Detailed investigating into the effects of spherical and chromatic abe
rrations, diffraction and the probe current allows the more general fo
rmulae for the optimized aperture and the minimum probe radius in low-
voltage scanning electron microscopes (LVSEMs) to be derived using bot
h wave optics and geometric optics. The probe sizes for a diversity of
electron sources in LVSEMs have been estimated, which may be useful f
or practical applications. The computed results indicate the possibili
ty of achieving 1.5-2.0-nm resolution at low voltages.