Charge transport model to predict dielectric breakdown as a function of voltage,temperature, and thickness

As the minimum pitch in interconnects continues to shrink, dielectric breakdown is becoming increasingly more difficult to qualify for each new technology node. Standard voltage-acceleration models provide quick, but general, assessments of the dielectric quality. Instead, a one-dimensional charge transport model has been developed as a tool to investigate the process of the dielectric breakdown and why it occurs. The model couples Poisson's equation with constitutive equations for mobile electrons, trapped electrons, and defects in the dielectric. Bonds in the dielectric matrix are weakened by the electric field, and broken by energetic electrons, creating defects. Failure occurs when a critical defect density is reached, causing trap-to-trap tunneling and an abrupt increase in the current.The model successfully replicates electrical data for leakage current and dielectric failure as a function of voltage, temperature, and thickness. The activation energy for dielectric failure is shown to increase as the electric field decreases, resulting in much higher activation energies at operating conditions compared to testing conditions. The dielectric strength also increases for decreasing thickness based on a previous theory for planar dielectrics, and is shown to cause the failure vs. field slope to increase for thinner dielectrics.