  Fast, large area patterning of arbitrary structures down to the nanometre
scale is of great interest for a range of applications including the
semiconductor industry, quantum electronics, nanophotonics and others. It was
recently proposed that nanometre-resolution mask lithography can be realised by
sending metastable helium atoms through a binary holography mask consisting of
a pattern of holes. However, these first calculations were done using a simple
scalar wave approach, which did not consider the dispersion force interaction
between the atoms and the mask material. To access the true potential of the
idea, it is necessary to access how this interaction affects the atoms. Here we
present a theoretical study of the dispersion force interaction between an atom
and a dielectric membrane with a hole. We look at metastable and ground state
helium, using experimentally realistic wavelengths (0.05-1 nm) and membrane
thicknesses (5-50 nm). We find that the effective hole radius is reduced by
around 1-7 nm for metastable helium and 0.5-3.5 nm for ground-state helium. As
expected, the reduction is largest for thick membranes and slow atoms.
