An evolutionary method for efficient computation of mutual capacitance for VLSI circuits based on the method of images Yiorgos I. Bontzios a , Michael G. Dimopoulos b,⇑ , Alkis A. Hatzopoulos a a Dept. of Electrical & Computer Eng., Aristotle Univ. of Thessaloniki, Thessaloniki 54124, Greece b Dept. of Electronics, Alexander Technological Educational Inst. of Thessaloniki, P.O. Box 141, Thessaloniki 57400, Greece article info Article history: Received 24 July 2010 Received in revised form 2 October 2010 Accepted 6 October 2010 Available online 11 October 2010 Keywords: Capacitance Capacitance modeling Genetic algorithms Charges Mixed analog–digital integrated circuits VLSI circuits Method of images abstract The problem of computing the capacitance coupling in Very Large Scale Integrated (VLSI) circuits is studied in this work. The proposed method is an approximate extended version of the method of images. The initial problem is formulated here as an optimization prob- lem for the solution of which a genetic algorithm (GA) is employed. The proposed method is fast, general, does not rely on fitting techniques and is applicable to an arbitrary 2D or 3D geometry configuration of conductors. Extensive simulation results are presented for sev- eral practical case studies. Comparative results are given with other methods from litera- ture and a commercial tool employing the Finite Element Method (FEM). The results show that the capacitance value computed by our method is in close agreement to the value obtained by the other methods from literature and also by the commercial tool with the average difference ranging between 2% and 5% while demonstrating better scalability as the problem complexity rises. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Modeling and prediction of the noise coupling is an important design consideration in modern mixed signal ICs. Errone- ous estimation of the coupling may lead, for example, to degradation on the performance of an analog amplifier or to the propagation of noise from one block to another. For this reason, the correct prediction of the coupling during the IC design phase is imperative. Three types of noise coupling are recognized in VLSI circuits; resistive, capacitive and inductive. The latter is a significant issue in special cases, where for example bonding wires or inductors are present. On the other hand, the resistive and mainly capacitive coupling should be always considered. The continuous scaling of the CMOS technologies, which in effect brings metallization at closer distances, makes the correct capacitive coupling computation and prediction in modern technologies critical. Many techniques for calculating the capacitive coupling have been proposed in literature. The most common ones are the FEM and BEM methods [1–3]. In these methods, the space is discretized into a finite number of cells. The problem is then solved using standard numerical integration techniques. Although general methods, they suffer from increased memory requirements and simulation time and in some complex problems they totally fail to converge. While the simulation time may not be considered as a significant problem in research, it turns out to be prohibitive for the design process. One other major approach is the modeling of the capacitance coupling with a small number of lumped capacitances [4–10]. In these methods every type of problem is first semi-explicitly solved, using mostly conformal mapping techniques and by imposing parameters the values of which are computed by fitting techniques, resulting in semi-empirical formulas. The main drawback of this approach is that its range of validity is limited to the specific type of problem solved. 1569-190X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2010.10.002 ⇑ Corresponding author. Tel.: +30 6972645452. E-mail addresses: gmpontzi@auth.gr (Y.I. Bontzios), mdimop@ieee.org (M.G. Dimopoulos), alkis@eng.auth.gr (A.A. Hatzopoulos). Simulation Modelling Practice and Theory 19 (2011) 638–648 Contents lists available at ScienceDirect Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat