Band-fluctuations model for the fundamental absorption of crystalline and amorphous semiconductors: a dimensionless joint density of states analysis

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 MnxN, as examples for direct bandgap materials, as well as amorphous Si:Hx, SiC:Hx and SiNx, 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.

Optoelectronic Properties of Hydrogenated Amorphous Substoichiometric Silicon Carbide with Low Carbon Content Deposited on Semi‐Transparent Boron‐Doped Diamond

“…Thus, the band gap and bond angle distortions are enhanced in the amorphous network with the formation of Si—C bonds . Tauc gap is sensitive to Urbach energy, and there are some new models estimating the band gap more precisely than the Tauc model …”

“…While hydrogenated amorphous substoichiometric silicon carbide a‐Si 1− x C x :H is often prepared at temperatures below 300 °C, CH 4 suppresses polycrystalline Si growth in favor of H‐rich amorphous a‐Si 1− x C x :H at elevated deposition temperatures . The increasing carbon concentration in a‐Si 1− x C x :H broadens the band gap and introduces unwanted localized tail states near the band edge …”

Sub-gap defect density characterization of molybdenum oxide: An annealing study for solar cell applications

“…The optical bandgap has been further evaluated by means of other two models. With respect to the Tauc's model, the Ulrich's empirical model for the direct bandgap or the band fluctuation models [59,60] allow distinguishing between the absorption edge and absorption tails [61]. The resulting optical bandgaps are summarized in Table 1.…”

Optical Bandgap Definition via a Modified Form of Urbach’s Rule

“…Models to fit the absorption coefficient α of semiconductors as a function of the incident photon energy E are important for the design of opto-electronic devices, and, therefore, their improvement and deeper understanding attract ongoing research activities [ 1 ]. As pointed out in Ref.…”

“…As pointed out in Ref. [ 1 ], which gives an excellent updated overview of the field, conventional models exclude thermal effects, and are based on crystalline materials, resulting for direct absorptive transitions in the well-known relationship below [ 1 , 2 ]: where A is a constant, whose order of magnitude is typically around the saturation of α , and E gDOS is the theoretical optical bandgap based on the three-dimensional density of states (DOS). However, Equation (1) possesses a considerable shortcoming because it does not consider tail states, which cause a red shift of the absorption edge.…”