Physics and Engineering of Radiation Detection

6.5. Photodetectors 413

photon counting capabilities. With a pulse resolution of as low as 20ps, a gain of
as high as 10^8 , and a quantum efficiency approaching 80%, the APDs are becoming
more and more popular in single photon counting applications.

C.5 NoiseConsiderations......................

APDs are generally operated at low light levels due to their signal amplification
characteristics. Their sensitivity is therefore limited by their inherent noise. There
are different sources of noise in an APD, the most important of which are listed
below.

Leakage Current:An APD can have two types of leakage currents: surface

leakage current and bulk leakage current. The bulk leakage current, which flows

in the bulk of the material, is affected by the high electric field in a manner

similar to the signal current, and hence gets amplified. We will represent the

gain associated with the bulk leakage current byGlto differentiate it from

the multiplication factor for the signal. IfIlsandIlbare the surface and bulk

leakage currents respectively then the total leakage currentIlin an APD having

a mean gain〈G〉can be expressed as

Il=Ils+〈Gl〉Ilb. (6.5.70)

The contribution of surface leakage current to the total leakage current is quite

small and can therefore be safely ignored for most computations. Hence we

can write

Il≈〈Gl〉Ilb. (6.5.71)

The fluctuations of this leakage ordarkcurrent is given by the shot noise

formula

σ^2 l=2eIlB〈Gl〉^2 Fl, (6.5.72)

whereeis the unit electrical charge,Bis the bandwidth of the system, andFl

is the excess noise factor for the leakage current. Note that here we have made

use of the definition of the excess noise factor given earlier, that is

Fl=

〈G^2 l〉

〈Gl〉^2

. (6.5.73)

The excess noise factor in terms of electron ionization rateα,depletionwidth

d, ionization rate ratiou, and gain factorGlis given by (see, for example (21))

Fl=

(1 +αd〈Gl〉)(1+uαd〈Gl〉)

〈Gl〉

. (6.5.74)

Determination of the noise factor and the fluctuations of the dark current

requires the knowledge of the multiplication factor or gain, which can be com-

puted from the relation (21)

〈Gl〉=

1 −e−αd(1−u)

αd

[

e−αd(1−u)−u

]. (6.5.75)