Poisson Equation

The Diffusion Poisson Coupled Model (DPCM) is presented to modelling the oxidation of a metal covered by an oxide layer. This model is similar to the Point Defect Model and the Mixed Conduction Model except for the potential profile which is not assumed but calculated in solving the Poisson equation. This modelling considers the motions of two moving interfaces linked through the ratio of Pilling-Bedworth. Their locations are unknowns of the model. Application to the case of iron in neutral or slightly basic solution is discussed. Then, DPCM has been first tested in a simplified situation where the locations of interfaces were fixed. In such a situation, DPCM is in agreement with Mott-Schottky model when iron concentration profile is homogeneous. When it is not homogeneous, deviation from Mott-Schottky model has been observed and is discussed. The influence of the outer and inner interfacial structures on the kinetics of electrochemical reactions is illustrated and discussed. Finally, simulations for the oxide layer growth are presented. The expected trends have been obtained. The steady-state thickness is a linear function of the applied potential and the steady-state current density is potential independent.

Numerical solution techniques for the pressure Poisson equation (which plays two distinct roles in the formulation of the incompressible Navier-Stokes equations) are investigated analytically, with a focus on the influence of the boundary conditions adopted. Solutions obtained for two cases of the inviscid stagnation problem of point flow using Dirichlet boundary conditions are presented in graphs and compared with solutions obtained using Neumann boundary conditions and a consistent finite-difference procedure on staggered grids: these solutions are shown to be identical, confirming the result of Gresho and Sani (1987).

The development of a new Smoothed Particle Hydrodynamics (SPH) method, called Adaptive Smoothed Particle Hydrodynamics (ASPH), generalized for cosmology and coupled to the Particle Mesh (PM) method for solving the Poisson Equation, for the simulation of galaxy and large-scale structure formation, will be described. The accurate numerical simulation of the highly nonlinear phenomena of shocks and caustics which occur generically in the process of structure formation requires enormous dynamic range and resolution. Previously existing numerical methods require substantial modification in order to achieve the required resolution with current computer technology. The ASPH method incorporates new, adaptive, anisotropic smoothing and shock-tracking algorithms, which significantly enhance the resolving power of the• SPH method. We describe tests of ASPH versus SPH against the difficult cosmological pancake collapse problem. All cosmological hydro methods should be required to reproduce this test. High resolution 2D simulations of galaxy and large-scale structure formation in the Hot Dark Matter (HDM) model are presented using ASPH, showing that ASPH can resolve pancake shocks with fewer than 40 particles per pancake per dimension.

The Caldeira-Leggett Hamiltonian describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira-Leggett model and the linearized Vlasov-Poisson equation are analyzed, and it is shown that the damping in the Caldeira-Leggett model is analogous to that of Landau damping in plasmas (Landau, 1946 [1]). An invertible linear transformation (Morrison and Pfirsch, 1992 [18]; Morrison, 2000 [19]) is presented that converts solutions of the Caldeira-Leggett model into solutions of the linearized Vlasov-Poisson system.

This paper presents a novel physics-based analytical
TSV model that allows fast and accurate design
space exploration of signal propagation and
attenuation properties in 3D ICs, and represents a
useful tool for circuit designers and process
engineers. A through silicon via(TSV), is a vertical
interconnection method between chips and also is the
critical enabling technology for three-dimensional
integrated circuits (3D ICs). The model equations are
based on simple process data including physical
dimensions, passivation thickness, substrate doping,
and TSV type without requiring full access to process
parameters of a particular TSV technology. Working
the other way around, by setting the parasitic
threshold voltage and minimum MOS capacitance of
a specific TSV, the model can provide a list of
process specifications. The model has been validated
against measured results published in literature. Our
experiments show that TSV parasitic MOS capacitor
threshold voltage and minimum capacitance values
computed using the aforementioned model are within
25% and 5 % of measured data. The resulting
complex RLC model, taking into account the
coupling effects between neighboring TSVs as well,
has been experimentally validated under DC and
high-frequency AC conditions. Moreover, timing
libraries compatible with conventional EDA tools
have been generated to run realistic timing analysis
for 3D stacked integrated circuits, such as 3D I/Os.

We study the liquid structure and solvation forces of dense monovalent electrolytes (LiCl, NaCl, CsCl, and NaI) in a nanometer slab-confinement by explicit-water molecular dynamics (MD) simulations, implicit-water Monte Carlo (MC) simulations, and modified Poisson-Boltzmann (PB) theories. In order to consistently coarse-grain and to account for specific hydration effects in the implicit methods, realistic ion-ion and ion-surface pair potentials have been derived from infinite-dilution MD simulations. The electrolyte structure calculated from MC simulations is in good agreement with the corresponding MD simulations, thereby validating the coarse-graining approach. The agreement improves if a realistic, MD-derived dielectric constant is employed, which partially corrects for (water-mediated) many-body effects. Further analysis of the ionic structure and solvation pressure demonstrates that nonlocal extensions to PB (NPB) perform well for a wide parameter range when compared to MC simulations, whereas all local extensions mostly fail. A Barker-Henderson mapping of the ions onto a charged, asymmetric, and nonadditive binary hard-sphere mixture shows that the strength of structural correlations is strongly related to the magnitude and sign of the salt-specific nonadditivity. Furthermore, a grand canonical NPB analysis shows that the Donnan effect is dominated by steric correlations, whereas solvation forces and overcharging effects are mainly governed by ion-surface interactions. However, steric corrections to solvation forces are strongly repulsive for high concentrations and low surface charges, while overcharging can also be triggered by steric interactions in strongly correlated systems. Generally, we find that ion-surface and ion-ion correlations are strongly coupled and that coarse-grained methods should include both, the latter nonlocally and nonadditive (as given by our specific ionic diameters), when studying electrolytes in highly inhomogeneous situations.

Silicon-based devices are currently the most attractive group because they are functioning at room temperature and can be easily integrated into conventional silicon microelectronics. There are many models and simulation programs available to compute CV curves with quantum correction [Choi C-H, This work deals with the simulation of electron transfer through SiO 2 barrier of metal-oxide-semiconductor structure (MOS). The carrier density is given by a self consistent resolution of Schro¨dinger and Poisson equations and then the MOS capacitance is deduced and compared with results available in literature. As it is well known, the MOS capacitance-voltage profiling provides a simple determination of structure parameters. The extracted tunnel oxide thickness and substrate doping are compared with those used in the simulation. For the purpose to investigate the electron tunnelling through the barrier, we have used the transfer matrix approach. Using I-V simulations, we have shown that the traps in SiO 2 matrix have a drastic influence on electron tunnelling through the barrier. The trap-assisted contribution to the tunnelling current is included in many models [Maserjian J, Zamani N. this is the basis for the interpretation of stress induced leakage current (SILC) and breakdown events. Memory effect becomes typical for this structure. We have studied the I-V dependence with trap parameters. r

The stress inversion method is developed to find a stress field which satisfies the equation of equilibrium for a body in a state of plane stress. When one stress-strain relation is known and data on the strain distribution on the body and traction along the boundary are provided, the method solves a well-posed problem, which is a linear boundary value problem for Airy's stress function, with the governing equation being the Poisson equation and the boundary conditions being of the Neumann type. The stress inversion method is applied to the Global Positioning System (GPS) array data of the Japanese Islands. The stress increment distribution, which is associated with the displacement increment measured by the GPS array, is computed, and it is found that the distribution is not uniform over the islands and that some regions have a relatively large increment. The elasticity inversion method is developed as an alternative to the stress inversion method; it is based on the assumption of linear elastic deformation with unknown elastic moduli and does not need boundary traction data, which are usually difficult to measure. This method is applied to the GPS array data of a small region in Japan to which the stress inversion method is not applicable. To cite this article: M. Hori et al., C. R. Mecanique 336 (2008). Résumé Méthode d'inversion des contraintes et analyse des données GPS. La méthode d'inversion est développée pour trouver un champ de contraintes satisfaisant les équations d'équilibre pour un corps en situation de contrainte plane. La relation entre contrainte et déformation étant connue et les données de distribution de déformation sur le corps et de traction sur le bord étant fournies, la méthode résout un problème bien posé, qui consiste en un problème aux limites linéaire pour la fonction de contrainte d'Airy, comprenant l'équation de Poisson et des conditions aux limites de type Neumann. La méthode d'inversion est appliquée aux données GPS (Global Positioning System) concernant les îles japonaises. Les incréments de contraintes associés aux incréments de déplacements mesurés par le système GPS sont calculés, et l'on trouve que leur distribution n'est pas uniforme sur les îles, certaines régions présentant un incrément relativement grand. La méthode d'inversion élastique est développée comme alternative à la méthode d'inversion des contraintes ; elle est fondée sur l'hypothèse d'une déformation linéaire élastique avec des coefficients d'élasticité inconnus, et ne requiert pas de données concernant les tractions au bord, généralement difficilement mesurables. La méthode est appliquée aux données GPS d'une petite région du Japon pour laquelle la méthode d'inversion des contraintes n'est pas utilisable. Pour citer cet article : M. Hori et al., C. R. Mecanique 336 (2008).

We present a second-order accurate algorithm for solving the free-space Poisson's equation on a locally-refined nested grid hierarchy in three dimensions. Our approach is based on linear superposition of local convolutions of localized charge distributions, with the nonlocal coupling represented on coarser grids. The representation of the nonlocal coupling on the local solutions is based on Anderson's Method of Local Corrections and does not require iteration between different resolutions. A distributed-memory parallel implementation of this method is observed to have a computational cost per grid point less than three times that of a standard FFT-based method on a uniform grid of the same resolution, and scales well up to 1024 processors.

The pseudo-MOS transistor (Psi-MOSFET characteristics) is a simple and successful technique for the monitoring of silicon-on-insulator (SOI) wafer quality. To characterize modern ultrathin films, a reconsideration and review of Psi-MOSFET physics and models is required. Selected numerical simulations are presented, which shed light on the intriguing features governing Psi-MOSFET characteristics. Updated models accounting for the density of interface states and

We focus on transport of electron spins, which spin-polarized currents can be controlled and manipulated via the electron energy and momentum. We study in this paper the electronic properties of ferromagnetic phase of a multilayer ferromagnetic semiconductor in the mean-field and effective mass approximations, as a result of the magnetic interaction between holes and Mn ions, the magnetic layers acts as potential barriers for holes with spin-up, and as potential wells for the inverse spin polarization. As an example we calculate the dependence of hole density and the spin polarization in terms of the band offset v w which describes the difference in electronegativity between the Mn and GaAs atoms. Our calculations are performed using a self-consistent procedure to solve Schrödinguer and Poisson equations taking into account the coulomb interaction between holes. q

This paper presents a new methodology for the deformation of soft objects by drawing an analogy between Poisson equation and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by the Poisson equation. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. A method is presented to derive the internal forces from the potential energy distribution. This proposed methodology not only deals with large-range deformations, but also accommodates both isotropic and anisotropic materials by simply changing the constitutive coefficients. Examples are presented to demonstrate the efficiency of the proposed methodology.

We have studied the time-dependent development of electric double-layers (ionic sheaths) in saline solutions by simultaneously solving the sodium and chlorine ion continuity equations coupled with Poisson's equation in one dimension. The study of the effects of time-varying electric fields in solution is relevant to the possible health effect of radio-frequency electric fields on cells in the human body and to assessing the potential of using external electric fields to orient proteins for attachment to surfaces for biosensing applications. Our calculations, for applied voltages of 10-175 mV between the electrode and the solution, predict time scales of ∼0.1-110 µs for the formation of double-layers in solutions of concentration between 0.001 and 1.0 M. We develop an empirical equation that can predict the double-layer formation time to within 10% over this wide parameter range. The method has been validated by comparing the solutions obtained, once the program has run to a steady state, with the standard non-linear Poisson-Boltzmann equations. Excellent agreement is found with the Gouy-Chapman solution of the non-linear Poisson-Boltzmann equation. Thus the method is not restricted in accuracy and applicability as is the case for the linear Poisson-Boltzmann equation. The method can also provide solutions for cases where there are orders of magnitude changes in the ion densities; this has not been the case for previous studies where small perturbation analysis has been employed. The method developed here can readily be extended to two and three dimensions using time-splitting methods.

The authors present a method for calculating the electrostatic potential directly in a straightforward manner. While traditional methods for calculating the electrostatic potential usually involve solving the Poisson equation iteratively, the authors obtain the electrostatic interaction potential by performing direct numerical integration of the Coulomb-law expression using finite-element functions defined on a grid. The singularity of the Coulomb operator is circumvented by an integral transformation and the resulting auxiliary integral is obtained using Gaussian quadrature. The three-dimensional finite-element basis is constructed as a tensor ͑outer͒ product of one-dimensional functions, yielding a partial factorization of the expressions. The resulting algorithm has, without using any prescreening or other computational tricks, a formal computational scaling of O͑N 4/3 ͒, where N is the size of the grid. The authors show here how to implement the method for efficiently running on parallel computers. The matrix multiplications of the innermost loops are completely independent, yielding a parallel algorithm with the computational costs scaling practically linearly with the number of processors.

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is

An analytical threshold voltage model for doublegate MOSFETs with localized charges is developed. From the 2-D Poisson's equation with parabolic potential approximation, a compact threshold voltage model is derived. The proposed model is then verified with a 2-D device simulator. The model can be used to investigate hot-carrier-induced device degradation for various device dimensions and various charge distributions. Index Terms-Double-gate (DG) MOSFETs, hot-carrier effects (HCEs), localized charge, surface potential, threshold voltage.

A symbolic procedure for deriving various finite difference approximations for the three-dimensional Poisson equation is described. Based on the software package Mathematica, we utilize for the formulation local solutions of the differential equation and obtain the standard second-order scheme (7-point), three fourthorder finite difference schemes (15-point, 19-point, 21-point), and one sixth-order scheme (27-point). The symbolic method is simple and can be used to obtain the finite difference approximations for other partial differential equations.

A two-dimensional (2-D) analytical model for the surface potential variation along the channel in fully depleted silicon-on-insulator MOSFETs is developed .Our Approach to solve poisson's equation using suitable boundary conditions, results high accuracy to calculate the potential of the channel as compare to various approaches. A Simple and accurate analytical expression for surface potential in channel are derived. The proposed model will help to reduce Short Channel Effect, Drain Induced Barrier Lowering in Fully Depleted SOI MOSFETs etc

A tutorial 2D MATLAB code for solving elliptic diffusion-type problems, including Poisson's equation on single patch geometries, is presented. The basic steps of Isogeometric Analysis are explained and two examples are given. The code has a very lean structure and has been kept as simple as possible, such that the analogy but also the differences to traditional finite element analysis become apparent. It is not intended for large-scale problems.

An approach to determine the optical modal gain spectra in multiple quantum-well semiconductor lasers based on InP in terms of the current at electrodes is presented. The link between the current at the electrodes and the density of carriers inside each quantum well was provided by rate equations with the inclusion of carrier transport effects. Description of hole dispersion is based on a 4 × 4 Luttinger-Kohn Hamiltonian and was done with the electrostatic effects of the carrier charges. Electrostatic effects were included via a self-consistent solution of electron and hole wave equations and the Poisson equation. The optical gain for the TE (transverse electric) mode has been determined with the inclusion of non-Markovian effects, Coulombic enhancement, and band-gap renormalization. The theoretical approach was compared with experimental measurements of the optical gain on a laser structure consisting of four quantum wells using the Hakki-Paoli method. The important role played by the leakage current was revealed when the results were compared.

In this paper we propose a new approach to the study of integrable cases based on intensive computer methods' application. We make a new investigation of Kovalevskaya and Goryachev -Chaplygin cases of Euler -Poisson equations and obtain many new results in rigid body dynamics in absolute space. Also we present the visualization of some special particular solutions.

La evaluación final se realizó por medio de la interpretación estratigráfica y estructural de los PayShales arrojando como resultado la zona 4 al NW del área de estudio como la mejor para profundizar la evaluación de un yacimiento del tipo no convencional.

Carrier concentration profiles of two-dimensional electron gases are investigated in wurtzite, Ga-face and N-face heterostructures used for the fabrication of field effect transistors. Analysis of the measured electron distributions in heterostructures with AlGaN barrier layers of ...

In the present paper, a two-dimensional (2-D) analytical model for graded channel fully depleted cylindrical/surrounding gate MOS-FET (GC FD CGT/SGT) has been developed by solving the Poisson's equation in cylindrical coordinates. An abrupt transition of silicon film doping at the interface has been assumed and the effects of the doping and the lengths of the high and low doped regions have been taken into account. The model is used to obtain the expressions of surface potential and electric field in the two regions. The analysis is extended to obtain the expressions for threshold voltage (V th ) and subthreshold swing. It is shown that a graded doping profile in the channel leads to suppression of short channel effects (SCEs) like threshold voltage roll-off, drain induced barrier lowering (DIBL) and hot carrier effects. The results so obtained have been compared with simulated results obtained using the device simulator ATLAS 3D and are found to be in good agreement.

A drain-current model for undoped symmetric double-gate MOSFETs is proposed. Channel-length modulation and drain-induced barrier lowering are modeled by using an approximate solution of the 2-D Poisson equation. The new model is valid and continuous in linear and saturation regimes, as well as in weak and strong inversions. Excellent agreement was found with Silvaco-ATLAS simulations. Index Terms-Compact device modeling, double gate (DG), MOSFET, short-channel effects.

In this paper, we present a full 3-D real-space quantum-transport simulator based on the Green's function formalism developed to study nonperturbative effects in ballistic nanotransistors. The nonequilibrium Green function (NEGF) equations in the effective mass approximation are discretized using the control-volume approach and solved self-consistently with the Poisson equation in order to obtain the electron and current densities. An efficient recursive algorithm is used in order to avoid the computation of the full Green function matrix. This algorithm, and the parallelization scheme used for the energy cycle, allow us to compute very efficiently the current-voltage characteristic without the simplifying assumptions often used in other quantum-transport simulations. We have applied our simulator to study the effect of surface roughness and stray charge on the I D -V G characteristic of a 6-nm Si-nanowire transistor. The results highlight the distinctly 3-D character of the electron transport, which cannot be accurately captured by using 1-D and 2-D NEGF simulations, or 3-D mode-space approximations.

A new formulation is introduced for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH). The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection. Unlike earlier approaches used to simulate incompressible flows with SPH, the pressure is not a thermodynamic variable and the Courant condition is based only on fluid velocities and not on the speed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per time-step. Efficiency comparisons show that the projection method has a significant potential to reduce the overall computational expense compared to weakly compressible SPH, particularly as the Reynolds number, Re, is increased. Simulations using this SPH projection technique show good agreement with finite-difference solutions for a vortex spin-down and Rayleigh-Taylor instability. The results, however, indicate that the use of an approximate projection to enforce incompressibility leads to error accumulation in the density field.

Turbulent flow measurements were conducted between two bluff bodies set in uniform flow in tandem arrangement. The velocity field obtained with PIV was averaged with respect to either time or phase of periodic pressure oscillation induced by vortex shedding from the bluff body, i.e., Reynolds decomposition or three-level decomposition. The Reynolds stresses caused by periodic fluid motion was found excessively large compared with those related to turbulent fluctuations in the entire flow field in observation. The PIV data were used to solve the discrete Poisson equation of instantaneous pressure. The effect of organized vortex motion caused strong correlations between velocity and pressure gradient when observed from the framework of the Reynolds averaging.

A quasi-two-dimensional charge transport model of AlGaN/GaN high electron mobility transistor has been developed that is capable of accurately predicting the drain current as well as small-signal parameters such as drain conductance and device transconductance. This model built up with incorporation of fully and partially occupied subbands in the interface quantum well, combined with a numerically self-consistent solution of the Schro¨dinger and Poisson equations. In addition, nonlinear polarization effects, self-heating, voltage drops in the ungated regions of the device are also taken into account. Also, to develop the model, the accurate two-dimensional electron gas mobility and the electron drift velocity have been used. The calculated model results are in very good agreement with existing experimental data for Al m Ga 1Àm N/GaN HEMT devices with Al mole fraction within the range from 0.15 to 0.50, especially in the linear regime of I-V curve. r

In this paper we propose the finite difference method for the second-order elliptic equation in the L-shape domain. The scheme is based on the non-overlap domain decomposition method. We use the coarse mesh difference scheme at the interface grids and fine mesh difference scheme at the interior mesh points. We derive the error estimate O(h 2 + H 3 ) with mesh size h and coarse mesh size H. Then we discuss some iterative methods for our scheme and derive the upper bound of the convergent rate 1 À H. Finally we present some numerical experiments.

This work presents a Multilevel Schwarz Shooting method for the numerical solution of the Poisson equation, using a five point finite difference molecule, and subject to Dirichlet boundary conditions, which arises in two dimensional incompressible flow simulations. The iterative simple shooting algorithm utilized has optimal complexity, but becomes unstable when the problem size is increased. In this work, this limitations is overcome using a domain decomposition technique, more specifically, the alternating Schwarz method, which is used to generalize the iterative multiple shooting approach in the partial differential equation (PDE) context. In order to accelerate the convergence of the algorithm a multilevel approach is used. The resulting iterative algorithm has optimal complexity and is scalable in terms of problem size. Results of computational experiments are presented for the Poisson equation and for the two dimensional incompressible Navier-Stokes equation using the stream function-vorticity formulation.

A high-order accurate, finite-difference method for the numerical solution of the incompressible Navier–Stokes equations is presented. Fourth-order accurate discretizations of the convective and viscous fluxes are obtained on staggered meshes using explicit or compact finite-difference formulas. High-order accuracy in time is obtained by marching the solution with Runge–Kutta methods. The incompressibility constraint is enforced for each Runge–Kutta stage iteratively either

We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic devices. The mathematical model consists of two coupled partial differential equations for the elastic wave propagation and the electric field, respectively, in anisotropic piezoelectric media. These equations are discretized by the finite element method in space and by a finite difference method in time. The latter method yields a convenient numerical decoupling of the governing equations. We describe how a computer implementation can utilize the decoupling and via object-oriented programming techniques reuse independent codes for the Poisson equation and the linear time-dependent elasticity equation. First we apply the simulator to a simplified model problem for verifying the implementation, and thereafter we show that the methodology is capable of simulating a real-world case from nanotechnology, involving surface acoustic waves in a geometrically non-trivial device made of Gallium Arsenide.

L'oggetto principale della prova finale è la teoria degli operatori m-dissipativi su spazi di Banach.
Nella tesi si analizzano alcune proprietà di tale classe di operatori. Il caso più studiato in letteratura è quello degli operatori m-dissipativi definiti su un dominio denso su spazi di Hilbert. Alcuni esempi di operatori m-dissipativi sono forniti dall'operatore Laplaciano con diversi domini di definizione.
Consideriamo ora il problema di evoluzione generale, soffermandoci nei casi particolari in cui A è un operatore autoaggiunto o antisimmetrico in uno spazio di Hilbert.
Nella nostra trattazione introdurremo la teoria dei semigruppi di contrazione, con particolare attenzione al semigruppo di contrazione  generato da un operatore m-dissipativo con dominio denso, analizzando un importante risultato, il Teorema di Hille-Yosida-Phillips, utile nello studio delle equazioni di evoluzione.
In Natura, molti fenomeni di propagazione sono descritti da equazioni di evoluzione, per esempio l'equazione del calore che modellizza il trasporto dell'energia termica in un mezzo omogeneo: essa è il più semplice esempio di equazione di diffuusione che analizziamo nella prova finale come applicazione della teoria dei semigruppi.
La trattazione è basata sui Capitoli 2-3 del libro "An Introduction to Semilinear Evolution Equations" di Thierry Cazenave e Alain Haraux [4].

The effects of Schottky gate on behavior of two-dimensional electron gas (2DEG) density and two-dimensional electron mobility (2DEM) in AlGaN/GaN heterostructures with different Al mole fraction in AlGaN barrier and its different thickness have been studied. The sheet carrier concentration, NS, was determined self-consistently from the coupled Schrö dinger and Poisson equations, by assuming a real model for heterostructures and by using Numerov's method.

We describe an interactive, computer-assisted framework for combining parts of a set of photographs into a single composite picture, a process we call "digital photomontage." Our framework makes use of two techniques primarily: graph-cut optimization, to choose good seams within the constituent images so that they can be combined as seamlessly as possible; and gradient-domain fusion, a process based on Poisson equations, to further reduce any remaining visible artifacts in the composite. Also central to the framework is a suite of interactive tools that allow the user to specify a variety of high-level image objectives, either globally across the image, or locally through a painting-style interface. Image objectives are applied independently at each pixel location and generally involve a function of the pixel values (such as "maximum contrast") drawn from that same location in the set of source images. Typically, a user applies a series of image objectives iteratively in order to create a finished composite. The power of this framework lies in its generality; we show how it can be used for a wide variety of applications, including "selective composites" (for instance, group photos in which everyone looks their best), relighting, extended depth of field, panoramic stitching, clean-plate production, stroboscopic visualization of movement, and time-lapse mosaics.

The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated long-range potential. This latter model can be formalized, in the continuum limit, as a field theory of scalar matter in interaction with a gauge field, in the su (2) algebra. This description has already offered the analytical derivation of the sinh-Poisson equation, which was known to govern the stationary coherent structures reached by the Euler fluid at relaxation. In order this formalism to become a familiar theoretical instrument it is necessary to have a better understanding of the physical meaning of the variables and of the operations used by the field theory. Several problems will be investigated below in this respect.

In the present study, we determine using Maple software the exact numerical solution of Poisson's equation in a Schottky barrier junction according to three different approaches. First, we consider the simple case where the space charge zone is depleted and the doping impurities are fully ionized. Then we treat the case where the space charge zone is non-depleted and the doping impurities are fully ionized. Finally, we solve rigorously the more general case where the space charge zone is non-depleted and the doping impurities are partially ionized. We use two different methods to solve the problem. In the former one, the distance of each point to the junction is calculated as a function of its potential. In the second one, we use a finite difference scheme to solve the Poisson's equation. The calculations may be integrated into a course on semiconductor devices to show the use of Maple capabilities in the resolution of the second order non-linear differential equation governing the potential in electronic devices.

Let P(E) be the space of probability measures on a measurable space (E, E). In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure π ∈ P(E). Non-linear Markov kernels (e.g. Del ; Del ) K : P(E) × E → P(E) can be constructed to admit π as an invariant distribution and have superior mixing properties to ordinary (linear) MCMC kernels. However, such non-linear kernels cannot be simulated exactly, so, in the spirit of particle approximations of Feynman-Kac formulae (Del Moral 2004), we construct approximations of the non-linear kernels via Self-Interacting Markov Chains (Del Moral & Miclo 2004) (SIMC). We present several non-linear kernels and demonstrate that, under some conditions, the associated self-interacting approximations exhibit a strong law of large numbers; our proof technique is via the Poisson equation and Foster-Lyapunov conditions. We investigate the performance of our approximations with some simulations, combining the methodology with population-based Markov chain Monte Carlo (e.g. Jasra et al. ). We also provide a comparison of our methods with sequential Monte Carlo samplers when applied to a continuous-time stochastic volatility model.

Based on nonpinned surface potential concept, in this paper we present a compact single-piece and complete I-V model for submicron lightly-doped drain (LDD) MOSFETs. The physics-based and analytical model was developed using the drift-diffusion equation and based on the quasi two-dimensional (2-D) Poisson equation. The important short-channel device features: drain-induced-barrier-lowering (DIBL), channel-length modulation (CLM), velocity saturation, and the parasitic series source and drain resistances have been included in the model in a physically consistent manner. In this model, the LDD region is treated as a bias-dependent series resistance, and the drain-voltage drop across the LDD region has been considered in modeling the DIBL effect. This model is smoothly-continuous, valid in all regions of operation and suitable for efficient circuit simulation. The accuracy of the model has been checked by comparing the calculated drain current, conductance and transconductance with the experimental data

We have calculated the subband structure and confinement potential of modulation-doped Ga1−xAlxAs-GaAs symmetric double quantum wells a function of the doping concentration. Electronic properties of this structure are determined by solving the Schrödinger and Poisson equations selfconsistently. To understand the exchange correlation potential effects on the band bending and subband populations, this potential has been included in the calculation at 0 K and, at room temperature. We find that at low doping concentrations the effect of the exchange correlation potential is more pronounced on the subband populations.