A MIXED FINITE ELEMENT METHOD FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device is described by a system of three quasilinear partial differential equations. One is elliptic in form for the electric potential and the other two are parabolic in form for the conservation of electron and hole concentrations. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by a Galerkin method that applies a variant of the method of characteristics to the transport terms. Optimal order convergence analysis in L2 is given for the proposed method.     

IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

The transient behavior of a semiconductor device consists of a Poisson equa-tion for the electric potential and of two nonlinear parabolic equations for the electrondensity and hole density.The electric potential equation is discretized by a mixed finiteelement method. The electron and hole density equations are treated by implicit-explicitmultistep finite element methods. The schemes are very efficient. The optimal order errorestimates both in time and space are derived.     

非矩形区域上半导体问题的交替方向有限元方法

Transient behavior of semiconductor with heat-conduction on nonrectangular is studied using isoparametric elements and an approximation to the Jacobian of the isoparametric map.Concentration and heat-conduction equations are solved by alternating-direction methods and electric potential equation is approximated by finite element method.Optimal order error estimates in L^2 are demonstrated using the theory and technique of a prior estimate of differential equation.     

RESEARCH ANNOUNCEMENTS ON “STABILITY OF RAREFACTION WAVES OF THE COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM WITH LARGE INITIAL PERTURBATION”

<正>1 Introduction and Main Results In this paper,we study the dynamics of compressible viscous charged particles consisting of two-species particles (e.g.,ions and electrons) under the influence of the self-consistent electrostatic potential force in semiconductor device or plasma physics (cf.[1,6]) which is modeled by the compressible Navier-Stokes-Poisson system (called NSP system in the sequel for simplicity).     

UPWIND FINITE VOLUME SCHEMES FOR SEMICONDUCTOR DEVICE

The mathematical model of semiconductor devices is described by the initial boundary value problem of a system of three nonlinear partial differential equations. One equation in elliptic form is for the electrostatic potential; two equations of convection-dominated diffusion type are for the electron and hole concentrations. Finite volume element procedure are put forward for the electrostatic potential, while upwind     

半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

ALTERNATING-DIRECTION MULTISTEP PRECONDITIONED ITERATIVE METHODS FOR SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.     

t-PBIB DESIGNS

A new type of design, called a t-PBIB design, is introduced by combining the notion of a t-design and the one of PBIB design. Some basic properties of a t-PBIB design are given, and a class of 3-PBIB designs is constructed by means of finite vector spaces.     

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.     

三维热传导型半导体器件问题在局部加密网格上的有限差分格式

局部网格加密技术能很好地解决局部性很强的问题,半导体器件问题的解在半导体的p-n结附近有很强的局部性质.热传导型半导体器件瞬态问题的数学模型由四个方程组成的非线性偏微分方程组的初边值问题决定,电场位势方程是椭圆型的,电子和空穴浓度方程是抛物型的,温度方程是热传导型的.依据实际数值模拟的需要,提出了一类三维热传导型半导体问题在时间上进行局部加密的复合网格上的有限差分格式,并给出了电子、空穴浓度和温度的最大模误差估计以及数值算例.这些研究结果对半导体器件数值模拟的算法理论、实际应用和工程软件系统的研制,均具有重要的价值.     

三维半导体器件问题在时空局部加密复合网格上的有限差分格式

半导体器件的瞬时状态由三个方程组成的非线性偏微分方程组的初边值问题决定,电子位势方程是椭圆型的,电子和空穴浓度方程是抛物型的．依据实际数值模拟的需要,提出了一类三维半导体问题在时间和空间上进行局部加密的复合网格上的有限差分形式,并给出了电子和空穴浓度的最大模误差估计,最后给出了数值算例．     

三维半导体问题的迎风有限体积格式

半导体器件的瞬时状态由包含三个拟线性偏微分方程所组成的方程组的初边值问题来描述.其中电子位势方程是椭圆型的,电子和空穴浓度方程是对流扩散型的.作者对三维半导体模型问题采用四面体网格上的有限体积元方法进行逼近,具体地,对电子位势方程采用一次元有限体积法来逼近,对电子浓度和空穴浓度方程采用迎风有限体积方法来逼近,并进行了详细的理论分析,得到了O(h+\Delta t)阶的L^2模误差估计结果.     

Application of the homotopy analysis method to the Poisson–Boltzmann equation for semiconductor devices

This paper describes the application of a recently developed analytic approach known as the homotopy analysis method to derive an approximate solution to the nonlinear Poisson–Boltzmann equation for semiconductor devices. Specifically, this paper presents an analytic solution to potential distribution in a DG-MOSFET (Double Gate-Metal Oxide Semiconductor Field Effect Transistor). The DG-MOSFET represents one of the most advanced device structures in semiconductor technology and is a primary focus of modeling efforts in the semiconductor industry.     

A parallel adaptive finite volume method for nanoscale double-gate MOSFETs simulation

We propose in this paper a quantum correction transport model for nanoscale double-gate metal-oxide-semiconductor field effect transistor (MOSFET) device simulation. Based on adaptive finite volume, parallel domain decomposition, monotone iterative, and a posteriori error estimation methods, the model is solved numerically on a PC-based Linux cluster with MPI libraries. Quantum mechanical effect plays an important role in semiconductor nanoscale device simulation. To model this effect, a physical-based quantum correction equation is derived and solved with the hydrodynamic transport model. Numerical calculation of the quantum correction transport model is implemented with the parallel adaptive finite volume method which has recently been proposed by us in deep-submicron semiconductor device simulation. A 20 nm double-gate MOSFET is simulated with the developed quantum transport model and computational technique. Compared with a classical transport model, it is found that this model can account for the quantum mechanical effects of the nanoscale double-gate MOSFET quantitatively. Various biasing conditions have been verified on the simulated device to demonstrate its accuracy. Furthermore, for the same tested problem, the parallel adaptive computation shows very good computational performance in terms of the mesh refinements, the parallel speedup, the load-balancing, and the efficiency.     

A finite difference scheme for two-dimensional semiconductor device of heat conduction on composite triangular grids

The momentary state of a semiconductor device of heat conduction is described by a system of four nonlinear partial differential equations. One elliptic equation is for the electrostatic, two parabolic equations are for the electron concentration and the hole concentration, and one heat exchange equation is for the temperature. According to the necessary of practical numerical simulations and based on the balance equation, finite difference schemes for two-dimensional transient behavior of a semiconductor device of heat conduction on composite triangular grids are constructed. Studying their stability and convergence properties, the error estimate in the energy norm is obtained. Finally, a numerical example is given.     

半导体瞬态问题特征变网格有限元法和分析

1 引 言考虑平面区域Ω　R2上的二维问题,其数学模型为[1]-△ψ=α（p-e+N（x））,（x,t）∈Ω×J,J（0,T],（1.1）     

三维热传导型半导体器件瞬态模拟问题的Crank-Nicolson差分-流线扩散有限元法及其数值分析

本文研究三维热传导型半导体器件瞬态模拟问题的数值方法.针对数学模型中各方程不同的特点,分别提出不同的有限元格式.特别针对浓度方程组是对流为主扩散问题的特点,使用Crank-Nicolson差分-流线扩散计算格式,提高了数值解的稳定性.得到的L2误差估计关于空间剖分步长是拟最优的,关于时间步长具有二阶精度.     

Finite volume element approximation and analysis for a kind of semiconductor device simulation

In this paper, we present a finite volume element scheme for a kind of two dimensional semiconductor device simulation. A general framework is developed for finite volume element approximation of the semiconductor problems. We construct a fully discrete finite volume element scheme based on triangulations with a piecewise linear finite element space and a general type of control volume. Optimal-order convergence in H ¹-norm is derived.     

A two-dimensional numerical analysis of a small geometry MOSFET

This paper describes the development of a computer model to simulate small geometry metal-oxide-semiconductor field effect transistors (MOSFETs). The model is developed by obtaining computer generated solutions to the phenomenological equations which describe carrier transport and the electric fields in a semiconductor device. Threshold voltage variations and breakdown effects are also discussed.