A Comprehensive Model to Predict the Timing Resolution of SiPM-Based Scintillation Detectors: Theory and Experimental Validation

Silicon photomultipliers (SiPMs) are expected to replace photomultiplier tubes (PMTs) in several applications that require scintillation detectors with excellent timing resolution, such as time-of-flight positron emission tomography (TOF-PET). However, the theory about the timing resolution of SiPM-based detectors is not yet fully understood. Here we propose a comprehensive statistical model to predict the timing resolution of SiPM-based scintillation detectors. It incorporates the relevant SiPM-related parameters (viz. the single cell electronic response, the single cell gain, the charge carrier transit time spread, and crosstalk) as well as the scintillation pulse rise and decay times, light yield, and energy resolution. It is shown that the proposed model reduces to the well-established Hyman model for timing with PMTs if the number of primary triggers (photoelectrons in case of a PMT) is Poisson distributed and crosstalk and electronic noise are negligible. The model predictions are validated by measurements of the coincidence resolving times (CRT) for 511 keV photons of two identical detectors as a function of SiPM bias voltage, for two different kinds of scintillators, namely LYSO:Ce and LaBr₃:5%Ce. CRTs as low as 138 ps ± 2 ps FWHM for LYSO:Ce and 95 ps ± 3 ps FWHM for LaBr₃:5%Ce were obtained, demonstrating the outstanding timing potential of SiPM-based scintillation detectors. These values were found to be in good agreement with the predicted CRTs of 140 ps FWHM and 95 ps FWHM, respectively. Utilizing the proposed model, it can be shown that the CRTs obtained in our experiments are mainly limited by photon statistics while crosstalk, electronic noise and signal bandwidth have relatively little influence.