Determination of effective capacitance and film thickness from constant-phase-element parameters

Two different mathematical formulas for estimating effective capacitance from Constant-Phase-Element (CPE) parameters, taken from the literature, are associated unambiguously with either surface or normal time-constant distributions. Application to different systems are used to illustrate the importance of using the correct formula that corresponds to a given type of distribution. Experiments and simulations are used to show that the effective capacitance obtained for a normal distribution yields correct values for the film thickness under conditions where the local resistivity does not vary significantly. When the local resistivity varies considerably over the thickness of a film, the experimental frequency range may preclude observation of the capacitance contribution of a portion of the film, resulting in under prediction of the film thickness.