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.

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.

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。

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.

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.

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.

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.

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.

Combined Electromagnetic and Drift Diffusion Models for Microwave Semiconductor Device

In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.

Nano-Electronic Simulation Software (NESS): A Novel Open-Source TCAD Simulation Environment

This paper presents the latest status of the open source advanced TCAD simulator called Nano-Electronic Simulation Software(NESS)which is currently under development at the Device Modeling Group of the University of Glasgow.NESS is designed with the main aim to provide an open,flexible,and easy to use simulation environment where users are able not only to perform numerical simulations but also to develop and implement new simulation methods and models.Currently,NESS is organized into two main components:the structure generator and a collection of different numerical solvers;which are linked to supporting components such as an effective mass extractor and materials database.This paper gives a brief overview of each of the components by describing their main capabilities,structure,and theory behind each one of them.Moreover,to illustrate the capabilities of each component,here we have given examples considering various device structures,architectures,materials,etc.at multiple simulation conditions.We expect that NESS will prove to be a great tool for both conventional as well as exploratory device research programs and projects.

New progress in the principle of nonequilibrium statistical physics

In recent years, a new fundamental equation of nonequilibrium statistical physics was proposed in place of the Liouville equation. That is the anomalous Langevin equation in (?) space or its equivalent Liouville diffusion equation of time-reversal asymmetry. This equation reflects that the form of motion of particles in statistical thermody-namic systems has the drift-diffusion duality and the law of motion of statistical thermodynamics is stochastic in essence, but does not obey the Newton equation of motion, though it is also constrained by dynamics. The stochastic diffusion of the particles is the microscopic origin of macroscopic irre-versibility. Starting from this equation, the BBGKY diffusion equation hierarchy was presented, the hydrodynamic equations, such as the generalized Navier-Stokes equation, the mass drift-diffusion equation and the thermal conductivity equation have been derived succinctly. The unified description of all three level equations of microscopic, kinetic and hydrodynamic

On fundamental equation of statistical physics (II)--Nonequilibrium entropy and its evolution equation

Some derivations based on the anomalous Langevin equation in Liouville space (i.e. Γ space) or its equivalent Liouville diffusion equation of time reversal asymmetry are presented. The time rate of change, the balance equation, the entropy flow, the entropy production and the law of entropy increase of Gibbs nonequilibrium entropy and Boltzmann nonequilibrium entropy are rigorously derived and presented here. Furthermore, a nonlinear evolution equation of Gibbs nonequilibrium entropy density and Boltzmann nonequilibrium entropy density is first derived. The evolution equation shows that the change of nonequilibrium entropy density originates from not only drift, but also typical diffusion and inherent source production. Contrary to conventional knowledge, the entropy production density σ ≥0 everywhere for all the inhomogeneous systems far from equilibrium cannot be proved. Conversely, σ may be negative in some local space of such systems.

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.