Physics and Engineering of Radiation Detection

414 Chapter 6. Scintillation Detectors and Photodetectors

It is instructive to compare equations 6.5.57 and 6.5.74, which represent the

gains of signal and dark currents respectively. It can be shown that they are

related through the relation

〈Gl〉=

1

αd

[〈Ge〉−1]. (6.5.76)

Excess Noise: We have already introduced the term excess noise factor to

characterize the fluctuations in the APD gain. This factor actually repre-

sents the so called excess noise that is related to the statistical nature of the

underlying particle interactions that take place during the process of charge

multiplication. Due to these fluctuations the distribution of amplitudes of the

output current pulses assume a finite width even if the incident light can be

described by an impulse or delta function.

We have already introduced the expression for the excess noise factor for the

dark current (see equation 6.5.74. For the signal current due to electrons the

noise factor can be written as (41)

Fe=u〈Ge〉+

[

2 −

1

〈Ge〉

(1−u)

]

, (6.5.77)

where, as before,urepresents the hole to electron ionization rate ratio and

〈Ge〉is the mean signal gain.


Thermal Noise:Thermal noise, though important, is not actually related to

the APD itself. It refers to the noise generated in the output circuitry due

to thermal agitations of the current carriers. During the discussion on PMT

noise, we introduced the termJohnson noiseto characterize the thermal noise

generated in the preamplifier. The same argument can be applied for the case

of APDs as well. Hence the variance of output current due to thermal noise is

given by

σt=

√

4 FtkBTB

Reqv

, (6.5.78)

whereFtis the noise figure for the noise source (the output circuitry),kBis the

familiar Boltzmann’s constant,Tis the absolute temperature,Bis the system

bandwidth, andReqvis the equivalent impedance of the output circuit.

The signal-to-noise ratio can be determined by noting that the noise sources
described above are independent of each other, since this allows us to represent the
total fluctuations or variance of the output current by

σ^2 out=σc^2 +σ^2 l+σ^2 t, (6.5.79)

where the subscriptsout,c,l,andtrefer to the variances corresponding to the
output signal, charge carriers, leakage current, and thermal noise respectively. If
the output signal is due to the electrons, as is usually the case, then the fluctuations
in the electron current can be written as

σ^2 c=2eIeB〈Ge〉^2 Fe, (6.5.80)