The Mott T−14 law from the rate equation formalism

The Mott $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}$ law for the dc hopping conductivity for amorphous semiconductors is derived from the rate equation formalism by using the methodology of Butcher and Hayden. This formula is then fitted to the experimental data for a-Si, a-Ge, partially compensated heavily doped n-type Ge and polymer PPIB at 640 atmospheric pressures. It is found that the “simplified Butcher formula” approximately fits the experimental data for a-Si and a-Ge. The values of the density of states at the Fermi level calculated from the expression for the prefactor of this formula are much more reasonable values than those obtained from the original Mott formula. The origin of this significant improvement is found to lie not in improved approximations but in the choice of the values of the characteristics frequency R₀.