Photoconductive gain of extrinsic semiconductor detectors

Abstract Photoconductive gain in extrinsic (doped) semiconductor devices has traditionally been described by the ratio of the constant carrier lifetime to the carrier transit time. In this work, the constant-lifetime approximation is replaced by an effective lifetime, obtained through spatial averaging of photocurrent density over the device length, resulting in photocurrent saturation with applied voltage bias. The concept of effective mobility, which incorporates contributions from both majority and minority carriers, is introduced. Analytical expressions for effective carrier distributions based on effective mobility and for photoconductive gain governed by effective carrier distributions and majority-carrier photocurrent are derived. It is further shown that the maximum gain depends only on the ratio of majority to minority carrier mobilities, eliminating the unphysical prediction of unbounded gain at high bias voltages, extreme mobilities, or short device lengths. The analysis reconciles classical theory with simulation and experimental results, recovering correct gain behaviour across low- and high-drift regimes.