230
8 Transport
8.3.5 Piezoelectric Potential Scattering
In piezoelectric crystals (see Sect. 16.4), i.e. crystals that show an electric polarization upon strain,
certain acoustic phonons lead to piezoelectric fields. In GaAs, with 111 being the piezoelectric
directions, this is the case for shear waves. In strongly ionic crystals, e.g. II–VI semiconductors, the
piezoelectric scattering can be stronger than the deformation potential scattering. The mobility due to
piezoelectric potential scattering is
μ pz.el. =
16
√
2π
3
0 r
m ∗3/2 e K 2 (kT )
−1/2
,
(8.22)
with K =
e
2
p /c l
0 r +e 2
p /c l
, e p being the piezoelectric coefficient.
8.3.6 Polar Optical Scattering
LO phonons are connected with an electric field antiparallel to the displacement (9.29). In the scattering
mechanism the absorbed or emitted phonon energy ω 0 is comparable to the thermal energy of the
carriers. Therefore, the scattering is inelastic and the relaxation-time approximation does not work. The
general transport theory is complicated. If the temperature is low compared to the Debye temperature,
T D
μ pol.opt. =
e
2 m ∗ α ω 0
exp
D
T
,
(8.23)
where α =
1
137
m ∗ c 2
2k D
1
(∞)
−
1
(0)
is the dimensionless polar constant.
8.3.7 Dislocation Scattering
Dislocations can contain charge centers and thus act as scattering centers citeyou. This has been first
demonstrated for n-Ge crystals that have been deformed [725, 726]. The deformation has introduced
acceptor-type defects reducing the mobility in particular at low temperatures (similar to ionized impurity scattering). The mobility due to dislocation scattering in an n-type semiconductor is given by [727,
728]
μ disl. =
30
√
2π π
2 d
2
(kT )
3/2
N disl e 3 f 2 L D
√
m ∗
∝
√
n
N disl
T ,
(8.24)
d being the average distance of acceptor centers along the dislocation line, f their occupation rate, N disl
the area density of dislocations and L D = (kT /(e
2 n))
1/2 the Debye screening length. The relation
μ ∝
√
n/N disl has been confirmed for various n-type GaN samples [729].
8 Transport
8.3.5 Piezoelectric Potential Scattering
In piezoelectric crystals (see Sect. 16.4), i.e. crystals that show an electric polarization upon strain,
certain acoustic phonons lead to piezoelectric fields. In GaAs, with 111 being the piezoelectric
directions, this is the case for shear waves. In strongly ionic crystals, e.g. II–VI semiconductors, the
piezoelectric scattering can be stronger than the deformation potential scattering. The mobility due to
piezoelectric potential scattering is
μ pz.el. =
16
√
2π
3
0 r
m ∗3/2 e K 2 (kT )
−1/2
,
(8.22)
with K =
e
2
p /c l
0 r +e 2
p /c l
, e p being the piezoelectric coefficient.
8.3.6 Polar Optical Scattering
LO phonons are connected with an electric field antiparallel to the displacement (9.29). In the scattering
mechanism the absorbed or emitted phonon energy ω 0 is comparable to the thermal energy of the
carriers. Therefore, the scattering is inelastic and the relaxation-time approximation does not work. The
general transport theory is complicated. If the temperature is low compared to the Debye temperature,
T D
μ pol.opt. =
e
2 m ∗ α ω 0
exp
D
T
,
(8.23)
where α =
1
137
m ∗ c 2
2k D
1
(∞)
−
1
(0)
is the dimensionless polar constant.
8.3.7 Dislocation Scattering
Dislocations can contain charge centers and thus act as scattering centers citeyou. This has been first
demonstrated for n-Ge crystals that have been deformed [725, 726]. The deformation has introduced
acceptor-type defects reducing the mobility in particular at low temperatures (similar to ionized impurity scattering). The mobility due to dislocation scattering in an n-type semiconductor is given by [727,
728]
μ disl. =
30
√
2π π
2 d
2
(kT )
3/2
N disl e 3 f 2 L D
√
m ∗
∝
√
n
N disl
T ,
(8.24)
d being the average distance of acceptor centers along the dislocation line, f their occupation rate, N disl
the area density of dislocations and L D = (kT /(e
2 n))
1/2 the Debye screening length. The relation
μ ∝
√
n/N disl has been confirmed for various n-type GaN samples [729].