A new high-granular compact time-of-flight neutron detector for the
identification and energy measurement of neutrons produced in nucleus-nucleus
interactions at the BM@N experiment, Dubna, Russia, at energies up to 4 AGeV is
under development. The detector consists of approximately 2000 fast plastic
scintillators, each with dimensions of 40×40×25 mm3, equiped
with SiPM (Silicon Photomultiplier) with an active area of 6×6 mm2.
The signal readout from these scintillators will employ a single-threshold
multichannel Time-to-Digital Converter (TDC) to measure their response time and
amplitude using the time-over-threshold (ToT) method. This article focuses on
the analytical description of the signals from the plastic scintillator
detectors equipped with silicon photomultipliers. This description is crucial
for establishing the ToT-amplitude relationship and implementing slewing
correction techniques to improve the time resolution of the detector. The
methodology presented in this paper demonstrates that a time resolution at the
70 ps level can be achieved for the fast plastic scintillator coupled with
silicon photomultiplier with epitaxial quenching resistors