Real image resolution of SEM and low-energy SEM and its optimization: distribution width of the total surface emission

The real point resolution of an SEM image is treated in a two-dimensional model where the decisive quantity is the root-mean-square distance of the emitted electron from the pixel centre. This quantity is computed taking into account the direct illumination of the specimen surface by the primary spot the dimensions of which are given by the electron optical column and the indirect illumination from a virtual source of the backscattered electrons in the specimen depth the properties of which depend on the specimen. Because the second order movement of the full distribution is considered here instead of some measure of the central narrow peak of secondaries, the backscattered electron influence significantly deteriorates the resulting resolution. Reasonable approximations regarding both contributions, particularly the Monte-Carlo modelling of the backscattering process by algorithms providing acceptable results down to 1 keV and the approximate relations describing the secondary and backscattered electron emission again down to 1 keV, enabled us to bring the considerations up to numerical results for some typical instruments, namely a "cheap" SEM, a "top" SEM and a low-energy SEM (LESEM) adapted from the cheap SEM by using the cathode lens. The optimum landing energy providing the best point resolution, computed for the individual chemical elements, falls into the range 1 to 5 keV for the cheap SEM and it remains around 1 keV (with some uncertainty caused by the approximations mentioned) for both the top SEM and LESEM. Similarly, the real resolution for the elements ranges between 16 and 45 nm when the cheap SEM with a 3.4 nm nominal spotsize at 30 keV is used, between 3.5 and 9 nm for the 0.7 nm top SEM and between 5.5 and 7 nm for the cheap SEM adapted to LESEM.