The Hall coefficient: a tool for characterizing graphene field effect transistors

Graphene field effect transistors are considered as a candidate for future high-frequency applications. For their realization, the optimal combination of substrate, graphene preparation, and insulator deposition and composition is required. This optimization must be based on an in-depth characterization of the obtained graphene insulator metal (GIM) stack. Hall effect measurements are frequently employed to study such systems, thereby focussing primarily on the charge carrier mobility. In this work we show how an analysis of the sheet Hall coefficient can reveal further important properties of the GIM stack, like, e.g., the interface trap density and the spacial charge inhomogeneity. To that end, we provide an extensive description of the GIM diode, which leads to an accurate calculation of the sheet Hall coefficient dependent on temperature and gate voltage. The gate dependent inverse sheet Hall coefficient is discussed in detail before we introduce the concept of an equivalent temperature, which is a measure of the spacial charge inhomogeneity. In order to test the concept, we apply it to evaluate already measured Hall data taken from the literature. This evaluation allows us to determine the Drude mobility, even at the charge neutrality point, which is inaccessible with a simple one band Hall mobility analysis, and to shed light on the spacial charge inhomogeneity. The formalism is easily adaptable and provides experimentalists a powerful tool for the characterization of their graphene field effect devices. (paper)