A quantum efficiency analytical model for complementary metal–oxide–semiconductor image pixels with a pinned photodiode structure

A quantum efficiency analytical model for complementary metal–oxide–semiconductor (CMOS) image pixels with a pinned photodiode structure is developed. The proposed model takes account of the non-uniform doping distribution in the N-type region due to the impurity compensation formed by the actual fabricating process. The characteristics of two boundary PN junctions located in the N-type region for the particular spectral response of a pinned photodiode, are quantitatively analyzed. By solving the minority carrier steady-state diffusion equations and the barrier region photocurrent density equations successively, the analytical relationship between the quantum efficiency and the corresponding parameters such as incident wavelength, N-type width, peak doping concentration, and impurity density gradient of the N-type region is established. The validity of the model is verified by the measurement results with a test chip of 160× 160 pixels array, which provides the accurate process with a theoretical guidance for quantum efficiency design in pinned photodiode pixels.