E. Malainho, M. I. Vasilevskiy, P Alpuim, S. A. Filonovich
Dielectric function of hydrogenated amorphous silicon near the optical absorption edge
Journal of Applied Physics 106 (2009) 073110
We report the results of the optical spectra modeling for hydrogenated amorphous silicon (aSi:H) thin films produced for photovoltaic cell applications, which allowed us to accurately determine the material's optical gap (Eg). While for thick films of aSi: H, as well as for other amorphous semiconductors, Eg is normally estimated from a so called Tauc plot, this is hardly possible for thin films because of the interference effects. We developed a physically founded semianalytical model for the complex dielectric function of aSi: H, valid below and above the optical gap and containing a small number of adjustable meaningful parameters, including Eg and the characteristic energy scales of the optical transition matrix element distribution and the joint density of states in the absorption tail region. With this model and using the transfer matrix formalism for multilayer optics, we have achieved a good agreement between the calculated and experimental transmittance spectra, which allowed us to selfconsistently determine the values of the above parameters. We found that both Eg and the characteristic scale of the subgap absorption tail increase with the hydrogen addition. We have also determined the absorption rate spectra of the films, relevant to any optical spectroscopy of subgap states, such as the photothermal deflection spectroscopy and constant photocurrent measurements.
Cited Articles

Franta D., Nečas D., Zajíčková L.,
Models of dielectric response in disordered solids,
Optics Express 15 (2007) 16230–16244 
Franta D., Ohlídal I., Klapetek P., Roca i Cabarrocas P.,
Complete characterization of rough polymorphous silicon films by atomic force microscopy and the combined method of spectroscopic ellipsometry and spectroscopic reflectometry,
Thin Solid Films 455–456 (2004) 399–403