Optical and Electrical Characterization and Modeling of Photon Detection Probability in CMOS Single-Photon Avalanche Diodes

Single-photon avalanche diodes (SPADs) are very attractive devices in optical detector applications where both CMOS integration and low light detection are critical. An important SPAD performance parameter is the photon detection probability (PDP) which has to be carefully characterized for the sensor design. In this article, we present a comprehensive modeling and experimental characterization of the PDP to obtain its optical and electrical dependency on different parameters including the wavelength and light incidence angle as well as the biasing condition. By calculating the optical absorption and the avalanche triggering probabilities within the silicon, the PDP of an n
⁺
/p-well CMOS-implemented SPAD is accurately modeled. It is shown that due to the formation of a standing wave in different layers above the silicon, which significantly affects the optical transmission and the PDP spectrum, the application of the presented approach is necessary especially when an anti-reflection coating layer is not available. The obtained result shows an excellent agreement to our measurements and, therefore, the model can be reliably used for accurate design and optimization of SPAD-based detectors and to avoid very time-consuming experimental investigations, e. g. for obtaining the detector performance for deviations in the light incidence angle.