  The present paper is dedicated to the structural study of crystallographic
peculiarities appearing in epitaxial films of metastable epsilon iron oxide
($\varepsilon$-Fe$_2$O$_3$) grown by pulsed laser deposition onto a
semiconductor GaN (0001) substrate. The columnar structure of the nanoscale
$\varepsilon$-Fe$_2$O$_3$ films has been for the first time investigated using
high resolution electron microscopy (HRTEM) direct space technique complemented
by reciprocal space methods of high-energy electron diffraction and
color-enhanced HRTEM image Fourier filtering. The study of
$\varepsilon$-Fe$_2$O$_3$ / GaN interface formation has been further expanded
by carrying out a depth resolved analysis of density and chemical composition
by neutron reflectometry and energy-dispersive X-ray spectroscopy. The obtained
results shed light onto the properties and the origin of the enigmatic
few-nanometer thick low density transition layer residing at the
$\varepsilon$-Fe$_2$O$_3$ / GaN interface. A detailed knowledge of the
properties of this layer is believed to be highly important for the development
of $\varepsilon$-Fe$_2$O$_3$ / GaN heterostructures that can potentially become
part of the iron-oxide based ferroic-on-semiconductor devices with room
temperature magneto-electric coupling.
