Surface Roughness of Sputtered Silicon. I. Surface Modeling

A mathematical model for the calculation of surface roughness was developed for focused ion beam (FIB) sputtering. The surface roughness function is a combination of the beam function and the material function. The beam function includes ion type, ion acceleration energy, and beam parameters. Furthermore, the beam parameter incorporates ion flux, the ion beam intensity distribution profile, tailing and neighboring of the successive beams, dwell time, etc. The intensity distribution inside the ion beam is considered to be Gaussian. The cumulative intensity over the total milling area is calculated by the algebraic summation of individual beam intensity delivered to every pixel successively. The material function includes the inherent material properties related to the ion beam micromachining. If one knows the beam function and material function, surface roughness at the bottom of the sputtered features can be calculated using this model.