  We present a first-principles computational study of cation-Se $\Sigma$3
(112) grain boundaries in CuGaSe$_2$. We discuss the structure of these grain
boundaries, as well as the effect of native defects and Na impurities on their
electronic properties. The formation energies show that the defects will tend
to form preferentially at the grain boundaries, rather than in the grain
interiors. We find that in Ga-rich growth conditions Cu vacancies as well as Ga
at Cu and Cu at Ga antisites are mainly responsible for having the equilibrium
Fermi level pinned toward the middle of the gap, resulting in carrier
depletion. The Na at Cu impurity in its +1 charge state contributes to this. In
Ga-poor growth conditions, on the other hand, the formation energies of Cu
vacancies and Ga at Cu antisites are comparatively too high for any significant
influence on carrier density or on the equilibrium Fermi level position. Thus,
under these conditions, the Cu at Ga antisites give rise to a $p$-type grain
boundary. Also, their formation energy is lower than the formation energy of Na
at Cu impurities. Thus, the latter will fail to act as a hole barrier
preventing recombination at the grain boundary, in contrast to what occurs in
CuInSe$_2$ grain boundaries. We also discuss the effect of the defects on the
electronic properties of bulk CuGaSe$_2$, which we assume reflect the
properties of the grain interiors.
