# Photocurrent shot noise correlation function

1. Aug 24, 2012

### Niles

Hi

I have stumpled upon the following expression for the correlation function of the photocurrent shot noise for a photodiode
$$<\delta i(t)\delta i(t+\tau)> = \frac{e^2\eta}{h\nu}P\delta(\tau)$$
where η is the quantum efficiency and P the power in the signal. δ(τ) denotes the Dirac delta, which makes good sense as shot noise is white noise. However I am unsure of how the prefactor is derived. Can anyone point me in the right direction?

Best,
Niles.

2. Aug 24, 2012

### Darwin123

I can point in a direction. Sorry that I don't have a text editor, but I think you will see what I am getting at.
{h\nu} is the energy per photon. "P" is the power of the light illuminating the photodiode, which means energy per second. So {h\nu}P is the number of photons per second illuminating the photodiode.

Last edited: Aug 24, 2012
3. Aug 24, 2012

### marcusl

No, P/(hv) is the photon flux, which equals the number of electrons/sec. The current is therefore eP/(hv). So I think the question from Niles is: why doesn't the expression above have units of {eP/hv}^2?

4. Aug 25, 2012

### Niles

Hi

Thanks, that is exactly my question.