Finite‐Element Analysis of Ceramic Multilayer Capacitors: Modeling and Electrical Impedance Spectroscopy for a Nondestructive Failure Test

Abstract

The opportunities are introduced to calculate the electrical, mechanical, and thermal couplings of ceramic multilayer capacitors (MLCs) with the finite-element method. The results may lead to improvements in the production, integration, and operation of MLCs. In this paper, a comparison is given of calculations and measurements of electromechanical resonances in the impedance spectra of MLCs. The simulation of defective capacitors with three different types of assumed faults reveals the changes in the impedance spectra due to these defects. This allows the prediction of flaws in MLCs based on measurement of the impedance spectra.

Physical origin of residual thermal stresses in a multilayer ceramic capacitor

“…The increase of the HM decreases the magnitude of the average in-plane stress components 11 and 22 more efficiently than the LM as seen in the right columns of Figs. 2͑a͒ and 3͑a͒ by the reason aforementioned.…”

“…This magnitude is presented herein for the purpose of extracting physical origin of the residual thermal stress. As can be seen, the in-plane residual stress components 11 and 22 develop even when no margins exist. In Figs.…”

“…An interesting point is that the role of the HM in reducing the magnitude of average in-plane stress in the active region is more enhanced when the LM coexists although the role of the LM itself is not apparent. For instance, 11 The reason for the synergistic effect is because the motion of the HM along axis 1 and 2, by the attached shrinking nickel electrode in the active region, is buttressed by the presence of the LM. This phenomenon resists the tendency of the nickel electrode in the active region to compress the dielectric layer in the same region along axis 1 ͑ 11 ͒ and 2 ͑ 22 ͒, respectively, thereby the synergistic effect results.…”

“…Thus, FEM has been widely used to analyze the stress state in many nano- 9 and microstructures including MLCCs. [10][11][12][13] It has thus been adopted herein to elucidate the physical origin of the evolution of residual stresses in a MLCC and the numerical result has been compared with some experimental data in the literature. Figure 1 shows the considered geometry of a MLCC as well as a one-eighth space of the three-dimensional ͑3D͒ geometry that was modeled with appropriate boundary conditions to reduce computational load.…”

“…2,3 Regarding the influence of the residual stress on the dielectric constant of a MLCC, it has been reported that outof-plane stress ͑vertical 33 component͒ in a ceramic layer increases the dielectric constant when it is tensile. 4 In the cases of the in-plane stresses 11 and 22 , they increase the dielectric constant when they are compressive. This knowledge successfully explained the increase in the dielectric constant with the increase in the number of layers in a MLCC.…”