  GaN/AlxGa1-xN quantum wells were grown by molecular beam epitaxy on high
quality bulk (0001) GaN substrates. The quantum well thickness was set in the
6-8 nm range to favor the photoluminescence emission of indirect excitons.
Indeed, such excitons are known to be spatially indirect, due to the presence
of the internal electric field which spatially separates the electron and hole
wave functions. The growth conditions were optimized in view of minimizing the
photoluminescence peak broadening. In particular, the impact of growth
temperature (up to 900{\deg}C) on the surface morphology, structural and
photoluminescence properties was studied. The diffusion of indirect excitons on
the scale of tens of microns was measured with a micro-photoluminescence setup
equipped with a spatially resolved detection. A dedicated model and its
analysis allow us to extract from these measurements the exciton diffusion
constant and to conclude on the optimum growth conditions for the GaN/AlxGa1-xN
quantum well structures suited for studies of quantum collective effects in
indirect exciton liquids.
