112 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS
102
ELECTRIC FIELD (V/cm)
CARRIER
DRIFT
VELOCITY
(cm/s)
103 104 105 106
105
106
107
108
GaAs
Si
InP
Electrons
Holes
Figure 3.10: Velocity–field relations for several semiconductors at 300 K.
The corresponding relaxation times are
τsc(1 kV/cm) =
(0. 26 × 0. 91 × 10 −^30 kg)(1400× 10 −^4 m^2 /V)
1. 6 × 10 −^19 C
=2. 1 × 10 −^13 s
τsc(100 kV/cm) =
(0. 26 × 0. 91 × 10 −^30 )(100× 10 −^4 )
1. 6 × 10 −^19
=1. 48 × 10 −^14 s
Thus the scattering rate has dramatically increased at the higher field.
Example 3.8The average electric field in a particular 0.1μm GaAs device is 50 kV/cm.
Calculate the transit time of an electron through the device (a) if the transport is ballistic;
(b) if the saturation velocity value of 10^7 cm/s is used.
For ballistic transport the transit time is
τtr=
√
2 L
a
with the acceleration,agiven by
a=
eE
m∗
