  We present a systematic study of the influence of elastic strain relaxation
on the built-in electrostatic potentials and the electronic properties of axial
(In,Ga)N/GaN nanowire heterostructures. We employ and evaluate analytical and
numerical approaches to compute strain and polarization potentials. These two
ingredients then enter an eight-band k.p model to compute electron and hole
ground states and energies. Our analysis reveals that for a sufficiently large
ratio between the thickness of the (In,Ga)N disk and the diameter of the
nanowire, the elastic relaxation leads to a significant reduction of the
built-in electrostatic potential in comparison to a planar system of similar
layer thickness and In content. However, a complete elimination of the built-in
potential cannot be achieved in axial nanowire heterostructures. Nevertheless,
the reduction of the built-in electrostatic potential leads to a significant
modification of the electron and hole energies. Our findings indicate that the
range of accessible ground state transition energies in an axial (In,Ga)N/GaN
nanowire heterostructure is limited due to the reduced influence of
polarization potentials for thicker disks. Additionally, we find that strain
and polarization potentials induce complex confinement features of electrons
and holes, which depend on the In content, shape, and dimensions of the
heterostructure.
