Theoretical Analysis of the Performance of One-Dimensional Photonic Crystal-Based Dye-Sensitized Solar Cells Gabriel Lozano, Silvia Colodrero, Ophelie Caulier, Mauricio E. Calvo, and Herna ´n Mı ´guez* Instituto de Ciencia de Materiales de SeVilla, Consejo Superior de InVestigaciones Cientı ´ﬁcas-UniVersidad de SeVilla, Ame ´rico Vespucio 49, 41092 SeVilla, Spain ReceiVed: October 8, 2009; ReVised Manuscript ReceiVed: January 18, 2010 A simple analytical model that allows designing one-dimensional photonic crystal based dye sensitized solar cells of optimized performance, accounting for the actual optical features of the device, is herein presented. Based on the theoretical description of the effect of coupling such Bragg mirrors to the light harvesting electrode, recently reported experimental values of the spectral dependence of incident photon to current conversion efﬁciency attained for such structures are fairly reproduced and rationalized. A thorough analysis of them in terms of the interplay between the effect of the electrode thickness and the characteristics of the Bragg reﬂection, such as intensity, spectral position, and width, is provided. Predictions on the maximum enhancement factors expected for realistic structures are also presented. Introduction The positive effect of coupling a photonic crystal to an absorbing electrode on power conversion efﬁciency has been demonstrated for a number of solar cells in the last years. 1–7 The different physical mechanisms of enhancement have been thoroughly analyzed theoretically. 8–10 Very recently, a signiﬁcant increase of both light harvesting efﬁciency (LHE) and power conversion efﬁciency has been observed in dye-sensitized electrodes coupled to highly reﬂecting porous nanoparticle based one-dimensional photonic crystals (1DPCs), which act as coherent scattering layers. 11,12 This approach, although not optimized yet, seeks to maximize the amount of light absorbed, while keeping some of the added values of the standard dye- sensitized solar cell, such as its semitransparency, which is lost when either a diffuse scattering layer or a metallic back mirror are used to enhance absorption. In this latter approach, besides, light must travel through a layer of absorbing electrolyte in which unproductive optical losses in terms of charge generation occur. On the other hand, 1DPCs are also capable of reﬂecting light of targeted wavelengths very intensely in spite of pos- sessing a small thickness (around 0.5 µm), so that no extra ohmic resistances that might cause a drop of the voltage are created. In fact, because the effect of the photonic crystal is similar to an increase of the photon ﬂux, a rise of the open circuit photovoltage is expected, 13 although it has not been observed yet. It has been experimentally shown that enhancement of optical absorption is due to both the partial localization of photons of certain narrow frequency ranges as well as to the increase of the optical path within the absorbing layer, which result from its coupling to the photonic crystal. 12 However, it is still lacking a theoretical description that allows devising actual 1DPC based solar cells, which must take into account the interplay between the effect of the working electrode thickness, the amount of dye absorbed, and the characteristics (spectral width and intensity) of the Bragg reﬂection resulting from the coupled photonic structure. In this letter, we report on theoretical simulations of both the optical reﬂectance and the incident photon to current conversion efﬁciency (IPCE) of porous one-dimensional pho- tonic crystal-based dye-sensitized solar cells (DSSC). An analytical model that accounts for the actual optical features of the device is proposed. Its validity is conﬁrmed by comparing its predictions with recently reported experimental values of the spectral dependence of the photogenerated current attained for such structures, which are fairly reproduced and rationalized. It is demonstrated that the interplay between the optical effect of the electrode thickness and the scattering strength of the photonic crystal determines the basic features of the performance of the cell and must be considered to design an optimized device. Predictions on the maximum enhancement factors expected for realistic structures are also presented. Theoretical Model. Both the actual dye-sensitized electrode and the porous 1DPC are consecutively deposited onto a conducting ﬂuorinated tin-oxide-coated transparent substrate. First, a layer of nanocrystalline titanium dioxide (TiO 2 ) particles was deposited onto a conducting transparent substrate by doctor blade, spin-coating, or a combination of both techniques. A course rough layer was attained through the former, but a uniform and smooth surface was achieved in the ﬁnal coating after a drop of a suspension of ﬁne TiO 2 particles was spun onto it. Then, to build the Bragg reﬂector onto this coated substrate, layers of SiO 2 and TiO 2 particles were deposited alternately by spin-coating so that a periodic modulation of the refractive index is built up in the direction perpendicular to the electrode surface. Optical interference effects occurring between the beams reﬂected and transmitted at the different interfaces created are at the origin of the photonic crystal properties of this type of periodic nanostructures. After performing the usual thermal annealing and sensitization processes, the cell is completed using a metal-covered counterelectrode and the internal space between the electrodes is ﬁlled with a liquid redox electrolyte that at the same time soaks the porous photonic crystal, thus yielding electrical contact between the different parts of the cell. This ensemble is herein modeled through a layered structure, as depicted in Figure 1, in which the notation used in the simulation to represent the thickness and refractive index of each relevant slab is included. The incoming and outgoing media are considered to be the upper and lower glass * Corresponding author. E-mail: hernan@icmse.csic.es. J. Phys. Chem. C 2010, 114, 3681–3687 3681 10.1021/jp9096315  2010 American Chemical Society Published on Web 02/09/2010