Polytypism in ZnS, ZnSe, and ZnTe: First-principles study

We report results of first-principles calculations based on the projector augmented wave (PAW) method to explore the structural, thermodynamic, and electronic properties of cubic (3C) and hexagonal (6H, 4H, and 2H) polytypes of II-VI compounds: ZnS, ZnSe, and ZnTe. We find that the different bond stacking in II-VI polytypes remarkably influences the resulting physical properties. Furthermore, the degree of hexagonality is found to be useful to understand both the ground-state properties and the electronic structure of these compounds. The resulting lattice parameters, energetic stability, and characteristic band energies are in good agreement with available experimental data. Trends with hexagonality of the polytype are investigated.

Figure 1

Stick-and-ball models of 3C and $p$H ($p=2$, 4, 6) of ZnX polytypes. Zinc: brown spheres, X (X = S, Se, and Te): gray spheres. The stacking sequence of the cation-anion bilayers are indicated by the symbols A, B, or C. Primitive unit cells are shown for the $p$H polytypes, while a nonprimitive hexagonal cell is depicted to illustrate the 3C symmetry.

Figure 2

Structural and energetic properties as function of the hexagonality of the polytype. (a) Renormalized lattice constant ratio $2c/\left(pa\right)$. (b) Lattice parameter $a$. (c) Cohesive energy per cation-anion pair relative to the 3C value. Lines are only given to guide the eye.

Figure 3

The uppermost valence and lowest conduction bands near $\Gamma$ of the hexagonal polytypes and 3C of (a) ZnS, (b) ZnSe, and (c) ZnTe. The valence band maximum is used as energy zero. The symmetry of the most important states is indicated.

Figure 4

Band gap (a), spin-orbit splitting (b), and crystal-field splitting (c) vs polytype hexagonality $h$.