Avalanche-Area Dependence of Gain in Passive-Quenched Single-Photon Avalanche Diodes by Multiple-Photon Injection

It is widely believed that the single-photon gain (SPG) of passive-quenched single-photon avalanche diodes (PQ-SPADs) is given by the product of the junction capacitance ( ${C}_{d}$ ) and the overvoltage ( ${V}_{\textsf {ov}}$ ) applied to the SPAD and that this gain remains constant even under multiple-photon injection. In this paper, we show that these are not always true. We found that the SPG of PQ-SPADs increases with increasing irradiation power of a picosecond pulse laser. This result is understood by considering that the avalanche area generated by a single-avalanche trigger is smaller than the active area of the diode, and that multiple-photon injection induces multiple-avalanche triggers in the depletion layer resulting in a variation in the avalanche area within the junction. Numerical transient simulation using a 1-D avalanche diode model coupled with 2-D junction capacitance reveals that the SPG increases from ${C}_{d}{V}_{\textsf {ov}}$ to $2{C}_{d} {V}_{\textsf {ov}}$ as the ratio of the avalanche area to diode active area increases.