8.4 High-Field Transport
239
Fig. 8.14 Charge-carrier distribution in a multi-valley band structure (e.g. GaAs, InP) for a zero, b small (E < E a ),
c intermediate and d large (E > E b ) field strength. The situation shown in e is reached temporarily during velocity
overshoot (see also Fig. 8.16)
Fig. 8.15 Temperature
dependence of the
saturation velocity for Si
(following v s = v s0 (1 +
0.8 exp(T /600 K )) −1 with
v s0 = 2.4 × 10 7 cm/s from
[759]) and GaAs [676,
767, 768]
8.4.4 Impact Ionization
If the energy gain in the field is large enough to generate an electron–hole pair, the phenomenon of
impact ionization occurs. The kinetic energy is ∝ v
2 . Momentum and energy conservation apply. Thus,
at small energies (close to the threshold for impact ionization) the vectors are short and collinear to
fulfill momentum conservation. At higher energy, larger angles between the velocity vectors of the
impact partners can also occur. If the process is started by an electron (Fig. 8.17a) the threshold energy
is given by [770]
E
thr
e =
1 +
m e
m e + m hh
E g .
(8.31)
If the process starts with a heavy hole, the threshold [770],