TDDB at low voltages: An electrochemical perspective

TDDB lifetime projections at operating voltages for backend of line (BEOL) dielectrics have been based on accelerated testing at high fields and extrapolation to operating conditions based on electric field dependent dielectric wearout models. As operating voltages are reduced to 1V range, such intrinsic field acceleration based wearout mechanisms become negligible making such extrapolations questionable. At the same time, as we scale the BEOL geometries, extrinsic wearout mechanisms involving copper and moisture can impact TDDB reliability. In this paper, we, for the first time, investigate extrinsic reliability in low voltage regime where electrochemical redox reactions are possible. We formulate a physical electrochemical model for TDDB. We present analytic solution for limiting cases that show TDDB lifetime dependence on voltage or electric field depending on relative rates of electrode reactions and field assisted ion transport. Generalization to higher voltages are also discussed.