Variable range hopping electric and thermoelectric transport in anisotropic black phosphorus

Black phosphorus (BP) is a layered semiconductor with a high mobility of up to ∼1000 cm2 V−1 s−1 and a narrow bandgap of ∼0.3 eV, and shows potential applications in thermoelectrics. In stark contrast to most other layered materials, electrical and thermoelectric properties in the basal plane of BP are highly anisotropic. To elucidate the mechanism for such anisotropy, we fabricated BP nanoribbons (∼100 nm thick) along the armchair and zigzag directions, and measured the transport properties. It is found that both the electrical conductivity and Seebeck coefficient increase with temperature, a behavior contradictory to that of traditional semiconductors. The three-dimensional variable range hopping model is adopted to analyze this abnormal temperature dependency of electrical conductivity and Seebeck coefficient. The hopping transport of the BP nanoribbons, attributed to high density of trap states in the samples, provides a fundamental understanding of the anisotropic BP for potential thermoelectric applications.