Determination of scattering time and of valley occupation in transition-metal dichalcogenides doped by field effect

The transition-metal dichalcogenides have attracted a lot of attention as a possible stepping-stone toward atomically thin and flexible field-effect transistors. One key parameter to describe the charge transport is the time between two successive scattering events - the transport scattering time. In a recent report, we have shown that it is possible to use density functional theory to obtain the band structure of two-dimensional semiconductors in presence of field effect doping. Here, we report a simple method to extract the scattering time from the experimental conductivity and from the knowledge of the band structure. We apply our approach to monolayers and multilayers of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, and WSe$_2$ in presence of a gate. In WS$_2$, for which accurate measurements of mobility have been published, we find that the scattering time is inversely proportional to the density of states at the Fermi level. Finally, we show that it is possible to identify the critical doping at which different valleys start to be occupied from the doping-dependence of the conductivity.