Trends in the band-gap pressure coefficients and bulk moduli in different structures of ZnGa₂S₄, ZnGa₂Se₄ and ZnGa₂Te₄

We have performed a first-principles investigation for the family of compounds ZnGa₂X₄ (X= S, Se, Te). The properties of two possible structures, defect chalcopyrite and defect famatinite are both calculated. We reveal that ZnGa₂S₄ and ZnGa₂Se₄ have direct band gaps, while ZnGa₂Te₄ has an indirect band gap. The local density approximation band gaps are found to be very different in two structures, while the lattice parameters and bulk moduli are similar. We extend Cohen's empirical formula for zinc-blende compounds to this family of compounds. The pressure coefficients are calculated and metallization pressures are discussed. We find that a_gⁱ remains fairly constant when the group-VI element X is varied in ZnGa₂X₄(II–III₂–VI₄).