Single photon avalanche diode (SPAD) operating in Geiger mode can be used to detect the extremely weak optical signal. In this paper, we present a novel bi-directional SPAD structure and apply it to the passive quenching circuit. We also apply a unidirectional SPAD to the passive quenching circuit for comparison. The traditional SPADs used for passive quenching circuit usually extract the voltage waveform from the cathode, which is often used for single photon detection. Interestingly, the research in this paper finds that the current-voltage characteristic (I-V) of the bi-directional SPAD applied to the passive quenching circuit is a complete 8-shaped by extracting the current and voltage waveforms from the anode, which has the characteristics of a generalized memristor. At the same time, the I-V curve of the unidirectional SPAD is only a half under the same parameters. And the results are verified by Cadence Spectre circuit simulator.