An extended proof of the Ramo-Shockley theorem

Abstract

An introduction of a new functional form of Green's theorem for inhomogeneous media has enabled us to show that the Ramo-Shockley theorem derived for inhomogeneous media with electrodes maintained at constant potentials is still valid even when the electrode potentials are time-varying. Our proof, which is based on this modified Green's theorem, is an extension of Ramo's original proof and is different from the energy balance method which is the existing method of proof of the theorem for inhomogeneous media at constant electrode potentials. Our proof provides a basis for calculations of the instantaneous currents in semiconductor devices using particle simulations such as the Monte-Carlo method since it differentiates clearly the current induced in the electrodes due to the moving charges from the current caused by the time-varying potentials of the electrodes through capacitive couplings among the electrodes.