Reexamination of Gain Theory for Intrinsic Photoconductive Devices

The quantum efficiency (QE) or gain (G) of a photoconductive device is most commonly given in literature as a ratio of carrier lifetime to transit time, allowing for a value much greater than unity. In this work, by assuming primary photoconductivity, we reexamine the photoconductive theory for the device with an intrinsic (undoped) semiconductor, with nearly zero equilibrium carrier densities. Analytic gain formula is obtained for arbitrary drift and diffusion parameters under a bias voltage and by neglecting the polarization effect due to the relative displacement in the electron and hole distributions. We find that the lifetime/transit-time ratio formula is only valid in the limit of weak field and no diffusion. Numerical simulations are performed to examine the polarization effect, confirming that it does not change the qualitative conclusions. We discuss the distinction between two QE definitions used in the literature: accumulative QE (〖QE〗_acc ), considering the contributions of the flow of all photocarriers, regardless of whether they reach the electrode; and apparent QE (〖QE〗_app), measuring the photocurrent at the electrode. In general, 〖QE〗_acc>〖QE〗_app, due to an inhomogeneous photocurrent in the channel; however, both approach the same unity limit for strong drift. We find that 〖QE〗_acc  〖 QE〗_app is a deficiency of the commonly adopted constant-carrier-lifetime approximation in the recombination terms.