This theoretical study provides a comprehensive analysis of the tunable influence of combined electric bias and magnetic fields on the thermoelectric properties of Tetragonal Silicene nanoribbons (T-SiNRs). The analysis focuses on both symmetric and asymmetric lattice configurations of T-SiNRs. The findings reveal that the application of a bias voltage induces an energy gap, transforming metallic T-SiNRs into semiconductors. In contrast, a magnetic field produces distinct effects: the Zeeman effect preserves the metallic nature by enhancing the density of states near the Fermi level, while the Peierls phase can induce a small band gap under specific field strengths. The thermodynamic properties, including thermal conductivity κ(T), heat capacity C(T) and Lorenz number L(T) exhibit distinct responses to these external perturbations: bias voltage significantly reduces these properties, particularly at higher temperatures, whereas a magnetic field enhances them. The emergence of a zero-intensity region in temperature-dependent functions, attributed to the suppression of charge carrier excitation, expands with increasing bias voltage but diminishes under a magnetic field. Moreover, the simultaneous application of bias voltage and a magnetic field enhances thermodynamic properties across various temperature ranges, compared to the unperturbed cases. Symmetric T-SiNRs exhibit higher thermal conductivity and heat capacity at low temperatures, while asymmetric structures dominate at higher temperatures. The behavior of the Lorenz number is particularly sensitive to external fields, with its peak position and intensity increasing under bias voltage but decreasing with the magnetic field. These findings highlight the potential of T-SiNRs for advanced nanoelectronic and thermophotonic applications, where precise modulation of thermal and electronic properties is critical for optimizing device performance.
