Theoretical evaluation of MTF and charge collection efficiency in CCD and CMOS image sensors

摘要

Classical models used to calculate the Modulation Transfer function (MTF) of a solid-state image sensor generally use a sinusoidal type of illumination. The approach, described in tins paper, consists in considering a point-source illumination to built a theoretical three-dimensional model of the diffusion and the collection of photo-carriers created within the image sensor array. Fourier transform formalism is used for this type of illumination. Solutions allow to evaluate the spatial repartition of the charge density collected in the space charge region, i.e. to get the Pixel Response Function (PRF) formulation. PRF enables to calculate analytically both MTF and crosstalk at every needed wavelengths. The model can take into account a uniformly doped substrate and an epitaxial layer grown on a highly doped substrate. The built-in electric field induced by the EPI/Substrate doping gradient is also taken into account. For these configurations, MTF, charge collection efficiency and crosstalk proportion are calculated. The study is established in the case of photodiode pixel but it can be easily extended to pinned photodiode pixels and photogate pixels.