On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.