Design guidelines for thermopower generators with multi-layered black phosphorus

We study a thermal gradient induced current $( I _{th})$ flow in potassium (K)-doped two-dimensional anisotropic black phosphorus (BP) with semi-Dirac dispersion. The prototype device is a BP channel clamped between two contacts maintained at unequal temperatures. The choice of BP lies in the predicted efficient thermolectric behaviour. A temperature-induced difference in the Fermi levels of the two contacts drives the current (typified by the electro-thermal conductance) which we calculate using the Landauer transport equation. The current shows an initial rise when the device is operated at lower temperatures. The rise stalls at progressively higher temperatures and $I _{th}$ acquires a plateau-like flat profile indicating a competing effect between a larger number of transmission modes and a corresponding drop in the Fermi level difference between the contacts. The current is computed for both n- and p -type BP and the difference thereof is attributed to the particle-hole asymmetry. We conclude by pointing out improved thermal behaviour that may arise in multi-layered BP through topological phase transitions induced by additional K-doping.