TDDB lifetime of asymmetric patterns and its comprehension from percolation theory

TDDB-lifetime distribution of asymmetric pattern (perpendicular-faced comb) was estimated using a 3-dimensional electrostatic model calculation and its statistical treatment based on the percolation theory. Nanometer-size small cells which represent the minimum unit of electric isolation are placed along the perimeter of an asymmetric pattern. In the model, a dielectric breakdown occurs when a series of defective cells form a path through the potential barrier. The local electric field near the cathode dictates the percolation-path length (tunneling distance). The model suggests that a negative bias at the pattern tips provides a shorter percolation path due to steep gradient of potential, resulting in a shorter lifetime. However, in contrast to the model predictions the experimental data do show only a small difference between positive and negative biases. Therefore, the theoretical estimation from the ideal electric field leads us too much shorter lifetime than the real case.