Electrode defects in multilayer capacitors part I: Modeling the effect of electrode roughness and porosity on electric field enhancement and leakage current

Multilayer capacitors consist of multiple, often hundreds of capacitors connected in parallel to maximize volumetric efficiency. As the dielectric and electrode layer thicknesses are scaled down, microstructural imperfections become increasingly influential on the device electrical performance. Specifically, the presence of nonplanar and discontinuous electrodes can lead to local field enhancements while the relative morphologies of two adjacent electrodes determine variations in the local dielectric thickness. To study the effects of electrode morphologies, an analytical approach is taken to calculate the field enhancement and leakage current with respect to an ideal parallel-plate capacitor. It is shown that the electrode roughness causes the leakage current to increase with respect to that of the ideal flat parallel-plate capacitor. To further include the effects of local curvature on electric field enhancements, finite element methods are used to calculate field distributions within capacitor structures containing rough interfaces and porosity. In these simulations, the effects of electrode pore diameters, dielectric layer thickness, and the amplitude and wavelength of the electrode roughness are studied.