Computing Capacitance

Name:    Prof. Michael Mascagni                 
Address: Department of Computer Science and
         Department of Mathematics and
	 Department of Scientific Computing and
         Graduate Program in Molecular Biophysics	
         Florida State University
         Tallahassee, FL  32306-4530  USA
         AND
         Information Technology Laboratory
         Applied and Computational Mathematics Division
         100 Bureau Drive M/S 8910
         National Institute of Standards and Technology (NIST)
         Gaithersburg, MD  20899-8910  USA

Offices: 498 Dirac Science Library/207A Love Building (FSU) Building 225/Room B154 (NIST)
Phone:   +1.850.644.3290 (FSU) +1.301.975.2051 (NIST)
FAX:     +1.850.644.0058
e-mail:  mascagni@fsu.edu (FSU) mascagni@nist.gov (NIST)

Title: Stochastic Computational Electrostatics and Applications: Computing Capacitance

We are interested in using stochastic (Monte Carlo) methods to solve problems that are relevant to electrostatics and specifically to semiconductor design. Thus, we begin by introducing what Monte Carlo are and show how they can be used to compute several numerical quantities. We then focus on Monte Carlo methods using the Walk on Spheres technique to solve partial differential equations of the elliptic type. These are equations that describe a state of physical equilibrium such as we see in electrostatics. One such important problem in electrostatics is computing the capacitance of an object in 3D. We discuss how this is done using both convential deterministic methods and the Walk on Spheres technique. We then show how one can use similar ideas from stochastic computing to compute relative capacitance and then mutual capacitance. Mutual capacitance is an important quantity used to evaluate the electrostatic suitability of semiconductor designs. As such, fast and accurate methods for mutual capacitance computations are important in facilitating the semicondutor design process. We then consider the computation of capacitance as a computational paradigm. Using the Walk on Spheres method is a very efficient computational approach for capacitance extraction, and so it has become the method of choice by a variety of vendors of software for semiconductor design and in many aspects of computer graphics. In particular, the Walk on Spheres technique has significantly improved the performance of the ZENO code developed at NIST by the author and various collaborators. At present, the author is seeking funding to continue this work using CHIPS funding.

References:

C.-O. Hwang, J. A. Given and M. Mascagni (2000) On the Rapid Calculation of Permeability for Porous Media Using Brownian Motion Paths, Physics of Fluids, 12: 1699–1709.
R. Sawhney and K. Crane (2020) Monte Carlo Geometry Processing: A Grid-FreeApproach to PDE-Based Methods on Volumetric Domains, ACM Trans. Graphics, 39(4): 18 pages. https://doi.org/10.1145/3386569.3392374
D. Juba, D. J. Audus, M. Mascagni, J. Douglas, W. Keyrouz (2016) ZENO: Software for calculating hydrodynamic, electrical, and shape properties of polymer and particle suspensions, Journal of Research of the National Institute of Standards and Technology, 122. https://doi.org/10.6028/jres.122.020
P. Hamlin, W. J. Thrasher, W. Keyrouz and M. Mascagni (2019) Geometry Entrapment in Walk-on-Subdomains, Monte Carlo Methods and Applications, 24(4): 178–193.