Multilayer capacitor margin stresses and electrode to dielectric thickness calculations

The mismatch of thermal expansion coefficients in co-fired multilayer capacitors (MLCs) leads to development of residual stress on cooling. These stresses are of a compressive nature for the multilayer stack and a tensile character for the ceramic margin. A closed-form stress calculation of the critical ratio of electrode thickness to ceramic dielectric thickness in the stack shows a limiting ratio of approximately 1:2. Design equations are given in order to calculate the multilayer electrode to dielectric thickness ratio. The required design parameters are the linear thermal expansion coefficients, the temperature difference, the Young's moduli, the strength of the ceramic margin, and the ratio of active to inactive capacitor area.