Fundamental Limits on the Subthreshold Slope in Schottky Source/Drain Black Phosphorus Field-Effect Transistors

The effect of thickness, temperature, and source-drain bias voltage, V_DS, on the subthreshold slope, SS, and off-state properties of black phosphorus (BP) field-effect transistors is reported. Locally back-gated p-MOSFETs with thin HfO₂ gate dielectrics were analyzed using exfoliated BP layers ranging in thickness from ∼4 to 14 nm. SS was found to degrade with increasing V_DS and to a greater extent in thicker flakes. In one of the thinnest devices, SS values as low as 126 mV/decade were achieved at V_DS = -0.1 V, and the devices displayed record performance at V_DS = -1.0 V with SS = 161 mV/decade and on-to-off current ratio of 2.84 × 10³ within a 1 V gate bias window. A one-dimensional transport model has been utilized to extract the band gap, interface state density, and the work function of the metal contacts. The model shows that SS degradation in BP MOSFETs occurs due to the ambipolar turn on of the carriers injected at the drain before the onset of purely thermionic-limited transport at the source. The model is further utilized to provide design guidelines for achieving ideal SS and meet off-state leakage targets, and it is found that band edge work functions and thin flakes are required for ideal operation at high V_DS. This work represents a comprehensive analysis of the fundamental performance limitations of Schottky-contacted BP MOSFETs under realistic operating conditions.