The impact of crystalline inhomogeneity on electrical transport and 1/$f$ noise in MoS$_{2}$ field effect transistor

We show that both conductivity and low frequency 1/$f$ noise are strongly influenced by the presence of localized trap states in ultra-thinMoS$_{2}$ field effect transistor. The trap states not only create Coulomb scattering of charge carriers but also slowly exchange carrier with channel. The trap density is quantitatively calculated which turns out two orders of magnitude higher than the typical SiO$_{2}$ surface trap density. This suggests a structural origin of the trap states in MoS$_{2}$ films. The result was also supported by similar noise measurement on MoS$_{2}$ devices on trap free hexagonal boron nitride substrate. The origin of these states is also investigated by spectroscopic studies, which indicate a possible presence of metallic 1T-patches inside the major semiconducting 2H phase.