In this paper, we establish the physical model of semiconductor-based epitaxial graphene. By considering the atomic non-harmonic vibration, we have the variations of the hybrid potential and thermoelectric potential of semiconductor-based epitaxial graphene with chemical potential and temperature are investigated, respectively. The influence of atomic non-harmonic vibration on the thermoelectric effect is also discussed. The results show that: 1) The hybrid potential is independent of temperature under the simple harmonic approximation. If the first non-harmonic term is considered, the hybrid potential increases with increasing temperature. However, if both the first and second non-harmonic terms are considered, the hybrid potential decreases with increasing temperature. 2) At a given temperature, the variation curve of thermoelectric potential of epitaxial graphene with chemical potential is left-right asymmetric at the chemical potential of zero, and there is a mutation near the chemical potential eV. 3) At a given chemical potential, the thermoelectric potential of epitaxial graphene is similar to that of single-layer graphene, namely that both decrease nonlinearly with increasing temperature, while the thermoelectric potential value of epitaxial graphene is larger than that of single-layer graphene. Compared with the simple harmonic approximation, the non-harmonic effect can reduce the thermoelectric potential value of the epitaxial graphene with a small amount. The influence of the non-harmonic effect on the thermoelectric potential increases slowly with increasing temperature, ranging from 0.23% to 0.25%.
