Please tell the methods to find them theoretically and also experimentally.How does higher mobility allows quantum dot detector to operate at relatively higher temperature?
The detectivity is a function of dark current and responsivity. Since the dark current grows up with temperature and responsivity degrades, it can be said that the detectivity is a decreasing function of temperature and you can't see any peak (maximum) in detectivity&temperature curve to say what temperature is optimum.
For high mobility operation, I'm not sure but I think it may relates to the increased photoconductive gain of detector. If you check the semi-empirical relation developed for the photoconductive gain of QDIPs (APPLIED PHYSICS LETTERS Vol. 83, No. 6, pp. 1234-6, 2003) it is strongly dependent on the capture probability of carriers by QDs. I think that higher mobility carriers exhibit lower capture probability and then the photoconductive gain and consequently responsivity are increased.