Derivation of Urbach's rule in terms of exciton interband scattering by optical phonons

The Urbach rule is derived by treating the exciton interband scattering by optical phonons in the dipole approximation in terms of a Green's-function theory. Our results contain in the limit of low phonon fields the quadratic Stark effect, but show that for typical microfields of thermal phonons in polar semiconductors the Urbach rule is caused by the broadening of the exciton level due to tunneling ionization transitions as proposed by Dow and Redfield. Furthermore, an analytic treatment of the electroabsorption model of Dow and Redfield is developed.