R. Nassar et al., MATHEMATICAL-MODELING OF FOCUSED ION-BEAM MICROFABRICATION, Journal of vacuum science & technology. B, Microelectronics and nanometer structures processing, measurement and phenomena, 16(1), 1998, pp. 109-115
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.