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We have developed a Kramers–Kronig consistent analytical expression to fit the measured optical functions of hydrogenated amorphous silicon (a-Si:H) based alloys, i.e., the real and imaginary parts of the dielectric function (e1,e2) (or the index of refraction n and absorption coefficient α) versus photon energy E for the alloys. The alloys of interest include amorphous silicon–germanium (a-Si1−xGex:H) and silicon–carbon (a-Si1−xCx:H), with band gaps ranging continuously from ∼1.30 to 1.95 eV. The analytical expression incorporates the minimum number of physically meaningful, E independent parameters required to fit (e1,e2) versus E. The fit is performed simultaneously throughout the following three regions: (i) the below-band gap (or Urbach tail) region where α increases exponentially with E, (ii) the near-band gap region where transitions are assumed to occur between parabolic bands with constant dipole matrix element, and (iii) the above-band gap region where (e1,e2) can be simulated assuming a single ...

Analytical model for the optical functions of amorphous semiconductors from the near-infrared to ultraviolet: Applications in thin film photovoltaics