Schrodinger-Poisson equations without Ambrosetti-Rabinowitz condition

We prove the existence of ground state solutions for a stationary Schrodinger-Poisson equation in R(3). The proof is based on the mountain pass theorem and it does not require the Ambrosetti-Rabinowitz condition. (C) 2010 Elsevier Inc. All rights reserved.

A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

This study considers the solution of a class of linear systems related with the fractional Poisson equation (FPE) (−∇2)α/2φ=g(x,y) with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f(A)=A−α/2 on a vector b. For large, sparse, and symmetric positive definite matrices, the Lanczos approximation generates f(A)b≈β0Vmf(Tm)e1. This method works well when both the analytic grade of A with respect to b and the residual for the linear system are sufficiently small. Memory constraints often require restarting the Lanczos decomposition; however this is not straightforward in the context of matrix function approximation. In this paper, we use the idea of thick-restart and adaptive preconditioning for solving linear systems to improve convergence of the Lanczos approximation. We give an error bound for the new method and illustrate its role in solving FPE. Numerical results are provided to gauge the performance of the proposed method relative to exact analytic solutions.

MODELING HETEROSTRUCTURES WITH SCHRODINGER-POISSON-NAVIER ITERATIVE SCHEMES, EFFECT OF CARRIER CHARGE, AND INFLUENCE OF ELECTROMECHANICAL COUPLING

This paper presents a detailed investigation of the erects of piezoelectricity, spontaneous polarization and charge density on the electronic states and the quasi-Fermi level energy in wurtzite-type semiconductor heterojunctions. This has required a full solution to the coupled Schrodinger-Poisson-Navier model, as a generalization of earlier work on the Schrodinger-Poisson problem. Finite-element-based simulations have been performed on a A1N/GaN quantum well by using both one-step calculation as well as the self-consistent iterative scheme. Results have been provided for field distributions corresponding to cases with zero-displacement boundary conditions and also stress-free boundary conditions. It has been further demonstrated by using four case study examples that a complete self-consistent coupling of electromechanical fields is essential to accurately capture the electromechanical fields and electronic wavefunctions. We have demonstrated that electronic energies can change up to approximately 0.5 eV when comparing partial and complete coupling of electromechanical fields. Similarly, wavefunctions are significantly altered when following a self-consistent procedure as opposed to the partial-coupling case usually considered in literature. Hence, a complete self-consistent procedure is necessary when addressing problems requiring more accurate results on optoelectronic properties of low-dimensional nanostructures compared to those obtainable with conventional methodologies.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

We propose an alternative crack propagation algo- rithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algo- rithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equa- tions is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algo- rithm, we use five quasi-brittle benchmarks, all successfully solved.

Damage and fracture algorithm using the screened Poisson equation and local remeshing

We propose a crack propagation algorithm which is independent of particular constitutive laws and specific element technology. It consists of a localization limiter in the form of the screened Poisson equation with local mesh refinement. This combination allows the cap- turing of strain localization with good resolution, even in the absence of a sufficiently fine initial mesh. In addition, crack paths are implicitly defined from the localized region, cir- cumventing the need for a specific direction criterion. Observed phenomena such as mul- tiple crack growth and shielding emerge naturally from the algorithm. In contrast with alternative regularization algorithms, curved cracks are correctly represented. A staggered scheme for standard equilibrium and screened equations is used. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests.

A Computationally Efficient Generalized Poisson Solution for Independent Double-Gate Transistors

Previous techniques used for solving the 1-D Poisson equation ( PE) rigorously for long-channel asymmetric and independent double-gate (IDG) transistors result in potential models that involve multiple intercoupled implicit equations. As these equations need to be solved self-consistently, such potential models are clearly inefficient for compact modeling. This paper reports a different rigorous technique for solving the same PE by which one can obtain the potential profile of a generalized IDG transistor that involves a single implicit equation. The proposed Poisson solution is shown to be computationally more efficient for circuit simulation than the previous solutions.

Bipolar Poisson Solution for Independent Double-Gate MOSFET

We propose a new set of input voltage equations (IVEs) for independent double-gate MOSFET by solving the governing bipolar Poisson equation (PE) rigorously. The proposed IVEs, which involve the Legendre's incomplete elliptic integral of the first kind and Jacobian elliptic functions and are valid from accumulation to inversion regimes, are shown to have good agreement with the numerical solution of the same PE for all bias conditions.

Novel applications of BEM based Poisson level set approach

Accurate and efficient computation of the distance function d for a given domain is important for many areas of numerical modeling. Partial differential (e.g. HamiltonJacobi type) equation based distance function algorithms have desirable computational efficiency and accuracy. In this study, as an alternative, a Poisson equation based level set (distance function) is considered and solved using the meshless boundary element method (BEM). The application of this for shape topology analysis, including the medial axis for domain decomposition, geometric de-featuring and other aspects of numerical modeling is assessed. © 2011 Elsevier Ltd. All rights reserved.

The influence of 1 nm AlN interlayer on properties of the Al0.3Ga0.7N/AlN/GaN HEMT structure

The sheet carrier concentrations, conduction band profiles and amount of free carriers in the barriers have been determined by solving coupled Schrodinger and Poisson equation self-consistently for coherently grown Al0.3Ga0.7N/GaN and Al0.3Ga0.7N/AlN/GaN structures on thick GaN. The Al0.3Ga0.7N/GaN heterojunction structures with and without 1 nm AlN interlayer have been grown by MOCVD on sapphire substrate, the physical properties for these two structures have been investigated by various instruments such as Hall measurement and X-ray diffraction. By comparison of the theoretical and experimental results, we demonstrate that the sheet carrier concentration and the electrons mobility would be improved by the introduction of an AlN interlayer for Al0.3Ga0.7N/GaN structure. Mechanisms for the increasing of the sheet carrier concentration and the electrons mobility will be discussed in this paper. (C) 2007 Elsevier Ltd. All rights reserved.

Properties of AlyGa1-yN/AlxGa1-xN/AlN/GaN Double-Barrier High Electron Mobility Transistor Structure

Electrical properties of AlyGa1-yN/AlxGa1-xN/AlN/GaN structure are investigated by solving coupled Schrodinger and Poisson equation self-consistently. Our calculations show that the two-dimensional electron gas (2DEG) density will decrease with the thickness of the second barrier (AlyGa1-yN) once the AlN content of the second barrier is smaller than a critical value y(c), and will increase with the thickness of the second barrier (AlyGa1-yN) when the critical AlN content of the second barrier y(c) is exceeded. Our calculations also show that the critical AlN content of the second barrier y(c) will increase with the AlN content and the thickness of the first barrier layer (AlxGa1-xN).

Effect of spontaneous and piezoelectric polarization on intersubband transition in AlxGa1-xN-GaN quantum well

A self-consistent solution of conduction band profile and subband energies for AlxGa1-xN-GaN quantum well is presented by solving the Schrodinger and Poisson equations. A new method is introduced to deal with the accumulation of the immobile charges at the AlxGa1-xN-GaN interface caused by spontaneous and piezoelectric polarization in the process of solving the Poisson equation. The effect of spontaneous and piezoelectric polarization is taken into account in the calculation. It also includes the effect of exchange-correlation to the one electron potential on the Coulomb interaction. Our analysis is based on the one electron effective-mass approximation and charge conservation condition. Based on this model, the electron wave functions and the conduction band structure are derived. We calculate the intersubband transition wavelength lambda(21) for different Al molar fraction of barrier and thickness of well. The calculated result can fit to the experimental data well. The dependence of the absorption coefficient a on the well width and the doping density is also investigated theoretically. (C) 2004 American Vacuum Society.

Observations on subband electron properties in In0.65Ga0.35As/In0.52Al0.48As MM-HEMT with Si delta-doped on the barriers

Magneto-transport measurements have been carried out on a Si delta-doped In0.65Ga0.35As/In0.52Al0.48As metamorphic high-electron-mobility transistor with InP substrate in a temperature range between 1.5 and 60 K under magnetic field up to 13 T. We studied the Shubnikov-de Haas (SdH) effect and the Hall effect for the In0.65Ga0.35As/In0.52Al0.48As single quantum well occupied by two subbands and obtained the electron concentration and energy levels respectively. We solve the Schrodinger-Kohn-Sham equation in conjunction with the Poisson equation self-consistently and obtain the configuration of conduction band, the distribution of carriers concentration, the energy level of every subband and the Fermi energy. The calculational results are well consistent with the results of experiments. Both experimental and calculational results indicate that almost all of the delta-doped electrons transfer into the quantum well in the temperature range between 1.5 and 60 K.

Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.