Relationship between constant-phase element (CPE) parameters and physical properties of films with a distributed resistivity

Several issues concerning constant-phase element (CPE) behavior in the impedance response of films with a distributed resistivity are addressed here. To carry it out we consider two theoretical distributed models that account for exact CPE behavior and which provided us with the phenomenology of power-law frequency responses usually found in the literature. We focus on the derivation of the relationship between CPE parameters and the physical properties of the film, which remains a challenging problem of paramount importance in impedance data interpretation. Results are compared to existing expressions widely used to extract film properties from CPE behavior, in particular to those derived by Hsu and Mansfeld [1] and by Hirschorn et al. [2]. A mathematical basis for the agreements or deviations observed in previous experimental works as well as for some conjectures formulated in related literature is provided. We also address some possible ambiguities that can arise when the experimental frequency range does not allow the recognition of the overall behavior.