Percolation models for gate oxide breakdown

Computer calculations of the formation of a percolation path across a finit e lattice are used to model dielectric breakdown. The classical scaling rel ations for percolation are expected to be valid only for large (finite) sys tems near p(c). We investigate the opposite limit of very small samples, co mparable to the lattice spacing. It is shown that relatively simple numeric al calculations can quantitatively describe the statistics and thickness de pendence of oxide breakdown in thin samples. The critical defect density fo r breakdown shows a strong decrease with thickness below about 5 nm, then b ecomes constant below 3 nm. Both of these features can be quantitatively ex plained by percolation on a finite lattice. The effective defect "size" of about 3 nm is obtained from the thickness dependence of the breakdown distr ibutions. The model predicts a singular behavior when the oxide thickness b ecomes less than the defect size, because in this limit a single defect nea r the center of the oxide is sufficient to create a continuous path across the sample. It is found that a given percolation path has a probability of about 10(-3) for initiating destructive breakdown. We investigate both homo geneous percolation and percolation in a nonuniform density of sites. (C) 1 999 American Institute of Physics. [S0021-8979(99)05222-6].