Exponential tail of the optical absorption edge of amorphous semiconductors

Abstract

The low energy tail of the absorption edge of amorphous films of Ge, GeTe, As₂Se₃, Se and Se doped with 1-5 wt. % As, and melt-quenched platelets of Se and doped Se has been found to vary exponentially with photon energy in a manner similar to the Urbach rule observed in various ionic compounds and crystalline semiconductors. Our critical examination of all known data on the Urbach tail suggests that the tail must have similar physical origin in all cases. The tail may be ascribed to the broadening of the absorption edge by random, localized electric fields (Franz-Keldysh effect) arising from the LO phonons of the polar modes of vibration, and/or frozen-in lattice distortions or fluctuations in the nearest neighbour distance for an amorphous material. This mechanism can also explain the observation that amorphous semiconductors lacking long range order exhibit the Urbach tail with slope independent of temperature up to the amorphous → crystalline transformation temperature. The observed temperature variation of the slope of the Urbach tail in liquid semiconductors and amorphous Se (a variation similar to that of crystalline materials) may, however, be understood on the basis that some long range order in the form of molecular or chain structures exists in these materials.