Temperature-Dependent Transport in Ultrathin Black Phosphorus Field-Effect Transistors

We studied the temperature-dependent transport properties of ultrathin black phosphorus (BP). We present measurements of BP Schottky barrier (SB) metal-oxide-semiconductor field-effect-transistors (MOSFETs) with various channel lengths, constructed from a single BP sample with nanoscale uniformity in thickness and width. The electrical characterization reveals a reversal in the temperature dependence of drain current as a function of gate voltage. This reversal indicates a transition in the charge conduction limiting mechanisms as the device is swept from the off-state into the on-state. In the off-state, charge transport is limited by thermionic emission over the energy barriers at the source/drain SB contacts, and drain current increases with temperature. In the on-state, carriers can easily tunnel across the SB at the contacts, and charge transport is limited by scattering in the channel. As a result, drain current decreases with temperature in the on-state, as scattering increases with temperature. Using Landauer transport theory, we derive a closed-form expression for thermionic emission current in SB-MOSFETs with two-dimensional channels. We use this expression to extract the SB height at metal contact interface with BP and demonstrate the impact of scattering on the extraction. We then use a comprehensive BP SB-MOSFET model to analyze on-state current as a function of temperature and demonstrate the effects of charged impurity and phonon scattering on the transport properties of BP through extractions of mobility at fixed carrier density.