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14 декабря, 2021
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Simulations
a) Two-layered systems
From the field of anti-reflection coatings, two-layered coating designs such as the V — and the W-design are known [24]. These systems owe their name to the shape of the reflection minimum. The effect of anti-reflection extends over a certain wavelength range, but aside from this region considerable reflectance peaks occur, which can be used to produce a colored reflection. The region of antireflection enhances the solar transmission. Creating a region of higher reflectance at short wavelengths, blue and green colors of reflection can be easily achieved in combination with a good solar transmission.
As an example we show the W- design. Both sides of the substrate are coated identically, as it occurs often in sol-gel dip coating. Our calculation takes into account the multiple reflections between the two sides. The optical model has the structure
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Fig.1: Simulated reflectance spectra for W-designs. The glass substrate has been assumed to be coated at both sides (optical model: air//L2H//glass//2HL//air. The design wavelength Ac has been chosen to 800 nm. |
air // L 2H // glass /2HL // air, where the letters "L” and "H” mean quarterwave layers of low and high refractive index, respectively. The corresponding layer thicknesses t(L) and t(H) have thus been chosen to n x t(H) = A.0/2 and
n x t(L) = A.0/4, where the
so-called "design wavelength A. o” indicates the center of the region of anti-reflection (here: Xo = 800 nm). A refractive index of 1.52 has been assumed for the glass substrate. The resulting reflectance spectra are displayed in Fig.1. For the shown examples, the resulting colors are in the region of bluish green. Within a rather large region the reflectance is lower than the one of an uncoated substrate (approx. 8%). Due to the partial antireflection, the achieved color saturation and as well the solar transmission are remarkable. A survey of the characteristic figures, the color coordinates x and y, the visible reflectance Rvis, the solar transmission Tsoi and the figure of merit M = Rvis/Rsoi, is given in TABLE I.
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TABLE i:
CIE color coordinates x and y, the visible reflectance RVIS, the solar transmission Tsol and the figure of merit M = RVIS/Rsol, as computed for the curves displayed in Fig. 1.
b) Three-layered system
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Fig. 2: Simulated reflectance spectra for the three-layered system. The glass substrate has been assumed to be coated at only one side. Adding the additional layer to the V-design results in a strong enhancement of the colored reflection. |
Starting from a classical V-design, we have studied the influence of adding a third layer. We consider a glass substrate with a refractive index of 1.52 being coated on one side by a stack of three layers, the first layer being 30 nm thick with a refractive index of 2.2, the second layer 140 nm thick with n = 1.46, and a third layer of variable thickness with n = 2.2. By variation of the thickness t3 of the topmost layer from 0 nm to 50 nm, we obtain the reflectance spectra displayed in Fig.2. The thin black line illustrates the reflectance for the two-layered V-design (thickness
t3 = 0 nm). Adding the additional layer results in an increase of the colored reflection. The spectrum corresponding to the case of a 30 nm thick top layer exhibits a strong enhancement of the reflection peak and still a region of anti-reflection at a wavelength of 1000 nm. For the top layer being 50 nm thick, the region of antireflection is already less pronounced. Also from the point of view of the solar transmission Tsol(%), the region between 10 nm and 40 nm appears most interesting. TABLE II shows the numerical results for the color coordinates x and y, the visible reflectance RVIS, the solar reflectance reflectance Rsol, the solar transmission Tsol and the figure of merit M = RVIS/Rsol, in dependence on the thickness t3 of the third layer.
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TABLE II:
CIE color coordinates x and y, the visible reflectance RVIS, the solar reflectance Rsol, the solar transmission Tsol and the figure of merit M = RVIS/Rsol, as computed for the curves displayed in Fig. 2.
c) Maxima of higher order
Towards shorter wavelengths, the reflectance spectra for dielectric thin film stacks exhibit rapid oscillations between the maxima and minima of higher order. By using high enough layer thicknesses, the maxima can be placed in the visible spectral region. Fig.3 illustrates an example showing the oscillations in the high wavelength region which are used for the coloration.
For e. g. a color of pink two peaks, corresponding to blue and red contributions, are necessary. The calculation is based on literature data for the refractive indices of SiO2 and TiO2 [27-29]. For
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Fig.3: Simulated reflectance spectra for the design ‘A’ (layer 1: 213 nm TiO2, layer 2: 258 nm SiO2). The glass substrate has been assumed to be coated at only one side. For a color of pink two peaks, corresponding to blue and red contributions, are necessary. |
simplicity, coatings have been assumed to be transparent within the solar spectral region. Layer thicknesses of 213 nm and 258 nm are assumed for the TiO2 and the SiO2 layers, respectively.
Color coordinates of x = 0.39 and y = 0.24 have been found, accompanied by a visible reflectance of 9.8 %, while the solar transmission amounts to 84.6 %. Some more examples are listed in TABLE III. The selection comprises two, three and four layered systems. Layer 1 is the next to the glass. A refractive index of 1.52 has been assumed for the glass, the coating is supposed to be only on one side of the substrate.
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TABLE III: color approx. M =
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Color coordinates x and y, the visible reflectance RVIS, the solar reflectance Rsol, the solar transmission Tsol and the figure of merit M = RvIS/Rsol, as computed for a variety of two, three and four layered systems.
d) Quarterwave stacks
In quarterwave stacks, all individual layers are of the optical film thickness n ■ t = 20/4 , where X0 is called the design wavelength. Usually layers of a high index material (H) alternate with layers of a low refractive index material (L), resulting in a stack of the form HLHLHL… . Often, these filters are employed as high reflectivity mirrors, exhibiting a nearly perfect reflectance over a large frequency band. The larger the difference in the refractive indices, the larger is the spectral region of high reflection. We are interested in the opposite, a narrow reflection peak, which can in principle be created by employing a large number of layers (e. g. forty layers for a linewidth in the order of 20 nm [30]). Here we consider a system, where both sides of the glass are coated each by a stack of five individual layers. Consequently, the structure of the optical model is air//HLHLH//glass//HLHLH//air.
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wavelength (nm) Fig. 4: Simulated reflectance spectra for a design based on a five-layered quarterwave stack on each side of the glass substrate (optical model: air//HLHLH//glass//HLHLH//air. The design wavelength Ло has been chosen to 550 nm. Angles of reflection from 0° to 60° have been assumed. |
The refractive indices n(H) = 1.65 and n(L) = 1.47 have been
chosen (in combination with a refractive index of the glass substrate of 1.52) . Our
calculation has been performed for various angles of incidence, rising from normal incidence in steps of 20°. A graphical representation is given in Fig.4, the figures are summarized in Table IV. For normal incidence, the FWHM amounts to 167 nm, the visible reflectance to 34 %.
The solar transmission (84%) is acceptable; the energy loss compared to an uncoated glass amounts only to 8 % . The angular dependence of the reflectance is nicely illustrated in Fig. 4. For an angle of incidence of 20° , the curve does not change significantly; the position of the maximum shifts slightly from 550 nm to 534 nm. For 40° , the shift continues to 499 nm. For 60 °, a blueshift in the order of magnitude of the peak width is accompanied by a rise of the background level. For 80°, the background level rises further, the peak is barely distinguishable, and the properties are quite close to those of uncoated glass (representation in Fig. 4 omitted for clarity). With increasing angle of incidence, the difference between the transmission of uncoated glass Tglass and the transmission Tsol of the coated system decreases, while the figure of merit M converges to unity. In TABLE IV a survey of the characteristic numbers is given.
TABLE IV:
Position of the reflectance maximum, color coordinates x and y, the visible reflectance RVIS, the solar transmission Tsoi, the transmission of an uncoated glass Tglass, the difference Tglass — Tsol between the latter and the solar transmission, and the figure of merit M = Rvis/Rsoi, as computed for the curves displayed in Fig. 4. The values for the angle of incidence of 80° are added.
By adapting film thicknesses according to the relation n ■ t = 20/4, the peak position X0 can be shifted easily. For design wavelengths X0 of 450 nm and 650 nm, colors of blue (x = 0.20 , y = 0.24 ) and orange (x = 0.44 , y = 0.36 ) are attained. The solar transmission increases slightly or changes barely ( 6 % and 84 %, respectively), while the visible reflectance decreases ( 17 % and 29 %, respectively).
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Several design types have been proposed to achieve an energy-efficient coloration of solar collector glazing. Known anti-reflection coatings such as the two-layered V — and W-design can be modified to create a colorful reflection in the visible spectral region and a region of antireflection e. g. in the infrared. This approach is especially suitable to create blue and green colors in combination with a high solar transmission. Addition of a third layer to a V-design leads to a strong enhancement of the reflectance peak. Already with such a three-layered coating design of moderate total coating thickness, considerable peak heights and thus a strong visible reflectance can be achieved. Therefore this design is attractive for large area coating processes where production costs scale with the number of individual layers and the total coating thickness. Another way to create a colored reflection is to make use of the maxima of higher order appearing towards short wavelengths. In this regime the shapes of the reflectance spectra become rather complex, but can be used to produce colors where more than one reflection peak is needed. A systematic approach to the problem of achieving a single, isolated reflectance peak is the one of quarterwave stacks. Already with stacks of five layers and a suitable choice of refractive indices, sufficiently narrow reflectance peaks can be produced. Interference colors are in general angle-dependent. This could both increase (nice effect, high-tech image) or decrease acceptance of the proposed collector covers, which is a subject of discussion with architects, manufacturers and end-users. However, for the shown example of a five-layered quarterwave stack, the peak shift at 60° angle of reflection is in the same order of magnitude as the half peak width. Additionally, if the multilayered coating is only applied at the inner side of the collector, the angular dependence can be reduced by diffusing elements, such as rough surfaces/interfaces or a diffusing interlayer. Common thin film deposition processes are magnetron sputtering, plasma enhanced chemical vapor deposition, vacuum evaporation, or SolGel dip coating. Transparent oxides such as silicon dioxide (n ~ 1.47), aluminum oxide (n ~ 1.65) , or titanium dioxide (n ~ 2.2) can routinely be deposited [24,31,32]. Intermediate refractive indices would be accessible by the synthesis of mixed oxides. Nanocomposite mixed oxides can be modeled in the framework of effective medium theories, such as e. g. the Bruggeman or the Ping Sheng theory [33,34],
both providing analytical expressions for the resulting optical properties. With all coating processes, care has to be taken for a superior film homogeneity, which is essential for interference filters. Vacuum processes yield in general high quality films, but a considerable investment into the vacuum coating machines is necessary already in the start-up phase. The scale-up of a vacuum process, which has been developed in the laboratory, is possible, but non-trivial [35]. This is much easier for SolGel dip-coating. Once the right solutions and withdrawal speeds are found, the size of the glass pane does not alter the basic process parameters. Here, one main problem is to avoid dust, which creates defects and harms the coating quality. Costs rise with the repeated baking of multilayered coatings on large glass panes. One solution to the problem can be special precursors, which enable a film hardening by ultraviolet light [36].
Multilayered interference filters of dielectric thin films have been designed for the application as energy-efficient coloration of collector cover glasses. The optical behavior of the designed multilayers is analysed by computer simulations yielding the CIE color coordinates, the relative luminosity, the degree of solar transmission, and a figure of merit which is a measure for the energy effectiveness of the coloration. For several types of multilayer design the computer simulations yield promising results. Hereby, constraints such as a realistic choice of refractive indices, a limited number of layers in the stack, and a not excessive total stack thickness have been respected. The way for the experimental realisation of energy-efficient colored glazed solar collectors has thus been opened up.
Financial support of this work has been provided by the Swiss Federal Office of Energy SFOE. Authors are grateful to Dr. I. Hagemann, and Dr. P. W. Oliveira for inspiring discussions.