Page 52 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Source: Photodetection and Measurement

Chapter
3

Fundamental Noise Basics

and Calculations

3.1 Introduction

We saw in Chap. 1 that many silicon photodiodes exhibit detection performance
in their region of best sensitivity within about 30 percent of the ideal respon-
sivity and limited by fundamental quantum processes r(A/W) = 0.807l(mm).
This quantum limited performance does not mean, however, that detectors
do everything we want, or even less that detection systems based on them
are perfect. The detector might be operating as well as possible but still not
well enough. All that really counts for your system is the final measure-
ment signal-to-noise ratio (S/N). We have spent some time looking at the
signal (photocurrent), how to maximize it, and how to measure it in a useful
bandwidth. Now we must look at the fundamental sources of noise. All detec-
tion systems are limited, at least, by shot noise and thermal (or Johnson)
noise.

3.2 Shot Noise
Shot noise is the uncertainty in determining the magnitude of a current.
It might be thought to be present in any current, whether generated by
photodetection or delivered by the wall-socket wiring, although not necessarily
with the same relative magnitude. In practice it appears to be relevant only in
junctions where there is a “barrier” that carriers must cross, and this includes
photocurrents generated in photodiodes. The term shot noise arose on listen-
ing to the fluctuations in current in vacuum diodes run in their “temperature-
limited” region with headphones. Current variations sound like lead shot
raining down on a metal plate. If a large number of precision measurements is
made of a nominally constant current and the results are plotted, the results
should be distributed evenly around the nominal value as shown in Fig. 3.1.
On the right of the figure is a histogram that shows the likelihood of measur-
ing a current in a given current “bin.” Clearly the most frequently encountered

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