Page 206 - Introduction to Information Optics

3.3. Critical Components i 91

power. Mathematically, the mean square of shot noise determined
current is

where / is the average current generated by the detector, e is the electron
charge unit, I d is the dark current (i.e., the current arisen from thermally
generated carriers without light illumination), and A/ is the bandwidth
over which the noise is being considered. Thermal noise (also referred to
as Jonshon noise or Nyquist noise) arises in the load resistor of the
photodiode circuit due to random thermal motion of electrons. Math-
ematically, it can be written as

/••/ \
VNT/ — ~ (3.44)
R,
23
where k B = 1.381 x 1CT J/K is the Boltzmann constant, T is the absolute
temperature, and R L is the resistance of the loading resistor. The thermal
noise is proportional to the absolute temperature. This is why, in some
cases, to reduce noise for very low light signal detection, we put the
photodetector in liquid nitrogen (i.e., T = 77 K).
Table 3.2 summaries typical performance characteristics of detectors.

Example 3.13. The band gap energy of a PIN photodetector is 0.73 eV. Obtain
the corresponding cutoff wavelength.
Solve:
m s

Table 3.2
Material Silicon Germanium InGaAs

Types PIN APD PIN APD PIN APD
Wavelength range (nm) 400- 1 100 800-1800 900 1700
Peak (nm) 900 830 1550 1300 1300 1300
1550 1550
Responsivity (A/W) 0.6 77-139 0.65-0.7 3-28 0.6-0.8
Quantum efficiency (%) 65 90 77 50-55 55 75 60-70 60 70
Gain (M) 1 150-250 1 5 40 1 10-30
Bias voitage ( — V) 45-100 220 6-10 20 35 5 < 30
Dark current (nA) 1-10 0.1-1.0 50-500 10-500 1-20 1 5
Capacitance (pF) 1.2-3 1.3-2 2-5 2 5 0.5-2 0.5
Rise time (ns) 0.5-1 0.1-2 0.1-0.5 0.5-0.8 0.06-0.5 0.1- -0.5