Statistical Analysis of Silicon Photomultiplier Output Signals

Abstract

Silicon photomultipliers are relatively new devices designed as a matrix of single-photon avalanche detectors, which have become popular for their miniature dimensions and low operating voltage. Their superior sensitivity allows detecting low-photon-count optical pulses, e.g., in ranging and LIDAR applications. The output signal of the photomultiplier is a non-stationary stochastic process, from which a weak periodic pulse can be extracted by means of statistical processing. Using the double-exponential approximation of output avalanche pulses the paper presents a simple analytical solution to the mean and variance of the stochastic process. It is shown that even for an ideal square optical pulse the rising edge of the statistically detected signal is longer than the edge of individual avalanche pulses. The knowledge of the detected waveform can be used to design an optimum laser pulse waveform or algorithms for estimating the time of arrival. The experimental section demonstrates the proposed procedure.

Understanding the Nonlinear Response of SiPMs

“…A detailed electrical model of a SiPM, such as the one described in [ 24 ], should include the rise and decay times of the charge avalanche, the parasitic capacitance of the quenching resistors, and their connections to the silicon substrate, as well as the input impedance of the readout electronics. As a consequence, the shape of the transients is not a simple exponential function, as assumed by Equation ( 2 ), but it can be modeled using multiple exponential terms [ 25 ]. In principle, the output charge Q is independent of the shape of the transients.…”