  As a prototypical example for a heterostructure combining a weakly and a
strongly interacting quantum many-body system, we study the interface between a
semiconductor and a Mott insulator. Via the hierarchy of correlations, we
derive and match the propagating or evanescent quasi-particle solutions on both
sides. While the propagation is described by a band-like dispersion in both the
weakly and the strongly interacting case, the inverse decay length across the
interface follows a different dependence on the band gap in the Mott insulator
and the semiconductor. As one consequence, tunnelling through a Mott insulating
layer behaves quite different from a semiconducting (or band insulating) layer.
For example, we find a strong suppression of tunnelling for energies in the
middle between the upper and lower Hubbard band of the Mott insulator.
