Linear Potential Approximation Research Articles

Precise determination of surface band bending in Ga-polar n-GaN films by angular dependent X-Ray photoemission spectroscopy

We present a systematic study of surface band bending in Ga-polar n-GaN with different Si doping concentrations by angular dependent X-ray photoelectron spectroscopy (ADXPS). The binding energies of Ga 3d and N 1 s core levels in n-GaN films increase with increasing the emission angle, i. e., the probing depth, suggesting an upward surface band bending. By fitting the Ga 3d core level spectra at different emission angles and considering the integrated effect of electrostatic potential, the core level energy at the topmost surface layer is well corrected, therefore, the surface band bending is precisely evaluated. For moderately doped GaN, the electrostatic potential can be reflected by the simply linear potential approximation. However, for highly doped GaN samples, in which the photoelectron depth is comparable to the width of the space charge region, quadratic depletion approximation was used for the electrostatic potential to better understand the surface band bending effect. Our work improves the knowledge of surface band bending determination by ADXPS and also paves the way for studying the band bending effect in the interface of GaN based heterostructures.

On the influence of the electron-velocity spread in a beam on the mechanism of Cherenkov beam–plasma interaction

The instability of an electron beam in cold plasma is considered in the linear potential approximation with different velocity-distribution functions of beam electrons. It is demonstrated that the mechanism of beam instability in plasma changes as the electron-velocity spread is increased: the hydrodynamic single-particle instability mode evolves into the hydrodynamic collective mode or the single-particle kinetic one. Instability growth rates in different modes are determined analytically and numerically.

An accurate modeling of piezoelectric smart beams with first-order shear deformation theory

A finite element model for piezoelectric smart beam in extension mode based on First-order Shear Deformation Theory (FSDT) with an appropriate through-thickness distribution of electric potential is presented. Accuracy of piezoelectric finite element formulations depends on the selection of assumed mechanical and electrical fields. Most of the conventional FSDT-based piezoelectric beam formulations available in the literature use linear through-thickness distribution of electric potential which is actually nonlinear. Here, a novel quadratic profile of the through-thickness electric potential is proposed to include the nonlinear effects. The results obtained show that the accuracy of conventional formulations with linear through-thickness potential approximation is affected by the material configuration, especially when the piezoelectric material dominates the beam cross section. It is shown that the present formulation gives the same level of accuracy for all regimes of material configurations in the beam cross section. Also, a modified form of the FSDT displacements is employed, which utilizes the shear angle as a degree of freedom instead of section rotation. Such a FSDT displacement field shows improved performance compared to the conventional field. The present formulation is validated by comparing the results with ANSYS 2D simulation. The comparison of results proves the improved efficiency and accuracy of the present formulation over the conventional formulations.

Quantum-mechanical calculation of carrier distribution in MOS accumulation and strong inversion layers

We derive a statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrödinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.

Effects of atomic and magnetic order on electronic transport in Pd-rich Pd-Fe alloys

The transport properties of Pd-rich PdFe alloys are investigated as a function of the atomic and magnetic order on the L2${}_{1}$ (Cu${}_{3}$Au) lattice. The residual resistivity, anisotropic magnetoresistance (AMR), and anomalous Hall effect are calculated from first principles in their dependence on the degree of atomic order. The calculations are based on the relativistic generalization of the transport Kubo-Greenwood approach as formulated in the framework of the first-principles tight-binding linear muffin-tin orbital (TB-LMTO) method and coherent potential approximation (CPA). The effect of the thermal magnetic disorder on the resistivity (thermal magnetoresistance) and AMR has been also studied using the disordered local moment approach based on the CPA. It is found that the experimentally observed fast decrease of AMR ratio with temperature can be mostly ascribed to the spin disorder effects. Our results are in an overall good agreement with available experimental data.

Electronic Energies in Delta Doped AlGaAs/GaAs Heterostuctures

The band bending of the potential at the AlGaAs/GaAs interface increases with the electrons concentration in the GaAs channel. This band bending is often ignored in the theoretical calculation of the electronic energies and a linear potential approximation was used. This led to imprecise energy values and occupied subband configurations. We have taken account of the band bending in the subband energies calculation. The potential expression was considered as sum of linear and quadratic terms. The quadratic term was considered as a time independent perturbation and the electronic energies were corrected to the first order. We have calculated the Fermi energy for different electronic concentrations. The relation between the Fermi energy and the electronic concentration at the interface leads to the desired configuration of the occupied subbands. When the fundamental subband is only occupied, the characteristics of those heterostructures are best enhanced. The corresponding electronic concentration was calculated. The theoretical results were used for the determination of the active electron concentration in two AlGaAs/GaAs heterostructures.

Energy diffusion controlled reaction rate of reacting particle driven by broad-band noise

The energy diffusion controlled reaction rate of a reacting particle with linear weak damping and broad-band noise excitation is studied by using the stochastic averaging method. First, the stochastic averaging method for strongly nonlinear oscillators under broad-band noise excitation using generalized harmonic functions is briefly introduced. Then, the reaction rate of the classical Kramers' reacting model with linear weak damping and broad-band noise excitation is investigated by using the stochastic averaging method. The averaged Ito stochastic differential equation describing the energy diffusion and the Pontryagin equation governing the mean first-passage time (MFPT) are established. The energy diffusion controlled reaction rate is obtained as the inverse of the MFPT by solving the Pontryagin equation. The results of two special cases of broad-band noises, i.e. the harmonic noise and the exponentially corrected noise, are discussed in details. It is demonstrated that the general expression of reaction rate derived by the authors can be reduced to the classical ones via linear approximation and high potential barrier approximation. The good agreement with the results of the Monte Carlo simulation verifies that the reaction rate can be well predicted using the stochastic averaging method.

Large amplitude spatial fluctuations in the boundary region of the Bose–Einstein condensate in the Gross–Pitaevskii régime

Abstract The Gross–Pitaevskii regime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas–Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations.

Correlated Doping in Semiconductors: the Role of Donors in III-V Diluted Magnetic Semiconductors

We investigate the compositional dependence of the total energy of the mixed crystals (Ga,Mn)As co-doped with As, Sn, and Zn. Using the ab initio linear muffin-tin orbital coherent potential approximation method we find acorrelation between the incorporation of acceptors (Mn, Zn) and donors (Sn, antisite As). In particular, the formation energy of Asia is reduced by approximately 0.1 eV in the presence of Mn, and vice versa. This leads to the self-compensating behavior of (Ga,Mn)As.

Local kinetic-energy density of the Airy gas

The Airy gas model is used to derive an expression for the local kinetic energy in the linear potential approximation. The expression contains an explicit Laplacian term $\frac{2}{5}({\ensuremath{\Elzxh}}^{2}/2m){\ensuremath{\nabla}}_{\ensuremath{\mu}}^{2}(\mathbf{r})$ that, according to jellium surface calculations, must be a universal feature of any accurate local description. Applied to the noble gases the expression reduces the errors by a factor of $50$ over previous results obtained by the linear potential approximation.

Accuracy of Nonlinear Approximations in Spheroidal Collapse: Why Are Zeldovich‐Type Approximations Good?

Among various analytic approximations for the growth of density fluctuations in the expanding universe, the Zeldovich approximation and its extensions in a Lagrangian scheme are known to be better than other approximations, even in mildly nonlinear regimes. We compare analytic approximations with true density evolution in the presence of spheroidal symmetry. We consider Eulerian and Lagrangian perturbation theories up to third order, and frozen-flow and linear potential approximation. We also introduce the Pade approximation in the Eulerian scheme which improves usual perturbation theories. In the course of comparison, we clarify the reason why these Zeldovich-type approximations effectively work beyond the linear regime, with reference to the two following aspects of the problem: (1) the dimensionality of the system and (2) the Lagrangian scheme on which the Zeldovich approximation is grounded. We mention which of these two aspects supports the validity of the Zeldovich-type approximations. We also give a suggestion for a better approximation method beyond the Zeldovich type.

Loop Corrections in Nonlinear Cosmological Perturbation Theory

Using a diagrammatic approach to Eulerian perturbation theory, we analytically calculate the variance and skewness of the density and velocity divergence induced by gravitational evolution from Gaussian initial conditions, including corrections *beyond* leading order. Except for the power spectrum, previous calculations in cosmological perturbation theory have been confined to leading order (tree level)-we extend these to include loop corrections. For scale-free initial power spectra, the one-loop variance \sigma^2 = \sigma^2_l + 1.82 \sigma^4_l and the skewness S_3 = 34/7 + 9.8 \sigma^2_l, where \sigma_l is the rms fluctuation of the linear density field. We also compute loop corrections to the variance, skewness, and kurtosis for several non-linear approximation schemes, where the calculation can be easily generalized to 1-point cumulants of higher order and arbitrary number of loops. We find that the Zel'dovich approximation gives the best approximation to the loop corrections of exact perturbation theory, followed by the Linear Potential approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative agreement with the relative behavior of tree-level results. In LPA and FFA, loop corrections are infrared divergent for spectral indices n < 0; this is related to the breaking of Galilean invariance in these schemes.

Itinerant magnetism of disordered Fe-Co and Ni-Cu alloys in two and three dimensions.

The electronic structure and band magnetism of disordered ${\mathrm{Fe}}_{100\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$ and ${\mathrm{Ni}}_{100\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Cu}}_{\mathit{x}}$ bulk alloys and of corresponding disordered overlayers on an fcc Cu(001) substrate were studied by means of the first-principles tight-binding linear muffin-tin orbital coherent potential approximation method. For the Fe-Co system, we found that the composition dependence of the averaged and the local Fe magnetic moments is strongly affected by the dimensionality of the system while the local Co moments remain nearly constant. In the bulk bcc alloys, a nonmonotonic behavior of the averaged magnetization occurs due to the transition from weak to strong ferromagnetism. The averaged magnetization of the random overlayers depends linearly on the composition while the local Fe and Co moments are constant since the strong ferromagnetism is stabilized by the substrate throughout the whole composition range. For the Ni-Cu system, a transition from ferromagnetism to paramagnetism is found both in the bulk fcc alloys and in the overylayers. The ferromagnetism of the overlayers is reduced in comparison to the bulk systems of the same composition. The concentration trends of local densities of states, local numbers of electrons, and work functions are discussed.

Electronic structure, thermodynamic and thermal properties of Ni-Al disordered alloys from LMTO-CPA-DFT calculations

The fast linear muffin-tin orbital coherent potential approximation method allied with density functional theory (LMTO-CPA-DFT) is used to calculate electronic structure and cohesive properties of Ni-Al random alloys on an underlying FCC lattice in all concentration intervals. Binding curves obtained in the calculations are used in the Debye-Gruneisen analysis to determine thermal properties and temperature-dependent Connolly-Williams cluster interactions. The calculated lattice constants, bulk moduli, enthalpies and free energies of formation are in good agreement with experiment. The globally and locally relaxed cluster interactions are compared with the results obtained from the total energy-band calculations for elements and ordered phases.

Metal surface dipole moment and work function in the linear potential model

Jellium metal surface properties such as the surface dipole barrier and work function are studied in the linear potential approximation to the effective potential at the surface. The metal surface position and field strength are determined respectively by the requirement of overall charge neutrality and the constraintst on the electrostatic potential by the Budd-Vannimenus theorem. The calculations are primarily analytic and these properties are given in terms of the universal function of the field strength. The results obtained employing the Ceperley-Alder expression for the correlation energy closely approximate those of Lang and Kohn.

Metal Surface Dipole Moment and Work Function in the Linear Potential Model

Jellium metal surface properties such as the surface dipole barrier and work function are obtained in the linear potential approximation to the effective potential at the surface. The metal surface position and field strength are determined respectively by the requirement of overall charge neutrality and the constraint set on the electrostatic potential by the Budd-Vannimenus theorem. The calculations are primarily analytic and these properties are given in terms of universal functions of the field strength. The results obtained employing the Ceperly-Alder expression for the correlation energy closely approximate those of Lang and Kohn

Study of the kinetic energy density functional in the locally linear potential approximation

A kinetic energy density functional based on a locally linearized approximation for the potential has been investigated through calculation using accurate Hartree–Fock densities for several atoms. The integrated and the local values of this kinetic energy density as well as the local behavior of its functional derivative are compared with corresponding quantities for Hartree–Fock and other existing kinetic energy functionals including a newly suggested one. With an N-dependent correction factor, this functional shows better agreement.

The Effect of Many‐Electron Correlation on Photothresholds of Semiconductors and Valence Band Discontinuities at Heterojunctions

AbstractPhotothresholds of semiconductors are known to deviate by 3 to 4 eV from the predictions of one‐electron band theory. It is shown that these discrepancies are due to many‐electron correlation effects, in particular, to electronic relaxation. The corrections to photothresholds due to electronic relaxation are calculated by means of Green's function technique applying the linear shielded potential approximation to the exchange‐correlation self‐energy. Within the uncertainties of LCAO theories the calculated photothresholds of group IV, III‐V, and II‐VI semiconductors agree with experimental data. A simple physical picture of the correlation effect is provided. Relaxation corrections to valence band discontinuities from one‐electron band theories are also calculated.

Constant field approximation for the crystal-assisted pair-creation process

The electron-positron production rate for the newly predicted crystal-assisted pair creation process is proportinal to squared matrix elements. Each matrix element is governed by the overlap of a channeled electron wavefunction and the wavefunction of a positron which is repelled by the same channeling potential. Closed form expressions for these matrix elements can be obtained by linearizing the channeling potential in the neighborhood of the classical turning points. Results obtained from the linear potential approximation were compared with more accurate numerical results for photons directed along the 〈110〉 axis of diamond. Agreement to within a factor of two was obtained over a wide range of incident energies. These approximate calculations have been extended to yield predictions for the crystal-assisted pair production rate for a number of different crystals, different axis orientations, and a variety of temperatures.

Study of the exchange energy of an inhomogeneous electron gas at a surface

In this work we have studied the exchange energy property of an inhomogeneous electron gas at a jellium surface. The nonlocal surface exchange energy is determined exactly for the accurate set of single-particle wave functions generated within the linear-potential approximation to the effective potential at a surface, and written in terms of a universal function of the field strength. It is shown, that over the wide range of density profiles considered, this universal function increases by a factor of 6 as the profile is changed from rapidly to slowly varying. For a Hartree-Fock gas with bulk density such that $5&gt;~{r}_{s}&gt;~1$, the corresponding increase in the surface exchange energy is three orders of magnitude. The local density approximation (LDA) functional of the surface exchange energy is also determined for the same set of wave functions, and for the first time its convergence to the exact results as the density profile is made slowly varying demonstrated. It is shown that this LDA functional is a poor approximation for metallic densities, overstimating the exact results by 17-55%. The results of a previous calculation within the step-model approximation are also reinterpreted, and similar conclusions with regard to the inaccuracy of the LDA functional arrived at. The applicability of the nonlocal calculation of this work to the evaluation of other approximate nonlocal exchange energy functionals, and to the study of the inhomogeneous Hartree-Fock and fully correlated systems is also indicated.