  Despite the widespread use of Scanning Transmission Electron Microscopy
(STEM) for observing the structure of materials at the atomic scale, a detailed
understanding of some relevant electron beam damage mechanisms is limited.
Recent reports suggest that certain types of damage can be modeled as a
diffusion process and that the accumulation effects of this process must be
kept low in order to reduce damage. We therefore develop an explicit
mathematical formulation of spatiotemporal diffusion processes in STEM that
take into account both instrument and sample parameters. Furthermore, our
framework can aid the design of Diffusion Controlled Sampling (DCS) strategies
using optimally selected probe positions in STEM, that constrain the cumulative
diffusion distribution. Numerical simulations highlight the variability of the
cumulative diffusion distribution for different experimental STEM
configurations. These analytical and numerical frameworks can subsequently be
used for careful design of 2- and 4-dimensional STEM experiments where beam
damage is minimised.
