62
3 Crystals
For a Ge x Si 1−x alloy this means that any given atom site has the probability x to have a Ge atom
and 1 − x to have a Si atom. The probability p n that a Si atom has n next-neighbor Ge atoms is
p n =
4
n
x
n
(1 − x)
4−n
,
(3.23)
and is depicted in Fig. 3.39 as a function of the alloy composition. The symmetry of the Si atom is
listed in Table 3.8. If it is surrounded by four of the same atoms (either Ge or Si), the symmetry is T d .
If one atom is different from the other three next neighbors, the symmetry is reduced to C 3v since one
bond is singled out. For two atoms each the symmetry is lowest (C 2v ).
In an alloy from binary compound semiconductors such as Al x Ga 1−x As the mixing of the Al and
Ga metal atoms occurs only on the metal (fcc) sublattice. Each As atom is bonded to four metal atoms.
The probability that it is surrounded by n Al atoms is given by (3.23). The local symmetry of the As
atom is also given by Table 3.8. For AlAs x P 1−x the mixing occurs on the nonmetal (anion) sublattice.
If the alloy contains three atom species it is called a ternary alloy. In Fig. 3.40 the (1 ¯
10) surface (UHV
cleave) of an In 0.05 Ga 0.95 As alloy is shown. Indium atoms in the first layer show up as brighter round
dots [247]. Along the [001]-direction the positions are uncorrelated, along [110] an anti-correlation is
Fig. 3.39 Probability that
a Si atom has n
next-neighbor Ge atoms in
a random Ge x Si 1−x alloy
Fig. 3.40 a STM empty-state image (17.5 × 17.5 nm 2 ) of the (1 ¯
10) surface of an MBE-grown In 0.05 Ga 0.95 As alloy
on GaAs, b curvature-enhanced image. c Schematic atomic arrangement of the first and second atomic layer. Adapted
from [248]
3 Crystals
For a Ge x Si 1−x alloy this means that any given atom site has the probability x to have a Ge atom
and 1 − x to have a Si atom. The probability p n that a Si atom has n next-neighbor Ge atoms is
p n =
4
n
x
n
(1 − x)
4−n
,
(3.23)
and is depicted in Fig. 3.39 as a function of the alloy composition. The symmetry of the Si atom is
listed in Table 3.8. If it is surrounded by four of the same atoms (either Ge or Si), the symmetry is T d .
If one atom is different from the other three next neighbors, the symmetry is reduced to C 3v since one
bond is singled out. For two atoms each the symmetry is lowest (C 2v ).
In an alloy from binary compound semiconductors such as Al x Ga 1−x As the mixing of the Al and
Ga metal atoms occurs only on the metal (fcc) sublattice. Each As atom is bonded to four metal atoms.
The probability that it is surrounded by n Al atoms is given by (3.23). The local symmetry of the As
atom is also given by Table 3.8. For AlAs x P 1−x the mixing occurs on the nonmetal (anion) sublattice.
If the alloy contains three atom species it is called a ternary alloy. In Fig. 3.40 the (1 ¯
10) surface (UHV
cleave) of an In 0.05 Ga 0.95 As alloy is shown. Indium atoms in the first layer show up as brighter round
dots [247]. Along the [001]-direction the positions are uncorrelated, along [110] an anti-correlation is
Fig. 3.39 Probability that
a Si atom has n
next-neighbor Ge atoms in
a random Ge x Si 1−x alloy
Fig. 3.40 a STM empty-state image (17.5 × 17.5 nm 2 ) of the (1 ¯
10) surface of an MBE-grown In 0.05 Ga 0.95 As alloy
on GaAs, b curvature-enhanced image. c Schematic atomic arrangement of the first and second atomic layer. Adapted
from [248]