Prediction of breakdown in ultrathin SiO_2 films with fractal distribution of traps

摘要

An approach to modeling of thin SiO_2 film degradation based on fractal distribution of traps is presented, which shows a high predictive power for ultrathin oxides breakdown. The fractal patterns of traps are produced by a modified version of the diffusion limited aggregation (DLA) model introduced in literature as to describe irreversible colloidal aggregation. In the present version of the DLA model, the trap generation in SiO_2 is not random. It occurs at an interface or the trap aggregates to another existing trap. The movement probabilities of particles creating traps are defined through two parameters, which describe the lateral and straight movement. The two parameter values have been set as to obtain a certain fractal dimension (1.7) derived from optical inspections on dielectrics already reported in literature. The model has been calibrated using breakdown data obtained on samples fabricated ad hoc. It is coherent with the Weibull statistics describing the oxide film failure. Finally, the results of the model have been compared with experimental data of breakdown taken from literature.