If the signal amplitude is large ( this can happen for the receivers which are close to the transmitter in an optical network) the shot noise dominates over the thermal noise, i.e. .

The SNR in this case

For shot noise limited regime the load resistance has no role to play in SNR improvement. Also the SNR improves linearly with the signal power.

The signal power requirement in the case increases linearly with bandwidth, i.e.

This very interesting, that at low signal powers, the receiver performance improves better with signal power than at high signal powers.