方块电阻测试中的有限元理论

介绍了用有限元方法计算半导体方块电阻四探针测试中二维点电流势场的模型并且证明了其正确性，由于有限元方法对边界没有限制，该方法为方块电阻测试中精确确定边界修正系数，更重要的是为微样品测试结构确定提供直接明了的理论依据。     

薄层方块电阻宽电极测试方法

设计一种用宽电极测试薄层方块电阻的方法,给出理论分析和实验结果,该方法可以作为对四探针方块电阻测试仪进行校对的原始方法．也可以开发为一个大学物理设计性实验。     

优化GaN基发光二极管的电极

针对以蓝宝石为衬底的GaN基发光二极管出现的电流扩展不均的问题,采用有限元方法建立了GaN基发光二极管的三维网络模型,并对四种常见结构的器件进行数值模拟,发现影响二极管电流的因素不仅与发光二极管电极的位置有关,而且依赖于器件的结构参数.以电流扩展不均为指标确定出这四种器件中最佳的电极位置分布,同时对最佳电极位置分布的器件进行了结构参数优化,结果表明当p型金属层方块电阻与n型GaN的方块电阻接近时,电流扩展均匀性最好,且p-GaN的接触电阻和厚度越小,电流扩展越不均匀.     

大圆片样品方块电阻测试及径向等高线图的绘制

本文用微机控制四探针测试系统,按着分区等差方法计算的连续点,描绘出半导体大圆片样品方块电阻的径向等高线图.     

ITO薄膜的电阻并联效应研究

采用电子束蒸发镀膜方法在K9玻璃基底上分别镀制了ITO/SiO₂/ITO,ITO/Ti₂O₃/ITO和ITO/MgF₂/ITO结构的多层薄膜,用四探针方块电阻仪测量薄膜表面的方块电阻,用原子力显微镜观测样品的表面微观形貌。结果显示,当ITO薄膜的粗糙度较大且介质薄膜的物理厚度小于100nm时,各层ITO薄膜之间通过山峰状的凸起结构相连通,导致样片表面的方块电阻测量值与各层ITO薄膜电阻的并联值相当。这表明,当ITO薄膜的粗糙度较大且介质薄膜厚度较小时,各层ITO薄膜表现出电阻并联效应。利用多层ITO薄膜的电阻并联效应设计并制备了450～1200nm超宽光谱透明导电薄膜,用四探针方块电阻仪测量了试验样片的表面方块电阻,用紫外-可见-近红外分光光度计测试了样片的光谱透射率。结果显示,在相同表面方块电阻条件下,相比于单层ITO薄膜,利用ITO薄膜电阻并联效应所制备的多层透明导电薄膜具有更高的光谱透射率。     

磷吸杂工艺研究

磷吸杂在晶体管芯片制造过程中对改善芯片表面态、减少漏电流等起着重要作用.文中确定了方块电阻为6-8Ω/□(欧姆/方块)的磷吸杂工艺条件,并对过程的相关影响因素进行分析和探讨,同时提出了解决方法.     

基于SiC MOSFET的霍尔迁移率在片测试方法

研究了一种霍尔迁移率在片测试方法,通过在片测量反型层电荷密度ns和反型层方块电阻Rs得到反型层载流子的霍尔迁移率。通过在待测芯片上固定一个环形磁体获得一个高强度磁场,并且测试磁体与芯片距离和磁场强度的关系。讨论了反型层电荷密度ns和反型层方块电阻Rs的测试原理和方法,采用多次测量求导的办法,消除了霍尔电压测试过程中由于样品制备和测试系统的原因引入漂移电压,提高了测试精度。基于该方法完成测试平台搭建,并应用该测试平台完成了对SiC MOSFET样品霍尔迁移率的测试,得到了霍尔迁移率随栅极电压变化的关系。     

BiCMOS工艺中纵向晶体管β和广义SPC

采用 SPC获得影响 Bi CMOS工艺中纵向晶体管电流放大系数 β值波动的因素仅和基区方块电阻相关。进一步采用 SUPREM3工艺模拟得到影响 β波动的重要因素是扩散炉温度。试验结果定量证明温度的影响 ,由此说明批量生产时测试基区方块电阻而无需测试结深就能预测其 β值。最后建议采用广义的 SPC使 β值受控达到设计规范     

双电测组合法测试半导体电阻率的研究

对双电测组合四探针法测试方块电阻 (Rs)和体电阻率 ( ρ)进行了研究 ,从理论和实践上揭示三种组合模式的共同优点 :测量结果与探针间距无关 ,可使用不等距探针头 ;具有自动修正边界影响的功能 ,不必寻找修正因子 ;不移动探针头即可得知均匀性 .推导出用于体电阻率时的厚度函数 .论述了Rs、ρ、大小样片及边界附近的测试原理 ,给出了Rs 和 ρ的计算公式.     

双电测组合法测试半导体电阻率的研究

对双电测组合四探针法测试方块电阻(Rs)和体电阻率(ρ)进行了研究,从理论和实践上揭示三种组合模式的共同优点:测量结果与探针间距无关,可使用不等距探针头;具有自动修正边界影响的功能,不必寻找修正因子;不移动探针头即可得知均匀性.推导出用于体电阻率时的厚度函数.论述了Rs、ρ、大小样片及边界附近的测试原理,给出了Rs和ρ的计算公式.     

A new FEM approach for open boundary Laplace's problem

An efficient improved finite element method (FEM) is presented for electromagnetic Laplace's problems with open boundary. The whole infinite domain is divided into a set of infinite elements instead of ordinary finite elements. Since a special FEM discretization and FEM solving procedure are used, it can not only take much less computer memory than that the conventional FEM needs, but also avoid the calculation error introduced by the truncated boundary or absorbing boundary condition used in conventional FEM     

On the modeling of a gapped power-bus structure using a hybrid FEM/MoM approach

A hybrid finite-element-method/method-of-moments (FEM/MoM) approach is applied to the analysis of a gapped power-bus structure on a printed circuit board. FEM is used to model the details of the structure. MoM is used to provide a radiation boundary condition to terminate the FEM mesh. Numerical results exhibit significant errors when the FEM/MoM boundary is chosen to coincide with the physical boundary of the board. These errors are due to the inability of hybrid elements on the boundary to enforce the correct boundary condition at a gap edge in a strong sense. A much better alternative is to extend the MoM boundary above the surface of the board.     

Micromechanical modeling of stress evolution induced during cure in a particle-filled electronic packaging polymer

Particle-filled polymers are widely used in electronic industries. From microscale view, cure-induced residual stress can be generated not only by the external constraints but also by the constraint effect among the particles. In this paper, a three-dimensional micromechanical finite element method (FEM) model has been setup for a silica particle filled epoxy. In the micromechanical model, the epoxy matrix is modeled with a previously developed cure-dependent viscoelastic constitutive model, whereas the silica particles are modeled as elastic with high stiffness. Cure shrinkage is applied to the matrix as an initial strain for each time increment. The cure-dependent viscoelastic properties were obtained from shear and tension-compression dynamical mechanical analysis measurements. Cure shrinkage and reaction kinetics were characterized with online density measurement and differential scanning calorimeter measurements, respectively. In order to simulate a partly constrained object, the micromechanical model is coupled with a macromodel FEM analysis. The displacements from the macromodel are used as boundary conditions for the micromodel. The effect of external constraints on the generation of the micro stresses is studied by using the boundary conditions related to different external constrained states.     

物体变形测量的相移数字散斑剪切干涉术

相移数字散斑剪切干涉技术可以提高检测精度,利用该方法对圆形铝板试件进行测量。为了实现全场相位的精确求解,运用等四步相移Carré算法定量计算相位。将该非接触测量技术与弹性力学理论分析相结合,对四周固支,中心受集中载荷试件的离面位移导数进行测量与分析,另外采用有限元方法进行模拟。最后将实验结果分别和理论结果、有限元结果进...     

Numerical absorbing boundary conditions for the scalar and vectorwave equations

Electromagnetic field computation may be carried out conveniently by using the finite element method (FEM). When solving open region problems using this technique, it becomes necessary to enclose the scatterer with an outer boundary upon which an absorbing boundary condition (ABC) is applied; analytically-derived ABCs have been used extensively for this purpose. Numerical absorbing boundary conditions (NABCs) have been proposed as alternatives to analytical ABCs. For the two-dimensional (2-D) Helmholtz equation, it has been demonstrated analytically that these NABCs become equivalent to many of the existing analytical ABs in the limit as the cell size tends to zero. In addition, the numerical efficiency of these NABCs has been evaluated by using as an indicator the reflection coefficient for plane and cylindrical waves incident upon an arbitrary boundary. We have extended this procedure to the study of the NABCs derived, for the three-dimensional (3-D) scalar and vector wave equations from the point of view of their numerical implementation in node- and edge-based FEM formulations, respectively     

复杂媒质电磁散射特性的有限元—边界元方法分析

通过有限元-边界元方法分析具有复杂媒质特性目标的电磁散射特性,如各向异性、双各向同性、双各向异性等.该混合方法能够利用有限元灵活地处理散射体内部的复杂材料,利用边界积分方法分析物体的非闭合区域,避免了使用吸收边界条件截断开放区域.通过推导基于有限元法的双各向异性媒质的泛函表达式,实现铁氧体、等离子体、手征等各类复杂媒质的统一建模,使该方法有很强的通用性.数值结果证明:本文发展的有限元-边界元方法对复杂媒质电磁散射问题分析的准确性和有效性.     

A numerical absorbing boundary condition for finite difference andfinite element analysis of open periodic structures

In this paper we present a novel approach to deriving local boundary conditions, that can be employed in conjunction with the Finite Difference/Finite Element Methods (FD/FEM) to solve electromagnetic scattering and radiation problems involving periodic structures. The key step in this approach is to derive linear relationships that link the value of the field at a boundary grid point to those at the neighboring points. These linear relationships are identically satisfied not only by all of the propagating Floquet modes but by a few of the leading evanescent ones as well. They can thus be used in lieu of absorbing boundary conditions (ABCs) in place of the usual FD/FEM equations for the boundary points. Guidelines for selecting the orders of the evanescent Floquet modes to be absorbed are given in the paper. The present approach not only provides a simple way to derive an accurate boundary condition for mesh truncation, but also preserves the banded structure of the FD/FEM matrices. The accuracy of the proposed method is verified by using an internal check and by comparing the numerical results with the analytic solution for perfectly conducting strip gratings     

介质周期结构频率选择特性有限元法分析

采用有限元方法分析了平面波入射时介质周期结构的频率选择特性.截取一个完整的周期单元,内部应用有限元(FEM)方法计算;采用理想匹配层(PML)吸收边界、周期边界、入射边界相结合的方法对无限空间进行截断.几种边界条件的联合应用大大简化了开放空间问题的计算,保证了计算精度.算例结果与理论值符合较好,表明有限元方法在分析此类问题中的正确性和有效性.     

3-D electrical impedance tomography for piecewise constant domains with known internal boundaries

Electrical impedance tomography (EIT) is a badly posed inverse problem, but can be stabilized if one assumes that the conductivity is piecewise constant, with a relatively small number of distinct regions, and that the region boundaries are known, for example from prior anatomical imaging. With this assumption, we introduce a three-dimensional (3-D) boundary element method (BEM) model for the forward EIT map from injected currents to measured voltages, and 3-D inverse solutions for both BEM and the finite element method (FEM) which explicitly take into account the parameterization implied by the known boundary locations. We develop expressions for the Jacobians for both methods, since they are nonlinear, to more rapidly solve the inverse problem. We show simulation results in a torso geometry with the heart and lungs as inhomogeneities. In a simulation study, we could reconstruct the conductive values of some internal organs of a human torso with more than 92% accuracy even with inaccurate internal boundary locations, a randomized rather than constant conductivity profile (with the standard deviation of the Gaussian-distributed conductivities set to 20% of their mean values), signal to measurement noise of 50 dB, and with different meshes used for the forward and inverse problems. BEM and FEM perform similarly, leading to the conclusion that the choice between them should be based on secondary considerations such as computational efficiency or the need to model conductivity anisotropies     

Vector one-way wave absorbing boundary conditions for FEMapplications

In the paper a derivation is presented which leads to a new and general class of vector absorbing boundary conditions (ABCs) for use with the finite element method (FEM). The derivation is based on a vector one-way wave equation and a polynomial approximation of the vector radical. It is shown that wide-angle absorbing boundary conditions, as proposed in Halpern and Trefethen (1988) for optimal absorption of out-going waves, can be obtained in vector form. Vector plane waves are used to evaluate the accuracy and the reflection performance of these boundary conditions in a wide range of incidence angles. The implementation of the vector ABCs in a FEM formulation is also provided to show how up to the fifth-order absorbing accuracy can be achieved with derivatives only up to the second-order. A possible formulation is described which not only yields a third-order accuracy with first-order derivatives, but also retains the symmetry of the FEM matrix