3D Time-of-flight distance measurement with custom - Universität ...

66 CHAPTER 3
The proportionality factor between the electrical field and the drift velocity is the
carrier mobility µn (here electron mobility), given by:
q ⋅ τ
µ
c
n ≡
m
Equation 3.11
eff
τ c is the mean free time, or the average time between collisions of the carriers with
the lattice or impurity atoms. It strongly depends on the semiconductor material, the
temperature and the doping concentration in the semiconductor (see also
Figure 3.12).
For very high electric fields this drift velocity approaches the thermal velocity, which
cannot be exceeded in silicon and thus defines the maximum drift velocity vmax (or
saturation velocity) in an electric field (10 7 cm/s for Si) (see Figure 3.13):
3kT
v max = v th =
m
Equation 3.12
eff
Figure 3.13 Drift of free charge carriers in an electric field: saturation velocity.
[SZ2].
The correct expression for the drift velocity, considering the saturation velocity is:
µ n ⋅ E
vn
=
µ n ⋅ E
1+
Equation 3.13
vmax
At this point it is worth mentioning two points:
(1) Generally, the carrier drift velocity in metal is much lower than in
semiconductors because of the lower mobility.