The power conversion efficiency (PCE) of the dye sensitized solar cell were calculated from the following factors: open circuit voltage (Voc),short circuit current (Jsc), fill factor (FF) and incident light energy (Pin)[26, 27],
$$\eta =\frac{{V}_{oc}{J}_{sc }FF}{{P}_{in}}$$………………………….1
In dye sensitized solar cell the Vocis calculated from disparity between Fermi level of the semiconductor to the redox potential to the redox electrolyte. The short circuit current is depends the factor of photon harvesting ability and injection of electron to the semiconductor. The Jsc and Voc should be high possess that the PCE of the solar cell will be high. The short circuit current of the solar cell was calculated to the equation,[28, 29]
$${J}_{sc}= \underset{\lambda }{\int }LHE\left(\lambda \right){\varphi }_{inject }{\eta }_{collect} d\lambda$$………………………….2
Where LHE is the light harvesting efficiency and ϕinjectis the electron injection efficiency of the sensitizers. for DSSC’s the electrode is same and dye sensitizers only differs. So the ηcollect of the DSSC is assumed to be constant.
The LHE of the sensitizers were calculate from the following equation,
LHE = 1–10− f ………………………….. (3)
Where, f is the oscillator strength of the sensitizers.
The ϕinject were calculated from electron driving force ΔGinject. The ΔGinject of the sensitizers were calculated from the equation,[30, 31]
$${{\Delta }G}_{inject }= {E}_{OX}^{*}- {E}_{CB}^{SC}$$…………………………..4
Where, \({E}_{OX}^{*}\) is the excited state oxidation potential of the sensitizers and \({E}_{CB}^{SC}\) is the ground state reduction potential of the conduction band edge of the TiO2. The excited state oxidation potential were calculated from the equation as,
$${E}_{OX }^{*}= {E}_{OX}- {\lambda }_{max}$$…………………………..5
Where, Eoxis the redox potential of the ground state of the sensitizers and vertical transition energy corresponding to the maximum absorption (λmax).
The elelctron regeneration efficiency of the sensitizers were determined from the driving force for regeneration ΔGreg is given by,[32]
ΔGreg = Eox – Eredox ………………………….. (6)
Where, Eredox is the redox potential of the I−/I3− electrolyte (4.8eV).
The Nonlinear optical properties of the sensitizers are determined from dipolemoment and static polarizability to the following equations,[33]
$${\mu }_{tot}= \sqrt{{(\mu }_{x}^{2}+{\mu }_{y}^{2}+{\mu }_{z}^{2}})$$…………………………..7
$${\alpha }_{0}= \frac{({\alpha }_{xx}+{\alpha }_{yy}+{\alpha }_{zz}}{3}$$…………………………..8
Where, αxx, αyy and αzz is the polarizability tensor componants.