Urbach tail, disorder, and localized modes in ternary semiconductors

We analyze the role of localized modes, produced by structural disorder, in the formation of the optical-absorption edge in semiconductors. Such modes give rise to an additional energy h δv_d, above the average of the optical modes in the ordered sample. In the present study, this interpretation is confirmed experimentally from a study of infrared absorption spectra of several samples of the semiconductor CuGaTe₂. The high value of h v_p found in these samples, higher than the average of the 14 Raman modes of the ordered sample, is in good agreement with the average of all the optical and localized modes. Previous models involving disorder are discussed and derived from the thermal/disorder broadening of a harmonic oscillator with average frequency associated with the measured phonon modes. Our quantitative interpretation in terms of phonon frequency shift can be extended to a more general class of crystalline/amorphous semiconducting materials.