  Based on theoretical arguments we propose a possible route for controlling
the band-gap in the promising photovoltaic material CdIn$_2$S$_4$. Our
\textit{ab initio} calculations show that the experimental degree of inversion
in this spinel (fraction of tetrahedral sites occupied by In) corresponds
approximately to the equilibrium value given by the minimum of the theoretical
inversion free energy at a typical synthesis temperature. Modification of this
temperature, or of the cooling rate after synthesis, is then expected to change
the inversion degree, which in turn sensitively tunes the electronic band-gap
of the solid, as shown here by accurate screened hybrid functional
calculations.
