The spatial resolution of cathodoluminescence (CL) technique only depends on minority carrier diffusion length  if no electric field is built in the local irradiation region. However, the electron beam can generate a local electrical potential that causes an internal current flow and then affects the resolution, for instance, in some structures such as p-n junctions and grain boundaries.
The reported resolution of cathodoluminescence technique is 10 nm for InGaN/GaN multiple quantum well structures .
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 J. Bruckbauer, P.R. Edwards, T. Wang, R.W. Martin: High resolution cathodoluminescence
hyperspectral imaging of surface features in InGaN/GaN multiple quantum well structures,
Appl. Phys. Lett. 98 (2011) 141908.