8.3 Low-Field Transport
227
Table 8.2 Mobilities of electrons and holes at room temperature for various semiconductors
Material
−μ n (cm 2 /Vs)
μ p (cm 2 /Vs)
Si
1300
500
Ge
4500
3500
GaAs
8800
400
GaN
300
180
InSb
77 000
750
InAs
33 000
460
InP
4600
150
ZnO
230
8
Chap. 12), the mobility can reach several 10
7 cm
2 /Vs at low temperature (Fig. 12.37). In bulk semiconductors with small band gap, a high electron mobility is caused by its small effective mass. Some
typical values are given in Table 8.2.
8.3.2 Microscopic Scattering Processes
The relaxation time constant summarizes all scattering mechanisms. If the relaxation times τ i of various
processes are independent, the Matthiesen rule can be used to obtain the mobility (μ i = q τ i /m
∗ )
1
μ
=
i
1
μ i
.
(8.12)
A more detailed book keeping is provided within the framework of the Boltzmann transport theory
(Appendix J).
The various scattering mechanisms have quite different temperature dependences such that the
mobility is a rather complicated function of temperature. In [716] the mechanisms determining the low
and high-field transport properties of (cubic) semiconductors are reviewed. A schematic overview of
the various carrier scattering processes discussed in the following is shown in Fig. 8.2.
8.3.3 Ionized Impurity Scattering
Theoretically, this problem is treated similar to Rutherford scattering. A screened Coulomb potential
is assumed, as the scattering potential
V (r ) = −
Z e
4ππ 0 r
1
r
exp
−
r
l D
,
(8.13)
where l D is the screening length. The problem has been treated classically by Conwell and Weisskopf
[717] and quantum mechanically by Brooks [718] and Herring. An expression for the mobility that
encompasses the Conwell–Weisskopf and Brooks–Herring results is derived in [719]. Further details
are given in [720, 721]. For the mobility it is found that
227
Table 8.2 Mobilities of electrons and holes at room temperature for various semiconductors
Material
−μ n (cm 2 /Vs)
μ p (cm 2 /Vs)
Si
1300
500
Ge
4500
3500
GaAs
8800
400
GaN
300
180
InSb
77 000
750
InAs
33 000
460
InP
4600
150
ZnO
230
8
Chap. 12), the mobility can reach several 10
7 cm
2 /Vs at low temperature (Fig. 12.37). In bulk semiconductors with small band gap, a high electron mobility is caused by its small effective mass. Some
typical values are given in Table 8.2.
8.3.2 Microscopic Scattering Processes
The relaxation time constant summarizes all scattering mechanisms. If the relaxation times τ i of various
processes are independent, the Matthiesen rule can be used to obtain the mobility (μ i = q τ i /m
∗ )
1
μ
=
i
1
μ i
.
(8.12)
A more detailed book keeping is provided within the framework of the Boltzmann transport theory
(Appendix J).
The various scattering mechanisms have quite different temperature dependences such that the
mobility is a rather complicated function of temperature. In [716] the mechanisms determining the low
and high-field transport properties of (cubic) semiconductors are reviewed. A schematic overview of
the various carrier scattering processes discussed in the following is shown in Fig. 8.2.
8.3.3 Ionized Impurity Scattering
Theoretically, this problem is treated similar to Rutherford scattering. A screened Coulomb potential
is assumed, as the scattering potential
V (r ) = −
Z e
4ππ 0 r
1
r
exp
−
r
l D
,
(8.13)
where l D is the screening length. The problem has been treated classically by Conwell and Weisskopf
[717] and quantum mechanically by Brooks [718] and Herring. An expression for the mobility that
encompasses the Conwell–Weisskopf and Brooks–Herring results is derived in [719]. Further details
are given in [720, 721]. For the mobility it is found that