Approximate methods for the solution of quantum wires and dots : Connection rules between pyramidal, cuboidal, and cubic dots

Energy eigenvalues of the electronic ground state are calculated for rectangular and triangular GaAs/Ga(0.6)Al(0.4)As quantum wires as well as for cuboidal and pyramidal quantum dots of the same material. The wire (dot) geometries are approximated by a superposition of perpendicular independent finite one-dimensional potential wells. A perturbation is added to the system to improve the approximation. Excellent agreement with more complex treatments is obtained. The method is applied to investigate the ground state energy dependence on volume and aspect ratio for finite barrier cubic, cuboidal, and pyramidal quantum dots. It is shown that the energy eigenvalues of cubes are equal to those of cuboids of the same volume and aspect ratio similar to one. In addition, a relationship has been found between the volumes of pyramidal quantum dots (often the result of self-assembling in strain layered epitaxy) and cuboidal dots with the same ground state energy and aspect ratios close to one. © 1999 American Institute of Physics

A model for time-dependent grain boundary diffusion of ions and electrons through a film or scale, with an application to alumina

A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern. Reactions with the environment constitute the boundary conditions and drive the transport between the surfaces. Time-dependent simulations solving the Poisson equation self-consistently with the Nernst-Planck flux equations for the mobile species are performed. In the resulting Poisson-Nernst-Planck system of equations, the electrostatic potential is obtained from the Poisson equation in its integral form by summation. The model is used to interpret alumina membrane oxygen permeation experiments, in which different oxygen gas pressures are applied at opposite membrane surfaces and the resulting flux of oxygen molecules through the membrane is measured. Simulation results involving four mobile species, charged aluminum and oxygen vacancies, electrons, and holes, provide a complete description of the measurements and insight into the microscopic processes underpinning the oxygen permeation of the membrane. Most notably, the hypothesized transition between p-type and n-type ionic conductivity of the alumina grain boundaries as a function of the applied oxygen gas pressure is observed in the simulations. The range of validity of a simple analytic model for the oxygen permeation rate, similar to the Wagner theory of metal oxidation, is quantified by comparison to the numeric simulations. The three-dimensional model we develop here is readily adaptable to problems such as transport in a solid state electrode, or corrosion scale growth

Finite pseudo orbit expansions for spectral quantities of quantum graphs

We investigate spectral quantities of quantum graphs by expanding them as sums over pseudo orbits, sets of periodic orbits. Only a finite collection of pseudo orbits which are irreducible and where the total number of bonds is less than or equal to the number of bonds of the graph appear, analogous to a cut off at half the Heisenberg time. The calculation simplifies previous approaches to pseudo orbit expansions on graphs. We formulate coefficients of the characteristic polynomial and derive a secular equation in terms of the irreducible pseudo orbits. From the secular equation, whose roots provide the graph spectrum, the zeta function is derived using the argument principle. The spectral zeta function enables quantities, such as the spectral determinant and vacuum energy, to be obtained directly as finite expansions over the set of short irreducible pseudo orbits.Comment: 23 pages, 4 figures, typos corrected, references added, vacuum energy calculation expande

Photoreflectance and surface photovoltage spectroscopy of beryllium-doped GaAs/AlAs multiple quantum wells

We present an optical study of beryllium delta-doped GaAs/AlAs multiple quantum well (QW) structures designed for sensing terahertz (THz) radiation. Photoreflectance (PR), surface photovoltage (SPV), and wavelength-modulated differential surface photovoltage (DSPV) spectra were measured in the structures with QW widths ranging from 3 to 20 nm and doping densities from 2×10(10) to 5×10(12) cm(–2) at room temperature. The PR spectra displayed Franz-Keldysh oscillations which enabled an estimation of the electric-field strength of ~20 kV/cm at the sample surface. By analyzing the SPV spectra we have determined that a buried interface rather than the sample surface mainly governs the SPV effect. The DSPV spectra revealed sharp features associated with excitonic interband transitions which energies were found to be in a good agreement with those calculated including the nonparabolicity of the energy bands. The dependence of the exciton linewidth broadening on the well width and the quantum index has shown that an average half monolayer well width fluctuations is mostly predominant broadening mechanism for QWs thinner than 10 nm. The line broadening in lightly doped QWs, thicker than 10 nm, was found to arise from thermal broadening with the contribution from Stark broadening due to random electric fields of the ionized impurities in the structures. We finally consider the possible influence of strong internal electric fields, QW imperfections, and doping level on the operation of THz sensors fabricated using the studied structures. © 2005 American Institute of Physic

Quantum box energies as a route to the ground state levels of self-assembled InAs pyramidal dots

A theoretical investigation of the ground state electronic structure of InAs/GaAs quantum confined structures is presented. Energy levels of cuboids and pyramidal shaped dots are calculated using a single-band, constant-confining-potential model that in former applications has proved to reproduce well both the predictions of very sophisticated treatments and several features of many experimental photoluminescence spectra. A connection rule between their ground state energies is found which allows the calculation of the energy levels of pyramidal dots using those of cuboids of suitably chosen dimensions, whose solution requires considerably less computational effort. The purpose of this work is to provide experimentalists with a versatile and simple method to analyze their spectra. As an example, this rule is then applied to successfully reproduce the position of the ground state transition peaks of some experimental photoluminescence spectra of self-assembled pyramidal dots. Furthermore the rule is used to predict the dimensions of a pyramidal dot, starting from the knowledge of the ground state transition energy and an estimate for the aspect ratio Q. © 2000 American Institute of Physics

Clear air turbulence

Research on forecasting, detection, and incidents of clear air turbulenc

A linear acoustic model for multi-cylinder IC engine intake manifolds including the effects of the intake throttle

This paper presents a linear acoustic model of a multi-cylinder intake manifold that can be used as part of a hybrid time/frequency domain method to calculate the intake wave dynamics of practical naturally aspirated engines. The method allows the user to construct a model of almost any manifold of complex geometry. The model is constructed as an assemblage of sub-models: (i) A model for a straight pipe with both ends open and through-flow. (ii) A model for an expansion chamber consisting of three lengths of pipe laid end-to-end: a narrow bore pipe expanding into a wide bore pipe contracting into a narrower bore pipe once more. (iii) A model of a side-branch, which includes a model for a straight pipe with one end closed and a model for the three way junction that joins the side-branch to a length of flow pipe. (iv) A model for an expansion with two (or more) side-branches, which combines the sub-models (i, ii, iii) into a multi-way (n-way) junction model. (v) A model for an intake throttle. Good agreement with measurement has been found for each sub-model when bench-tested in isolation and encouraging agreement has been found when many sub-models are used together to model a complex intake manifold on a running engine

Absorption in atomic wires

The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously treated to recover unitarity for the non-hermitian hamiltonians. In contrast to other models of parametrized scatterers we assemble explicit potentials profiles in the form of delta arrays, Poschl-Teller holes and complex Scarf potentials. The techniques developed provide analytical expressions for the scattering and absorption probabilities of arbitrarily long wires. The approach presented is suitable for modelling molecular aggregate potentials and also supports new models of continuous disordered systems. The results obtained also suggest the possibility of using these complex potentials within disordered wires to study the loss of coherence in the electronic localization regime due to phase-breaking inelastic processes.Comment: 14 pages, 15 figures. To appear in Phys. Rev.