Capacitance of Thin Dielectric Structures

Abstract

The capacitance contribution from the space charge and associated potential distribution in the metal electrodes of a parallel‐plane capacitor has been estimated by a classical, electrostatic calculation. The electron density is assumed to be given by the absolute zero temperature, Fermi‐Dirac distribution function. The first integration of Poisson's equation and application of the boundary conditions for the electric field at the metal‐dielectric interfaces result in two nonlinear, algebraic equations (one for each electrode) for the potential distribution as a function of the dielectric thickness and applied voltage. These equations were solved numerically. The results show that for reasonable electric fields in the dielectric (8 V/cm) the lumped‐series capacitance of the electrodes is practically constant and independent of applied voltage and dielectric thickness, in good, qualitative agreement with previously reported experimental results. The total capacitance is the series combination of the capacitances of the dielectric and the electrodes. The electrodes are effectively a capacitor with a thickness 2.3 L, where L is a length characteristic of the metal. This electrode series capacitance for metals such as gold is of the order of 1 μF/cm².