Efficiency Enhancement in Dye Sensitized Solar Cell Using 1D Photonic Crystal

A detailed theoretical investigation of one dimensional SiO2/TiO2 photonic crystal based ZnO-Pt dye sensitized solar cell with N719 dye is carried out. The optical properties of the theoretically designed dye sensitized solar cell such as transmittance, absorptance and reflectance are calculated using transfer matrix method in order to calculate numerically the key parameters like open circuit voltage (VOC), short circuit current (Jsc) and efficiency of the DSSC. The efficiency of the porous one-dimensional 1D SiO2/TiO2 photonic crystal coupled ZnO-Pt dye sensitized solar cell is studied for various periods of photonic crystal layers. It is found that the desired integrated system enables to maximize the absorption in the selective spectrum region (400-900 nm) and hence the maximum efficiency achieved is 4.5% for a ZnO-Pt dye sensitized solar cell having a 1D SiO2/TiO2 photonic crystal.


Introduction
Dye-sensitized solar cells (DSSCs) are emerging as a technical and economical sustainable substitute to the p-n junction photovoltaic devices. The absorption of dye increases the light harvesting efficiency (LHE). The chlorophyll-form sensitized zinc oxide electrode based DSSC was synthesized in 1972 [1]. Recently developed sensitized solar cells like quantum dot sensitized solar cells and DSSCs are the potential substitutes for traditional photovoltaic systems. These systems were mainly based on materials such as silicon, cadmium telluride etc., due to their low costs and efficient production procedures [2]. Single ZnO crystals which are mostly dealt in research work deliver limited output as only about 1 % of the dye molecules' nanostructure are capable to absorb incident light intensity [3]. In this way, the optimization of porosity of the electrode composed of refined oxide powder, improves the efficiency of DSSC.
In 1991, nano porous titanium dioxide DSSC was discovered with 7% efficiency [3]. Even if different studies have been reported, the actual efficiency of TiO 2 DSSCs is often higher than the efficiency of ZnO DSSCs [4]. This is because of the presence of the high carboxylic acid essential groups in the dyes in which the dissolution of ZnO and precipitation of dye-Zn 2+ complexes occur. The overall power conversion efficiency have been focused on to increase the photovoltage through function of the oxide, improving the photocurrent with new dyes, and boosting stability by better encapsulation [5]. Intense research efforts extensively directed on synthesizing new organic dye molecules with higher absorptivity materials [6,7].
Nanostructured materials, such as photonic crystal (PhC), large particle aggregation scattering layers, and plasmonic nanometals have opened to increase LHE in the thirdgeneration solar cells [8][9][10][11][12][13][14]. PhCs, with periodic dielectric nanostructures, view strong ability to attain a unique level of control the light propagation and also light energy distribution in photovoltaic devices [15][16][17]. In these devices via several mechanisms, such as photon localization increase the red-light absorption near the red edge of a photonic bandgap, light reflection within the photonic bandgap at different angles and formation of photon resonance modes within the solar cell are used to increase the LHE [14,15]. Hence, in photovoltaic devices integrated with PhCs, photons absorption increases which results in increased LHE with lower usage of absorbing materials. PhC coupled sensitized solar cells in 2003 has stimulated more efforts to design PhCs with different optical structural properties that permits for light management in the DSSC [18].
This work intended to explore the theoretical configuration of the porous structure of ZnO-Pt DSSC with N719 dye. Optical properties of theoretically designed DSSCs such as transmittance, reflectance and absorptance are calculated using transfer matrix method (TMM), in order to calculate numerically, the key parameters like open circuit voltage (V oc ), photo current density (J ph ), efficiency(ŋ) etc. In addition, the efficiency of porous 1D SiO 2 /TiO 2 PhC coupled ZnO-Pt DSSC is calculated and compared with ZnO-Pt DSSC without PhC. It is concluded that the presence of porous 1D SiO 2 /TiO 2 PhC enhance the efficiency of DSSC.

Construction of DSSC
The DSSC structure is theoretically designed which consists of FTO plates, ZnO photoelectrode, N719 dye, KI electrolyte solution with platinum counter electrode. Probably, DSSCs are usually built with two layers of conductive transparent media, that allow a semiconductor medium and catalyst to deposit. Here the porous ZnO nano-particle semiconductor film is deposited on transparent conducting oxide (TCO)-coated glass substrate which serve as a photo electrode and platinum deposited TCO serves as a counter electrode [19]. The N719 dye is used in the DSSC to get maximum absorption. The ZnO photo electrode and Pt counter electrode are then bound together and an electrolyte KI is then loaded with a syringe.The oxidised dye can be regenerated successfully by the redox couple of KI electrolyte. Counter electrode catalyses the reduction of I − /I 3− liquid electrolyte and gathers holes from the hole transport material. The Fig. 1 shows the schematic structure of ZnO-Pt DSSC.

Optical Properties of ZnO Working Electrode
The optical properties of the N719 loaded ZnO working electrode, are essential to evaluate the absorption of the entire structure of the ZnO DSSC with and without 1D PhC. From the recent literature of experimental research, the estimated absorbance values of the N719 loaded ZnO working electrode is found to be 34.28% for a wavelength of 534 nm having the electrode thickness of 330 nm [20]. The transmission of Dyed ZnO is calculated from the absorbance using Beer's lambert law [21].
The reflectance is calculated from the following equation where R -Reflection, A -Absorptance and T -Transmission The refractive index of N719 loaded ZnO working electrode is calculated from the following equation [22].
The refractive index of N719 loaded ZnO working electrode is calculated and is found to be comparable with various experimental work [23]. The calculated value and values of refractive index of other components from the literature is listed in the Table 1. DSSC consists of multiple thin layers with distinct optical properties. A classical interaction exists between the electromagnetic radiation and a finite one-dimensional non-periodic multilayer, where the corresponding maxwell's equations are solved using TMM formalism. This interaction system fulfils the conditions proposed by the reflection, transmission and absorption, within the layers, and optical interference between incoming and outgoing optical electric fields [23,24].
The effective index of refraction which may be expressed a s e γ j λ  thickness d j for each layer j. Here γ j is the real refractive index, k j is the imaginary refractive index, and α j is the absorption coefficient j = 1, 2...n. Figure 1 shows the theoretically designed DSSC with actual parameters of different layers. Light of intensity I 0 is assumed to be incident normal to the substrate for a centre wave length of 550 nm (λ 0 ) and multiple reflections at the air/substrate and substrate/ multilayer interfaces are taken into account for the study of transmission spectra of DSSC [25].

Integration of 1D Photonic Crystal in DSSC
Photonic crystal with multilayers having different lattice parameters is fabricated which can increase the photogenerated current for the whole spectral region in which the dye absorbs.
Hence the presence of photonic crystal inside the ZnO-Pt DSSC enhances the light harvesting efficiency. In this section, we numerically analyse the integrated system of the ZnO-Pt DSSC with 1D porous SiO 2 /TiO 2 photonic crystals shown in Fig. 2. Initially the optical properties of ZnO-Pt DSSC structure are analyzed using TMM method. Secondly the optical properties of 1D porous SiO 2 /TiO 2 photonic crystals coupled ZnO-Pt DSSC are calculated. The PhC structure consist of alternative porous SiO 2 and TiO 2 dielectric layers, whose optical parameters are taken from the literature [26,27]. The thickness of SiO 2 /TiO 2 layers are taken as d Sio2 = 95 nm and d Tio2 = 80 nm. The Fig. 2 shows that the porous 1D SiO 2 /TiO 2 PhC coupled DSSC. The matrices are formed for the intersection between two layers and wave propagation through each layer. The product of all the transfer matrices forms the actual transfer-matrix of solar cell. The photon absorption of these two solar cell designs (with and without PhC) has been favorably compared with the state-of-art solar cell designs. The combination of sub cell layers has yielded very high photon absorption through the entire solar radiation spectrum. The layers can represent in a matrix form in which the product of the individual layers are matrices. Finally, this method involves the system converting the matrix into reflection, transmission and absorption coefficient [7].
A common mathematical approach, transfer-matrix method is used to compute the spectral properties of 1D multilayered photonic structures,which is tailored for the analysis of the optical characteristics of DSSCs that incorporate a porous 1D PhC absorber layer. The model showed excellent quantitative agreement with angle-dependent spectral transmittance measurements recorded from complete DSSCs, allowing detailed analysis of the LHE by the dye from the 1D PhC [28].
According to TMM, each single layer has a transfer matrix the M is given by [7,29].
The phase difference is δ ¼ 2π The product of each intermediate layer starting with air layer, the resulting products describes entire stack in the order in which lights encounter them. Since each layer associated with its own transfer matrix, for our theoretically designed photonic crystal based DSSC system, the matrix describing the number of layers between the air and substrate according to Macleod et.al is given by italic M H and M L are the corresponding components of the porous SiO 2 /TiO 2 photonic crystal and N is the period of photonic crystal.
For the entire structure of photonic crystal based DSSC, the total transfer matrix is given by where the matrix elements can be calculated in terms of the elements of the single-period matrix. From the total matrix, the reflection coefficient ρ, reflectivity R, transmission coefficient τ, transmittivity T, and absorptivity A can be found.

The reflection coefficient
The reflectivity is where the asterisk denotes the complex conjugate The transmission coefficient τ The transmittivity is given by 30 The absorptivity is calculated from By substuting R and T from the Eqs. (8) and (10) in Eq. (11), the equation for absorptivity is given by where γ 1 and γ s -Refracted indices of first and last layer of the DSSC structure.

Photovoltaic Properties of ZnO-Pt DSSC with 1D SiO 2 /TiO 2 PhC
In this work, the photocurrent density (J ph ), open circuit voltage (V oc ), saturation current (J 0 ), quantum efficiency and power conversion efficiency of ZnO-Pt DSSC are theoretically calculated. It is compared with corresponding numerical calculations carried out through 1D SiO 2 /TiO 2 PhC coupled ZnO-Pt DSSC. The photocurrent density is calculated from the following equation [30].
where e-electron charge, A-Total absorbtion of Zno-Pt DSSC calculated from (12) The photoflux is given by where p in -incident flux at solar spectrum A.M 1.5 is 1000 W/m 2 f g frequency that corresponds to ZnO bandgap value (3.37 eV) The saturation current is given by The open circuit voltage is given by J ph and J 0 are calculated from Eqs. (13) and (14). The fill factor can be calculated using the following equation [28], where v oc ¼ eV oc = k B T is a normalised voltage. The efficiencies of the theoretical designed DSSC with and without PhC are calculated using the equation 6 Results and Discussions The optical parameters such as transmittance, absorptance and reflectance of the DSSC with and without PhC can be calculated using TMM method, by solving the Eqs. (7) to (12) with MATLAB software. Figure 3 shows the optical characteristics of ZnO-Pt DSSC with 1D SiO 2 / TiO 2 PhC coupled layers (n = 0,2,3). The effect is more pronounced in the range of 500 nm-800 nm. In Table 1, the absorptivity without PhC result indicates that the photo electrode does not consume incident light in a single pass owing to the low light scattering of the multilayer nonperiodic structure. But the presence of 1D SiO 2 /TiO 2 PhC coupled inside the working electrode can be form the scattering centres and strengthen the scattering process by its periodic structure. Light scattering is employed in dye-sensitized solar cells to improve the optical absorption of the incident light [31][32][33][34].
From the absorbtion graph it is understood that more absorbtion takes place when DSSC is coupled with PhC. It gets maximum absorption of light in DSSC with PhC having period n = 2 compared with PhC having period n = 3.It may due to the refractive index contrast make a disorder in the interface of PhC layers. The optimized periods of layers can increase the path length as well as diffused or multiple scattered/reflected and localized the incident light at longer time. As a result, significant optical absorption amplification in a broad spectral range is achieved by 1D photonic crystal and a multi-layer non-periodically structured absorbing material.
The photo current density, open circuit voltage for 1D SiO 2 /TiO 2 PhC integrated ZnO-Pt DSSC are analysed using Eqs. (13) & (14). The effect is maximum when the DSSC coupled with 1D PhC with period n = 2.The effect of photo current density with number of period of PhC layers is studied and is shown in the Fig. 4.The short-circuit current increases and attains the maximum value with number of periods n = 2 at the wavelength of 700 nm.
Because of the increase of optical absorption by multiple reflection / scattering in the interface of PhC structure, it can localize the maximum number of photons on the electrode therefore the short-circuit current is increased in the DSSC. The 1D PhC acts as absorber or bottom reflector can trap the incident light. It reduces the group velocity of the photons which can prevent recombination of the exciton`for a longer time, hence it leads to the higher rate of photoelectron generation. The lowering of short-circuit current after n = 2 is due to the maximum reflection in the forbidden bandgap of PhC. By analysing all the optical parameters and substituted in Eq. (13), the efficiency of DSSC may be investigated. The calculated J sc , V oc , FF and η for various number of periods in the PhC are shown in the Table 2. It is concluded that the DSSC having PhC with period of n = 2 get a maximum value of 4.5%.
The theoretical results revealed the porous 1D SiO 2 /TiO 2 PhC as absorbing layer and act as a potential couple layer to improve the efficiency by trapping the photons and initiate the photons drive gradually back through the absorbing electrode in the selective spectrum range 400 nm -900 nm.

Conclusion
The photovoltaic parameters of ZnO-Pt with N719 dye based DSSC are calculated. ZnO-Pt DSSC coupled with porous 1D SiO 2 /TiO 2 PhC is theoretically designed. The absorptance of the integrated system of ZnO-Pt DSSC with and without 1D SiO 2 /TiO 2 PhC are calculated using TMM method. It is found that the desired integrated system enable to maximize the absorption in the selective spectrum region (400-900 nm). The solar cell parameters are studied for various periods of PhC in the integrated system. The short circuit current (J sc ), open circuit Voltage (V oc ), fill factor (FF) and hence the efficiency(ŋ), are calculated theoretically at 700 nm wavelength. The optical design of 1D SiO 2 /TiO 2 PhC absorbing layer enhance the cell efficiency without affecting kinetic balance between charge separation and recombination. The maximum short circuit current (J sc ) is found to be 440 μA cm −2 which leads to a maximum efficiency of 4.5%. for a DSSC having 1D SiO 2 /TiO 2 PhC.