Interpolation of numerically computed potential using finite element approach

Abstract

Finite difference method (FDM) is a very useful and simple tool in determining electrical potential field of two‐dimensional geometries, such as integrated circuit (IC) planar resistors. It is very accurate and its accuracy can be easily controlled by changing the grid size. One limitation of the FDM, however, is that it computes potentials at predetermined grid points only. Unlike the finite element method (FEM), it does not compute potential functions that can be used to interpolate potentials at the points that are not located at the grid, or to use these functions in determining other quantities based upon the computed potential such as electric field intensity. This paper describes a method that is a combination of the FDM and FEM. It retains the simplicity and accuracy of the FDM. Yet, like the FEM, it provides potential functions that can be used for interpolation and post‐processing of potential. The combined FDM‐FEM method is used to determine the potential functions of an IC planar resistor. The results are in agreement with analytically derived results. The approach we have developed is simple yet accurate and thus of use in professional engineering work.