Analytical extraction of the single-diode model parameters for macro-porous silicon-based dye-sensitized solar cells using Lambert W-function

In this work, based on the Lambert W -function and a single-diode five-parameter model, the electrical characteristics of the macro-porous silicon-based dye-sensitized solar cell (PSi-DSSC) and its photovoltaic performance are investigated. As the first step, PSi-DSSCs with different silicon porosities were formed and characterized. In the next step, using the equivalent circuit of the single diode model, the derivation of DSSC parameters from a single I–V curve under only one constant illumination level was carried out. It was found that the I–V curves rebuilt with the extracted parameters are in good agreement with the original experimental I–V curves. The influence of silicon porosity upon the five equivalent circuit parameters, including the reverse diode saturation current I 0 , the photocurrent I ph , the series resistance R s , the shunt resistance R sh , and the ideality factor n , was examined. It was demonstrated that the higher optical absorption coefficient of the porous silicon structure increases I ph and that providing a larger contact area for electrolytes with dye-adsorbed TiO 2 is effective in accelerating the rate of the oxidized dye reduction by I − and of decreasing R s . R sh was also increased by reduction of the chance of charge recombination across the TiO 2 /dye/electrolyte junctions. An increase in the porosity of the silicon photoanode to 65% demonstrated improved cell performance with ~32%, ~3.7%, and ~6.3% enhancement in the short current circuit ( I sc ), open-circuit voltage ( V oc ), and fill factor ( FF ), respectively. Finally, the highest efficiency value of 5.45% was achieved for PSi-DSSC (sample 4), which is about 45% higher than 3.76% of the standard DSSC (sample 1).