A stochastic model for characterizing the conversion gain of Active Pixel Complementary metal-oxide-semiconductor (CMOS) image sensors (APS) with at least four transistors is presented. This model, based on the fundamental principles of electronic noise, may provide a reliable calibration of the gain conversion, which is one of the most important parameters of CMOS Image Sensor pixels. The new model revisits the "gold standard" ratio method of the measured variance of the shot noise to the mean value. The model assumes that shot noise is the dominant noise source of the pixel. The microscopic random time-dependent voltage of any shot noise electron charging the junction capacitance C of the sensing node may have either an exponential form or a step form. In the former case, a factor of 1/2 appears in the variance to the mean value, namely, q/2C is obtained. In the latter case, the well-established ratio q/C remains, where q is the electron charge. This correction factor affects the parameters that are based on the conversion gain, such as quantum efficiency and noise. The model has been successfully tested for advanced image sensors with six transistors fabricated in a commercial FAB, applying a CMOS 180 nm technology node with four metals. The stochastic modeling is corroborated by measurements of the quantum efficiency and simulations with advanced software (Lumerical).
Keywords: CMOS Image Sensor; conversion gain; global shutter; low read noise; photon counting; pinned photodiode; shot noise.