Flexural and acoustic phonon-drag thermopower and electron energy loss rate in silicene

We have performed a comprehensive numerical and analytical examination of two crucial transport aspects in silicene: the phonon-drag thermopower,Sp, and the electron's energy loss rate,Fe. Specifically, our investigation is centered on their responses to out-of-plane flexural phonons and in-plane acoustic phonons in silicene, a two-dimensional allotrope of silicon as a function of electron temperature,T,and electron concentration,n,upto the room temperature. It is found that the calculated quantities have a non-monotonic dependence for the phonon modes for both parameters(T and n)considered while analytical results predict definite dependencies up to the complete low-temperature Bloch-Gruneisen (BG) regime. To provide a more comprehensive picture, we contrast the complete numerical outcomes with the approximated analytical BG results, revealing a convergence within a specific range of temperature and carrier concentration. In light of this convergence, we put forth suggestions to elucidate the underlying factors responsible for this behavior. A comparison based on the magnitude of the calculated quantities can be made from the figures between the two considered phonon modes, which clearly shows that the out-of-plane flexural phonons are effective throughout the considered temperature range. This observation leads us to posit that the dominating contribution of the out-of-plane flexural phonon modes hinges upon the deformation potential constant and phonon energy associated with the phonon mode. Our study carries significant implications for estimating the electrical and thermal properties of silicene and provides valuable insights for the development of devices based on silicene-based technologies.