Graphene FETs with high and low mobilities have universal temperature-dependent properties.

We use phenomenological modelling and calculations of charge carrier scattering to investigate the dependence of the electrical resistivity, Ro, on gate voltage, Vg, for a series of monolayer graphene field effect transistors with mobilities, mu, ranging between 5,000 and 200,000 cm2/Vs at low-temperature. Our measurements over a wide range of temperatures from 4 K to 400 K can be fitted by the relation μ=4/eδnRo_max for all devices, where Ro_max is the resistivity maximum at the neutrality point and delta-n is an "uncertainty" in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of n. This relation is consistent with thermal broadening of the carrier distribution and the presence of the disordered potential landscape consisting of so-called electron-hole puddles near the Dirac point. To demonstrate its utility, we combine this relation with linearised temperature-dependent Boltzmann transport calculations that include the effect of optical phonon scattering. This approach demonstrates the similarity in the temperature-dependent behaviour of carriers in different types of single layer graphene transistors with widely differing carrier mobilities. It can also account for the relative stability, over a wide temperature range, of the measured carrier mobility of each device.