238
8 Transport
(a)
10
2
10
3
10
4
10
6
10
5
10
8
10
10
10
7
6
5
Si
Ge
GaAs
electrons
holes
(b)
7
ZnO
100
200
300
3.0
2.0
1.0
0
0
GaN
Si
InP
GaAs
InGaAs
Fig. 8.13 Drift velocity at room temperature as a function of applied electric field for a high-purity Si, Ge, and GaAs
on a double-logarithmic plot and b on linear plots for Si [759], Ge [760], GaAs [676], InP [761], (In, Ga)As [762], GaN
and ZnO [763]
Table 8.4 Material parameters for multi-valley bandstructure of GaAs and InP. denotes the energetic separation of
the two lowest valleys of the conduction band, E thr the threshold field for NDR and v P the peak velocity (at E thr ). Most
values from [766]
Material
Lower valley (
Upper valley (L)
E g
(eV)
(eV)
E thr
(kV/cm)
v P
(10 7 cm/s)
m ∗
(m 0 )
μ n
(cm 2 /Vs)
m ∗
(m 0 )
μ n
(cm 2 /Vs)
GaAs
1.42
0.36
3.2
2.2
0.068
≈8000
1.2
≈180
InP
1.35
0.53
10.5
2.5
0.08
≈5000
0.9
≈100
regime, above the threshold field of E thr = 3.2 kV/cm in GaAs, is called negative differential resistivity
(NDR) and was predicted in [764]. This phenomenon can be used in microwave oscillators, e.g. the
Gunn element (Sect. 21.5.11).
The effect occurs in a multi-valley band structure (see Fig. 8.14, for values cf. Table 8.4), e.g. in
GaAs or InP, when the carrier energy is high enough to scatter (Fig. 8.14c,d) from the minimum
(small mass and high mobility) into the L valley (large mass and low mobility) [765].
The temperature dependence of the saturation velocity is shown in Fig. 8.15. With increasing temperature the saturation velocity decreases since the coupling with the lattice becomes stronger.
8.4.3 Velocity Overshoot
When the electric field is switched on, the carriers are at first in the minimum (Fig. 8.14a). Only
after a few scattering processes are they scattered into the L minimum. This means that in the first
moments transport occurs with the higher mobility of the lowest minimum (Fig. 8.14e). The velocity is
then larger than the (steady-state) saturation velocity in a dc field. This phenomenon is called velocity
overshoot and is a purely dynamic effect (Fig. 8.16). Velocity overshoot in GaN is discussed in [769].
It is an important effect in small transistors.
8 Transport
(a)
10
2
10
3
10
4
10
6
10
5
10
8
10
10
10
7
6
5
Si
Ge
GaAs
electrons
holes
(b)
7
ZnO
100
200
300
3.0
2.0
1.0
0
0
GaN
Si
InP
GaAs
InGaAs
Fig. 8.13 Drift velocity at room temperature as a function of applied electric field for a high-purity Si, Ge, and GaAs
on a double-logarithmic plot and b on linear plots for Si [759], Ge [760], GaAs [676], InP [761], (In, Ga)As [762], GaN
and ZnO [763]
Table 8.4 Material parameters for multi-valley bandstructure of GaAs and InP. denotes the energetic separation of
the two lowest valleys of the conduction band, E thr the threshold field for NDR and v P the peak velocity (at E thr ). Most
values from [766]
Material
Lower valley (
Upper valley (L)
E g
(eV)
(eV)
E thr
(kV/cm)
v P
(10 7 cm/s)
m ∗
(m 0 )
μ n
(cm 2 /Vs)
m ∗
(m 0 )
μ n
(cm 2 /Vs)
GaAs
1.42
0.36
3.2
2.2
0.068
≈8000
1.2
≈180
InP
1.35
0.53
10.5
2.5
0.08
≈5000
0.9
≈100
regime, above the threshold field of E thr = 3.2 kV/cm in GaAs, is called negative differential resistivity
(NDR) and was predicted in [764]. This phenomenon can be used in microwave oscillators, e.g. the
Gunn element (Sect. 21.5.11).
The effect occurs in a multi-valley band structure (see Fig. 8.14, for values cf. Table 8.4), e.g. in
GaAs or InP, when the carrier energy is high enough to scatter (Fig. 8.14c,d) from the minimum
(small mass and high mobility) into the L valley (large mass and low mobility) [765].
The temperature dependence of the saturation velocity is shown in Fig. 8.15. With increasing temperature the saturation velocity decreases since the coupling with the lattice becomes stronger.
8.4.3 Velocity Overshoot
When the electric field is switched on, the carriers are at first in the minimum (Fig. 8.14a). Only
after a few scattering processes are they scattered into the L minimum. This means that in the first
moments transport occurs with the higher mobility of the lowest minimum (Fig. 8.14e). The velocity is
then larger than the (steady-state) saturation velocity in a dc field. This phenomenon is called velocity
overshoot and is a purely dynamic effect (Fig. 8.16). Velocity overshoot in GaN is discussed in [769].
It is an important effect in small transistors.