This study theoretically explores the effects of external fields and doping on the electronic and thermoelectric properties of tetragonal silicon (T-Si) and tetragonal germanium (T-Ge) structures using a tight-binding model, Green’s function formalism, and the Kubo formula. External parameters modify the positions and intensities of the density of states (DOS) peaks, influencing charge carrier excitation and conductivity trends. Applying bias voltage introduces zero-intensity regions in thermal conductivity due to band gap opening, reducing thermal properties. In contrast, chemical potential and magnetic field significantly enhance thermal properties by increasing intensity and shifting the peak position. T-Ge exhibits higher thermal properties than T-Si across the selected parameter ranges. The findings highlight the potential for optimizing and enhancing the thermoelectric properties of tetragonal structures through external controllable parameters.
