1. Introduction

Dye sensitized solar cells (DSCs) are photovoltaic devices which provide a technically feasible and cost effective alternative to silicon based devices. Since their discovery in 1991 by Graetzel and O’Reagan [1,2] conversion efficiency higher than 10% have been recently reached [3–6]. A prototypical DSC consists of a ≈10 μm thick active layer composed by mesoporous titania (TiO₂), a wide band-gap oxide, doped with fluorescent dye molecules and an electrolyte layer of about 40 μm, both enclosed between two transparent conducting glasses (Fluorine doped Tin Oxide, FTO). One of the most common molecules employed as “dye sensitizer” is a complex named SQ2 [7]. Exposure of a DSC to solar light through the upper electrode results in the photoexcitation of the dye producing photogenerated electrons which can reach the bottom photoelectrode giving rise to an electrical signal. The dye’s electrical neutrality is re-established by an electrolyte (the redox couple I^-/I₃^-). On the counterelectrode a thin (≈10 nm) platinum layer acts as a catalyst for the reaction between I₃^- and I^-.

So far different strategies have been pursued to improve the efficiency of such devices. These include: improvement of the mesoporous oxide film morphology (which has an impact on electron transport) [8,9], research of new dyes /dye blends capable of harvesting solar light over a broad spectral range extending to the near IR region [10–12], optimization of the electrolyte species to obtain a good matching between the energy levels and an improvement of the ionic conductivity [13].

In addition to the above reported traditional approaches novel strategies to improve the light harvesting of the DSCs appeared recently. These belong to a wider framework of efficient photon management techniques and include the use of scattering centers [14,15], photonic crystals [16–18], superstructures [19–21] and scattering layers [22] either inside the TiO₂ layer or in its backside. Also prism coupling [23] and waveguides DSCs [24] have been proposed. All these strategies aimed at an enhancement of the radiation absorption by increasing the light path in the active layer either by scattering or light confinement. Introduction of periodic structures (such as gratings) into the cell architecture is a very promising way to obtain such an enhancement as recently demonstrated for thin film organic solar cells [18,19,25].

In the present work we studied by two-dimensional (2D) finite-elements method (FEM) the effect of periodic grating structures on DSC performances. The simulations have been accomplished by COMSOL Multiphysics software package [26]. A typical DSC model has been considered for the calculation. Such model has been slightly modified by introducing grating structures in different position along the cell. In the simulation both the pitch of the grating and the height have been varied. Energy density distribution and absorption of the active layer (the titania layer where the fluorescent dye is inserted) have been calculated and compared with the cell without nanostructurization. We found that the best results regarding enhancement of the energy density and absorption in the DSC active layer are obtained for a grating structure inserted between the dye-sensitized TiO₂ and the electrolyte layer.

Concerning the evaluation of the grating parameters, we took into account, in order to optimize pitch and height of the structures, the geometrical constraints connected to their practical feasibility by means of low-cost standard soft-lithographic techniques. These methods can be straightforwardly applied to dielectric materials attainable via sol-gel process. A grating pitch of 500 nm with a height of 300 nm results to be a good choice considering the optical properties of these materials. With such a nanostructurization an improvement in the overall absorption of the active layer of 23.4% (integrated in the spectral range 500-750 nm) with respect to the bare DSC has been found.

2. Structure

The model structure of the DSC device we have used in our simulations is showed in Fig. 1 . It closely resembles the actual cells (except for the lack of the top and bottom soda lime glass substrates) produced and characterized by the Center for Hybrid and Organic Solar Energy (CHOSE) [27]. It can be schematized as a stack of parallel sections of different materials consisting, from top to the bottom, in:

 

Fig. 1 (a) A cross-section of the DSC model. The scheme is not in scale and without top and bottom macroscopic glass substrates. (b) Illustrative figure of the type of 1D rectangular grating structure. (c) Definition of the grating parameters: height and pitch.

Download Full Size | PDF

With respect to the above described model, our actual cells have a very thin platinum layer (about few tens of nanometers) located between the electrolyte and the FTO layer. We have decided to exclude such thin layer from the simulation since the mesh parameters used for calculation cannot account for too small sizes in order to have reasonable computation time.

Since the main goal of this paper is the evaluation of the effect of the inclusion of nanostructures between the layers of the DSC, the model presented in Fig. 1 has been consequently modified with inclusion of periodic 1-dimensional nanostructures, i.e. a periodic grating, in different positions (vide infra).

In order to perform the most reliable simulations, the physical and geometrical parameters, i.e. the refractive indices, the absorption coefficients and the thicknesses of each layers, have been either taken from tabulated values when available or experimentally determined by means of absorption and spectroscopic ellipsometry measurements on actual cells (doped with SQ2 dye) provided by CHOSE. In particular, in Table 1 are reported the n and k values used for simulation for DSC layers at 700 nm wavelength.

Table 1. Refractive index (n) and absorption coefficient (k) at 700 nm wavelength for the DSC layers and for dielectric sol-gel based material.

View Table

3. Modeling method

We performed two-dimensional (2D) FEM calculations of energy density, Poynting vector and absorption on the model cell described above. The solar light illumination (in the range 500-750 nm which is relevant for the used dye) has been assumed as an incident plane wave of constant intensity and only TE polarization on the top edge of the structure was taken into account for the sake of simplicity. The width of the repeated unit used in the simulation has been set to 20 micrometers. Periodical boundary conditions have been imposed on the lateral edges of the unit. Its dimension has been chosen only after several comparisons with different widths in order to verify their irrelevance for the simulation results and to ensure reasonable computing time. The errors given by the results of our simulations with COMSOL are given by a quality factor dependent on the ratio between the real areas of the layers and the areas of the bi-dimensional meshes (used to cover the real areas) and implemented in the simulations. We have estimated a maximum error of about 6% of the numerical results regarding electric field, Poynting vector and local energy density.

The numerical results for the absorption have been calculated by an integration of the divergence of the Poynting vector in the active layer:

4. Results and discussion

In order to estimate the impact on the energy density of the inclusion and location of nanostructures, the basic model shown in Fig. 1 was suitable modified by the inclusion of periodic 1-dimensional rectangular grating. In Fig. 2 we report the relative energy density defined as:

 

Fig. 2 Relative energy density in the dye-sensitized titania for different grating position along the DSC layers.

Download Full Size | PDF

The values of the energy density have been obtained by a numerical integration on the absorbing dye-sensitized titania layer, where we want to get maximum light confinement. It has to be noted that the results of the integration has been divided by the lateral size of the integration domain (the unit of 20 µm) in order to have an energy density independent from the particular lateral width. A grating having a pitch of 500 nm and a height of 100 nm was employed for the simulation. The energy density distribution was estimated for an incident wavelength of 700 nm. Such wavelength has been chosen on the basis that an increase of the energy density and absorption in this spectral region is desirable since the availability of the solar energy is quite relevant while the commercial dye absorption is usually quite low.

We notice that the energy density (normalized for the lateral width as explained above), which in the case of no grating (case A) was about 6.91 * 10⁻¹⁰ J/m², increases with the inclusion of a surface structurization. In the case B a very little effect can be observed. In case C a more visible effect has been found and the improvement in the energy density was about 20%. Case D where a sol-gel based layer was included between titania and electrolyte layer gives better results with respect to the previous cases. Moreover, a double grating (case E) does not produce any significant increasing of the energy density with respect to the case of only one grating. Similar behavior for the energy density enhancement respect to the grating position has been obtained also varying grating pitch and depth. In the following we report a detailed study on the grating parameters (pitch and height) for the case where the grating is made of a dielectric material and is positioned at the interface between titania and electrolyte layers (case D). We decided to deepen such case, instead of the more simple case of the direct modulation of the titania layer for two reasons. The first one is related to the higher relative energy density, even if the improvement is only of 1.2% with respect to the bare modulation of the titania layer, and the second one and more important is related to the experimental possibility to engineerize the dielectric layer changing its composition thanks to the sol-gel technique [28,29].

In Fig. 3(a) we plot a typical result given by 2D FEM for the energy density distribution at the edge between the titania (upper layer) and electrolyte layer (lower part of the sketch) for the bare DSC model. The color scale for the energy density is given in the figure and the vertical and horizontal numerical scales show the real dimensions of the 2D cell in meters. The energy density distribution is represented for an incident wavelength of 700 nm.

 

Fig. 3 Energy density distribution at the interface between titania and electrolyte layers without (a) and with grating (b).

Download Full Size | PDF

In Fig. 3(b) is reported the energy density distribution for 700 nm wavelength at the same interface (titania/electrolyte layer) with the presence of a dielectric grating having 300 nm height and 500 nm periodicity. The resulting effect, governed by the light diffraction of the grating, is an evident redistribution of the radiation. The energy density is concentrated in bunches both in the electrolyte and in the active layer. Integrating the energy density on the whole active layer, the value results higher compared to the case without grating and such an effect yields useful absorption in that zone.

On the basis of these results we decided to adopt the configuration with the grating between the titania and the electrolyte in the following simulations aimed at optimize the grating shape (height and pitch).

We started calculating the energy density in the active layer for a fixed periodicity of 500 nm and different height of the grating, ranging from 100 to 700 nm. Figure 4(a) shows the relative energy density as a function of the grating height. We report the relative energy density as a function of four incident wavelengths, namely: 500, 600, 650 and 700 nm. The effect of the grating, regarding the increasing of the energy density, is more evident for 500 and 700 nm wavelength, while for the 600 and 650 nm we don’t record any effect of the nanostructures on the energy density in the DSC active layer. Such an effect can be explained considering that at the intermediate wavelengths the dye absorption is very high and therefore the solar radiation arriving at the grating position is very low since it is already absorbed in the first part of the doped titania layer. As a consequence the total integral gives a minor contribution and the diffractive effect is strongly hampered. Figure 4(b) shows the effect on the relative energy density calculated in the active layer as a function of the periodicity for a fixed grating height of 300 nm. In a similar way as discussed above, the effect of the grating is more evident for the wavelengths where the absorption is low (500 and 700 nm), while the effect is negligible for wavelengths where the absorption is quite high.

 

Fig. 4 Relative energy density confined in the dye-sensitized titania layer as a function of the height for a 500 nm pitch grating (a) and as a function of the pitch grating for a 300 nm grating height (b). Values are reported for different wavelengths (see labels in the figure).

Download Full Size | PDF

In view of a possible practical implementation of nanostructures on actual DSC devices, we have focused on the case of a grating having a pitch of 500 nm and with height equal to 300 nm. With this configuration we have simulated the absorption spectrum of the dye-sensitized titania layer starting from the parameters of a real DSC as reported in Fig. 5(a) . A broadband enhancement in the spectral range 500 - 750 nm due to the presence of the grating structure can be noticed. Figure 5(b) shows the difference between the simulated absorption spectra with and without grating displaying that the enhancement in the absorption is more pronounced for longer wavelengths. This physical effect is extremely important, since in this range the absorption of many commercial dyes is usually quite low, while the availability of solar energy is relevant.

 

Fig. 5 (a) Absorption spectra of the active layer given by numerical simulation of the DSC with (red line-filled squares) and without grating (green line-open circles). (b) Difference in the absorption spectra with and without grating.

Download Full Size | PDF

In order to evaluate the overall effect of the nanostructurization on the DSC device we performed the calculation of the absorption enhancement factor defined as:

5. Conclusions

The influence of different light trapping schemes on the performance of a realistic DSC device has been investigated with numerical simulations. We demonstrated that it is possible to achieve a broadband absorption enhancement by integrating a dielectric sol-gel based grating at the interface between the dye-sensitized titania and the electrolyte layer. Grating pitch and height have been studied by means of an accurate analysis of the cell performances and grating parameters (500 nm pitch and 300 nm height) for an efficient result have been precisely evaluated. The improvement in the absorption, integrated in all the analyzed range (500-750 nm) was 23.4%. In addition the more relevant improvement was found for wavelengths above 700 nm where the solar energy is still intense but the absorption of the sensitizer is low. The choice to investigate dielectric gratings fabricated by sol-gel technique is related to the great advantages offered by such process regarding the simplicity of the fabrication via soft lithography and the possibility of an easy fine tuning of the optical properties of the structure that could give even best results in terms of light management.