Contact hole model for etch depth dependence

The dependence of the etch depth of a contact hole or circular via on the d iameter of the hole opening is derived for a simple model which includes th e effect of the bombarding ions and the neutral radicals on the etching. Th e ion etch rate at the center of the contact hole is proportional to the io n energy flux and the neutral etch rate is proportional to the neutral flux expression for molecular flow in a pipe. The total etch rate expression is found by Langmuir kinetics. The linear experimental relation for the etch depth versus the inverse diameter holds in this model for etching in the ne ar ion flux-limited regime. The dependence of the etch depth and average et ch rate on the etch time is given for this model. (C) 1999 American Vacuum Society. [S0734-211X(99)02901-7].