  We theoretically investigate two different magnetic tunneling junctions
(MTJs) with semiconductor barriers, CuInSe${}_{2}$ (CIS) and CuGaSe${}_{2}$
(CGS), which are the terminal compounds of recently reported mixed
semiconductor barrier, CuIn${}_{1-x}$Ga$_{\it x}$Se${}_{2}$. To discuss the
transport properties of these systems, we analyze complex band structures,
magnetoresistance (MR) ratios, and resistance-area products ($RA$) by using
first-principles based calculations in combination with the Landauer formula.
It is found that the $\Delta_{1}$ wave functions have dominant contributions to
the spin-dependent tunneling transport in both CIS- and CGS-based MTJs. We also
find that the CGS-based MTJ has a much larger MR ratio and slightly higher $RA$
than those of the CIS-based MTJ, which indicates that a larger MR ratio is
expected for a higher Ga concentration $x$ in the
CuIn${}_{1-x}$Ga${}_{x}$Se${}_{2}$-based MTJs. We further study the
relationship between the band gaps in the barriers and MR ratios by changing
the Coulomb repulsions in the Cu 3$d$ states of the CIS and CGS. It is shown
that the barrier with a larger band gap yields a larger MR ratio. The
comparison of MR ratios and $RA$ between the CIS-, CGS-, and MgO-based MTJs are
also given.
