  We present a theoretical model of matter-wave diffraction through a material
nanostructure. This model is based on the numerical solution of the
time-dependent Schr{\"o}dinger equation, which goes beyond the standard
semi-classical approach. In particular, we consider the dispersion force
interaction between the atoms and the material, which is responsible for high
energy variations. The effect of such forces on the quantum model is
investigated, along with a comparison with the semi-classical model. In
particular, for atoms at low velocity and close to the material surface, the
semi-classical approach fails, while the quantum model accurately describes the
expected diffraction pattern. This description is thus relevant for slow and
cold atom experiments where increased precision is required, e.g. for
metrological applications.
