Page 55 - Photodetection and Measurement - Maximizing Performance in Optical Systems

Fundamental Noise Basics and Calculations

48 Chapter Three

3.4 What Shot Noise Can We Expect?
Replacing the electronic charge with its numerical value and translating to
more useful engineering units we can write for the shot current noise density:
)
.
i n = 057 I p (mApA Hz (3.5)
As the shot noise dictates the ultimate precision with which the photocurrent
can be measured, it is important to have a feel for its magnitude. Table 3.1
shows a few values.
This shows the precision that is possible in principle if the measurement
system is shot noise limited. If we have 1mA of photocurrent, it should be
possible to determine its magnitude with a precision of 1 in 55 million in 1Hz
bandwidth, far beyond the resolution of the best analog-to-digital converters.
In practice, many effects conspire to limit our precision to a value much worse
that that.
Another big issue is what currents actually show full shot noise? This is a
matter of some uncertainty in the literature. Netzer (1981) suggests that shot
noise is seen in situations where charge carriers cross a barrier independently
of one another, such as pn-junction diodes where the passage occurs by diffu-
sion, a vacuum-tube cathode where electron emission occurs as a result of
thermal motion, and photodiodes.

3.4.1 TRY IT! (In)visible shot noise
Instead of looking for parts per million (ppm) variations in milliampere currents, let’s
try to make an AC optical measurement, with the shot noise as visible as possible.
Connect a photodiode and reverse bias it with a 15-V battery, passing the photo-
current directly into a 1-MW impedance oscilloscope input (Fig. 3.2). It might be a
good idea to carefully filter the battery voltage and put the whole thing in a well-
screened metal box. Otherwise, all you will see is line pickup. Illuminate the photo-
diode with a flashlight or LED to give 1-V DC on the oscilloscope.
This gives us a 1mA photocurrent, which should exhibit a current noise spectral
density of 0.57pA/ Hz . With the detection bandwidth of 20MHz, such as that of a
modest oscilloscope without bandwidth restriction, the current noise level will be

TABLE 3.1 Some Examples of Shot Noise Values
Shot noise Relative noise
current spectral currents i n :I p in
Current (I p) density (i n) 1Hz BW
1mA 18pA/ Hz 1:55,000,000
1mA 0.57pA/ Hz 1:1,754,000
1nA 0.018pA/ Hz 1:55,000
1pA 0.57fA/ Hz 1:1,754

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