Guerra, J.A.; Tejada, A.; Töfflinger, J.A.; Grieseler, R.; Korte, L.: Band-fluctuations model for the fundamental absorption of crystalline and amorphous semiconductors: a dimensionless joint density of states analysis. Journal of Physics D: Applied Physics 52 (2019), p. 105303/1-11
10.1088/1361-6463/aaf963

Abstract:
We develop a band-fluctuations model which describes the absorption coefficient in the fundamental absorption region for direct and indirect electronic transitions in disordered semiconductor materials. The model accurately describes both the Urbach tail and absorption edge regions observed in such materials near the mobility edge in a single equation with only three fitting parameters. An asymptotic analysis leads to the universally observed exponential tail below the bandgap energy and to the absorption edge model at zero Kelvin above it, for either direct or indirect electronic transitions. The latter feature allows the discrimination between the absorption edge and absorption tails, thus yielding more accurate bandgap values when fitting optical absorption data. We examine the general character of the model using a dimensionless joint density of states formalism with a quantitative analysis of a large amount of optical absorption data. Both heavily doped p-type GaAs and nano-crystalline Ga 1-x Mn x N, as examples for direct bandgap materials, as well as amorphous Si:H x , SiC:H x and SiN x , are modeled successfully with this approach. We contrast our model with previously reported empirical models, showing in our case a suitable absorption coefficient shape capable of describing various distinct materials while also maintaining the universality of the exponential absorption tail and absorption edge.