Analytical study of the thermoelectric properties in silicene

Theoretically, we investigate the thermoelectric (TE) properties namely, electrical conductivity ( σ ), diffusion thermopower ( S d ), power factor ( PF ), electronic thermal conductivity ( κ e ) and thermoelectric figure of merit ( ZT ) for silicene on Al 2 O 3 substrate. TE coefficients are obtained by solving the Boltzmann transport equation taking account of the electron scattering by all the relevant scattering mechanisms in silicene, namely charged impurity (CI), short-range disorder (SD), intra- and inter-valley acoustic (APs) and optical (OPs) phonons, and surface optical phonons (SOPs). The TE properties are numerically studied as a function of temperature T (2–400K) and electron concentration n s (0.1–10 × 10 12 cm −2 ). The calculated σ and S d are found to be governed by CIs at low temperatures ( T < ∼ 10 K), similar to that in graphene. At higher T , they are found to be mainly dominated by the intra- and inter-valley APs. The resultant σ ( S d ) is foun d to decrease (increase) with increasing T , whereas PF remains nearly constant for T > ∼ 100 K. On the other hand, n s dependence shows that σ ( S d ) increases (decreases) with increasing n s ; with PF relatively constant at lower n s and then decreases with increasing n s . At room temperature, the calculated σ ( S d ) in silicene is closer to that in graphene and about an order of magnitude greater (less) than that in monolayer (ML) MoS 2 . The κ e is found to be weakly depending on T and Wiedemann–Franz law is shown to be violated. We have predicted a maximum PF ∼3.5 mW m −1 K −2 , at 300 K for n s = 0.1 × 10 12 cm −2 from which the estimated ZT = 0.11, taking a theoretically predicted lattice thermal conductivity κ l = 9.4 Wm −1 K −1 , is a maximum. This ZT is much greater than that of graphene and ML MoS 2 . The ZT is found to decrease with the increasing n s . The ZT values for other values of n s in silicene, at 300 K, also show much superiority over graphene, thus making silicene a preferred thermoelectric material because of its relatively large σ and very small κ l .