Modeling photon detection efficiency and temporal response of single photon avalanche diodes

In this paper we present a physically-based model aimed at calculating the Photon Detection Efficiency (PDE) and the temporal response of a Single-Photon Avalanche Diode (SPAD) with a given structure. In order to calculate these quantities, it is necessary to evaluate both the probability and the delay with which a photon impinging on the detector area triggers an avalanche. Three tasks are sequentially performed: as a first step, the electron-hole generation profile along the device is calculated according to the silicon absorption coefficient at the considered wavelength; successively, temporal evolution of the carriers distribution along the device is calculated by solving drift diffusion equations; finally, the avalanche triggering probability is calculated as a function of the photon absorption point. Validation of the model has been carried out by comparing simulation and experimental results of a few generations of detectors previously realized in our laboratory. Photon detection efficiency has been measured and calculated for wavelengths ranging from 400nm to 1000nm and for excess bias voltages ranging from 2 to 8V. Similarly, temporal response has been investigated at two different wavelengths (520 and 820nm). A remarkable agreement between experimental and simulation results has been obtained in the entire characterization domain simply starting from the measured doping profile and without the need of any fitting parameter. Consequently, we think that this model will be a valuable tool for the development of new detectors with improved performances.