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 listening 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 measuring a current in a given current "bin." Clearly the most frequently encountered measured value is the nominal current, here I _mean = 1.0, but there will always be some fuzziness.

Figure 3.1: Multiple measurements of a photocurrent should provide a Gaussian (actually Poisson) histogram, with a variance equal to its mean.

A constant photocurrent ( I _p) exhibits a current noise power spectral density given by:

where q is the charge on the electron (1.602 10 ^?19C) and B is the measurement bandwidth in hertz. This is called the Schottky formula.