6.5. Photodetectors 409
Now, using this value ofαdwe can calculate the gain atu=0.01 as follows.〈Ge〉 =
1 −u
e−αd(1−u)−u
=1 − 0. 01
e−^2 .37(1−^0 .01)− 0. 01
=11. 5The relative change in gain is
〈Ge〉 =50 − 11. 5
50
× 100
= 77%.
In general, the gain of an APD can be any value between 1 and 10^8. However the
standard APDs are mostly operated between gains of 10 and 1000. APDs of gains
higher than this are also used, though in situations where light level is extremely
low, such as in single photon counting experiments.
The mean internal gain of an APD is a function of the applied voltage since
the energy gained by the electrons between collisions depends on the electric field
strength. The bias-gain curve of a typical APD is shown in Fig.6.5.25. It is apparent
from this figure that an APD can, in principle, be operated in a range of gains, which
makes it a versatile device that can be tuned according to the level of the incident
light.
103
102
1
10
0 200 400 600
Reverse Bias (V)G
ain Figure 6.5.25: Variation of gain
with applied reverse bias in a
typical APD.In most applications, APDs are used in a region of the voltage-gain curve where
the relationship is approximately linear. In such a region the variation of gain with