  A first-principles study of the structural and electronic properies of carbon
impurities in CuIn$_{1-x}$Ga$_x$Se$_{2}$ is presented. Carbon is present in
organic molecules in the precursor solutions used in nonvacuum growth methods,
making more efficient use of material, time and energy than traditional vacuum
methods. The formation energies of several carbon impurities are calculated
using the hybrid HSE06 functional. C$_{\mathrm{Cu}}$ acts as a shallow donor,
C$_{\mathrm{In}}$ and interstitial C yield deep donor levels in CuInSe$_{2}$,
while in CuGaSe$_{2}$ C$_{\mathrm{Ga}}$ and interstitial C act as deep
amphoteric defects. So, if present, these defects reduce the majority carrier
(hole) concentration by compensating the acceptor levels and become trap states
for the photogenerated minority carriers (electrons). However, the formation
energies of the calculated carbon impurities are high, even under C-rich growth
conditions. Therefore, these impurities are not likely to form and will
probably be expelled to the intergranular region and out of the absorber layer.
