For a photo-active materials which has band gab of ~1.6 eV can exhibit, theoretical calculation, solar to hydrogen conversion efficiency about 30%. What about silicon (1.1 eV )?
Please refer to http://www.sciencedirect.com/science/article/pii/0927024894902097
The Detailed Balance Theory was used in the past by a number of authors to calculate the limiting efficiency of photovoltaic energy conversion. Values of 40.8% for optimum single gap devices and of 86.8% for infinite number of gaps were calculated for the maximum efficiencies of conversion of the radiation of the Sun, considered as a black body at a temperature of 6000 K. This work extends the generality of those results and introduces new refinements to the Theory: the cell absorptivity is justified to be equal to the emissivity under bias operation and under certain idealistic conditions, the optimization of the absorptivity is discussed and the concepts of solid angle and energy restriction are explained. Also, as a consequence of the review, new results arise: the maximum efficiency is found to be independent on the concentration and although the limiting efficiency of optimum devices is confirmed, the limiting efficiency previously established for non-optimum devices is found to have been underestimated under certain circumstances.
(Conversion efficiency) = (power out) / (power in), where (power in) is the solar flux (100 mW/cm2 is typically used). (Power out) for water splitting can be calculated by 1.23 V * (current density in mA/cm2). Therefore, you just need to determine the maximum photocurrent density possible for your material, which involves integrating the photon flux of the solar spectrum across your bandgap-dependent absorption range (so up to 1127 nm for bandgap 1.1 eV).
But a material with bandgap 1.1 eV can never generate enough voltage to drive water splitting. So your current toward water splitting would be zero, and thus solar-to-hydrogen would be zero!
http://rredc.nrel.gov/solar/spectra/am1.5/
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