162
6 Band Structure
Table 6.5 Longitudinal direction of effective mass ellipsoid, longitudinal and transverse effective electron mass in
several semiconductors. For the density of states mass m d,e see (6.72). Mass values in units of the free electron mass m 0
Long. dir.
m l
m t
m l /m t
m d,e
Ref.
C
100
1.4
0.36
3.9
1.9
[514]
Si
100
0.98
0.19
5.16
1.08
[515]
Ge
111
1.59
0.082
19.4
0.88
[515]
ZnO
[00.1]
0.21
0.25
0.88
[516]
CdS
[00.1]
0.15
0.17
0.9
[517]
Fig. 6.36 Effective
electron mass from
cyclotron resonance
experiments (at T = 4 K)
on a Si and b Ge for the
magnetic field in the (110)
plane and various
azimuthal directions θ.
Experimental data
(symbols) and fits (solid
lines) using (6.45) with a
m l = 0.98, m t = 0.19 and
b m l = 1.58, m t = 0.082.
Adapted from [515]
(a)
(b)
(m l /m t ≈ 0.8 for ZnO [513]), see Fig. 6.35b. In [512] also an anisotropy within the (00.1) plane is
predicted.
The directional dependence of the mass can be measured with cyclotron resonance experiments
with varying direction of the magnetic field. In Fig. 6.36, the field B is in the (110) plane with different
azimuthal directions. When the (static) magnetic field makes an angle ϑ with the longitudinal axis of
the energy surface, the effective mass is given as [518]
1
m ∗ =
cos 2 ϑ
m
2
t
+
sin
2
ϑ
m t m l
.
(6.45)
6.9.3 Nonparabolicity of Electron Mass
The dispersion around the conduction-band minimum is only parabolic for small k. The further away
the wavevector is from the extremum, the more the actual dispersion deviates from the ideal parabola
(see, e.g., Fig. 6.10). This effect is termed nonparabolicity. Typically, the energy increases less quickly
with k than in the parabolic model. This can be described in a so-called two-level model with the
dispersion relation
6 Band Structure
Table 6.5 Longitudinal direction of effective mass ellipsoid, longitudinal and transverse effective electron mass in
several semiconductors. For the density of states mass m d,e see (6.72). Mass values in units of the free electron mass m 0
Long. dir.
m l
m t
m l /m t
m d,e
Ref.
C
100
1.4
0.36
3.9
1.9
[514]
Si
100
0.98
0.19
5.16
1.08
[515]
Ge
111
1.59
0.082
19.4
0.88
[515]
ZnO
[00.1]
0.21
0.25
0.88
[516]
CdS
[00.1]
0.15
0.17
0.9
[517]
Fig. 6.36 Effective
electron mass from
cyclotron resonance
experiments (at T = 4 K)
on a Si and b Ge for the
magnetic field in the (110)
plane and various
azimuthal directions θ.
Experimental data
(symbols) and fits (solid
lines) using (6.45) with a
m l = 0.98, m t = 0.19 and
b m l = 1.58, m t = 0.082.
Adapted from [515]
(a)
(b)
(m l /m t ≈ 0.8 for ZnO [513]), see Fig. 6.35b. In [512] also an anisotropy within the (00.1) plane is
predicted.
The directional dependence of the mass can be measured with cyclotron resonance experiments
with varying direction of the magnetic field. In Fig. 6.36, the field B is in the (110) plane with different
azimuthal directions. When the (static) magnetic field makes an angle ϑ with the longitudinal axis of
the energy surface, the effective mass is given as [518]
1
m ∗ =
cos 2 ϑ
m
2
t
+
sin
2
ϑ
m t m l
.
(6.45)
6.9.3 Nonparabolicity of Electron Mass
The dispersion around the conduction-band minimum is only parabolic for small k. The further away
the wavevector is from the extremum, the more the actual dispersion deviates from the ideal parabola
(see, e.g., Fig. 6.10). This effect is termed nonparabolicity. Typically, the energy increases less quickly
with k than in the parabolic model. This can be described in a so-called two-level model with the
dispersion relation