  We investigate the feasibility of epitaxial growth of a three-dimensional
semiconductor on a two-dimensional substrate. In particular, we report for the
first time on molecular beam epitaxy growth of cadmium telluride (CdTe) quantum
wells on hexagonal boron nitride (hBN). The presence of the quantum wells is
confirmed by photoluminescence measurements conducted at helium temperatures.
Growth of quantum wells on two dimensional, almost perfectly flat hBN appears
to be very different from growth on bulk substrates, in particular it requires
70-100$^\circ$C lower temperatures.
