Biophotonics_Concepts_to_Applications

statistics follow a Poisson process. Because thefluctuations in the number of
photocarriers created are a fundamental property of the photodetection process, the
shot noise sets the lower limit on the receiver sensitivity when all other conditions
are optimized. Theshot noise currentishothas a mean-square value in a receiver
electrical bandwidth Bethat is proportional to the average value of the photocurrent
ip, that is,

i^2 shot

¼2qipBeM^2 FðMÞð 5 : 13 Þ

where F(M) is anoisefigureassociated with the random nature of the avalanche
process. For an APD the noisefigure is typically 3–6 dB. Forpinphotodiodes M
and F(M) are unity.
The photodiodedark currentis the current iDthat continues toflow through the
bias circuit of the device when no light is incident on the photodiode. This is a
combination of bulk and surface dark currents, but in general the surface dark
current is negligible. Thebulk dark currentiDBarises from electrons and/or holes
that are thermally generated in the pn junction of the photodiode. In an APD, these
liberated carriers also get accelerated by the high electricfield present at the pn
junction, and are therefore multiplied by the avalanche gain mechanism. The
mean-square value of this dark current is given by

i^2 DB

¼2qiDM^2 FðMÞBe ð 5 : 14 Þ

where iDis the primary (unmultiplied) detector bulk dark current, which is listed on
component data sheets.
To simplify the analysis of the receiver circuitry, one can assume that the
amplifier input impedance is much greater than the load resistance RL, so that the
thermal noise from Rais much smaller than that of RL. The photodetector load
resistor then dominates and contributes a mean-squarethermal noise current

i^2 T

¼

4kBT

RL

Be ð 5 : 15 Þ

where kBis Boltzmann’s constant and T is the absolute temperature. Using a load
resistor that is large but still consistent with the receiver bandwidth requirements
can reduce this noise.

Example 5.8An InGaAspinphotodiode has the following parameters at a

wavelength of 1300 nm: iD= 4 nA,η= 0.90, RL= 1000Ω, and the surface

leakage current is negligible. Assume the incident optical power is 300 nW

(–35 dBm), the temperature is 293 K, and the receiver bandwidth is 20 MHz.

Find (a) The primary photocurrent; (b) The mean-square shot noise current;

130 5 Fundamentals of Optical Detectors