The purpose of this work is to study the effects of carbon doping on the thermoelectric properties of monolayer hexagonal boron nitride (h-BN) and hexagonal silicon carbide (h-SiC) in the presence of a magnetic field. We use a tight-binding model and Kubo formalism to calculate the effects of doping concentration, dopant type and applied magnetic field on the heat capacity, electrical conductivity, magnetic susceptibility, and thermoelectric figure of merit. Heat capacity displays a Schottky anomaly that is more prominent at lower dopant concentrations. In the presence of the magnetic field, the Schottky anomaly shifts to lower temperature and its intensity is reduced. The magnetic susceptibility of the doped structures is enhanced by both doping and a magnetic field. The p-type doped structures exhibit higher magnetic susceptibility intensity compared to the n-type doped structures, especially for h-SiC structure. The electrical and thermal conductivities rise from zero at low temperatures, with higher intensity for p-doped structures. Doped h-SiC has higher conductivity at low temperatures, but doped h-BN exceeds it at higher temperatures. A comparison of p- and n-doped h-SiC and h-BN reveals enhanced thermoelectric performance for p-doped structures, further improved by lower dopant concentrations and applied magnetic fields. Overall, the work provides new insights into optimizing the thermoelectric properties of doped h-BN and h-SiC nanostructures through doping and external fields.
