Chemistry Reference
In-Depth Information
Table 4.1
Selected properties of group IV and III-V tetrahedrally bonded semicon-
ductors. [Data compiled from Madelung (1982); estimates of GaN effective
masses from Meney
et al
. (1996)]
Bond
length
d
(Å)
Direct
gap
E
g
(eV)
Indirect
gap
E
ind
Electron
relative
mass m
cr
LH relative
mass m
lr
HH
relative
mass m
hr
Dielectric
constant
ε
r
(eV)
g
C
1.54
6.5
5.5
0.36
1.08
5.7
Si
2.35
4.2
1.17
0.153
0.54
12.1
Ge
2.44
0.90
0.74
0.038
0.043
0.35
16.5
GaN
1.94
3.5
0.15
0.21
0.90
10
GaP
2.36
2.88
2.35
0.17
0.67
9.1
InP
2.54
1.42
0.079
0.12
0.6
9.6
AlAs
2.43
3.13
2.23
0.26
0.5
9.1
GaAs
2.45
1.52
0.067
0.082
0.45
12.8
InAs
2.61
0.42
0.023
0.026
0.41
12.3
AlSb
2.66
2.32
1.69
0.11
0.5
10.2
GaSb
2.65
0.81
0.041
0.05
0.4
14.4
InSb
2.8
0.235
0.0139
0.018
0.4
15.7
Table 4.2
Spin-orbit splitting energy (in meV) at the valence band
maximum in III-V zinc-blende (upper part of table) and
group IV tetrahedrally bonded semiconductors. (III-
V data from Krijn (1991); nitride data from Wei and
Zunger (1996) and group IV data from Madelung (1982))
N
P
As
Sb
Al
19
70
280
650
Ga
15
80
340
820
In
6
110
380
810
C
Si
Ge
6
45
290
isolatedatom. The atomic p states there are alsodegeneratewhenwe ignore
the electron spin. In reality, the electrons experience an additional potential
due to the interaction of the spinmagneticmoment with the vector product
of the velocity and electric field. This effect, spin-orbit coupling, splits the
p states in an isolated atom. It persists in solids and splits the degeneracy of
the valence band maximum (as well as splitting other degenerate states in
the band structure). Two of the six p states at the valence band maximum
are split off from the other four, and shifted down to lie at an energy
E
so
below the valence band maximum. Table 4.2 lists the spin-orbit splitting,
E
so
, for the group IV and III-V semiconductors. It can be seen how the
magnitude of the spin-orbit splitting,
E
so
, increases with atomic number
and is determined primarily by the group V element in III-V materials.
