Biophotonics_Concepts_to_Applications

The multiplication M for all carriers generated in the photodiode is defined by

M¼

iM

ip

ð 5 : 9 Þ

where iMis the average value of the total multiplied output current and ipis the
primary unmultiplied photocurrent defined in Eq. (5.6). In practice, the avalanche
mechanism is a statistical process, since not every carrier pair generated in the diode
experiences the same multiplication. Thus, the measured value of M is expressed as
an average quantity.
Analogous to thepinphotodiode, the performance of an APD is characterized by
its responsivityRAPD, which is given by

RAPD¼

gq

hm

M¼RM ð 5 : 10 Þ

whereRis the unity gain responsivity.

Example 5.7A given silicon avalanche photodiode has a quantum efficiency

of 65 % at a wavelength of 900 nm. Suppose 0.5μW of optical power

produces a multiplied photocurrent of 10μA. What is the multiplication M?

Solution: First from Eq. (5.8) the primary photocurrent generated is

ip¼RPin¼

gqk

hc

Pin¼

ðÞ 0 : 65 ðÞ 1 : 6  10 ^19 CðÞ 9  10 ^7 m

ðÞ 6 : 625  10 ^34 JsðÞ 3  108 m=s

5  10 ^7 W



¼ 0 : 235 lA

Then from Eq. (5.9) the multiplication is

M¼

iM

ip

¼

10 lA

0 : 235 lA

¼ 43

Thus the primary photocurrent is multiplied by a factor of 43.

5.3 Photodiode Noises

5.3.1 Signal-to-Noise Ratio

When detecting a weak optical signal, the photodetector and its following ampli-
fication circuitry need to be designed so that a desired signal-to-noise ratio is

128 5 Fundamentals of Optical Detectors