Modeling and verification of capacitive quenching in a single photon avalanche diode

We present modeling and analysis of carrier dynamics in a single-photon avalanche diode (SPAD) operated with a capacitive quenching (CQ) method. The CQ method is regarded as a conventional resistive quenching (RQ) with its quenching resistance infinite or an open circuit. The SPAD is modelled as a lumped circuit consisting of a voltage dependent charge generator representing an avalanching depletion region and a capacitance of the depletion region and parasitic components. The carrier dynamics inside the device is described by time-dependent bipolar continuity equations (BCE) derived from the carrier continuity equations. We solve the BCE numerically with a 0.1 ps time resolution and investigate numbers of carriers in each circuit element as functions of time and of excess bias voltage (|𝑉ex|). We find two important characteristics of the CQ method; (1) a single-photon triggered Geiger-mode pulse is guaranteed to be quenched in a stable state (2) a voltage drop of the internal bias of SPAD due to the charges stored on the capacitance is proportional to |𝑉ex| with the proportionality factor of two. The results, in turn, enables one to design a SPAD free from after-pulse and from overflow. Such a SPAD pixel is shown to be compatible with a conventional complementary metal-oxide semiconductor (CMOS) image sensor (CIS) with a four transistors configuration pixel circuit. Finally, effectiveness of the present methodology is demonstrated by the subrange synthesis (SRS) time-of-flight (ToF) ranging experiments using a 6 μm size 400 × 400 pixels SPAD-based CIS.