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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 (⑀ 1 ,⑀ 2) ͑or the index of refraction n and absorption coefficient ␣͒ versus photon energy E for the alloys. The alloys of interest include amorphous silicon-germanium (a-Si 1Ϫx Ge x :H) and silicon-carbon (a-Si 1Ϫx C x :H), with band gaps ranging continuously from ϳ1.30 to 1.95 eV. The analytical expression incorporates the minimum number of physically meaningful, E independent parameters required to fit (⑀ 1 ,⑀ 2) versus E. The fit is performed simultaneously throughout the following three regions: ͑i͒ the below-band gap ͑or Urbach tail͒ region where ␣ increases exponentially with E, ͑ii͒ the near-band gap region where transitions are assumed to occur between parabolic bands with constant dipole matrix element, and ͑iii͒ the above-band gap region where (⑀ 1 ,⑀ 2) can be simulated assuming a single Lorentz oscillator. The expression developed here provides an improved description of ⑀ 2 ͑or ␣͒ in the below-band gap and near-band gap regions compared with previous approaches. Although the expression is more complicated analytically, it has numerous applications in the analysis and simulation of thin film a-Si:H based p-in and n-i-p multilayer photovoltaic devices. First, we describe an approach whereby, from a single accessible measure of the optical band gap, the optical functions can be generated over the full solar spectrum for a sample set consisting of the highest quality intrinsic a-Si:H based alloys prepared by plasma-enhanced chemical vapor deposition using the principle of maximal H 2 dilution. Second, we describe quantitatively how such an approach can be modified for sample sets consisting of lower quality alloy materials. Finally, we demonstrate how the generated optical functions can be used in simulations of the absorption, reflection, and quantum efficiency spectra of a-Si:H based single-junction and multijunction solar cells.

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In studies of hydrogenated amorphous silicon (a-Si:H) n-i-p solar cells fabricated by rf plasma-enhanced chemical vapor deposition ͑PECVD͒, we have found that the maximum open circuit voltage (V oc) is obtained by incorporating p-type doped Si:H layers that are protocrystalline in nature. Specifically, these optimum p layers are prepared by PECVD in the a-Si:H growth regime using the maximum hydrogen-to-silane flow ratio possible without crossing the thickness-dependent transition into the mixed-phase (amorphousϩmicrocrystalline) growth regime for the ϳ200 Å player thickness. The strong dependence of the player phase and solar cell V oc on the underlying i-layer phase also confirms the protocrystalline nature of the optimum Si:H p layer.

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