  A density functional study is presented of the interstitial Zn$_i$, Ge$_i$,
and N$_i$ in ZnGeN$_2$. Corrections to the band gap are included by means of
the LDA+U method.
  The Zn and Ge interstitials are both found to strongly prefer the larger
octahedral site compared to the two types of tetrahedral sites.
  The Zn interstitial is found to be a shallow double donor but has higher
energy than previously studied antisite defects. It has a resonance in the
conduction band which is Zn-$s$ like.
  The Ge interstitial is an even higher energy of formation defect and also
behaves as a shallow double donor but has also a deep level in the gap,
corresponding to a Ge-$s$ orbital character while the Ge-$p$ forms a resonance
in the conduction band.
  The nitrogen interstitial forms a split-interstitial configuration, as also
occurs in GaN. Its electronic levels can be related to that of a N$_2$
molecule. The defect levels in the gap correspond to the $\pi_g$-like lowest
unoccupied molecular orbital (LUMO) of the molecule, which here becomes filled
with 3 electrons in the defect's neutral charge state. They are found to prefer
a high-spin configuration in the $q=+1$ state.
  The corresponding transition levels are obtained and show that this is an
amphoteric trap level occurring in $+2$, $+1$, 0 and $-1$ charge states. The
two possible sites for this split interstitial, on top of Zn or on top of Ge
differ slightly in N$_2$ bond-length. While the N$_i$ defects have the lowest
formation energy among the interstitials, it is still higher than that of the
antisites.
  Hence they are not expected to occur in sufficient concentration to affect
the intrinsic Fermi level position. In particular, they do not contribute to
the unintentional n-type background doping.
