Scaling size distribution of oxide defects, trema-fractal oxide layer, and breakdown statistics of metal-oxide-semiconductor devices

Yadava, R. D. S.
February 1989
Applied Physics Letters;2/27/1989, Vol. 54 Issue 9, p834
Academic Journal
The extreme value distribution, characteristic of the defect-related dielectric breakdown in thin SiO2 films, is derived by assuming that (i) the defects are Poisson distributed in space with their mean densities scaling with their sizes as D(a)∼a-γ, where D(a) is the total density of defects having sizes more than a and γ is a constant, and (ii) the dielectric strengths of weak spots associated with the defects are logarithmically related to their sizes as E∝-ln a. It is argued that γ<1. This implies that the defect-free region of the oxide film is a non-self-similar random fractal with fractal dimension df =2 and topological dimension dt =1.


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