Behavior modeling of a CaCu3Ti4O12 ceramic for capacitor applications

In pursuit of high permittivity materials for microelectronics application, there has been a considerable interest recently in the dielectric properties of the cubic perovskite related CaCu₃Ti₄O₁₂ (CCT), since this material has a so called giant permittivity value (~100000). In this paper a model of the electrical behavior of the capacitor realized with this material is presented. This model is particularly well suited for time domain simulations. Two types of electrical measurements are realized: conduction current measurements (giving static I(V) characteristics) and impedance spectroscopy measurements for different levels of static polarization. The proposed non linear electrical model includes three components: a constant resistor in serial with a capacitor having Cole-Davidson relaxations in parallel with a non linear resistor (describing the non linear dependency of the conduction current when the voltage increases). A good accuracy is obtained for the description of the dynamical behavior in a wide range of frequency and bias voltage, with only five parameters. This frequency model is converted into a time domain model (state space representation) using the Diffusive Representation tool. This approach allows predicting losses and reveals itself efficient to get simple input-output behavioral models which are useful for general nonlinear circuit simulations in the field of electrical engineering.