48
3 Crystals
Table 3.3 c/a ratio of various wurtzite semiconductors. Listed is ξ = (c/a − ζ 0 )/ζ 0 . Data based on [210]
Material
ξ (%)
Material
ξ(%)
Material
ξ (%)
Material
ξ (%)
AlN
−2.02
CdS
−0.61
CuBr
0.43
BeO
−0.61
GaN
−0.49
CdSe
−0.18
CuCl
0.55
ZnO
−1.9
InN
−1.35
CdTe
0.25
CuI
0.74
6H-SiC
0.49
ZnS
0.25
MgS
−0.80
AgI
0.12
BN
0.74
ZnSe
0.06
MgSe
−0.67
ZnTe
0.74
MgTe
−0.67
Many important semiconductors with large band gap crystallize in the wurtzite structure, such as
GaN, AlN, InN, [211] ZnO, [212] SiC, [213], CdS und CdSe.
3.4.6 Chalcopyrite Structure
The chalcopyrite [214] (ABC 2 , named after ‘fool’s gold’ CuFeS 2 , space group 122, I ¯
42d) structure is
relevant for I–III–VI 2 (with chalcogenide anions) and II–IV–V 2 (with pnictide anions) semiconductors
such as, e.g., (Cu,Ag)(Al,Ga,In)(S,Se,Te) 2 and (Mg,Zn,Cd)(Si,Ge,Sn)(As,P,Sb) 2 .
In Fig. 3.21, the derivation of zincblende and chalcopyrite compounds is shown schematically,
including the kesterite materials of type I 2 -II-IV-VI 6 .
In the chalcopyrite structure, a nonmetallic anion atom (‘C’) is tetrahedrally bonded to two different
types of cation atoms (‘A’ and ‘B’) as shown in Fig. 3.22. The local surrounding of each anion is
identical, two of both the A and B atoms. The structure is tetragonal. The aspect ratio η = c/(2a)
deviates from its ideal value 1; typically η < 1 [215, 216].
If the C atom is in the tetrahedral center of the two A and two B atoms, the bond lengths R AC and
R BC of the A–C and B–C bonds, respectively, are equal. Since the ideal A–C and B–C bond lengths
d AC and d BC are typically unequal, this structure is strained. The common atom C is therefore displaced
Fig. 3.21 Scheme of II–VI
zincblende and related
chalcopyrite and kesterite
compounds
Fig. 3.22 Chalcopyrite
structure, red and yellow
spheres denote the metal
species. The bigger green
spheres represent the
nonmetal anion
3 Crystals
Table 3.3 c/a ratio of various wurtzite semiconductors. Listed is ξ = (c/a − ζ 0 )/ζ 0 . Data based on [210]
Material
ξ (%)
Material
ξ(%)
Material
ξ (%)
Material
ξ (%)
AlN
−2.02
CdS
−0.61
CuBr
0.43
BeO
−0.61
GaN
−0.49
CdSe
−0.18
CuCl
0.55
ZnO
−1.9
InN
−1.35
CdTe
0.25
CuI
0.74
6H-SiC
0.49
ZnS
0.25
MgS
−0.80
AgI
0.12
BN
0.74
ZnSe
0.06
MgSe
−0.67
ZnTe
0.74
MgTe
−0.67
Many important semiconductors with large band gap crystallize in the wurtzite structure, such as
GaN, AlN, InN, [211] ZnO, [212] SiC, [213], CdS und CdSe.
3.4.6 Chalcopyrite Structure
The chalcopyrite [214] (ABC 2 , named after ‘fool’s gold’ CuFeS 2 , space group 122, I ¯
42d) structure is
relevant for I–III–VI 2 (with chalcogenide anions) and II–IV–V 2 (with pnictide anions) semiconductors
such as, e.g., (Cu,Ag)(Al,Ga,In)(S,Se,Te) 2 and (Mg,Zn,Cd)(Si,Ge,Sn)(As,P,Sb) 2 .
In Fig. 3.21, the derivation of zincblende and chalcopyrite compounds is shown schematically,
including the kesterite materials of type I 2 -II-IV-VI 6 .
In the chalcopyrite structure, a nonmetallic anion atom (‘C’) is tetrahedrally bonded to two different
types of cation atoms (‘A’ and ‘B’) as shown in Fig. 3.22. The local surrounding of each anion is
identical, two of both the A and B atoms. The structure is tetragonal. The aspect ratio η = c/(2a)
deviates from its ideal value 1; typically η < 1 [215, 216].
If the C atom is in the tetrahedral center of the two A and two B atoms, the bond lengths R AC and
R BC of the A–C and B–C bonds, respectively, are equal. Since the ideal A–C and B–C bond lengths
d AC and d BC are typically unequal, this structure is strained. The common atom C is therefore displaced
Fig. 3.21 Scheme of II–VI
zincblende and related
chalcopyrite and kesterite
compounds
Fig. 3.22 Chalcopyrite
structure, red and yellow
spheres denote the metal
species. The bigger green
spheres represent the
nonmetal anion