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Owing to the difficulties associated with substitutional doping of low-dimensional nanomaterials, most field-effect transistors built from carbon nanotubes, two-dimensional crystals and other low-dimensional channels are Schottky barrier MOSFETs (metal-oxide-semiconductor field-effect transistors). The transmission through a Schottky barrier-MOSFET is dominated by the gate-dependent transmission through the Schottky barriers at the metal-to-channel interfaces. This makes the use of conventional transistor models highly inappropriate and has lead researchers in the past frequently to extract incorrect intrinsic properties, for example, mobility, for many novel nanomaterials. Here we propose a simple modelling approach to quantitatively describe the transfer characteristics of Schottky barrier-MOSFETs from ultra-thin body materials accurately in the device off-state. In particular, after validating the model through the analysis of a set of ultra-thin silicon field-effect transistor data, we have successfully applied our approach to extract Schottky barrier heights for electrons and holes in black phosphorus devices for a large range of body thicknesses.

Analysing black phosphorus transistors using an analytic Schottky barrier MOSFET model