Discretization schemes for high-frequency semiconductor devicemodels

This paper provides an overview on the numerical issues involved in the spatial and time-domain discretization of the coupled transport-electromagnetic models used in the simulation of high-frequency semiconductor devices. The physical transport models derived from the Boltzmann transport equation (BTE) are reviewed in order of decreasing complexity, from the full hydrodynamic model to the drift-diffusion approach. Spatial discretization is introduced starting from ad hoc approaches developed in the field of semiconductor modeling, like the Scharfetter-Gummel (1969) scheme; a critical comparison is then provided with the upwind finite-element schemes. Finally, time-domain discretization issues are reviewed, with particular stress on innovative developments in the area of hydrodynamic and of coupled transport-full-wave EM models     

半导体器件模拟技术的研究

主要介绍了半导体器件模拟中常用的HD模型与DD模型和三角网格划分的常用算法。以泊松方程为例，简要说明了如何在三角网络上离散化方程。同时，介绍了几种求解非线形方程组常用的数值方法。     

Accurate current calculation in two-dimensional MOSFET models

Two-dimensional simulations of MOSFET's are widely used for the design of short-channel transistors used in VLSI circuits. These models use low order methods of discretization of solution variables. In this paper, a method of current calculation is presented which works with these methods and yields good accuracy. The method uses integration of the solution variables, rather than differentiation, and is similar to applying Ohm's law in two dimensions.     

VLSI Process modeling—SUPREM III

Over the past several years, the process-simulation tool SUPREM II has proven useful in the design and optimization of both bipolar and MOS technologies. This paper describes a new and significantly more capable version of the program--SUPREM III--which incorporates process models suitable for VLSI device design. This new version of the program is now generally available and should provide a powerful new tool in VLSI design. For the first time, the program models multilayer structures (up to five material layers). It also incorporates substantially upgraded diffusion, oxidation, ion implantation, and other process models. These models incorporate, where possible, recent thinking about underlying physical mechanisms. The program remains a one-dimensional simulator; extensions to two dimensions are discussed. This paper concentrates on the process models and their underlying physics; implementation issues are addressed elsewhere.     

短沟道MOSFET阈值电压辐照增强漂移效应

本文对γ辐照环境下,小尺寸MOSFET的性能进行了研究,发现了短沟MOSFET阈值电压辐照增强漂移效应;提出了辐照损伤电荷非均匀分布概念;开发了二维数值模拟程序,对辐照损伤电荷引起的器件物理作用进行了分析;建立了辐照环境下短沟道MOSFET的简化模型,成功地解释了实验现象;在理论分析的基础上,提出了适用于VLSI的抗核加固措施,并经实验证实其有效性。     

The impact of supercomputers on IC technology development and design

Very large scale integration (VLSI) has evolved at an enormous rate, progressing from hundreds of components on an integrated circuit (IC) in the 1960's to a million components on a chip in the foreseeable future. This paper reviews some of the computer-aided design (CAD) tools that are essential for VLSI technology development and circuit design and that also require large amounts of computer resources. Specifically, we describe programs for process simulation, device simulation, and circuit simulation. This paper also reviews the impact of high-performance computing facilities on the development and use of these programs at AT & T Bell Laboratories.     

Finite boxes—A generalization of the finite-difference method suitable for semiconductor device simulation

A two-dimensional numerical device-simulation system is presented. A novel discretization scheme, called "finite boxes," allows an optimal grid-point allocation and can be applied to nonrectangular devices. The grid is generated automatically according to the specified device geometry. It is adapted automatically during the solution process by equidistributing a weight function which describes the local discretization error. A modified Newton method is used for solving the discretized nonlinear system. To achieve high flexibility the physical parameters can be defined by user-supplied models. This approach requires numerical calculation of parts of the coefficients of the Jacobian. Supplementary algorithms speed up convergence and inhibit the commonly known Newton overshoot. The advantages and computer resource savings of the new method are described by the simulation of a 100-V diode. We also present results for thyristor and GaAs MESFET simulations.     

Characteristics of double-gate SOI CMOS nanotransistors for promising technologies with a low power consumption level

A procedure, allowing one to optimize topological and electrophysical parameters of double gate SOI nanotransistors with a thin unalloyed working area, with underlap gate and drain/source regions with regard to the physical restrictions and process requirements, without recourse to the 2D-simulation, is considered. Based on the numerical simulation results, the selection criteria of the key topological parameters of transistors for implementing the requirements in accordance with the International Technology Roadmap for Semiconductor 2010 Edition program for promising applications with a low power consumption level are discussed. The complex analysis of the VACs of transistors and gate characteristics, such as a time switching delay, as well as active and static power, shows that prototypes of the considered units are applicable for implementing high-performance VLSI projects.     

硅通孔中含有加速剂的电镀铜仿真

Filling high aspect ratio through silicon vias(TSVs) without voids and seams by copper plating is one of the technical challenges for 3D integration. Bottom-up copper plating is an effective solution for TSV filling. In this paper, a new numerical model was developed to simulate the electrochemical deposition(ECD) process, and the influence of an accelerator in the electrolyte was investigated. The arbitrary Lagrange-Eulerian(ALE) method for solving moving boundaries in the finite element method(FEM) was used to simulate the electrochemical process. In the model, diffusion coefficient and adsorption coefficient were considered, and then the time-resolved evolution of electroplating profiles was simulated with ion concentration distribution and the electric current density.     

An accurate scheme for the solution of the time-domain Integral equations of electromagnetics using higher order vector bases and bandlimited extrapolation

Despite the numerous advances made in increasing the computational efficiency of time-domain integral equation (TDIE)-based solvers, the stability and accuracy of TDIE solvers remain problematic. This paper introduces a new numerical method for the accurate solution of TDIEs for scattering from arbitrary perfectly conducting surfaces. The work described in this paper uses the higher order divergence-conforming basis functions of Graglia et al. for spatial discretization and bandlimited interpolation functions for the temporal discretization of the relevant integral equations. Since the basis functions used for the temporal representation are noncausal, an extrapolation scheme is employed to recover the ability to solve the problem by marching on in time. Numerical results demonstrate that the proposed method is stable and that it exhibits superlinear convergence with regard to the spatial discretization and exponential convergence with respect to the temporal discretization.     

Analytical thermal model for multilevel VLSI interconnectsincorporating via effect

The authors present compact analytical thermal models for estimating the temperature rise of multilevel VLSI interconnect lines incorporating via effect. The impact of vias has been modeled using (1) a characteristic thermal length and (2) an effective thermal conductivity of ILD (interlayer dielectric), k_ILD,eff, with k _ILD,_eff=k_ILDη/, where η is a physical correction factor, with 0<η<1. Both the spatial temperature profile along the metal lines and their average temperature rise can be easily obtained using these models. The predicted temperature profiles are shown to be in excellent agreement with the three-dimensional (3-D) finite element thermal simulation results. The model is then applied to estimate the temperature rise of densely packed multilevel interconnects. It is shown that for multilevel interconnect arrays, via density along the lines can significantly affect the temperature rise of such interconnect structures     

硅低温双极晶体管的数值模拟

本文讨论了有关低温双极器件模拟物理参数的低温模型和各种低温物理效应,确立了适用于低温双极器件模拟的数值分析方法,建立了适用于77-300K温度范围内硅双极器件模拟程序,最后模拟分析了一典型结构品体管的常温和低温时的工作特性。     

Impatt diode simulation

A set of programs is established for IMPATT (Impact Avalanche Transit Time) diode simulation. It can be used to obtain the DC small and large signal solution of the IMPATT diodes made of different materials and having different doping profiles. The physical principles, numerical methods and program design are discussed, and the half-implicit method is presented in detail. Those programs can be used to simulate all kinds of transit-time devices, but the calculation results only of the Si IMPATT Diode are given.     

Numerical methods for semiconductor device simulation

This paper describes the numerical techniques used to solve the coupled system of nonlinear partial differential equations which model semiconductor devices. These methods have been encoded into our device simulation package which has successfully simulated complex devices in two and three space dimensions. We focus our discussion on nonlinear operator iteration, discretization and scaling procedures, and the efficient solution of the resulting nonlinear and linear algebraic equations. Our companion paper [13] discusses physical aspects of the model equations and presents results from several actual device simulations.     

天线耦合和极化对空分复用MIMO系统误码性能的影响

文章目的在于研究天线的互耦、匹配和极化特性对于基于空分复用的分层结构空时编码多输入多输出（Multiple Input Multiple Output,MIMO）系统误码性能的影响。采用了基于电路网络参数的信号分析模型,精确描述了匹配/未匹配天线阵列的发射、接收特性,接着使用蒙特卡罗分析方法对空分复用MIMO系统的误码性能进行了分析,包括匹配/未匹配线性阵列和极化分集阵列,并且讨论了极化失配特性对误码性能的影响。结果表明,匹配网络的应用能够有效地降低空分复用MIMO系统的误码率;同时极化分集天线的应用能够降低耦合和极化失配的影响,降低系统的误码率。     

Recent advances and trends in numerical techniques for process simulation

The gradually increasing complexity of the processing models and necessity to simulate in higher dimensions persistently challenges computational efficiency of the modern process simulators. In this paper, an outlook on the current status and trends in numerical techniques for efficient multidimensional bulk process simulation is given. Grid generation, grid adaptation, discretization and solving techniques are considered as the principle numerical building blocks of modem process simulation tools. The major task and obstacles for each of these numerical segments are recognized, and some recently proposed techniques to circumvent current limitations, as well as possible directions for future research are discussed.     

Moving dipole inverse solutions using realistic torso models

A noniterative numerical solution for the potentials on the surfaces of a piecewise homogeneous volume conductor due to a current dipole is described. This forward solution has been used in electric and magnetic single moving dipole (SMD) inverse solutions that employ a torso volume conductor model whose boundaries are specified numerically. Thus, the volume conductor model used by the inverse solutions need not be limited to simple geometric shapes; torso models of realistic shape can be used.     

Integration of VLSI circuits and mechanics for vibration control of flexible structures

The approach to modeling and control of smart flexible structures presented in this paper is based on the concept that an intelligent structure requires an internal knowledge of self to act intelligently. This knowledge can be acquired from local analog models of substructure dynamics and can be used in model-based controller designs. The key to this approach is the synergistic integration of analog VLSI circuit models and control with the sensing and actuation which are then to be embedded into the mechanical structure. This paper presents the motivation, development, and test results of analog VLSI circuit models for use in model-based control of smart flexible structures. Furthermore, control applications for these VLSI circuits are developed and simulation results are presented in which the VLSI circuits are used in adaptive vibration control of a simple mass-spring system.     

A New State-space-based Algorithm to Assess the Stability of the Finite-difference Time-domain Method for 3D Finite Inhomogeneous Problems

The finite-difference time-domain (FDTD) method is an explicit time discretization scheme for Maxwell's equations. In this context it is well-known that explicit time discretization schemes have a stability induced time step restriction. In this paper, we recast the spatial discretization of Maxwell's equations, initially without time discretization, into a more convenient format, called the FDTD state-space system. This in turn allows us to derive a new algorithm in order to determine the stability limit of FDTD for lossy, inhomogeneous finite problems. It is shown that a crucial parameter is the spectral norm of the matrix resulting from the spatial discretization of the curl operator. In a rectangular simulation domain the time step upper bound can be calculated in closed form and results in a time step limit less stringent than the Courant condition. Finally, the validity of the technique is illustrated by means of some pertinent numerical examples.