Although the coupling of inverse opals to dye sensitized electrodes demonstrated an increased IPCE with respect to that of a reference cell (Nishimura et al., 2003), the main drawback of these 3D structures is the difficult assembly process to achieve reasonable reflecting periodic materials, which leads usually to thick structures (between 5-10 micron thick). This might have a deleterious effect on charge transport and recombination through the cell. Very recently, new types of one-dimensional photonic crystals (1DPC) have been prepared by alternate deposition of either mesoporous (Choi et al., 2006); (Fuertes et al., 2007) or nanoparticles (Wu et al., 2007); (Colodrero et al., 2008) based films. These structures
Fig. 6. (a) Circles: Photogenerated current observed for a bilayer DSSC like the one shown in the inset when illuminated from the rear side. Squares: Photocurrent corresponding to a non periodically structured, standard DSSC. These data have been extracted from Nishimura et al., 2004. The curve in (b) shows the calculated absorptance (or LHE) for the structure shown in the inset under rear illumination. (c) Averaged absorptance of bilayer DSSCs formed by nc-TiO2 inverse opals of different width (from 3 to 17 sphere monolayers), each one of them having in turn different nc-TiO2 layer thickness on top (from 6.5 pm to 7.5 pm). Dotted lines in (b) and (c) are the calculated absorptance spectra of standard DSSC having the same amount of absorbing material than in the bilayer system. The insets show schemes of the modelled structure. The corresponding illumination direction is indicated by an arrow. (Extracted with permission from Mihi & Miguez, 2005)
are usually easier to build and integrate than those abovementioned of higher dimensionality and present attractive features, such as very intense and wide Bragg reflections and reduced thickness (less than a micron versus the several micron thickness of opals). Furthermore, the advantage of such lattices lies on the wide range of materials available to be deposited as multilayers, which implies accurate control over the optical properties of the periodic ensemble, and on the high structural and optical quality attainable. These nanostructures could therefore be a potentially interesting alternative to other type of light scattering layers used within the solar cell field, having created high expectations due to the large improvement of the performance achieved for this type of devices.
In this section, we will focus on mesostructured Bragg reflectors in which the building blocks are nanoparticles of different sort (Colodrero et al., 2008) that can be easily coupled to DSSC to enhance the optical absorption. The novelty of these nanostructures is mainly the large and highly accessible interconnected mesoscopic porosity that they can present, which makes them suitable for this type of solar devices. In fact, some of the most successful approaches developed to improve the LHE in silicon photovoltaic systems are based on the implementation of coherent scattering devices such as highly reflecting distributed Bragg reflectors (Johnson et al., 2005), surface gratings (Llopis & Tobias, 2005), or a combination of both (Zeng et al., 2006). However, the implementation of such structures in DSSC had been no possible due to the need for porous back reflectors that allowed a proper flow of the electrolyte through the cell and, at the same time, due to the complicated deposition process of solid layers from colloidal suspensions.
The fabrication of DSSC containing nanoparticle based 1DPC involves two basic steps: first, the deposition of the nanocrystalline TiO2 layer that acts as electrode onto a transparent conducting substrate, and second, the stacking of layers made of nanoparticles of different kind deposited alternately by spin-coating onto the sintered electrode. In this case, silica and titanium dioxide suspensions are employed because of the very high refractive index contrast they present, which allows achieving broad and intense Bragg reflections. The nanoparticle multilayer is periodic with a period of around a hundred nanometers, the thickness of these layers being controlled through either the concentration of the precursor suspensions or the rotation speed of the substrate during the spin coating process. Figure 7 shows a scheme of the described 1DPC based cell, as well as FESEM images corresponding to a cross section of both the nanocrystalline-TiO2 electrode and the periodic structure deposited onto the former. The uniformity in the thickness of both types of layers composing the 1DPC, and even the different morphology of the particles employed, can be clearly distinguished in the picture below. The total thickness of the photonic crystal can vary between 0.5 to less than 2 microns, depending mainly on the lattice parameter of the structure and the number of layers that compose the periodic stack.
Fig. 7. Left: Design of a DSSC coupled to a nanoparticle based 1DPC. Right: FESEM images showing the TiO2 nanocrystals forming the solar cell electrode (top), on which the porous periodic stack made of nanoparticles of different kind is deposited (bottom). In this case, a six layer photonic crystal has been implemented.
The procedure that follows to complete the solar cell is the same than the one usually employed for standard DSSC. It should be noticed that the nanoparticle multilayer integrated into the solar cell in this way behaves as a distributed Bragg reflector, providing the cell with a brilliant metallic reflection whose colour can be tuned by varying the thickness of the layers forming the periodic nanostructure. This can be readily seen in the photographs shown in Figure 8, in which the appearance of a reference cell and the same cell including two different 1DPC under perpendicular illumination are shown. Another remarkable issue from these systems is that the multilayer implemented like that does not alter significantly the cell semi-transparency, contrary to what happens when other scattering layers made of large titania nanoparticles are employed in DSSC to increase the photogenerated current. When these diffuse scattering layers are used, the solar cell becomes almost completely opaque as a consequence of the lack of spectral selectiveness of the incoherent scattering by slurries with a wide particle-size distribution. The comparison between the optical transmission spectra for the case of a standard reference cell (7.5 micron thick) and those corresponding to solar cells possessing the same TiO2 electrode thickness but coupled to different 1DPC and to a diffuse scattering layer are also included in Figure 8.
Fig. 8. Left: Images of a reference cell and different photonic crystal based DSSC. The brilliant colours displayed by the cell (bottom) arise from the periodic structures with different lattice parameter coupled to the dyed electrode (top image). Right: Transmittance spectra of a DSSC composed of a 7.5 micron thick electrode (black curve) and of the same electrode coupled to periodic structures with different lattice parameters (green and red curves). For comparison, the transmittance spectrum of a DSSC with the same electrode thickness but coupled to a 7.5 micron thick porous diffuse scattering layer is also plotted (black dashed line). (Extracted with permission from Colodrero et al., 2009 [b])
As explained in section 3.3.1, enhancement of optical absorption is primarily due to the partial localization of photons of certain narrow frequency ranges within the dyed TiO2 electrode (that acts as absorbing layer) as a result of its coupling to the photonic crystal, which acts as a porous low-loss dielectric mirror (Mihi & Miguez, 2005). These optical modes could, in principle, be recognized as narrow dips in the reflectance spectra at frequencies located within the photonic band gap, the enhancement range being determined by the spectral width of the photonic band gap (Mihi et al., 2005). The first experimental demonstration of the mechanism of light harvesting enhancement that takes place in DSSC coupled to photonic crystals has been recently reported using the nanostructures under the scope of this section (Colodrero et al., 2009[a]). The effect of well defined optical absorption resonances was detected both in optical spectroscopy and photogenerated current experiments of very thin and uniform dye-sensitized TiO2 electrodes coupled to high quality porous 1DPC, an unambiguous correspondence between them being established. This study demonstrated that light trapping within absorbing electrodes is responsible for the absorption enhancement that had previously been reported. Figure 9 shows the spectral response of the IPCE for three DSSC having increasing electrode thicknesses range from 350 nm thick to 1.5 micron thick but the same 1DPC implemented. In each case, an enhancement factor у was calculated as the ratio between the IPCE of the 1DPC based cell and that of the reference one. The spectral behaviour of у for each cell is compared to its corresponding optical reflectance measured under front-side illumination. It can be clearly seen that peaks of photocurrent correspond to the dips in reflectance are obtained, which are the fingerprint of optical resonant modes localized in a film coupled to a photonic crystal.
For these modes, matter-radiation interaction times are much longer; thus, the probability of optical absorption, and therefore the photogenerated current, is enhanced. As the thickness of the dye-sensitized electrode increases, the number of localized modes rises and so does the number of peaks in the у curve. The presence of a photonic crystal not only enhances the photogenerated current but also allows one to vary the spectral photoelectric response of thin electrodes in a controlled manner. For instance, in the example shown in Figure 9a, the largest current is attained at X = 470 nm instead of at X = 515 nm, where the dye absorption curve reaches its maximum. Thus, the photonic crystal allows tailoring to measure the enhanced absorption window of the dye, and thus, its overlap with the solar spectrum.
Fig. 9. Top: IPCE versus wavelength for cells containing the same 6 layer-1DPC coupled to dyed electrodes of increasing thicknesses in each case (from left to right). It is also plotted the IPCE for reference cells of the same electrode thickness without photonic crystal (blue circles). Bottom: Reflectance spectra of the 1DPC based solar cells (solid line) and the corresponding photocurrent enhancement factor (red circles). (Extracted with permission from Colodrero et al., 2009 [a])
On the other hand, besides the experimental demonstration and confirmation of the light harvesting enhancement mechanism achieved using 1DPC based solar cells, great improvements in power conversion efficiency (n) have also been observed in this type of solar devices coupled to highly reflecting nanostructures (Colodrero et al., 2009 [a]), (Colodrero et al., 2009 [b]). After analyzing the photocurrent density-voltage (J-V) curves under 1 sun illumination of DSSC, on which photonic crystals reflecting different ranges of wavelengths were coupled, it was found that the photocurrent was largely improved while leaving the open-circuit voltage almost unaltered. The magnitude of this effect depends mainly on two factors: first, the spectral width and position of the photonic band gap relative to the absorption band of the ruthenium dye; second, the degree of optical coupling to the dye-sensitized electrode, which depends in turn on the thickness of that electrode. The magnitude of the photocurrent enhancement effect caused by the coupling to the 1DPC is therefore expected to be lower as the thickness of the electrode increases, since more photons are absorbed by the dyed nc-TiO2 layer when they first pass through it. For this case, red reflecting 1DPCs might perform better, since the ruthenium dye captures less effectively solar radiation precisely for A>600 nm. Results on the power conversion efficiency (n) for DSSC with a 7.5 micron thick electrode coupled to 1DPC reflecting different ranges of wavelengths (green and red) are shown in figure 10. An enhancement in the efficiency close to 20% with respect to that of the reference cell was obtained for the 1DPC based solar cell showing a better matching with the absorption spectrum of the dye.
Fig. 10. Left: IV curves of a 7.5 micron thick electrode coupled to different 1DPC under 1 sun illumination. The corresponding IV curve for a reference cell is also plotted (black line). Right: Reflectance spectra measured under frontal illumination conditions of the PC-based solar cells together with the absorption spectrum of the Ru-dye (arbitrary units).
The photocurrent enhancement reported using PC based solar cells could be even larger at lower incident radiation intensities, reaching up to 30% of the reference value under 0.1 sun for the samples above described. This is mainly due to the decrease of density of carriers when so does the incident light intensity, which has a positive effect on electron transport and recombination through the cell. Besides, any resistance potentially introduced by the photonic crystal will have a minor effect at lower illumination conditions, since its effect increases with the number of carriers. In order to illustrate this effect, values of efficiency, photogenerated current and open-circuit voltage obtained for DSSC having 7.5 micron thick electrodes coupled to different 1DPC are presented in Figure 11. The variation of Jsc and Voc with intensity of the incident radiation confirms that the presence of the PC enhances the photocurrent significantly, but has a minor effect on the photovoltage. The linear and logarithmic dependence observed for Jsc and Voc, respectively, versus incident radiation intensity are in good agreement with theoretical predictions (Nazeerudin et al., 1993); (Sodergren et al., 1994).
To conclude this section and in order to prove the performance of these nanoparticle based structures as light harvesters, DSSC based on both 1DPC and diffuse scattering layers were evaluated and compared. For this purpose, a 7.5 micron diffuse scattering layer made of titania spheres 130 nm in diameter mixed with a paste similar to that employed to prepare the nanocrystalline titania layer was deposited onto a 7 micron thick reference electrode. A similar electrode was coupled to a 700 nm thick highly reflecting 1DPC. In order to perform a comparison of the effect on light harvesting these different architectures have, the 7 micron thick diffuse scattering layer was electrically isolated from the dye-sensitized electrode by introducing a thin layer of silica spheres 30 nm in diameter between them. By doing so, no contribution to the photocurrent from the different scattering layers employed is measured, since the 1DPC is also based on alternate layers of SiO2 and TiO2 nanoparticles, the first layer deposited onto the electrode being insulating. The effect of the PC on the short circuit photocurrent is observed to be similar and comparable to that of a diffuse scattering layer, provided that a suitable PC is chosen, as displayed in figure 12. Furthermore, the open circuit voltage is slightly higher in the case of the PC, which might be due to its much smaller width. It should be reminded that the enhancement in the case of PC is based on the partial confinement of light of a selected frequency range within the absorbing electrode, whereas in the case of diffuse scattering layers, the increase in efficiency is based on the random and non-selective scattering of visible light in all directions.
Fig. 11. Efficiency (n), short-circuit current density (Jsc) and open-circuit voltage (Voc) for a reference cell (open black circles) and for those PC based cells having the same electrode thickness coupled to 1DPC with different lattice parameters (green and red symbols) under illumination at different light intensities. (Extracted with permission from Colodrero et al., 2009 [b])
Fig. 12. Comparison between the efficiencies for a DSSC made of a 7 micron thick electrode and those corresponding to the same electrode thickness coupled to a diffuse scattering layer and a 1DPC. The thicknesses employed for the diffuse scattering layer and the periodic structure are 7.5 micron and 700 nm, respectively. (Extracted with permission from Colodrero et al., 2009 [b])
Colloidal chemistry approaches are suitable for implementing optical devices of high quality in DSSC in order to improve their performance. This opens the door for the conscious optimization of the photonic design of DSSC, as is commonly done for their silicon counterparts. This may also open the way to amplifying the absorption of other dyes with low extinction coefficients that cover other regions of the visible and near-IR solar spectrum. In this respect, a thorough analysis in terms of the interplay between the effect of the electrode thickness, the dye absorption spectrum, and the characteristics of the Bragg reflection, such as intensity, spectral position and width, is needed for designing 1DPC based DSSC of optimized performance. On the other hand, the greater enhancement of efficiency attained for thin electrodes coupled to these photonic structures highlight the potential that they might have in other cells using very thin absorbing layers, in which the main source of loss of efficiency is frequently the low amount of light absorbed.
 In 1768, Johann Elert Bode (1747-1826), director of Berlin Astronomical Observatory, published his popular book, "Anleitung zur Kenntnis des gestirnten Himmels" (Instruction for the Knowledge of the Starry Heavens), printed in a number of editions. He stressed an empirical law on planetary distances, originally found by J. D. Titius (1729-96), now called "Titius-Bode Law".
 (JPL 1998)
 Earth without Moon
 Mean for Martian latitude and year
Table 2. Comparative Mars and Earth astrophysical data
The data in table 2 are based on the mean eccentricities of the year 2009 as given in the reference. Accordingly, a value of g=6.6742810-11 is used for the universal constant of gravitation. Second is the time unit used to define the sidereal periods of revolution around the Sun and is derived, on its turn, from the solar conventional day of 24 hours in January 1, 1900. The atmosphere of Mars is presently very well known and consists, in order, of Carbon dioxide (CO2) 95.32%, Nitrogen (N2) 2.7%, Argon (Ar) 1.6%, Oxygen (O2) 0.13%, Carbon monoxide (CO) 0.07%, Water vapor (H2O) 0.03%, Nitric oxide (NO) 0.013%, Neon (Ne) 2.5 ppm, Krypton (Kr) 300 ppb, Formaldehyde (H2CO) 130 ppb , Xenon (Xe) 80 ppb, Ozone (O3) 30 ppb, Methane (CH4) 10.5 ppb and other negligible components. This composition is further used to assess the effect of solar radiation upon the dissociation and los of the upper Mars atmosphere and upon potential greenhouse gases.
 1 = x2
X2 = x3 (45) x3 = – KI (x1 – x1) – KP (x2 – x2) – KD (x3 – x3) = v(t)
Mn +Mp = 0.8