Size Dependence of Residual Thermal Stresses in Micro Multilayer Ceramic Capacitors by Using Finite Element Unit Cell Model Including Strain Gradient Effect

Abstract

The residual thermal stresses induced by the high-temperature sintering process in multilayer ceramic capacitors (MLCCs) are investigated by using a finite-element unit cell model, in which the strain gradient effect is considered. The numerical results show that the residual thermal stresses depend on the lateral margin length, the thickness ratio of the dielectrics layer to the electrode layer, and the MLCC size. At a given thickness ratio, as the MLCC size is scaled down, the peak shear stress reduces significantly and the normal stresses along the length and thickness directions change slightly with the decrease in the ceramic layer thickness t d as t d > 1 μm, but as t d < 1 μm, the normal stress components increase sharply with the increase in t d. Thus, the residual thermal stresses induced by the sintering process exhibit strong size effects and, therefore, the strain gradient effect should be taken into account in the design and evaluation of MLCC devices