Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films

Constant-phase element (CPE) behavior may be attributed to the distribution of physical properties in films, in the direction normal to the electrode surface. Numerical simulations were used to show that under assumption that the dielectric constant is independent of position, a normal power-law distribution of local resistivity is consistent with the CPE. An analytic expression for the impedance corresponding to a power-law distribution of resistivity was developed and used to establish a relationship between parameters for the CPE and physical properties of the film. The resulting impedance response was compared to that obtained from the Young resistivity distribution.