Calculation of the electrical capacitance of a truncated cone

The paper presents a method for the evaluation of the capacitance and charge distribution of a metallic truncated cone of finite length with top and bottom circular flat plates and isolated in free space, the integral equations relating the potential and unknown charge distribution on the surfaces are solved using the moment method employing pulse and delta functions as basis function and testing functions, respectively. The elements of the matrix to be inverted are found by dividing the surfaces into subsections which are combination of curvilinear rectangles and triangles. Capacitance and charge distribution are evaluated as a function of the geometrical parameters of the structure, numerical results on capacitance and charge distribution are presented     

Computation of the Capacitance Matrix for Systems of Dielectric-Coated Cylindrical Conductors

The method of moments is applied to the computation of the charge distributions and capacitance matrix for electrostatic systems of bare and dielectric-coated cylindrical wires. Several choices of expansion functions are investigated in detail and compared. Harmonic series expansion functions are shown to be especially well suited to problems involving systems of closely-spaced dielectric-coated cylindrical wires.     

Capacitance computations in a multilayered dielectric medium usingclosed-form spatial Green's functions

An efficient method to compute the 2-D and 3-D capacitance matrices of multiconductor interconnects in a multilayered dielectric medium is presented. The method is based on an integral equation approach and assumes the quasi-static condition. It is applicable to conductors of arbitrary polygonal shape embedded in a multilayered dielectric medium with possible ground planes on the top or bottom of the dielectric layers. The computation time required to evaluate the space-domain Green's function for the multilayered medium, which involves an infinite summation, has been greatly reduced by obtaining a closed-form expression, which is derived by approximating the Green's function using a finite number of images in the spectral domain. Then the corresponding space-domain Green's functions are obtained using the proper closed-form integrations. In both 2-D and 3-D cases, the unknown surface charge density is represented by pulse basis functions, and the delta testing function (point matching) is used to solve the integral equation. The elements of the resulting matrix are computed using the closed-form formulation, avoiding any numerical integration. The presented method is compared with other published results and showed good agreement. Finally, the equivalent microstrip crossover capacitance is computed to illustrate the use of a combination of 2-D and 3-D Green's functions     

Capacitance of dielectric coated cylinder of finite axial lengthand truncated cone isolated in free space

The capacitance of dielectric coated metallic cylinder and truncated cone are evaluated using the method of moments based on the pulse function and point matching. The analysis is based on the boundary condition for the potential on the conductor surface and the normal component of the displacement density at the dielectric-free space interface. The total free charge on the conductor surface is found from the inversion of a matrix partitioned into submatrices. Numerical data on the capacitance and charge distribution are presented     

Shape sensitivities of capacitances of planar conducting surfacesusing the method of moments

In this contribution, a new method is presented to obtain the sensitivities of the capacitance or the charge with respect to a geometrical parameter of planar conducting surfaces. The charge density is found by an integral equation technique. By applying the flux-transport theorem, a new integral equation for the total derivative of the charge with respect to a geometrical parameter is derived from the original electrostatic integral equation for the charge distribution. This new integral equation is solved together with the original integral equation by the method of moments using the same set of basis and test functions. The method is also applied to obtain derivatives for the inductance, impedance and effective dielectric constant. Some simple electrostatic problems are presented, which illustrate the capabilities of our approach. In these examples we also discuss the difference between the geometrical derivatives obtained in this way with geometrical derivatives which are obtained by a central finite difference estimate. Next, some examples of the calculation of geometrical derivatives of capacitance and inductance matrices of multilayer, multiconductor thin microstrip lines are discussed     

The Electrostatic Field of Conducting Bodies in Multiple Dielectric Media

A method for computing the electrostatic fields and the capacitance matrix for a multiconductor system in a multiple dielectric region is presented. The number of conductors and the number of dielectrics in this analysis are arbitrary. Some of the conductors maybe of finite volume and others may be infinitesimally thin. The conductors can be either above a single ground plane or between two parallel ground planes. The formulation is obtained by using a free-space Green's function in conjunction with total charge on the conductor-to-dielectric interfaces and polarization charge on the dielectric-to-dielectric interfaces. The solution is effected by the method of moments using triangular subdomains with piecewise constant expansion functions and point matching for testing. Computed results are given for some finite-length conducting lines, compared to previous results obtained by two-dimensional analysis.     

Direct computation of multiconductor transmission line capacitance and charge distribution

The per-unit-length capacitance parameter of multiconductor transmission line (MTL) is commonly extracted with indirect matrix transform method, which is complex and time-consuming. To solve the problem, an improved method to directly compute the MTL capacitance is proposed, which can be applied in the transmission line structure with arbitrary shaped cross-section and arbitrary separate distance. This method imports voltage conversions and matrix operations to simplify the complexity, improves computational efficiency by about 600% with results as accurate as previous method. The novel method presents a clear charge distribution map of MTL, whereas precious method will experience a tortuous process to get charge distribution.     

On the two-dimensional capacitance calculation of multiconductor multilayered interconnects

In this paper a method for analysis and modelling of transmission interconnect lines on multilayered dielectric media is presented. The analysis is based on semianalytical layered Green’s function and the electromagnetic concept of free charge density. It allows us to obtain integral equations between electric scalar potential and charge density distributions. These equations are solved by the Galerkin procedure of the Method of Moments. After this, the capacitance matrix of multiconductor interconnect lines in the presence of planar dielectric interfaces is calculated. When there exists no infinite ground plane, we enforce the constraint that the sum of all free charges is zero. The feasibility of the method has been shown by simulations of several transmission-line problems. The results have been compared with reported data obtained by free-space Green’s function method, conformai mapping formulas, generalized method of lines and inverted capacitance coefficient matrix technique. The proposed approach is not inferior to other procedures in terms of generality and memory requirements. At the same time, a reduction of the central processing unit (cpu) time is achieved because the integral equations are solved numerically only on the surface of conductor lines.     

Multiconductor Transmission Lines In Multilayered Dielectric Media

A method for computing the capacitance matrix and inductance matrix for a multiconductor transmission line in a multilayered dielectric region is presented. The number of conductors and the number of dielectric layers are arbitrary. Some of the conductors may be of finite cross section and others may be infinitesimally thin. The conductors are either above a single ground plane or between two parallel ground planes. The formulation is obtained by rising a free-space Green's function in conjunction with total charge on the conductor-to-dielectric interfaces and polarization charge on the dielectric-to-dielectric interfaces. The solution is effected by the method of moments using pulses for expansion and point matching for testing. Computed results are given for some cases where all conducting lines are of finite cross section and other cases where they are infinitesimally thin.     

A capacitance model for GaAs MESFETs

A capacitance model for a GaAs MESFET suitable for implementation in the circuit analysis program SPICE is presented. The model consists of nonlinear capacitances that are a function of two voltages. Such a model gives rise to ordinary nonlinear capacitances and transcapacitances. The placement of these elements in the Y matrix is shown. The empirical equations for the gate charge of a GaAs MESFET given provide an accurate SPICE model for the gate charge and capacitances of a MESFET. A comparison of measured capacitance values with the modeled values gives close enough agreement for circuit simulation purposes     

An efficient solver for the three-dimensional capacitance of theinterconnects in high speed digital circuit by the multiresolutionmethod of moments

The computation of the equivalent capacitances for three-dimensional (3-D) interconnects features large memory usage and long computing time. In this paper, a matrix sparsification approach based on multiresolution representation is applied with the method of moments (MoM) to calculate 3-D capacitances of interconnects in a layered media. Instead of direct expansion of the charge distribution by the orthogonal wavelet basis functions, the large full matrix resulting from discretization of the integral equations is taken as a discrete image and sparsified by two-dimensional (2-D) multiresolution representations. The inverse of the obtained sparse matrix is efficiently implemented by Schultz's iterative approach. Several numerical examples are given and the results obtained show that the proposed method significantly sparsifies the matrix equation and the capacitance parameters computed by the matrix equation with high sparsity agree well with the results of other reports and those computed by an established capacitance extractor FASTCAP     

An introduction to spectral domain method-of-moments formulations

The capacitance per unit length of a microstrip transmission line is obtained using a spectral-domain method-of-moments (MoM) formulation. The paper emphasizes this problem as a teaching tool to introduce students of electromagnetics to this technique. Firstly, the derivation of the spectral-domain Green's function is outlined. Using this, the relevant integral equation is derived to which the Galerkin MoM approach is then applied. The MoM problem is solved in the spectral domain by also transforming the expansion and weighting functions. The inverse Fourier transform is then applied to find the spatial-domain charge distribution, and, hence, capacitance. The issues that arise here - both of selecting how much of the spectrum to include, and how to choose the number of integration points - are discussed, and the results of typical numerical experiments are presented. The time required to compute the elements of the immittance matrix is shown to be 0(N/sup 3/); the use of translational symmetry (and thus Toeplitz matrix structure) to reduce this is outlined. Classroom experience with this material is discussed. Finally, a hybrid spectral/spatial-domain formulation, introducing asymptotics, is outlined to accelerate the evaluation of the immittance matrix.     

高速IC互连线分布参数提取的一种新方法:采用Pade逼近的介质格林函数法

本文提出采用Ｐａｄｅ逼近的介质格林函数方法计算多导体互连线分布参数。由于采用了分层介质的格林函数，只需在导体表面进行剖分，大大降低了未知变量的规模，本文首先提出利用Ｐａｄｅ逼近对Ｌａｐｌａｃｅ方程的级数形式的格林函数进行收敛性加速。文中给出了加速收敛的结果，表明这种方法是很有效的。     

Space-domain Green's function approach to the capacitancecalculation of multiconductor lines in multilayered dielectrics withimproved surface charge modeling

An integral equation method for the calculation of capacitance and inductance matrices is presented. The method is suitable for multiconductor transmission lines embedded in a multilayered dielectric medium on top of a ground plane. Conductors of arbitrary polygonal cross section can be handled, as well as infinitely thin conductors. The method is new in two respects. The kernel of the integral equation is the space-domain Green's function of the layered medium. The accuracy of the solution is enhanced by using basis functions that exactly model the singular behavior of the charge density in the neighborhood of a conductor edge. Numerical examples show the accuracy of the calculations and the complexity of the configurations that can be treated     

Small-signal gate-to-drain capacitance of MOSFET as a diagnostic tool for hot-carrier induced degradation

In this paper a method for the study of hot-carrier induced charge centers in MOSFETs based on a small-signal gate-to-drain capacitance measurement is described. Numerical modeling and simulation is used to provide an understanding of the effects of spatially localized trapped carriers and interface states on this capacitance. Experimental gate-to-drain capacitance results are presented and compared with charge pumping measurements. This method is used to investigate hot-carrier degradation of n- and p-channel MOSFETs after drain avalanche hot-carrier stress conditions. It is concluded that under this stress condition the degradation of both n- and p-channel devices is due to the trapping of majority carriers and the generation of acceptor type interface states in the top half of the silicon bandgap.     

An accurate model for power DMOSFETs including interelectrodecapacitances

A SPICE-compatible circuit model for power MOSFETs is presented. It is based on device physics and uses a subcircuit representation. The interelectrode capacitances are modeled accurately as nonlinear functions of the applied biases. Various second-order effects relating to the gate capacitance model are discussed, and strategies are presented to include them in the model. The model parameters can be obtained from device measurements. The model is verified by comparing measured and simulated waveforms from a gate charge test circuit     

Charge-injection noise in CCDs

An analysis of the noise associated with electronic charge injection in charge-coupled devices (CCDs) is presented, including the effects of diffusion currents. The capacitance of the injection circuit determines the charge-injection noise, and specification of the noise requires consideration of the quoted capacitance; for large charge packets, the noise has a characteristic variance of kTC/2 or kTC, depending on whether the capacitance is defined by microscopic (internal) or macroscopic (external) potentials. The variance is Poissonian for small charge packets. The noise values presented in this paper may serve as a target when optimizing charge-injection operation of a CCD.     

棱边元分区的区域分解算法及其在电磁问题中的应用

针对三维电磁问题,该文提出了采用非结构化网格剖分计算区域,并按单元进行区域划分的区域分解算法。将原求解区域划分为若干个不重叠的子区域,先通过求解容量矩阵获得子区域之间连接边界上的场值,再利用矢量有限元快速计算出每个子区域内部的场值,显著地降低了计算复杂度和存储量。通过引入预条件的Krylov子空间法求解容量矩阵方程,加速了收敛,进一步提高了效率。数值算例验证了该方法的准确性和有效性。     

小波多分辨率分析改进互连结构电容提取

本文将点匹配矢量法矩阵视作类似离散图像信号的一组数字信号矢量,进行小波多分辨率分解对该矩阵进行拟对角化压缩,克服了以往小小基直接展开的矩量法在求解二维与三维电在问题时的困难。文章例子的计算结果说明了这种方法在将矩量法得到的满矩阵变换为稀疏矩阵时具有的效率。电容参数提取的效率也由于矩阵的稀疏化得到了提高。文中的数据值结果与文献及ＦＡＳＴＣＡＰ软件的结果吻合。     

Explicit Analytical Charge and Capacitance Models of Undoped Double-Gate MOSFETs

An analytical, explicit, and continuous-charge model for undoped symmetrical double-gate (DG) MOSFETs is presented. This charge model allows obtaining analytical expressions of all total capacitances. The model is based on a unified-charge-control model derived from Poisson's equation and is valid from below to well above threshold, showing a smooth transition between the different regimes. The drain current, charge, and capacitances are written as continuous explicit functions of the applied bias. We obtained very good agreement between the calculated capacitance characteristics and 2-D numerical device simulations, for different silicon film thicknesses.