  Despite the concerted effort of several research groups, a detailed
experimental account of defect dynamics in high-quality single- and few-layer
transition metal dichalcogenides remain elusive. In this paper we report an
experimental study of the temperature dependence of conductance and
conductance-fluctuations on several few-layer MoS$_{2}$ exfoliated on hexagonal
boron nitride and covered by a capping layer of high-$\kappa$ dielectric
HfO$_{2}$. The presence of the high-$\kappa$ dielectric made the device
extremely stable against environmental degradation as well as resistant to
changes in device characteristics upon repeated thermal cycling enabling us to
obtain reproducible data on the same device over a time-scale of more than one
year. Our device architecture helped bring down the conductance fluctuations of
the MoS$_2$ channel by orders of magnitude compared to previous reports. The
extremely low noise levels in our devices made in possible to detect the
generation-recombination noise arising from charge fluctuation between the
sulphur-vacancy levels in the band gap and energy-levels at the conductance
band-edge. Our work establishes conduction fluctuation spectroscopy as a viable
route to quantitatively probe in-gap defect levels in low-dimensional
semiconductors.
