This paper presents a heuristic model for scanning helium ion beam lithography (SHIBL) in a EUV chemically amplified resist. The model employs a point-spread function to account for all physical and chemical phenomena involved in the resist activation. Ion shot noise effects are accounted for using Poisson statistics. Our model shows a good agreement with earlier single-pixel SHIBL experiments for determining line width as a function of dose for a desired line-and-space pattern. Furthermore, we propose optimized-pixel-dose SHIBL to improve exposure latitude, LCDU and LWR. Dose optimization is advantageous to single-pixel exposure when the feature size is at least about twice the width of the FWHM of the point-spread function. We confirm this by comparing our modeling results for single-pixel and optimized-pixel-dose exposure modes for line-and-space patterns.