Synchrotron X-ray nano computed tomography was used to investigate the microstructural evolution during co-sintering of multi-layer ceramic capacitors (MLCC) consisting of Ni electrodes and BaTiO3 dielectric layers stacked alternately. As the electrode thickness reduced to submicron at the scale of a few particle diameters, the process produced the defect of inner electrode leading to capacitance loss. The discontinuous electrode region contained round holes and irregularly-shaped channels. The formation of discontinuity was associated with the increase of characteristic length of heterogeneous electrode structure, i.e., the coarsening occurred. The evolution of electrode morphology by surface/interface diffusion caused the breakup of ligament between two holes driven by instability induced by surface tension and stress. The ligament pinch-off inevitably generated sharp points which might enhance the local electric field bringing about the dielectric breakdown. A model was presented to explain the formation of defect from the heterogeneous particles packing in the electrode layer.