A linear relation between the etch depth and the inverse diameter of a contact hole is derived approximately. The linear relation was found experimentally for contact holes etched in silicon dioxide and several models for it were computed.@super 1@ This linear relation can also be reexpressd as a function of time for which there is also data.@super 2@ The new feature is the application of Langmuir kinetics with synergistic etching of neutrals and the ions. The neutrals are modeled for molecular flow in a pipe with a sticking coefficient equal to one.@super 2@ This assumption is supported by a recent finding that the etching (nondepositive) neutrals are not adsorbed appreciably on top of the same neutrals on the passivated walls of contact holes etched in silicon dioxide.@super 3@ The ions are modeled simply by a vertical beam since the directed ion energy fluxes at the center of the contact hole fall off slowly with depth. The effect of the depositive neutrals on the etch depth relation is estimated. Etch rates for the neutrals and ions are computed from data.@super 1@
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@footnote 1@ 1. S. C. McNevin, M. Cerullo and J.T.C. Lee, Bull. Am. Phys. Soc. 42 1707 (1997). @footnote 2@ H. H@um u@bner and M. Engelhardt, J. Electrochem. Soc. 141, 2453 (1994). @footnote 3@ A. Misaka and K. Harafuji, IEEE Trans. Elect. Dev. 44, 751 (1997).