Impedance Spectroscopy Models for X5R Multilayer Ceramic Capacitors

High capacitance X5R MLCCs based on $BaTiO_3$ ceramic dielectric layers exhibit a single broad, asymmetric arc shape impedance and modulus response over the wide frequency range between 1 MHz to 0.01 Hz. Analysis according to the conventional brick-layer model for polycrystalline conductors employing a series connection of multiple RC parallel circuits leads to parameters associated with large errors and of little physical significance. A new parametric impedance model is shown to satisfactorily describe the experimental spectra, which is a parallel network of one resistor R representing the DC conductivity thermally activated by 1.32 eV, one ideal capacitor C exactly representing bulk capacitance, and a constant phase element (CPE) Q with complex capacitance $A(i{\omega})^{{\alpha}-1}$ with ${\alpha}$ close to 2/3 and A thermally activated by 0.45 eV or ca. 1/3 of activation energy of DC conductivity. The feature strongly indicate the CK1 model by J. R. Macdonald, where the CPE with 2/3 power-law exponent represents the polarization effects originating from mobile charge carriers. The CPE term is suggested to be directly related to the trapping of the electronic charge carriers and indirectly related to the ionic defects responsible for the insulation resistance degradation.