A comparison of the exact and an approximate solution for the resistance between two coplanar circular discs

摘要

One approach for modelling substrate noise coupling in mixed-signal integrated circuits is to calculate the surface potential at each point of interest caused by currents injected into the semiconductor substrate by different aggressor elements. However, calculation of the surface potential analytically is a very complicated problem and exact solutions are only available for a few simple configurations such as a single circular disc and two coplanar circular discs on a uniform semi-infinite substrate. For more complex situations approximate models using superposition of one-contact potentials is a more attractive approach. Therefore, this work compares the approximate superposition-model for the resistance between two coplanar circular discs on a uniform semi-infinite substrate with the exact solution, in order to give an estimate of the error introduced by using the superposition-model. It is seen that the error is very small when the separation distance between the discs are larger than roughly one contact radius, thus giving theoretical support for the already experimentally tested superposition-model.