Proposed universal relationship between dielectric breakdown and dielectric constant

Dielectrics with high dielectric constant k will likely be required for future replacement of conventional SiO2 gate dielectric. Physical models are needed which describe the reliability tradeoffs associated with the high-k material selection. In this paper we report on a fundamental relationship existing between the dielectric breakdown E-bd and dielectric constant k. An approximate E-bd similar to (k)(-1/2) relation is found and seems to be universal, i.e., the relation holds over nearly two decades of dielectric constant. A physics-based model has been developed to understand this critically important relationship. The good fit of the physical model (with no adjustable parameters) to the experimental data suggests that the local electric field (Lorentz-relation/Mossotti-field) in these high-k materials plays a very important role in the observed E-bd similar to (k)(-1/2) behavior. The very high local electric field (in high-k materials) tends to distort/weaken polar molecular-bonds thereby lowering the enthalpy of activation required for bond breakage by standard Boltzmann processes.