a Fundamental Theory of the Urbach Optical Absorption Edge in Crystalline and Disordered Semiconductors.

The band tail density of states and the optical absorption coefficient for electronic transitions between valence- and conduction-band tail states is calculated using a first principles method. The calculations are based on the Feynman path integral representation of the one electron propagator. Electron-static Gaussian correlated random potential, and electron-TA, LA, TO and LO phonon interactions are considered. There exists a synergetic interplay between static disorder and the nonadiabatic quantum dynamics of the finite temperature electron-phonon interaction. Static potential fluctuations provide nucleation centers for small polaron formation. The temperature dependence of the absorption edge is dominated by multiple phonon emission and absorption sidebands, which arise as a consequence of the nonlinear electron-phonon interaction. LA phonon sidebands and electron-static disorder interactions are responsible for Urbach behavior whereas TA, LO, and TO phonon sidebands produce bumps in absorption spectra. The theory is found to be in excellent agreement with experimental data on several crystalline and amorphous semiconductors. A detailed comparison is made between the predictions of the first principles theory and a physically intuitive argument based on the probability of the most probable potential well configuration.