Biophotonics_Concepts_to_Applications

(c) The mean-square dark current noise; and (d) The mean-square thermal

noise current.

Solution:

(a) From Eq. (5.8) the primary photocurrent is

ip¼RPin¼

gqk

hc

Pin

¼

ð 0 : 90 ÞðÞ 1 : 6  10 ^19 C 1 : 3  10 ^6 m



ðÞ 6 : 625  10 ^34 JsðÞ 3  108 m=s

3  10 ^7 W



¼ 0 : 282 lA

(b) From Eq. (5.13) the mean-square shot noise current for apinphotodiode

is

i^2 shot

¼2qipBe¼ 21 : 6  10 ^19 C



0 : 282  10 ^6 A



20  106 Hz



¼ 1 : 80  10 ^18 A^2

or i^2 shot

(^1) = 2
¼ 1 :34 nA
(c) From Eq. (5.14) the mean-square dark current is
i^2 DB
¼2qiDBe¼ 21 : 6  10 ^19 C


4  10 ^9 A


20  106 Hz


¼ 2 : 56  10 ^20 A^2
or i^2 DB
(^1) = 2
¼ 0 :16 nA
(d) From Eq. (5.15) the mean-square thermal noise current for the receiver is
i^2 T
¼
4kBT
RL
Be¼
41 ðÞ: 38  10 ^23 J=KðÞ293 K
1000 X
20  106 Hz


¼ 323  10 ^18 A^2
or i^2 T
(^1) = 2
¼18 nA
Thus for this receiver the rms thermal noise current is about 14 times
greater than the rms shot noise current and about 100 times greater than the
rms dark current.

5.3.3 Noise-Equivalent Power and Detectivity

The sensitivity of a photodetector is describable in terms of theminimum detectable
optical power. This is the optical power necessary to produce a photocurrent of the
same magnitude as the root-mean-square (rms) of the total noise current, or
equivalently, to yield a signal-to-noise ratio of 1. This optical signal power is

5.3 Photodiode Noises 131