Nanotech 2001 Vol. 1
Nanotech 2001 Vol. 1
Technical Proceedings of the 2001 International Conference on Modeling and Simulation of Microsystems

Compact Modeling and Model Order Reduction Chapter 3

Using Pseudo Transient Continuation and the Finite Element Method to Solve the Nonlinear Poisson-Boltzmann Equation

Authors: A.I. Shestakov, J.L. Milovich and A. Noy

Affilation: Lawrence Livermore National Laboratory, United States

Pages: 39 - 43

Keywords: Poisson-Boltzmann, chemical force microscopy, pseudo transient continuation, finite elements

The nonlinear Poisson-Boltzmann (PB) eequation is solved using Pseudo Transient Continuation. The PB solver is constructed by modifying the nonlinear diffusion modeule of a 3D, massively parallel, unstructured grid, finite element, radiation-hydrodynamics code. The solver also computes the electrostatic energy and evaluates the force on a user-specified contour. Either Dirichlet or mixed boundary conditions are allowed. The latter specifies surface charges, approximates far-field conditions, or lineariezes conditions "regulating" the surface charge. The code may be run in either Cartesian, cylindrical, or spherical coordinates. THe potential and force due to a conical probe interacting with a flat plate is computed and the result compared with direct force measurements by chemical force microscopy.

ISBN: 0-9708275-0-4
Pages: 638