232
8 Transport
(a)
(b)
Fig. 8.5 a Temperature dependence of the electron mobility in n-doped Ge (for various doping levels from N D ≈ 10 18 for
sample A to 10 13 cm −3 for sample F in steps of a factor of ten). Dashed line indicates T −3/2 dependence of deformation
potential scattering, solid lines are guides to the eye. Adapted from [594]. b μ n (T ) for n-type GaAs (N D ≈ 5×10 13 cm −3 ,
N A ≈ 2 × 10 13 cm −3 ). Solid lines are theoretical mobilities for various scattering mechanisms and combined mobility
according to (8.12). Adapted from [736]
being the volume of the unit cell over which the alloy-scattering potential is effective. Such effect
is present in any alloy such as In x Ga 1−x As [591] of Al x Ga 1−x N [592]. For the latter material, see also
the following section.
8.3.10 Dipole Scattering
In alloys of polar semiconductors (Chap. 16), i.e. lower-symmetric (non-cubic) semiconductors with an
electric polarization, the additional potential due to the random variation of the polarization introduces
an additional scattering mechanism, the so-called dipole scattering [592]. Dipole scattering originally
has been studied in the context of scattering in highly compensated semiconductors due to ionized
donor-acceptor pairs [593].
8.3.11 Temperature Dependence
The sum of all scattering processes leads to a fairly complicated temperature dependence of the mobility
μ(T ). In covalent semiconductors (Si, Ge) the most important processes are the ionized impurity
scattering (μ ∝ T
3/2 ) at low temperatures and the deformation potential scattering (μ ∝ T
−3/2 ) at high
temperatures (Fig. 8.5a). In polar crystals (e.g. GaAs) at high temperatures the polar optical scattering
is dominant (Fig. 8.5b).
In Fig. 8.6 the electron mobility of bulk and thin-film ZnO is compared. Since ZnO is polar the
mobility at room temperature is limited by polar optical phonon scattering. In the thin film, grainboundary scattering (Sect. 8.3.8) additionally occurs and limits the mobility.
In Fig. 8.7 the temperature dependence of the mobility is depicted for an alloy of polar semiconductors, namely Al 0.25 Ga 0.75 N. The contributions of alloy scattering and dipole scattering determine
the mobility [592].
8 Transport
(a)
(b)
Fig. 8.5 a Temperature dependence of the electron mobility in n-doped Ge (for various doping levels from N D ≈ 10 18 for
sample A to 10 13 cm −3 for sample F in steps of a factor of ten). Dashed line indicates T −3/2 dependence of deformation
potential scattering, solid lines are guides to the eye. Adapted from [594]. b μ n (T ) for n-type GaAs (N D ≈ 5×10 13 cm −3 ,
N A ≈ 2 × 10 13 cm −3 ). Solid lines are theoretical mobilities for various scattering mechanisms and combined mobility
according to (8.12). Adapted from [736]
being the volume of the unit cell over which the alloy-scattering potential is effective. Such effect
is present in any alloy such as In x Ga 1−x As [591] of Al x Ga 1−x N [592]. For the latter material, see also
the following section.
8.3.10 Dipole Scattering
In alloys of polar semiconductors (Chap. 16), i.e. lower-symmetric (non-cubic) semiconductors with an
electric polarization, the additional potential due to the random variation of the polarization introduces
an additional scattering mechanism, the so-called dipole scattering [592]. Dipole scattering originally
has been studied in the context of scattering in highly compensated semiconductors due to ionized
donor-acceptor pairs [593].
8.3.11 Temperature Dependence
The sum of all scattering processes leads to a fairly complicated temperature dependence of the mobility
μ(T ). In covalent semiconductors (Si, Ge) the most important processes are the ionized impurity
scattering (μ ∝ T
3/2 ) at low temperatures and the deformation potential scattering (μ ∝ T
−3/2 ) at high
temperatures (Fig. 8.5a). In polar crystals (e.g. GaAs) at high temperatures the polar optical scattering
is dominant (Fig. 8.5b).
In Fig. 8.6 the electron mobility of bulk and thin-film ZnO is compared. Since ZnO is polar the
mobility at room temperature is limited by polar optical phonon scattering. In the thin film, grainboundary scattering (Sect. 8.3.8) additionally occurs and limits the mobility.
In Fig. 8.7 the temperature dependence of the mobility is depicted for an alloy of polar semiconductors, namely Al 0.25 Ga 0.75 N. The contributions of alloy scattering and dipole scattering determine
the mobility [592].