Modeling and Analysis of Capacitive Relaxation Quenching in a Single Photon Avalanche Diode (SPAD) Applied to a CMOS Image Sensor

We present an analysis of carrier dynamics of the single-photon detection process, i.e., from Geiger mode pulse generation to its quenching, in a single-photon avalanche diode (SPAD). The device is modeled by a parallel circuit of a SPAD and a capacitance representing both space charge accumulation inside the SPAD and parasitic components. The carrier dynamics inside the SPAD is described by time-dependent bipolar-coupled continuity equations (BCE). Numerical solutions of BCE show that the entire process completes within a few hundreds of picoseconds. More importantly, we find that the total amount of charges stored on the series capacitance gives rise to a voltage swing of the internal bias of SPAD twice of the excess bias voltage with respect to the breakdown voltage. This, in turn, gives a design methodology to control precisely generated charges and enables one to use SPADs as conventional photodiodes (PDs) in a four transistor pixel of a complementary metal-oxide-semiconductor (CMOS) image sensor (CIS) with short exposure time and without carrier overflow. Such operation is demonstrated by experiments with a 6 µm size 400 × 400 pixels SPAD-based CIS designed with this methodology.