2D dark-count-rate modeling of PureB single-photon avalanche diodes in a TCAD environment

PureB silicon photodiodes have nm-shallow p+n junctions with which photons/electrons with penetration-depths of a few nanometer can be detected. PureB Single-Photon Avalanche Diodes (SPADs) were fabricated and analysed by 2D numerical modeling as an extension to TCAD software. The very shallow p+ -anode has high perimeter curvature that enhances the electric field. In SPADs, noise is quantified by the dark count rate (DCR) that is a measure for the number of false counts triggered by unwanted processes in the non-illuminated device. Just like for desired events, the probability a dark count increases with increasing electric field and the perimeter conditions are critical. In this work, the DCR was studied by two 2D methods of analysis: the "quasi-2D" (Q-2D) method where vertical 1D cross-sections were assumed for calculating the electron/hole avalanche-probabilities, and the "ionization-integral 2D" (II-2D) method where crosssections were placed where the maximum ionization-integrals were calculated. The Q-2D method gave satisfactory results in structures where the peripheral regions had a small contribution to the DCR, such as in devices with conventional deepjunction guard rings (GRs). Otherwise, the II-2D method proved to be much more precise. The results show that the DCR simulation methods are useful for optimizing the compromise between fill-factor and p-/n-doping profile design in SPAD devices. For the experimentally investigated PureB SPADs, excellent agreement of the measured and simulated DCR was achieved. This shows that although an implicit GR is attractively compact, the very shallow pn-junction gives a risk of having such a low breakdown voltage at the perimeter that the DCR of the device may be negatively impacted.