  We address the determination of the time resolution for the $\rm 100~\mu m$
4H-SiC PIN detectors fabricated by Nanjing University (NJU). The time response
to $\rm \beta$ particles from a $\rm ^{90}$Sr source is investigated for the
detection of the minimum ionizing particles (MIPs). We study the influence of
different reverse voltages, which correspond to different carrier velocities
and device sizes, and how this correlates with the detector capacitance. We
determine a time resolution $\rm (94\pm1)~ps$ for $\rm 100~\mu m$ 4H-SiC PIN
detector. A fast simulation software, termed RASER (RAdiation SEmiconductoR),
is developed, and validated by comparing the waveform obtained from simulated
and measured data. The simulated time resolution is $\rm (73\pm 1)~ps$ after
considering the intrinsic leading contributions of the detector to time
resolution.
