The mechanical and electrical properties of thin films have been become important and urgent in recent years, especially, the laminated structure made by films stacked over hundreds of layers. For example, the Multi-Layered Ceramic Capacitors (MLCCs) are such structures fabricated by one layer ceramic film interleaves with one layer electrode film repeatedly a hundred times. Thus, the advantages of MLCCs include small volume, mass product, and high capacity. That makes the MLCCs the necessary part of passive components. The Finite element method is adopted in the study. The model is built by the simulation program of ANSYS. After meshing and setting boundary conditions, the numerical process is performed. The numerical simulation was started first by applying a uniformly distributed pressure on the top of near hundred layers of MLCCs before sintering process with the bottom plate fixed. Then, the displacement and stress fields of MLCCs under five pressures were obtained and discussed. In order to visualize the results, the data of displacement and the stress fields were listed in Tables and plot in Figures. In addition to the MLCCs under vertically and uniformly distributed pressure, the slightly slant distributed pressure and gradient distributed pressure had been simulated. Next, the results of changing Young¡¦s modulus had also been received. It is found that the vertical distributed pressure and slant distributed pressure were not the main factor led to the side deformation. The lateral constraint of gradient distributed pressure would influence the deformation of the MLCCs significantly.

The complicated process may cause the internal defects of multi-layered ceramic capacitors (MLCCs) and result in the malfunctions. This work aims to investigate the deformations of MLCCs that composed of nearly a hundred of BaTiO3 and Ni electrode films interleaved and stacked due to high pressure at elevated temperature. This study focuses on theoretical and numerical analyses. Classical laminated plate theory, linear elastic assumptions and equilibrium equations were adopted. Associated with the texts by Timoshenko and practical manufacturing process, three types of boundary conditions were considered, such as all edges simple-supported, two opposite edges simple-supported and the other two free, and four edges free. Also, two more conditions need be added, including four fixed points at corners and the elastic foundation at bottom. The numerical simulation by finite element method (FEM) incorporated with software ANSYS was used to obtain the displacement field of MLCCs due to high pressure at elevated temperature. The MLCCs were divided into nine regions with suitably different boundary conditions. Compared with the numerical results the analytical solutions of nine regions were found satisfactorily acceptable, i.e., the errors were about 0.1% - 6.2% for the boundary conditions of four edges free and four corners fixed. The errors about 0.13% - 6.15% were also acceptable for the boundary conditions of two opposite edges simple-supported and the others free. However, the analytical solutions did not agree with the numerical results for the case of all the boundary conditions simple-supported. Finally the proposed theoretical methodology provides an analytical method alternatively, instead of FEM and ANSYS, to analyze a nearly hundred layered MLCCs.