase transitions of the Peierls type leading to one-dimensional as well as two- and/or three-dimensional ordering are analyzed in a tight-binding framework. There exists a large range, where the one-dimensional dimerization is suppressed, but where n-dimensional (n=2, 3) ordering can still exist. Fermi-surface nesting in materials with smaller anisotropy ratios allows for the conservation of metastable solid-state configurations, i.e., configurations where the electron–lattice interaction is enhanced, but where a metal–insulator transition is suppressed. For the quasi-one-dimensional metals with D+2A− and A−2D+ stoichiometry it is shown that electronic correlations lead to a remarkable enhancement of the metal–insulator transition temperature TP. Experimental data available for the respective 2:1 CT salts can be rationalized by simple analytic models. A possible violation of particle–hole symmetry between D+2A− and A−2D+ compounds in their ability to stabilize a low-temperature superconducting ground state is suggested.

A comparative theoretical analysis of superconducting organic charge transfer salts and high- Tc cuprates

The normal- and superconducting-state properties of organic charge transfer (CT) salts and high- T c cuprates are compared. Fermi-surface (FS) nesting on nonplanar surfaces is possible in both classes of metals as a result of approximate particle-hole symmetry. The charge fluctuations 〈(Δ n 2 i )〉 in the corresponding solids are described by the method of the local approach in the many-particle representation and the bond orbital approximation in the independent-particle scheme. The electronic configurations in the above systems allow for a coincidence of sizeable electronic correlations and large charge fluctuations which are even of extremal character. A simple strong coupling scheme is used to calculate the superconducting transition temperature T c in organic superconductors and high- T c cuprates. The estimated T c values are of reliable accuracy. The different temperatures scales in the organic systems and the high- T c cuprates are prevailingly determined by the Debye-temperature of the corresponding solids. A conventional mechanism of the BCS-type seems to be consistent with the experimental data. A possible violation of particle-hole symmetry for the stabilization of a superconducting ground state can be explained qualitatively. Electronic prerequisites supporting superconductivity in organic CT salts are summarized.

Dispersion relations of low-energy branches in the vibrational spectrum of cleaved GaAs(110).

A realistic calculation of the low-frequency phonon spectrum of cleaved GaAs(110) is presented. Our calculation is based on Chadi's tight-binding theory for structural energies and the structural energies are simply determined by the bond-orbital approximation. A variety of interesting surface vibrational modes are found which agree well with the observation, in He-atom scattering experiments, of some acoustic branches of surface phonons.

Physical picture of electron correlations in three-center four-electron bonds

It is shown that the strong electron correlations of π electrons in the O3 molecule may be well understood in terms of a simple analytic model which is a natural extension of a bond orbital approximation to the case of a three-center bond. Electron correlations are here responsible for the increase of density at the central atom and for enhanced correlations at both terminal ones. This result is confirmed by a numerical calculation of the interatomic correlations by using a local ansatz imposed on a semiempirical selfconsistent field ground state. It is argued that the discussed increase of the bond polarity in the O3 molecule is a universal phenomenon for three-center bonds filled (on the average) by more than one electron per atom, as, for example within the CuO2 planes of Cu based perovskites.

A Model Study of Instabilities Present in the Mean-Field Description and in Linearized Correlation Schemes

Abstract In this work we discuss the cooperative occurrence of instabilities in the Hartree-Fock (HF) approximation and linearized correlation models. Both breakdown phenomena can be analyzed via eigenvalues of characteristic matrices. The well known HF instabilities follow from a quasidegeneracy between the symmetry-adapted mean-field state and singly excited configurations. Quasi-degeneracies between the HF wave function and doubly excited configurations restrict the applicability of linearized correlation models. In the theoretical calculations the method of the local approach (LA) has been employed to derive the correlated ground state. For a system of the general topology XH2 (X = C, Si, etc.) the bond orbital approximation (BOA) has been used to derive analytic formulae indicating the stability range of linearized correlation schemes. Numerical calculations on the basis of a simple model-Hamiltonian are given for the π systems C2H4 and C2H2, respectively, which have been studied as a function of the CC bondlength. The comparison of the respective numerical data indicates that both breakdown phenomena are enhanced via coupling terms between strongly correlated bonds.

A Simple Scheme for Studies of Surface Phonons of Covalent Semiconductors. I. Calculation of Force Constants

AbstractA framework is given for calculating and interpreting vibrational surface properties of covalent semiconductors. The bond orbital approximation (BOA) in a tight‐binding theory for electronic structural energies is developed and applied to deriving atomic force constants that are essential for calculating dynamical matrix and phonon dispersion relations in these systems. The method used connects force constants with electronic structure directly and is able to predict phonon spectra as well as the change of force constant at the surface. Some analytical expressions for force constant calculation are obtained for the first time with this semiempirical models. It is shown that the scheme is fairly simple, yet accurate enough within the frame of tight‐binding theory.

A simple method to calculate the correlation energy in molecules based on the bond orbital approximation

It is the main scope of this work to present a transparent numerical approach for the determination of interatomic correlation energies in molecules. The analysis is of model character, i.e. the presentation of quantitative numerical data is not intended. Our simple analytical method to calculate the correlation energy is based on the bond orbital approximation (BOA) for the mean-field ground state and on the local approach (LA) to electron correlation. The interatomic correlation energy is obtained as a sum of various intrabond and interbond contributions, for which simple analytic formulae are derived. In this way, the dependence of electron correlation on bond polarities, two-electron integrals and kinetic hopping elements becomes transparent. The remaining intra-atomic part of the correlation energy is described by analytic expressions which depend only on the total charge and the number of p and s electrons on a given atom. Therefore, the total correlation energy may be estimated by using the information available from the self-consistent field calculation. As an example, an application of the method to a number of molecules of the general topology X-Y≡Y-Z is presented. The correlation energies obtained in an analytic way agree rather well with those given by a direct numerical evaluation within the LA.

A SIMPLE APPROACH FOR THE CALCULATION OF FORCE CONSTANTS OF SEMICONDUCTORS——APPLICATION TO THE STUDY OF PHONONS AT THE GaAs(111)-2×2 SURFACE

An analytical expression for the force constants of semiconductors with arbitrary hybridization is derived by using the bond orbital approximation to simplify the calculation of electronic band structure energy of the system. This method is shown to be simple and effective by the comparison between the theoretical calculation and experimental results of phonon dispersion curves of several materials. Applying this method to the study of phonon at GaAs (111)-2×2 sarface, the dispersion curves of phonons that are strongly localized at the surface are obtained.

Electron correlations in molecules. III. Strength of electron correlations in localized and aromatic bonds of main-group atoms

We investigate electron correlations within a minimal basis of various chemical bonds formed by second- and third-row atoms and hydrogen. The effects of correlations are characterized by two quantities: (i) intrabond correlation energy ϵ corr and (ii) the correlation strength parameter Σ. The latter describes the relative suppression of the charge fluctuations within a bond. The quantities ϵ corr and Σ can be associated with chemical bonds due to the local nature of the correlation phenomenon. It is found that one may distinguish between different classes of chemical bonds which are characterized by similar values of Σ parameter within each class. For instance, all considered bonds between hydrogen and main-group atoms fall into one class. The homopolar bonds formed by the atoms of the third row are characterized by a weaker σ but stronger π correlation strength than the respective bonds of the second row. The strongest correlations are found in homopolar single π bonds of third-row atoms. A particular detailed discussion is given of heteropolar bonds. The electron correlations of aromatic π electrons are found to be considerably weaker than those within the corresponding localized bonds. For the SCF input of the correlation calculation a semi-empirical method is used. The bond orbital approximation allows for a transparent interpretation of the computational results.

Structural phase transition in SiO x

For the two structural phases of the geometrically and chemically disordered solid SiO x , i.e. the random-bonding and the random-mixture phase, the temperature-composition phase diagram is calculated in dependence on an ordering energy E o . It is shown that the random-bonding phase is the high-temperature structure of SiO x , which is metastable or even unstable at low temperatures, revealing there a spinodal decomposition into two coexisting components with different chemical compositions and random-mixture structure. The corresponding immiscibility dome has its highest point at the temperature T = 0.5 E o /k for x = 1 . The phase transition is of first order. The ordering energy E o depends on the interaction between the microscopic structural basic units, i.e. the Si-Si and Si-O-Si bonds, and is calculated in terms of the bond-orbital approximation. The value of E o does probably not exceed 0.15 eV. The results are in agreement with experimental experience. The predictions derived could induce systematic experimental investigations of the phase transition in SiO x and, especially, of its spinodal decomposition.

Transferability of interatomic correlation energies

A simple procedure is presented to estimate the interatomic correlation energy of a bond A-B on the basis of intrabond correlations of the homopolar parents A-A and B-B and the bond polarity of A-B. We use a local approach supplemented by a semiempirical mean-field Hamiltonian within the bond orbital approximation. The capability of the interpolation scheme is demonstrated for several molecules formed by main-group atoms.

π-bonded model of an oxygen-vacancy center in SiO2

Tight-binding total energy calculations of the two possible states of the neutral oxygen-vacancy center in SiO2 have been performed within the bond orbital approximation. It has been shown that the lowest energy state is realized by a transfer of one electron from a nonbonding p oxygen orbital (next to the vacancy) into an opposite silicon dangling hybrid, and then by the formation of a π bond between the remaining oxygen p electron and the nearest silicon dangling hybrid. The new π-bonded model of the oxygen-vacancy center is discussed and the results obtained are compared with experimental data. The most important aspect of this work is the demonstration that for defects in SiO2, the π interactions are very important and should not be neglected in describing the physics of many problems in SiO2.

Electron correlations in molecules. I Bond orbital approximation

A simple and fairly accurate approach to electron correlations in the ground state of molecules is presented. The two parts of electron correlations, inter- and intra-atomic correlations, are treated separately and by different methods. The interatomic correlations are studied by means of a variational local ansatz. It starts from the self-consistent field (SCF) ground state and optimizes the energy by the appropriate reduction of charge fluctuations. This procedure is qualitatively illustrated in the bond orbital approximation (BOA). It is found that the correlation energy decreases with increasing bond polarity α p, being proportional to the factor (1 – α 2 p) 5 2 . It is also shown that the contributions to the correlation energy due to one-particle excitations become important only in more strongly correlated polar bonds. The intraatomic correlations are obtained from an atoms-in-molecule-type of approach. It makes use of a population analysis of the correlated ground state wavefunction. The used probability distribution P( n), where n is the valence electron number, is found to be well approximated by a normal distribution. The advantages and limitations of the method are shortly discussed.

Electron correlations in the ground state of covalent semiconductors.

We describe a simple and transparent method for studying electronic correlations in the ground state of covalent semiconductors. The starting point is a single-determinantal ground-state wave function in the bond-orbital approximation. Electronic correlations are taken into account by applying a variational ansatz. Analytical expressions are obtained for the interatomic or bond correlation energy as well as for the pair-correlation function. Both are discussed in detail. The intra-atomic correlation energy is estimated in two different ways which give identical results. One is based on an ``atoms in solids'' method which requires a population analysis of the ground-state wave function, while the other is based on an analysis of the correlation energies of hydrocarbon molecules. The theory is applied to diamond, Si, Ge, and \ensuremath{\alpha}-Sn. The correlation-energy contributions to the cohesive energy and the radial force constant are discussed and compared with experimental data. By using a diagrammatic representation, a comparison is made with ground-state correlation-energy calculations which use the ``GW approximation'' of Hedin [Phys. Rev. 139, A796 (1965)].

New tight-binding parameters for covalent solids obtained using Louie peripheral states

Excited $s$ states are added to the minimal-basis tight-binding theory of covalent solids using Louie's perturbation approach. This brings the conduction bands into better accord with experiment without appreciably complicating the calculation of properties in the bond-orbital approximation. Universal interatomic matrix elements are obtained by fitting the free-electron bands, and then adjusted to accord with the bands of germanium. Bands based upon these interatomic matrix elements, and upon Hartree-Fock term values, are then compared with pseudopotential bands for Si, Ge, Sn, GaAs, InSb, ZnSe, and CdTe. A single set of metallic, covalent, and polar energies for $s{p}^{3}$ hybrids obtained from the new matrix elements are found to predict good values for both the dielectric and elastic properties; in contrast, two different sets were required for the two classes of properties in the earlier theory.

A model of interface states and charges at the Si-SiO2 interface: Its predictions and comparison with experiments

We develop a model for states and charges at the Si-SiO2 interface based on the expected existence at this interface of threefold coordinated Si atoms, strained Si-Si bonds, etc. The associated electronic states are studied by using a generalized bond orbital approximation (supplemented in some cases by multiband cluster Bethe lattice calculations), where the various configurations ofinterest are allowed to relax in order to minimize the energy of the system. It is shown that the reconstructing character of interface states so obtained has a number of interesting experimental implications, and in particular it is found that by including reconstruction effects one is able to understand and in some cases correlate many different experimental results. Among others, these include some observed metal-oxide-semiconductor device instabilities, the dependence of the interface density of states on the conductivity type of the semiconductor substrate, and the amphoteric character of interface states.