Anomalously small resistivity and thermopower of strongly compensated semiconductors and topological insulators

In the recent paper, we explained why the maximum bulk resistivity of topological insulators (TIs) such as Bi₂Se₃ is so small [B. Skinner, T. Chen, and B. I. Shklovskii, Phys. Rev. Lett. 109, 176801 (2012)]. Using the model of completely compensated semiconductor we showed that when the Fermi level is pinned in the middle of the gap the activation energy of resistivity is Δ=0.3(Eg/2), where Eg is the semiconductor gap. In this paper, we consider a strongly compensated n-type semiconductor. We find the position of the Fermi level μ calculated from the bottom of the conduction band Ec and the activation energy of resistivity Δ as a function of compensation K, and show that Δ=0.3(Ec-μ) holds at any 0<1-K1. In the same range of relatively high temperatures, the Peltier energy (heat) Π is even smaller: ΠΔ/2=0.15(Ec-μ). We also show that at low temperatures, the activated conductivity crosses over to variable range hopping (VRH) and find the characteristic temperature of VRH, TES, as a function of K.