Application of Johnson's approximation in finite element modeling for electric field-dependent materials for use in multi-layer ceramic capacitor applications.

This thesis investigates the complex relationships between material properties and their response to electric fields, with a particular focus on voltage-dependent capacitance. A key objective was to develop and validate a simulation code based on Johnson’s equation to model the voltage dependency of dielectric materials. The code successfully captures the nonlinear behaviour of relative permittivity under varying electric fields, with simulation results closely aligned with established models and experimental data. This verification process demonstrates the reliability of the code for predicting dielectric behaviour.
The thesis further explores the impact of parameters such as Johnson’s parameter, applied electric field strength, material thickness, and intrinsic permittivity on the dielectric response. Results reveal that effective permittivity is highly sensitive to Johnson’s parameter and field strength, particularly in high-permittivity materials like barium titanate, where a decline in dielectric response is observed at higher values of these parameters. A saturation effect is also noted at higher Johnson’s parameter and field strengths. Additionally, material thickness plays a critical role in the final temperature coefficient of capacitance (TCC), with thickness having a stronger influence than other factors like volume fraction and conductivity ratio.
The thesis also compares analytical and simulated models, demonstrating that the simulations provide accurate results with minimal deviations from analytical solutions (less than 2%). A finite element modeling approach is developed to study multilayer ceramic capacitors (MLCCs), revealing how the core-shell structure of BaTiO3 influences voltage-capacitance characteristics. The findings offer new insights into the design of MLCCs with improved performance, tailored voltage dependence, and enhanced breakdown strength. Overall, this research contributes significantly to understanding dielectric material behaviour.