The thermoelectric properties of carbon-doped monolayer hexagonal boron nitride (h-BN) are studied using a tight-binding model employing Green function approach and the Kubo formalism. Accurate tight-binding parameters are obtained to achieve excellent fitting with Density Functional Theory results for doped h-BN structures with impurity type and concentration. The influence of carbon doping on the electronic properties, electrical conductivity, and heat capacity of h-BN is studied, especially under an applied magnetic field. Electronic properties are significantly altered by doping type, concentration, and magnetic field due to subband splitting, merging of adjacent subbands, and band gap reduction. These modifications influence the number, location, and magnitude of DOS peaks, generating extra peaks inside the band gap region. Heat capacity displays pronounced dependence on both magnetic field and impurity concentration, exhibiting higher intensity at lower dopant levels. Electrical conductivity is increased by double carbon doping compared to single doping, but is reduced at high magnetic fields because of high carrier scattering. The electronic figure of merit ZT increases with lower impurity concentration and is higher for CB versus CN doping at a given field strength. The power factor can be improved by increasing magnetic field and decreasing doping concentration. In summary, controlling doping and magnetic field demonstrates the ability to effectively engineer the thermoelectric properties of monolayer h-BN.
