Abstract
In Chapter 6 of their book, N.F. Mott and E.A. Davis1 treat the optical properties of amorphous semiconductors. The object of the present paper is to derive some of their results from first principles by means of a relatively simple microscopic model. This exactly soluble model provides an interpolation formula for materials which retain some crystalline characteristics, and may also lead to some new insights into the physics of the problem.
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References
N.F. Mott and E.A. Davis, “Electronic Processes in Non-Crystalline Materials,” 2nd Ed., Oxford Univ. Press, 1979, cf. §§6.7 and 9.12 for example.
Below Eg optical absorption in crystalline materials exhibits a temperature-dependent exponential (“Urbach”) tail, while below Eo the amorphous material has a similar exponential tail which is “frozen-in” at some effective temperature (see various explanations in ref. 1, or the more recent analysis by D.J. Dunstan, J. Phys. C16:L567 (1983)).
It follows that the mean free path of carriers in amorphous materials is limited not by any simple phase disorder such as is considered in the present model, but rather by amplitude variations in the eigen-states or by frustrations in the bond networks, neither of which phenomena are taken into account here.
At this stage of our understanding of the electronic states in amorphous solids, and within the context of the present simple model of disorder, it may not be useful to consider arbitrary band structures; but if this should become necessary, the first line in Eq. (15) can be evaluated—numerically, if need be—for arbitrary band structures.
The Wannier-Mott excitons and the Frenkel excitons are, in fact, just the two extremes of a possible continuum of behavior. This was recently proved in an article entitled “What is the mass of an exciton?” by D.C. Mattis and J.-P. Gallinar, Phys. Rev. Lett. 53: 1391 (1984).
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© 1985 Plenum Press , New York
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Mattis, D.C. (1985). Optical Absorption in Amorphous Semiconductors. In: Adler, D., Fritzsche, H., Ovshinsky, S.R. (eds) Physics of Disordered Materials. Institute for Amorphous Studies Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2513-0_27
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DOI: https://doi.org/10.1007/978-1-4613-2513-0_27
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