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

Abstract

We use phenomenological modelling and detailed experimental studies of charge carrier transport to investigate the dependence of the electrical resistivity,<i>ρ</i>, on gate voltage,<i>V</i>_<i>g</i>, for a series of monolayer graphene field effect transistors with mobilities,<i>μ</i>, ranging between 5000 and 250 000 cm²V^-1s^-1at low-temperature. Our measurements over a wide range of temperatures from 4 to 400 K can be fitted by the universal relationμ=4/eδnmaxfor all devices, whereρmaxis the resistivity maximum at the neutrality point and<i>δn</i>is an 'uncertainty' in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of carrier density,<i>n</i>. 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 temperature-dependent linearised 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.