  In this paper the optical gain mechanism in phototransistor detectors (PTDs)
is explored in low light conditions. An analytical formula is derived for the
physical limit on the minimum number of detectable photons for the PTD. This
formulation shows that the sensitivity of the PTD, regardless of its material
composition, is related to the square root of the normalized total capacitance
at the base layer. Since the base total capacitance is directly proportional to
the size of the PTD, the formulation shows the scaling effect on the
sensitivity of the PTD. We used the extracted formula to study the sensitivity
limit of a typical InGaAs/InP heterojunction PTD. Modeling predicts that a PTD
with a nanoscale electronic area can reach to a single photon noise equivalent
power even at room temperature. The proposed model can also be used to explore
the sensitivity and speed of the nanowire-based photodetectors. To the best of
our knowledge, this is the first comprehensive study on the sensitivity of the
PTD for low light detection.
