Computer calculations of the formation of a percolation path across a finite lattice are used to model dielectric breakdown. The classical scaling relations for percolation are expected to be valid only for large (finite) systems near pc. We investigate the opposite limit of very small samples, comparable to the lattice spacing. It is shown that relatively simple numerical calculations can quantitatively describe the statistics and thickness dependence of oxide breakdown in thin samples. The critical defect density for breakdown shows a strong decrease with thickness below about 5 nm, then becomes constant below 3 nm. Both of these features can be quantitatively explained by percolation on a finite lattice. The effective defect “size” of about 3 nm is obtained from the thickness dependence of the breakdown distributions. The model predicts a singular behavior when the oxide thickness becomes less than the defect size, because in this limit a single defect near 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 homogeneous percolation and percolation in a nonuniform density of sites.

The rate of defect generation by electrical stress in silicon dioxide has been measured as a function of gate voltage down to 2 V on a variety of MOSFETs with oxide thickness in the range 1.4 -5 nm. The critical defect density necessary for destructive breakdown has also been measured in this thickness range. These quantities are used to predict time to breakdown for ultra thin oxides at low voltages. The properties of the breakdown distribution, which becomes broader as the oxide thickness is reduced, are used to provide reliability projections for the total gate area on a chip. It is predicted that oxide reliability may limit oxide scaling to about 2.6 nm (CV extrapolated thickness) or 2.2 nm (QM thickness) for a 1 V supply voltage at room temperature and that the current SIA roadmap will be unattainable for reliability reasons by sometime early next century.

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Experimental and theoretical investigations are reported for defect generation by electrical stress in silicon dioxide and for the critical number of defects necessary to trigger destructive breakdown. Experimental evidence is presented showing that the critical number of defects reaches a limit when the oxide thickness is reduced below 2.7 nm. Percolation calculations are shown to be consistent with this oxide thickness limit representing the “effective size” of one defect spanning the oxide, connecting anode and cathode together. Also, these calculations show that not all of the defects are capable of triggering a destructive breakdown event.