Thermoelectric properties of gated phosphorene junctions

The reduced dimensions of nanostructures offer opportunities to control and improve the performance of thermoelectric devices based on two-dimensional materials. Here, we investigate theoretically the thermoelectric properties of gated phosphorene junctions (GPJs). We focus on the electronic contribution due to the possible ultralow phononic thermal conductivity in GPJs. The effects of nanostructuration, temperature, and phosphorene anisotropy are analyzed. The hybrid matrix method and the Landauer-B\"uttiker formalism are implemented to obtain the transmission coefficient and thermoelectric properties, respectively. We consider electronic transport mediated by holes or equivalently $n\ensuremath{-}p\ensuremath{-}n$ transport, finding that nanostructuration induces a strong anisotropy in all thermoelectric properties. The Seebeck coefficient, figure of merit, and efficiency have a better response in the zigzag direction, whereas, the electronic conductance, power factor and electronic thermal conductance have higher values in the armchair direction. In the case of large chemical potentials, large electrostatic potentials and narrow barriers the temperature generates an increase and broadening in all thermoelectric properties. In the zigzag direction, the figure of merit attains values above the technological limit value $ZT=3$, owing to the significant reduction of the ratio of conductances with respect to the Wiedemann-Franz law and the large values of the Seebeck coefficient. On the contrary, for low chemical potentials, small electrostatic potentials and wide barriers the thermoelectric properties diminish with the temperature. In this case, the figure of merit is dictated essentially by the Seebeck coefficient due to the slight variation of the ratio of conductances with respect to the Wiedemann-Franz law.