172
6 Band Structure
Fig. 6.50 Schematic band
structure of GaAs in
unstrained state (center)
and under compressive and
tensile biaxial strain as
labeled. Dashed lines
indicate shift of band edges
due to hydrostatic part of
strain
electrons
k
unstrained
k
E
k
E
E
unstrained
compressive
tensile
m =3/2
j
m=1/2 j
m=3/2 j
m =1/2
j
m=1/2 j
m=3/2 j
Table 6.7 Deformation potentials for some III–V semiconductors. All values in eV
Material
a
b
d
GaAs
−9.8
−1.7
−4.6
InAs
−6.0
−1.8
−3.6
Table 6.8 Deformation potentials for silicon and germanium. All values in eV from [542]
material
(()
d
(()
u
(L)
d
(L)
u
a
b
d
Si
1.1
10.5
−7.0
18.0
2.1
−2.33
−4.75
Ge
4.5
9.75
−4.43
16.8
2.0
−2.16
−6.06
E C,i = E
0
C,i + d Tr() + u a i a i ,
(6.59)
where E
0
C,i denotes the energy of the unstrained conduction-band edge. The deformation potentials for
Si and Ge are given in Table 6.8.
6.12.2 Strain Effect on Effective Masses
In the presence of strain the band edges are shifted (cf. Sect. 6.12). Since the electron mass is related
to the band gap, it is expected that the mass will also be effected. In the presence of hydrostatic strain
H the electron mass is [543] (cf. to (6.43) for H → 0)
m 0
m ∗
e
= 1 +
E P
E g + 0 /3
1 − H
2 +
3a
E g + 0 /3
,
(6.60)
with a being the hydrostatic deformation potential and H = Tr((). In [543], formulas are also given for
biaxial and shear strain and also for hole masses. Since the effective mass enters the mobility, the electrical conductivity depends on the stress state of the semiconductor (piezoresistivity, see Sect. 8.3.14).
6 Band Structure
Fig. 6.50 Schematic band
structure of GaAs in
unstrained state (center)
and under compressive and
tensile biaxial strain as
labeled. Dashed lines
indicate shift of band edges
due to hydrostatic part of
strain
electrons
k
unstrained
k
E
k
E
E
unstrained
compressive
tensile
m =3/2
j
m=1/2 j
m=3/2 j
m =1/2
j
m=1/2 j
m=3/2 j
Table 6.7 Deformation potentials for some III–V semiconductors. All values in eV
Material
a
b
d
GaAs
−9.8
−1.7
−4.6
InAs
−6.0
−1.8
−3.6
Table 6.8 Deformation potentials for silicon and germanium. All values in eV from [542]
material
(()
d
(()
u
(L)
d
(L)
u
a
b
d
Si
1.1
10.5
−7.0
18.0
2.1
−2.33
−4.75
Ge
4.5
9.75
−4.43
16.8
2.0
−2.16
−6.06
E C,i = E
0
C,i + d Tr() + u a i a i ,
(6.59)
where E
0
C,i denotes the energy of the unstrained conduction-band edge. The deformation potentials for
Si and Ge are given in Table 6.8.
6.12.2 Strain Effect on Effective Masses
In the presence of strain the band edges are shifted (cf. Sect. 6.12). Since the electron mass is related
to the band gap, it is expected that the mass will also be effected. In the presence of hydrostatic strain
H the electron mass is [543] (cf. to (6.43) for H → 0)
m 0
m ∗
e
= 1 +
E P
E g + 0 /3
1 − H
2 +
3a
E g + 0 /3
,
(6.60)
with a being the hydrostatic deformation potential and H = Tr((). In [543], formulas are also given for
biaxial and shear strain and also for hole masses. Since the effective mass enters the mobility, the electrical conductivity depends on the stress state of the semiconductor (piezoresistivity, see Sect. 8.3.14).