Electrical and thermoelectric transport by variable range hopping in thin black phosphorus devices

The moderate band gap of black phosphorus (BP) in the range of 0.3-2 eV, along a high mobility of a few hundred cm² V^-1 s^-1 provides a bridge between the gapless graphene and relatively low-mobility transition metal dichalcogenides. Here, we study the mechanism of electrical and thermoelectric transport in 10-30 nm thick BP devices by measurements of electrical conductance and thermopower (S) with various temperatures (T) and gate-electric fields. The T dependences of S and the sheet conductance (σ) of the BP devices show behaviors of T^1/3 and exp[-(1/T)^1/3], respectively, where S reaches ∼0.4 mV/K near room T. This result indicates that two-dimensional (2D) Mott's variable range hopping (VRH) is a dominant mechanism in the thermoelectric and electrical transport in our examined thin BP devices. We consider the origin of the 2D Mott's VRH transport in our BPs as trapped charges at the surface of the underlying SiO₂ based on the analysis with observed multiple quantum dots.