# Shot noise in a photo diode

1. Jun 14, 2014

### aaaa202

Not really sure where this belongs... But here goes:
If you illuminate a photo diode it generates a current because electrons are being emitted from its cathode. Since each emission is however an independent stochastic process the output current will be subject to fluctuations, which can be described using Poisson statistics.
Now in my book a result is that for the variance of the current in a frequency interval df, is given by:
d(Var(I)) = 2eI*df
, where I is the average current measured over long times.
This formula shows that current fluctuations are true white noise, since they are independent of the frequency. However it also confuses me a bit. To obtain the total fluctuations one will have to integrate over all possible frequencies. Doing so the integral of the above will diverge. What have I misunderstood?

I would also like to understand why in general integrating over the power spectral function gives us the total voltage fluctuations. It follows from the above when the noise is shot noise, but how do you know it to be true in general?

2. Jun 14, 2014

### UltrafastPED

3. Jun 26, 2014

### itaischles

Read about Wiener-Khinchine theorem to figure out why integrating the power spectral density results in total fluctuation.