Vast Structural and Polymorphic Varieties of Semiconductors AMM′Q₄ (A = K, Rb, Cs, Tl; M = Ga, In; M′ = Ge, Sn; Q = S, Se)

Nine new chalcogenide semiconductors AInM′Q₄ (A⁺ = K⁺, Rb⁺, Cs⁺, Tl⁺; M′⁴⁺ = Ge⁴⁺, Sn⁴⁺; Q^2– = S^2–, Se^2–) have been prepared by solid-state syntheses and structurally characterized by single-crystal X-ray diffraction techniques. These new phases fill in the missing links in these quaternary systems and crystallize in various two-dimensional layered polymorphs, while combinations containing large M³⁺ and M′⁴⁺ cations also adopt an extended three-dimensional (3D) network structure. The AMM′Q₄ materials exhibit a wide range of band gaps with colored selenides (1.8 eV < E_g < 2.3 eV) and mostly white sulfides (2.5 eV < E_g < 3.6 eV). These phases have direct band gaps except for the thallium analogues and the cubic AGaSnSe₄-cP84. First-principles theoretical calculations of the electronic band structures reveal critical insight into the structure/property relationships of these materials. The distinct polymorphism of these quaternary phases is studied by discussing kinetic and thermodynamic factors responsible for the crystallization, structural considerations, and complementary density functional theory (DFT) calculations.