  In this work, the consequence of the high band-edge density of states on the
carrier statistics and quantum capacitance in transition metal dichalcogenide
two-dimensional semiconductor devices is explored. The study questions the
validity of commonly used expressions for extracting carrier densities and
field-effect mobilities from the transfer characteristics of transistors with
such channel materials. By comparison to experimental data, a new method for
the accurate extraction of carrier densities and mobilities is outlined. The
work thus highlights a fundamental difference between these materials and
traditional semiconductors that must be considered in future experimental
measurements.
