Analytical model for the optical functions of amorphous semiconductors and its applications for thin film solar cells

摘要

We have developed a Kramers-Kronig consistent analytical expression to fit the dielectric functions (ε_1, ε_2) of hydrogenated amorphous silicon (a-Si:H)-based alloys measured using a combination of photoconductivity, transmission and reflection, and ellipsometric spectroscopies. The alloys of interest include amorphous silicon-germanium (a-Si_(1-x)Ge_x:H) and silicon-carbon (a-Si_(1-x)C_x:H), with optical bandgaps ranging from ～1.30 to 1.95 eV. The fit can be performed simultaneously throughout the following regions: (ⅰ) the sub-bandgap (or Urbach tail) region where the absorption coefficient increases exponentially with photon energy, (ⅱ) the band-to-band onset region where transitions are assumed to occur between parabolic bands with constant dipole matrix element, and (ⅲ) the above-bandgap region where a Lorentz oscillator model is applicable. We describe an approach whereby, from a single accessible measure of the optical bandgap, (ε_1, ε_2) can be generated for a sample set consisting of optimum electronic quality a-Si:H-based alloys prepared by plasma-enhanced chemical vapor deposition.