44
3 Crystals
(a)
(b)
Fig. 3.14 a Radial atomic distribution functions of crystalline (c-Ge, solid line) and amorphous (a-Ge, dashed line)
germanium, determined from EXAFS (extended X-ray absorption fine structure [201]). Adapted from [202]. b A continuous random network model of amorphous silicon containing a dangling bond in the center of the figure. Reprinted
with permission from [203]
genides and a-Ge [197] and since the late 1960s a-Si [198] are researched. The field of amorphous
oxides started in the mid 1950s with vanadate glasses [199] and is currently very active with mixedmetal-based oxides [200] (cmp. Chap. 20).
The local quantum mechanics provides almost rigorous requirements for the bond length to next
neighbors. The constraints for the bond angle are less strict. Covalently bonded atoms arrange in an
open network with the next-neighbor distance essentially preserved and correlations up to the third and
fourth neighbors (Fig. 3.14a). The short-range order is responsible for the observation of semiconductor
properties such as an optical absorption edge and also thermally activated conductivity. In Fig. 3.14b
a model of a continuous random network (with a bond-angle distortion of less than about 20%) of
a-Si is depicted. The diameter d SR of the short-range order region is related to a disorder parameter α
via [204]
d SR =
a
2 α
,
(3.7)
where a is the next-neighbor interatomic distance. For a diamond structure it is related to the lattice
constant by a =
√
3 a 0 /4.
Typically, a significant number of dangling bonds exists. Bonds try to pair but if an odd number of
broken bonds exists locally, an unsaturated, dangling bond remains. This configuration can be passivated by a hydrogen atom. Thus, the hydrogenation of amorphous semiconductors is very important,
in particular for a-Si. A hydrogen atom can also break an overlong (and therefore weak) bond, saturate
one side and eventually leave a dangling bond.
Amorphous material can be (re-)crystallized into crystalline, mostly polycrystalline material upon
annealing. This is technologically very important for a-Si (see Sect. 24.6.1).
3.4 Important Crystal Structures
Now the crystal structures that are important for semiconductor physics will be discussed. These are
mainly the rocksalt (PbS, CdO, . . .), diamond (C, Si, Ge), zincblende (GaAs, InP, . . .) and wurtzite
(GaN, ZnO, . . .) structures.
3 Crystals
(a)
(b)
Fig. 3.14 a Radial atomic distribution functions of crystalline (c-Ge, solid line) and amorphous (a-Ge, dashed line)
germanium, determined from EXAFS (extended X-ray absorption fine structure [201]). Adapted from [202]. b A continuous random network model of amorphous silicon containing a dangling bond in the center of the figure. Reprinted
with permission from [203]
genides and a-Ge [197] and since the late 1960s a-Si [198] are researched. The field of amorphous
oxides started in the mid 1950s with vanadate glasses [199] and is currently very active with mixedmetal-based oxides [200] (cmp. Chap. 20).
The local quantum mechanics provides almost rigorous requirements for the bond length to next
neighbors. The constraints for the bond angle are less strict. Covalently bonded atoms arrange in an
open network with the next-neighbor distance essentially preserved and correlations up to the third and
fourth neighbors (Fig. 3.14a). The short-range order is responsible for the observation of semiconductor
properties such as an optical absorption edge and also thermally activated conductivity. In Fig. 3.14b
a model of a continuous random network (with a bond-angle distortion of less than about 20%) of
a-Si is depicted. The diameter d SR of the short-range order region is related to a disorder parameter α
via [204]
d SR =
a
2 α
,
(3.7)
where a is the next-neighbor interatomic distance. For a diamond structure it is related to the lattice
constant by a =
√
3 a 0 /4.
Typically, a significant number of dangling bonds exists. Bonds try to pair but if an odd number of
broken bonds exists locally, an unsaturated, dangling bond remains. This configuration can be passivated by a hydrogen atom. Thus, the hydrogenation of amorphous semiconductors is very important,
in particular for a-Si. A hydrogen atom can also break an overlong (and therefore weak) bond, saturate
one side and eventually leave a dangling bond.
Amorphous material can be (re-)crystallized into crystalline, mostly polycrystalline material upon
annealing. This is technologically very important for a-Si (see Sect. 24.6.1).
3.4 Important Crystal Structures
Now the crystal structures that are important for semiconductor physics will be discussed. These are
mainly the rocksalt (PbS, CdO, . . .), diamond (C, Si, Ge), zincblende (GaAs, InP, . . .) and wurtzite
(GaN, ZnO, . . .) structures.