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In this paper, we develop an analytic physics-based model to describe currentconduction in ultra-thin black phosphorus (BP) field-effect transistors (FETs).The model extends the concept of virtual source charge calculation to capturethe effect of both hole and electron charges for ambipolar transportcharacteristics. The model comprehends the in-plane band-structure anisotropyin BP, as well as the asymmetry in electron and hole current conductioncharacteristics. The model also includes the effect of Schottky-typesource/drain contact resistances, which are voltage-dependent and cansignificantly limit current conduction in the on-state in BP FETs. Modelparameters are extracted using measured data of back-gated BP transistors withgate lengths of 1000 nm and 300 nm with BP thickness of 7.3 nm and 8.1 nm, andfor the temperature range of 180 K to 298 K. Compared to previous BP modelsthat are validated only for room-temperature and near-equilibrium biasconditions (low drain-source voltage), we demonstrate excellent agreementbetween the data and model over a broad range of bias and temperature values.The model is also validated against numerical TCAD data of top-gated BPtransistors with a channel length of 300 nm. The model is implemented inVerilog-A and the capability of the model to handle both dc and transientcircuit simulations is demonstrated using SPECTRE. The model not only providesa physical insight into technology-device interaction in BP transistors, butcan also be used to design and optimize BP-based circuits using a standardhierarchical circuit simulator.

An analytic virtual-source-based current-voltage model for ultra-thin black phosphorus field-effect transistors