In order to take account of the solar spectrum, a multilayer sample is characterized by its solar transmission Tsol, its solar reflectivity Rsoi defined respectively by the following relations:

_ JT(A) Iso, (A) dA

J Iso. (A) dA

We note here Isol the intensity of the solar spectrum AM1.5. The integration range is given by the limits of the solar spectrum. The visible reflectance Rvis is determined from the photopic luminous efficiency function V(l), the standard illumination D6s(A) and the hemispherical reflectivity R(A):

R _ fR(A) • Р65(Л) • V(A)dA vis f 065(Л) • V(Л)dЛ

For the theoretical case of a delta-distribution-shaped reflectivity, Schuler et al. [18] introduced a merit factor M defined as the ratio of the visible reflectance Rvis and the solar reflectivity Rsoi. M is then large for a high visible reflectance or low solar energy losses and consequently describes the energy efficiency of the visual perception.

Numerical simulations allow optimizing the reflectivity and transmission of the multilayer films as a function of the film thicknesses, the refractive indexes and the number of alternating layer. They show a correlation between the difference of the refractive index of the two materials. For example, a lower refractive index difference increases the optimal thicknesses of the individual layers and the layer number, but the solar transmission is high. The simulation optimization results based on the experimental optical constants of single layers will be published elsewhere [19].

Table 2 shows the solar transmission, the solar reflectivity, the relative visible reflectance and the merit factor M = Rvis/Rsoi in the case of the Ti02/Si02 multilayers. We indicated the experimental and calculated values. We see that for a given number of alternating layers, it is always possible to obtain either a high solar transmission or a high relative visible reflectance by adapting the thicknesses of both oxide materials. In order to obtain the best compromise between the energy losses by reflectivity and the visual effect, both parameters have to been optimized. Samples a and c show that the merit factor is not a sufficient indicator and one has to take into account the absolute Rsol. In fact, in these examples, the solar transmission is low and results in a uselessly high visible reflectance.

Table 3 shows the solar transmission, the solar reflectivity, the relative visible reflectance and the merit factor M in the case of the Al203/Si02 multilayers. The solar transmission is slightly decreasing by increasing layer number, but stays at a high level superior to 89%, which is comparable to the solar transmission of uncoated glass (92 %). As mentioned above, this is due to the small refractive index difference between Si02 and Al203. The relative visible reflectance and hence the factor M increases.

The result shows that the prepared coatings can meet the requirements for obtaining different reflected colors. More efforts are needed to improve at the same time the solar transmission and the visible reflectance by considering other oxides and by optimizing the layer thicknesses.

4. CONCLUSION

In this work, colored glass to cover solar collectors has been obtained by alternative deposition of dielectric layers with high and low refractive indices. The stoichiometry was first checked by XPS. The deposition rate has been controlled by in-situ laser reflectometry and confirmed by ex-situ ellipsometry for complex systems with several layers. The optical properties of individual oxides of titanium, silicon and aluminium have been determined. A Cauchy dispersion model is adequate for extracting the refractive and extinction index in the case of reactive magnetron sputtering deposition.

The reflectivity and the solar transmission depend on the thicknesses and the number of the alternative dielectric layers. The fabricated multilayers fulfilled the fixed requirements: quasi-zero absorption, reflectivity peak in the visible, solar transmission above 85% up to 89% and an acceptable visible reflectance.

More effort will be directed to study the lifetime of the multilayer coatings by aging tests in orderto investigate theirapplicabilityfor architectural integration in buildings.

ACKNOWLEDGEMENTS

The authors wish to thank Dr. M. Ley for helpful discussions and R. Steiner for the technical support. This work is supported by the Swiss Federal Office of Energy and the Swiss National Science Foundation.