Analysis of photoconductive gain as it applies to single-photon detection

We detail a mathematical framework for photoconductive gain applied to the detection of single photons. Because photoconductive gain is derived from the ability to measure current change for an extended period, its magnitude is reduced as detection speed is increased. We theoretically show that high-speed detection is still possible as long as the noise spectrum of the device is 1 / f in nature. Using signal analysis techniques, we develop tools to apply to device noise spectra to determine the performance of single-photon detectors that utilize photoconductive gain. We show that there is no speed penalty when one considers the signal-to-noise ratio for the fundamental 1 / f noise typical of high electron mobility transistors. We outline a technique for quickly characterizing a detector's sensitivity and speed through purely electrical measurements of the device's noise spectra. Consequently, the performance of the detector can be determined and optimized without conducting optical measurements. Finally, we employ this analysis to a quantum dot, optically gated field-effect transistor and verify our results with optical measurements.