Theoretical studies of optical absorption in amorphous semiconductors

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Abstract
The tight-binding model of a disordered two-band semiconductor due to Abe and Toyozawa (1981) is studied. Using three basically different approaches the imaginary part of the dielectric constant is calculated. First, for a short-ranged disorder potential, a mode-coupling theory is formulated which allows one to go beyond the convoluted density-of-states approach. Second, the optical spectra for a Bethe lattice, both with and without disorder, are calculated. This allows the identification of matrix-element effects in terms of the coupling to nearest, next-nearest sites, etc. The mode-coupling theory is then tested against the numerical Bethe-lattice results. Both methods yield a maximum of the matrix elements for transitions just below the gap of the ordered system. However, the absorption tail is essentially given by the convoluted density of states. Third, a long-ranged spatial correlation of site energies due to charged centres is treated by numerically solving for the eigenvalues and eigenvectors of a one-dimensional system. The absorption tail turns out to be exponential. This tail, in contrast to the case of short-ranged disorder potential, is dominated by the matrix elements.