Empirically, a photomultiplier tube (PMT) is said to present better signal-to-noise ratio (SNR) than an avalanche photodiode (APD). Some materials say that it is attributed to the higher gain and lower dark current of PMT.
The benefit of higher gain is confusing to me, since I suppose that noise (from incident photons and from the PMT detector) and signal are both amplified by gain. Why does higher gain result in better SNR?
You have quoted that photomultiplier tubes have a higher gain and lower dark current than avalanche photodiodes and considered that noise and signal are both amplified by gain, but what is important is the lower dark current of photomultiplier tubes compared with avalanche photodiodes.
This means that there is less inherent noise associated with photomultiplier tubes, so for the same signal they will present a better signal-to-noise ratio than avalanche photodiodes.
