Solving Poisson Equation Research Articles

MEASUREMENT OF THE BAND OFFSET IN GexSi1-x/Si SINGLE QUANTUM WELL BY USING SINGLE FREQUENCY ADMITTANCE SPECTROSCOPY

A single frequency admittance spectroscopy technique is introduced for determining the band discontinuity on Si/GexSi1-x/Si single quantum well (SQW). By using this method, the more accurate experimental results can be obtaind from a single frequency admittance spectrum. For an alloy with composition x=0.33，we get the activation energy Ea＝0.20eV. In order to obtain the value of the band offset，it is necessary to determine the position of Fermi level which depends on the dopam concentration inside and outside the well, the band offset of hetero-interface and temperature. By solving Poisson equation, we get the energy band diagram and Fermi level of the test sample. It is shown that the Fermi level lies about 40 meV above the top of valance band in the well. And due iv the carrier transfer at the hetero-interface, the carrier concentration (about ２×１０17ｃｍ－３) in the well is one order large than dopant concentration(1×１０16ｃｍ－３). The energy bands at two sides of the interfaces are bent by about 0.006 eV in the well and O.11eV in the barrier, hence the valance band offset can be calculated as 0.16eV. The accuracy of this technique can also be verified from reconstruction of C-T and G-T curves by cumputer simulation.

Parallel Computation of a Two-Dimensional Flow Field Using the MAC Methods.

This paper describes the basic issues in parallel computation of computational fluid dynamics (CFD) which are analyzed with a parallel computer. The parallel computer used is a cellular array processor called the AP 1000, operated by Fujitsu Parallel Computing Research Facilities. This paper is concerned with the adaptation of a Poisson equation solver, based on the successive over-relaxation method (SOR), to parallel computation. The convergence and relaxation factors of the SOR and the Red-Black SOR are examined. The optimum relaxation factor of the SOR decreases in the parallel computation ; while a high value of relaxation factor can be retained in the Red-Black SOR. Consequently, the Red-Black SOR is found to be a more effective solver in parallel computation. The present paper deals with parallel computation by means of the MAC. SMAC and HSMAC methods applied to a cavity flow. The computed field is decomposed into several domains. Each domain is assigned to one processor. With the methods tested, a high efficiency could be obtained by the present algorithms.

Application of an improved boundary element method on the problem of elastic torsion

An improved boundary element method has been used in analyzing and calculating the problems of the torsion of a prismatic bar with elliptical cross-section. In this paper the calculated results correspond with the values of boundary element method. However, the quantity of data required by the improved boundary element method is much less than that required by boundary element method, and the calculating time will be greatly reduced. Therefore, the procedure of this paper is an economical and efficient numerical computational way for solving Poisson equation problem.

Particle-method solution of two-dimensional convection-diffusion equations

We present a new method for solving two-dimensional convection-dominated convection-diffusion equations containing spatially and temporally localized source terms. The method uses grid-free transport: particles which carry point values of the concentration gradient move by convection and undergo random-walk to simulate diffusion. No numerical diffusion is introduced. Equations for the evolution of the gradient values are solved. The concentration is recovered from the particle data by solving Poisson equations. The method is applied to problems in rotational and elongational flow fields. Numerical results demonstrating convergence of the method are presented.

Optimizations of Fuzzy Controller for Solving Poisson Equations with Fast Convergence.

Fuzzy control was applied to speed up the convergence of a Poisson equation solver for the numerical calculations of incompressible fluid. The optimizations of the control rule were carried out by means of a hybrid method of the conjugate gradient method and the improved random walk method. The residual of the equation and the relaxation parameter are employed as input for the controller. It is found that this method is effective in obtaining fast convergence. Moreover, it is clarified that this control does not affect the bifurcation characteristics of the solution. The changes in optimized relaxation parameter are similar to Bang-Bang control.

Bipolar-Complementary-Metal-Oxide-Semiconductor (BiCMOS) Technology with Polysilicon Self-Aligned Bipolar Devices

An advanced bipolar-complementary-metal-oxide-semiconductor (BiCMOS) technology providing uncompromised high-performance, double polysilicon self-aligned (PSA) n-p-n bipolar and 1.25 µm gate length CMOS transistors is described. The polysilicon self-aligned-BiCMOS technology (PSA-BiCMOS) is intended for high-speed logic circuit operation at 5 V, where a high level of circuit integration and power consumption is involved. Features include vertical n-p-n transistors with a self-aligned n+ polysilicon emitter and p+ polysilicon base. The CMOS transistor features n+ polysilicon gates and lightly doped drain (LDD) NMOSFET. A process simulator, Stanford University process engineering models (SUPREM III) and device simulator, Poisson and continuity equation solver (PISCES II) were used to optimize the process steps and to enhance device characteristics, respectively. The performance of N- and PMOS transistors is comparable to those of a conventional CMOS process. The driving capability of CMOS and PSA-BiCMOS was compared according to fan-out. Compared to CMOS, PSA-BiCMOS has good driving capability from about 2.5 fan-out and PSA-BiCMOS with 1.25 µm N- and PMOS transistors and a bipolar transistor with 2 µm emitter width exhibits an average ring oscillator delay of 6.25 ns/stage at 1 pF load capacitance at 5 V.

Electro-optic mode-displacement silicon light modulator

A new type of guided-wave electro-optical intensity modulator is proposed and analyzed. The waveguide consists of an N-type Si core layer on a P-type Si substrate. Foward bias on the N+-N-P-P+ diode decreases the refractive index of the core and displaces the fundamental guided mode downward into the substrate. However, the mode is not extinguished because the substrate is bounded by a P+ contact. A spatial filter at the output converts the mode displacement into optical intensity modulation. A Poisson and continuity equation solver and multilayer waveguide simulation were used to obtain numerical estimates of mode displacement in a realistic structure.

Charged collected by diffusion from an ion track under mixed boundary conditions

Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be governed by an ambipolar diffusion equation with temporally constant and spatially uniform carrier lifetime and diffusion coefficient. Present results apply to a normally incident track but could easily be generalized to arbitrary track direction. The collected charge is found to depend on track length and on the electrostatic capacitance, rather than the area, of the sink. Theoretical predictions are compared to the results of a numerical simulation called the Poisson and Continuity Equation Solver (PISCES) for three cases and are found to agree within a factor of two in the worst case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Direct analytical methods for solving Poisson equations in computer vision problems

Direct analytical methods are discussed for solving Poisson equations of the general form Delta u=f on a rectangular domain. Some embedding techniques that may be useful when boundary conditions (obtained from stereo and occluding boundary) are defined on arbitrary contours are described. The suggested algorithms are computationally efficient owing to the use of fast orthogonal transforms. Applications to shape from shading, lightness and optical flow problems are also discussed. A proof for the existence and convergence of the flow estimates is given. Experiments using synthetic images indicate that results comparable to those using multigrid can be obtained in a very small number of iterations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Numerical analysis of nonequilibrium electron transport in AlGaAs/InGaAs/GaAs pseudomorphic MODFETs

Nonequilibrium electron transport in InGaAs pseudomorphic MODFETs has been analyzed with the moment equations approach. In the model, the momentum and energy balance equations for the two-dimensional electrons in the InGaAs channel are solved with relaxation times generated from a Monte Carlo simulation. The two-dimensional electron wave functions and the quantized state energies in the InGaAs quantum well are calculated exactly from the Schrodinger equation along the direction perpendicular to the quantum well. Also included is a two-dimensional Poisson equation solver. In the calculation, all of the equations are solved iteratively until a self-consistent solution is achieved. The simulation results for a realistic device structure with a 0.5- mu m recessed gate show a significant overshoot velocity of 4.5*10/sup 7/ cm/s at a drain bias of 1.0 V. Electron temperature reaches a peak value of around 2500 K under the gate. In energy transport, the diffusive component of the energy flux is found to be dominant in the high-field region. >

Deducing the Wind from Vorticity and Divergence

Abstract The horizontal wind field may be deduced from the vorticity and divergence by solving Poisson equations for the velocity potential and streamfunction or, more directly, by the solution of a single Poisson equally accurate. If the domain is of limited extent, boundary conditions must be specified. It is sufficient to prescribe a single component of the boundary velocity. Methods which use both components overdetermine the solution and may not converge in general.

Asymptotic Approximation and Perturbation Stream Functions in Viscous Flow Calculations

An asymptotic approximation technique is shown to substantially decrease the number of interations necessary for the accurate computation of steady solutions for viscous incompressible flows. A numerical study of flows exterior to a circular cylinder indicates that the technique reduces the required number of iterations by a factor of 10. The flux formulation of the vorticity stream function solution for the flow of a viscous incompressible fluid external to a circular cylinder requires the solution of the Poisson equation for the stream function. The use of the FACR (1), fast direct Poisson equation solver leads to serious errors in the computation of the stream function near the cylinder. However it is shown that these errors are eliminated through the introduction of a perturbation stream function.

Parallel marching Poisson solvers

The paper presents parallel algorithms for solving Poisson equation at N2 mesh points. The methods based on marching techniques are structured for efficient parallel realization. Using orthogonal decomposition properties of arising matrices, the algorithms can be formulated in terms of transformed vectors. On a MIMD computer with not more than N processors, the computations can be performed in horizontal slices with minimal synchronization requirements. Considering an SIMD machine with N2 processors, the complexity bound O(log N) has been achieved, whereby the single marching requires 10 log N steps only.

Finite difference procedure for solution of poisson equation over complex domains with Neumann boundary conditions

A generalized finite difference scheme for solving Poisson equation over multiply connected domain bounded by irregular boundaries at which Neumann boundary conditions are specified, is presented in this paper. The method used to treat the Neumann condition is a six-point gradient approximation method given by Greenspan[6]. The method is generalized to treat all types of grid intersections with the boundary. An efficient computational procedure is devised by eliminating the calculations at the boundary during the interations. The scheme is applied to the problem of forced convection heat transfer in a fully developed laminar flow through seven and nineteen rod-cluster assemblies. Fluid properties are assumed to be uniform. In arriving at the fast converging and efficient method from computational point of view, different iterative techniques, overrelaxation methods and boundary treatments were tried. The results of computations and the computer times are reported in the present paper.

A Poisson equation solver for rectangular or annular regions

AbstractA FORTRAN subroutine is presented which solves the system of simultaneous linear equations associated with the finite difference representation of the Poisson equation for rectangular or annular regions. The code is arranged to require minimum storage, and all possible operations involving known zeros and ones are suppressed. Single subscripting is employed to minimize execution time.

Electrical potential of an asymmetric membrane

Abstract A theory is proposed on the transmembrane potential caused by a membrane with asymmetrical distribution with respect to the surface charges of the membranes. The transmembrane potential is calculated by solving Poisson equation for the asymmetric membrane-electrolyte system, for both cases of linearized Poisson equation and nonlinearized Poisson equation. For the linear case, the magnitude of the transmembrane potential is proportional to the difference between two surface charge densities. However, for the nonlinearized case, the magnitude of the potential is smaller than that for the linearized case, and is no longer proportional to the difference between two surface charge densities of the membrane.

Large plane deformations of thin elastic sheets of neo-Hookean material

Es werden grosse ebene Verformungen dünner elastischer Scheiben aus Neo-Hookeschem Material betrachtet und eine Methode der sukzessiven Substitutionen entwickelt, um Probleme im Rahmen der zweidimensionalen Theorie endlicher ebener Spannungszustände zu lösen. Die erste Näherung wird durch lineare Randwertprobleme für zwei harmonische Funktionen bestimmt, und sie wird asymptotisch angenähert für sehr grosse Dehnungen in der Ebene der Scheiben. Die zweite und die höheren Annäherungen werden durch Lösung Poissonscher Gleichungen gewonnen. Es werden verschiedene Beispiele behandelt, und für rotationssymmetrische Verformungen wird gute übereinstimmung zwischen den Näherungen und den exakten Lösungen gefunden.