  Scattering of charge carriers and flicker noise in electrical transport are
the central performance limiting factors in electronic devices, but their
microscopic origin in molybdenum disulphide~(MoS$_2$)-based field effect
transistors remains poorly understood. Here, we show that both carrier
scattering and low-frequency $1/f$ noise in mechanically exfoliated ultra-thin
MoS$_2$ layers are determined by the localized trap states located within the
MoS$_2$ channel itself. The trap states not only act as Coulomb scattering
centers that determine transport in both equilibrium ($eV< k_BT$) and
non-equilibrium ($eV>k_BT$) regimes, where $V$ and $T$ are the source drain
bias and temperature respectively, but also exchange carriers with the channel
to produce the conductivity noise. The internal origin of the trap states was
further confirmed by studying noise in MoS$_2$ films deposited on crystalline
boron nitride substrates. Possible origin and nature of the trap states is also
discussed.
