MATHEMATICAL-MODELING OF FOCUSED ION-BEAM MICROFABRICATION

A mathematical model for sputtering a shape or cavity with an arbitrar y cross-sectional profile has been developed for focused ion beam mill ing. The ion beam is assumed to have a Gaussian intensity distribution and a submicron width. The model solves for ion beam dwell times on a pixel grid which yields the desired feature depth as a function of th e pixel (x,y) coordinate. The solution is unique and accounts for the ion beam flux contribution at any point from all other pixels in the a ddress matrix. A semiempirical sputter yield treatment allows for a ve ry wide range of ion beam/solid combinations and for yield variations with ion energy and angle of incidence. Solutions have been obtained f or parabolic surfaces of revolution, a parabolic trench (with a plane of symmetry) and a hemispherical pit. Either a square or a circular pi xel matrix was used for the parabolic shapes. Correspondence between t he predictions of the model and experimental 20 keV Ga+ sputtering of a parabolic cross-section trench in Si(100) was within the limits of t he accuracy of the experimental control. (C) 1998 American Vacuum Soci ety.