In this study, we investigate the electrical and thermodynamic properties of trilayer boron nitride (BN) nanoribbons with varying stacking orders (AAA, ABA) using the tight-binding approach. Our findings demonstrate that the large bandgap of the pristine BN structure is strongly dependent on the stacking order and can be effectively modulated through the substitution of the middle layer with graphene (BNC structure) and the application of a perpendicular bias voltage and magnetic field. These modifications also shift the peaks of the density of states (DOS) toward the Fermi level, leading to notable enhancements in electrical conductivity and heat capacity. Thermodynamic analysis reveals that the negligible thermal properties of pristine BN structures below 2000 K, are enhanced significantly with the incorporation of a graphene layer and application of a bias voltage and magnetic field. Comparisons between the different structures show that, under similar conditions, the ABA stacking order offers better thermodynamic performance compared with AAA stacking. Investigation of the Lorenz function shows that the BNC structure exhibits a main peak at lower temperatures with reduced magnitude compared with pristine BN and this peak shifts towards lower temperatures with variations in system parameters. These results indicate that bias voltage can serve as a highly effective control parameter for enhancing the electrical conductivity of BN nanoribbons to levels comparable with graphene nanoribbons. The theoretical findings of this research can be used in the design and fabrication of nanodevices based on BNC nanoribbons for electronic and thermal applications with tunable high efficiency.
