Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

SEMICLASSICAL LIMIT FOR BIPOLAR QUANTUM DRIFT-DIFFUSION MODEL

Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.

Weak solutions to one-dimensional quantum drift-diffusion equations for semiconductors

The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.

ASYMPTOTIC BEHAVIOR OF THE DRIFT-DIFFUSION SEMICONDUCTOR EQUATIONS

This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) denned by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.

On Global Boundedness of Solutions for the Drift-diffusion Semiconductor Equations

This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.

The Semiclassical Limit in the Quantum Drift-Diffusion Equations with Isentropic Pressure

The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.

The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model

The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.

The Bipolar Quantum Drift-diffusion Model

A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassieal limit describes the relation between quantum and classical drift-diffusion models, Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.

Quasi-neutral limit of the drift-diffusion model for semiconductors with general sign-changing doping profile

The quasi-neutral limit of time-dependent drift diffusion model with general sign-changing doping profile is justified rigorously in super-norm (i.e., uniformly in space). This improves the spatial square norm limit by Wang, Xin and Markowich.

半导体drift-diffusion模型的局部间断Galerkin方法及数值模拟

考虑半导体drift-diffusion(DD)模型一维和二维问题的局部间断Galerkin(LDG)方法,并进行数值模拟。模拟一维问题时,在浓度变化剧烈的部分采用细网格,在浓度变化平缓的地方采用粗网格,并与均匀网格的数值模拟进行比较,实现了在非均匀剖分下节省空间剖分单元数并加快了运行速度的目的。模拟二维问题时,采用了Dirichlet和Neumann相结合的边界。数值结果验证了LDG方法的稳定性。

Existence of Global Attractor for the One-Dimensional Bipolar Quantum Drift-Diffusion Model

In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.

Asymptotic Behavior of Solutions of the Bipolar Quantum Drift-Diffusion Model in the Quarter Plane

In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.

Mixed Layer Problem of a Three-Dimensional Drift-Diffusion Model for Semiconductors

The quasineutral limit and the mixed layer problem of a three-dimensional drift-diffusion model is discussed in this paper. For the Neumann boundaries and the general initial data, the quasineutral limit is proven rigorously with the help of the weighted energy method, the matched asymptotic expansion method of singular perturbation problem and the entropy production inequality.

Dirichlet-Neumann Problem for Unipolar Isentropic Quantum Drift-Diffusion Model

This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.

The Semiclassical Limit in the Quantum Drift-Diffusion Model

Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.

A POSITIVITY-PRESERVING FINITE ELEMENT METHOD FOR QUANTUM DRIFT-DIFFUSION MODEL

In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi levels.We propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction equations.The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations.Moreover,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi levels.The Poisson equation of electrical potential is solved with standard Lagrangian finite elements.We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete problem.Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.

Asymptotic Behavior of Solutions for the One-Dimensional Drift-Diffusion Model in the Quarter Plane

In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.

Study of the Discharge Mode in Micro-Hollow Cathode

In this study, micro-hollow cathode discharge （MHCD） is investigated by a fluid model with drift-diffusion approximation. The MHC device is a cathode/dielectric/anode sandwich structure with one hole of a diameter D=200 um. The gas is a Ne/Xe mixture at a pressure p=50-500 Torr. The evolutions of the discharge show that there are two different discharge modes. At larger pD the discharge plasma and high density excited species expand along the cathode surface and, a ringed discharge mode is formed. At smaller pD, the discharge plasma and the excited species expand along the axis of the cathode aperture to form a columnar discharge.

EXISTENCE OF WEAK SOLUTIONS TO A DEGENERATE STEAD-STATE SEMICONDUCTOR EQUATIONS

In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is （）（s） = s~α（α 〉 1）. We present existence results for general nonlinear diffhsivities for the degenerate Dirichlet-Neumann mixed boundary value problem.

Asymptotic Behavior of Global Smooth Solution of 1-D Quasineutral Drift Diffusion Model for Semiconductors

In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close to equilibrium）of the problem converge to the unique stationary solution.