An Improved 2-D Photon Detection Probability Model for Single-Photon Avalanche Diodes With Experimental Calibrations

Single-photon avalanche diodes (SPADs) enable ultrasensitive photodetection while being compatible to cost-effective standard CMOS technology. However, accurate characterization of their photon detection probability (PDP) remains underexplored, limiting the optimization of SPAD performance in standard CMOS processes. This work presents an efficient and robust PDP modeling approach that accounts for key process-dependent and experimental nonidealities. The model considers effects of interlayer dielectric (ILD), intermetal dielectric (IMD), and passivation layers, capturing their impact on optical transmission and PDP. To address experimental limitations, the simulated PDP is calibrated using measured transmission spectra of bandpass filters (BPFs). A Monte Carlo (MC) method further optimizes the PDP model with the consideration of process variations, enabling improved agreement with measurements. The proposed model achieves a mean absolute error (MAE) of 2.74% over the spectrum from 400 to 660 nm and an absolute difference of 0.44% at peak PDP at 420 nm when compared to the measured PDP results.