Correlation Between TDDB and VRDB for Low- $k$ Dielectrics With Square Root $E$ Model

A concise relation between voltage ramp dielectric breakdown (VRDB) and time-dependent dielectric breakdown (TDDB) based on the square-root (SQRT) E model for low- k dielectric-reliability evaluation was established. VRDB and TDDB experiments on low- k dielectrics in Cu interconnects were conducted and showed a very well correlation by this relation. The electric field acceleration parameter of the SQRT E model can be estimated with the dual ramping rate VRDB test. The characteristic of the statistic distribution of VRDB is shown to relate to that of TDDB.