3.4 Important Crystal Structures
47
Fig. 3.19 a Top view
(along the c-axis) and b
side view of the wurtzite
structure with the
tetragonal bonds indicated.
The top (bottom) surface of
the depicted structure is
termed the Zn-face, (00.1)
(O-face, (00. ¯
1))
(a)
(b)
Fig. 3.20 Comparison of
the tetragonal bonds in the
a zincblende and b wurtzite
structure (i: inversion
center, m: symmetry plane)
Thus the cation and anion sublattices are shifted with respect to each other by a quarter of the body
diagonal of the fcc lattice. The atoms are tetrahedrally coordinated, a Zn atom is bonded to four S atoms
and vice versa. However, no inversion center is present any longer (point group T d ). In the zincblende
structure the stacking order of diatomic planes along the body diagonal is aAbBcCaAbBcC. . .
Many important compound semiconductors, such as GaAs, InAs, AlAs, InP, GaP and their alloys
(cf. Sect. 3.7), but also the II–VI compounds ZnS, ZnSe, ZnTe, HgTe and CdTe and halides, including
AgI, CuF, CuCl, CuBr, and CuI, crystallize in the zincblende structure.
Four-fold coordinated materials (zincblende and wurtzite) typically undergo a phase transition into
6-fold coordinated structures upon hydrostatic pressure [208]. For GaAs under pressure see [209].
3.4.5 Wurtzite Structure
The wurtzite structure (ZnS, space group 186, P6 3 mc) is also called the hexagonal ZnS structure
(because ZnS has both modifications). It consists of a hexagonal lattice with a unit cell of four atoms
(Fig. 3.19). Typically, it is thought of as a hcp structure with a diatomic base. The c/a ratio typically
deviates from the ideal value ζ 0 =
√
8/3 ≈ 1.633 (3.4) as listed in Table 3.3. The c-axis is a 6 3 screw
axis.
The Zn atom is located at (0, 0, 0), the S atom at (0, 0,
√
3/8)a. This corresponds to a shift of 3/8 c
along the c-axis. This factor is called the cell-internal parameter u. For real wurtzite crystals u deviates
from its ideal value u 0 = 3/8 = 0.375, e.g. for group-III nitrides u > u 0 . The diatomic planes have a
stacking order of aAbBaAbB. . . along the [00.1]-direction as visualized in Fig. 3.17b.
In Fig. 3.20 the different local structural environment of the atoms in the zincblende and wurtzite
structure is shown.
47
Fig. 3.19 a Top view
(along the c-axis) and b
side view of the wurtzite
structure with the
tetragonal bonds indicated.
The top (bottom) surface of
the depicted structure is
termed the Zn-face, (00.1)
(O-face, (00. ¯
1))
(a)
(b)
Fig. 3.20 Comparison of
the tetragonal bonds in the
a zincblende and b wurtzite
structure (i: inversion
center, m: symmetry plane)
Thus the cation and anion sublattices are shifted with respect to each other by a quarter of the body
diagonal of the fcc lattice. The atoms are tetrahedrally coordinated, a Zn atom is bonded to four S atoms
and vice versa. However, no inversion center is present any longer (point group T d ). In the zincblende
structure the stacking order of diatomic planes along the body diagonal is aAbBcCaAbBcC. . .
Many important compound semiconductors, such as GaAs, InAs, AlAs, InP, GaP and their alloys
(cf. Sect. 3.7), but also the II–VI compounds ZnS, ZnSe, ZnTe, HgTe and CdTe and halides, including
AgI, CuF, CuCl, CuBr, and CuI, crystallize in the zincblende structure.
Four-fold coordinated materials (zincblende and wurtzite) typically undergo a phase transition into
6-fold coordinated structures upon hydrostatic pressure [208]. For GaAs under pressure see [209].
3.4.5 Wurtzite Structure
The wurtzite structure (ZnS, space group 186, P6 3 mc) is also called the hexagonal ZnS structure
(because ZnS has both modifications). It consists of a hexagonal lattice with a unit cell of four atoms
(Fig. 3.19). Typically, it is thought of as a hcp structure with a diatomic base. The c/a ratio typically
deviates from the ideal value ζ 0 =
√
8/3 ≈ 1.633 (3.4) as listed in Table 3.3. The c-axis is a 6 3 screw
axis.
The Zn atom is located at (0, 0, 0), the S atom at (0, 0,
√
3/8)a. This corresponds to a shift of 3/8 c
along the c-axis. This factor is called the cell-internal parameter u. For real wurtzite crystals u deviates
from its ideal value u 0 = 3/8 = 0.375, e.g. for group-III nitrides u > u 0 . The diatomic planes have a
stacking order of aAbBaAbB. . . along the [00.1]-direction as visualized in Fig. 3.17b.
In Fig. 3.20 the different local structural environment of the atoms in the zincblende and wurtzite
structure is shown.