Computations of the optical properties of metal/insulator-composites for solar selective absorbers

Renewable Energy 28 (2003) 1421–1431www.elsevier.com/locate/renene

Computations of the optical properties ofmetal/insulator-composites for solar selective

absorbers

M. Farooqa,∗, Z.H. Leeb

a Pakistan Council for Renewable Energy Technologies, 25, H-9, Islamabad, Pakistanb Department of Materials Science and Engineering, Korea Advanced Institute of Science and

Technology, Kusung-Dong 373-1, Yusung-Gu, Taejon, South Korea 305-701

Received 22 December 2001; accepted 19 February 2002

Abstract

Solar selective absorbers are very useful for photo thermal energy conversion. The absorbersnormally consist of thin films (mostly composite), sandwiched between the antireflection layerand (base layer on) a metallic substrate, selectively absorbing in the solar spectrum andreflecting in the thermal spectrum. The optical performance of the absorbers depends on thethin film design, thickness, surface roughness and optical constants of the constituents. Thereflectivity of the underlying metal and porosity of the antireflection coating plays importantroles in the selectivity behavior of the coatings. Computer simulations, applying effectivemedium theories, have been used to investigate the simplest possible design for compositesolar selective coatings. A very high solar absorption is achieved when the coating has a non-uniform composition in the sense that the refractive index is highest closest to the metalsubstrate and then gradually decreases towards the air interface. The destructive interferencecreated in the visible spectrum has increased the solar absorption to 98%. This paper alsoaddresses the optical performance of several metals/dielectric composites like Sm, Ru, Tm,Ti, Re, W, V, Tb, Er in alumina or quartz on the basis of their refractive indices. The anti-reflection coating porosity and surface roughness has been analyzed to achieve maximum solarabsorption without increasing the thermal emittance. Antireflection layer porosity is a functionof dielectric refractive index and has nominal effect on the performance of the coating. While,up to the roughness of 1× 10�7m RMS, the solar absorption increases and for higher rough-ness, the thermal emittance increases only. 2002 Published by Elsevier Science Ltd.

∗ Corresponding author.E-mail address: [email protected] (M. Farooq).

0960-1481/03/$ - see front matter 2002 Published by Elsevier Science Ltd.doi:10.1016/S0960-1481(02)00033-2

1422 M. Farooq, Z.H. Lee / Renewable Energy 28 (2003) 1421–1431

Keywords: Selective absorbers; Optical constants; Interference; Graded multilayers; Roughness andporosity

1. Introduction

In solar energy applications, a spectrally selective surface should capture themaximum solar energy and should have minimum emittance for thermal IR radiation[1]. To enhance the total solar absorptance of the coating, the high intensity visiblespectral region should have the lowest possible reflectance and, to suppress the emit-tance, the thermal radiation should have highest possible reflectance. A practicablesolar selective absorber is produced if a metal of high infrared reflectance is coatedwith a thin film of high solar absorptance. The highest solar absorptance is obtainedif the film is a metal/dielectric graded composite where the graded compositionshould be designed with a continuously decreasing refractive index (n) and an extinc-tion coefficient (k) from the substrate to the air interface. The ideal case is to havea refractive index n � 1 and extinction coefficient, k � 0 at the front surface (onAR coating). The lowest thermal emissivity is achieved when the coating has non-metallic properties, i.e. that k does not increase with wavelength, rather the opposite.It means that a metal-dielectric composite coating should be so thin that thermalradiations can not see the composite coating.

The graded composition is termed here as graded multilayered coating due tolimited gradation with three or four layers. This multilayered coating not only easesthe radiation to penetrate into it but also can be used to create destructive interferencein the coating, resulting in higher solar absorptance. To achieve the interferenceeffect and easy solar radiation penetration, the design of graded multilayered coatingsfor selective solar absorbers requires a detailed knowledge of the optical constantsof the considered materials. The optical constants of the studied material have beentaken from literature [2–4] for simulation. Many researchers have studied the gradedmultilayered designs [5–7] but our four-layer design [8] produced comparativelybetter results.

In this paper we compare the results of a new 3-layered and previous 4-layereddesigns for solar selective absorber coatings. We analyze the possible metals candi-dates which are capable of producing � 90% absorptance in graded multilayer solarabsorbers. Finally, the effect of surface roughness and porosity in the antireflectionlayer will also be described.

2. Need of graded multilayered design

Mainly, four designs for solar selective absorbers have been investigated. Themetal/insulator multilayer (stack) design [9] for solar selective absorber is not popularbecause it is difficult to accurately fabricate a thin (5–10 nm interference) metal

1423M. Farooq, Z.H. Lee / Renewable Energy 28 (2003) 1421–1431

layer. Also the problem of inter-diffusion during application among the metal anddielectrics layers changes the physical structure, resulting in decreased absorption.Ungraded (unilayer) composites [10] on metal substrates and covered by antireflec-tion coating have around 80% solar absorption. In order to achieve more than 90%absorption, most researchers used highly graded metal/insulator composite absorbers[11–13]. For graded composites, the reflectance at cut-off point increases slowly,resulting in higher emittance. During the last decade, through fundamental analysis,researchers [14–16] came to the conclusion that graded multilayer (2–5 layer) com-posites can produce more than 95% absorption with low thermal emittance.

Among graded multilayer composite design, 4-layered produced better results. Inour previous (4-layer) design, the destructive interference was created in the visiblespectrum and, in the NIR spectrum no interference effect was observed. For thisreason, the design has been simplified from four to three layers so that an extrainterface, which is not creating destructive interference, should not produce reflectionin the NIR spectrum. This design is more simple (layers have been reduced from 4to 3) and produced slightly better results than the previous design. The slightlyimproved results are due to the removal of extra interface, which is not producingdestructive interference but causing reflection in NIR spectrum. The metallic gra-dation with the depth profile for 3 and 4 layer designs is shown in Fig. 1. Herethe investigated solar selective absorbers consists of the following structure unlessotherwise described.

A 75 nm thick antireflection coating of alumina or quartz on a 200 nm thick, 0.65volume fraction (VF) and graded 3-layers absorber was coated. The top two layers(near AR layer) produce an interference effect in the visible spectrum. To suppressemittance, copper substrate is covered with 100 nm thick metal; this is the samemetal that is used for graded multilayers.

Fig. 1. Metallic gradation with depth profile for graded 3- and 4-layered designs.


3. Theory for multilayered thin film optics

The direct matrix method has been applied to calculate the reflection coefficientof a multiplayer design on a copper substrate. The system of N layers, as shown inFig. 2, has been characterized by the matrix method, which relates the amplitudesof the electromagnetic field components at the interface with the incident electromag-netic field components.

[Em�1Hm�1] � �cosfm

incm

sinfmincmsinfmcosfm�[EmHm] (1)

where E and H are mth layer’s electric and magnetic field vectors of the electromag-netic radiation. The matrix in Eq. (1) characterizes one layer and the determinant ofthe equation is unity, which acts as a check on the calculations.

For N number of layers we can rewrite Eq. (1) as:

[E0H0] � �Nm=1MatN[ENHN] (2)

where

[ENHN] � [1nsub]E+sub (3)

Matm � (cosfm�(i /ncmi)sinfm�incmsinfmcosfm) (4)

where ncm is the complex refractive index of the composite “mth” layer and “ i” isthe square root of minus one (√�1).

fm � 2pncmtm /l, (5)

where “ tm” is film thickness of “mth” layer and l is wavelength. The compositefilms are normally fabricated on metallic substrates, so there is no transmission of

Fig. 2. A multilayer stack scheme of N layers on a metallic substrate.


radiation. The only parameter from which to deduce the absorptance and emittanceof the system is reflectance, which is calculated as [17] for non-transparent substrates.

Rl � | cosf�(�incsinf) � ((�i /nc)sinf�cosj)ns

cosf � (�incisinf) � ((�i /nc)sinf � cosf)ns| (6)

where Rl is the reflectance at a single wavelength point and ns is the complex refrac-tive index of the substrate.

3.1. Calculation of solar absorption and thermal emittance

Solar absorption and thermal emittance of the coatings can be calculated from thereflectance spectra which is defined as:

R �

�l2

l1

RlIldl

�l2

l1

Ildl

(7)

where Il is the spectral incident radiation, Rl is the spectral reflectance, and, l1 andl2 define the spectral range

If the solar spectral distribution is divided into twenty bands of equal energy, thenthe selected ordinates method can be used and Eq. (7) is written as:

Rl1l20�

�20

i � 1

R�li

20(8)

To calculate the solar absorptance, the reflectance was taken on the 20 selectedordinates [18] for air mass (AM) 2.

The spectral emittance is evaluated using the Planck black body spectral distri-bution for 300 K at 20 selected ordinates for thermal emittance [19].

4. Results and discussion

4.1. Comparison of three and four layer design

The optical performance of 3- and 4-layer design was compared by calculatingthe solar absorption and thermal emittance for V:Al2O3, Ru:Al2O3, Tb:Al2O3 andTb:SiO2 composites. The suitability of different refractive index metal and dielectricin composites has already been published [20], so there is no need to discuss it here.


The 3-layer design is more simple and has produced slightly better solar absorptionas shown in Fig. 3. By changing the design, the thermal emittance (about ε300k �0.43) remained unchanged, so the results are not being presented here. The elimin-

ation of one layer has reduced the interface effect between adjacent layers in theNIR spectrum, where the destructive interference effect is negligible or zero. Dueto the top two layers, the destructive interference for 3-layer design was designedat 0.5 µm and 0.7 µm wavelengths, where maximum solar energy is available. Simu-lations predict that very good selective absorbers can be fabricated with this newsimplified design for most of the studied materials. It is clear from Fig. 3 that with3-layered design, a � 0.95 can be achieved, keeping ε300k � 0.05 for most of thecomposites studied here (dependant on their optical constants) and a/ε300 k ratio wasobserved to be more than 22 for Ru: Al2O3 and V: Al2O3 composites.

4.2. Analysis of various composites

Various metal/dielectric composites such as V:Al2O3, Ru:Al2O3, Re:SiO2 Tb:SiO2,Er:SiO2, Tm:SiO2 and Sm:SiO2 were investigated using 3-layered design to evaluatetheir optical performance (α, ε) for solar selective absorbers. To date, some metalslike Tb, Tm and Re have not been investigated thoroughly for solar absorbers. Mostof these combinations showed a�0.95. The selection of dielectra between SiO2 andAl2O3 depends on the refractive index and concentration of the metal in the com-posite. For higher metallic concentration and metal refractive index, a higher refrac-tive index dielectric is required. We have optimized the combination of the compositeon this principle and found it working but for detail, the reader is referred to refer-ence [8].

On the basis of refractive indices, we have divided the metals into three categories;low, medium and high. We will evaluate these composites on the basis of their

Fig. 3. Solar absorptance comparison for graded 3- and 4-layered designs.


refractive indices to understand the physics of the composition. The calculationssuggest that, to create destructive interference, refractive index “n” of the compositeat the top two interfaces should be 2.5 and 2.7 for 0.5 µm and 0.7µm wavelengths.To achieve this, the refractive index of the metal should be 3.2 and 3.5. Here thecomposite films have 0.65 metallic VF and the required dielectric should haven � 168. Alumina and quartz have 1.76 and 1.55 refractive index, so any one ofthe dielectrics can be used but alumina is comparatively more suitable for high refrac-tive index metals. For medium and low refractive index metals, quartz as a dielectricin composite and AR layer is the ultimate choice.

V (n � 3.3�3.8), W (n � 3.5�3.45), Ru (n � 3�5), and Re (n � 3.5�3.7) haverefractive index (high) “n”�3 in the visible region so interference effect is prominent,which resulted in comparatively higher absorption. Erbium (n � 2�2.3) and thulium(n=2–2.2) have medium refractive index and have quite good solar absorptance buterbium is the metal, which has strong absorption in the infrared spectrum causinghigher emittance. On the other hand Sm (n � 1.1�1.3) and Tb (n � 1.4�1.8) arethe lower refractive index metals and the interference effect is comparatively lowerbut the gradation effect may be prominent. Low refractive index composites havereasonably good solar absorption but remained lower than the interference occurringcoatings as shown in the Fig. 4. The α/ε ratio for higher refractive index compositesis higher than that of the medium and lower refractive index.

4.3. Effect of roughness and porosity

V:Al2O3, Ru:Al2O3 and Tb:SiO2 composites were investigated to observe the effectof porosity and surface roughness, created in AR layer. The porosity, which wasstudied for 0.05 to 0.3 air’s VF, decreased the refractive index of the AR dielectric.The refractive index of alumina was slightly higher than the optimized, so theporosity effect was clear as shown from the result of Ru:Al2O3 and V:Al2O3. On

Fig. 4. Optical performance of various metal/insulator graded 3-layered composites.


Fig. 5. Effect of porosity on the spectral reflectance of Ru: Al2O3 graded 3-layered composites.

the other hand there was nominal porosity effect for quartz composites as the refrac-tive index is already matching for medium refractive index metals like Er:SiO2 andTm:SiO2. The results are not being presented, as it is difficult to distinguish. In lowerrefractive index metal composites, the refractive index of dielectric might be slightlyhigher which enhanced absorptance slightly as shown from the (Sm:SiO2 and)Tb:SiO2 results. The effect of porosity on spectral reflectance for Ru:Al2O3 is shownin Fig. 5. Porosity effects on solar absorptance and thermal emittamce for V:Al2O3,Ru:Al2O3 and Tb:SiO2 absorbers are shown in Figs. 6 and 7, respectively. It can beobserved that there is a minor effect of porosity on α and ε.

Roughness is a key factor, which decreases the front surface reflection, and theabsorption increases with the increase of roughness. But if we go on increasing theroughness the absorption will not increase but the NIR radiation will also be absorbed

Fig. 6. Effect of porosity on the solar absorptance of graded 3-layered various composites.


Fig. 7. Effect of porosity on the thermal emittance of graded 3-layered various composites.

as shown from the spectral reflectance of Ru:Al2O3 in Fig. 8, which resulted inhigher emittance. We simulated for 5 × 10�9m to 5 × 10�7m RMS roughness andobserved that up to 1 × 10�7 RMS, absorption increases with the roughness but anyfurther increase causes only higher emittance. The effects of roughness on absorpt-ance and thermal emittance are shown in Figs. 9 and 10, respectively, and it is theconfirmation that beyond 1 × 10�7m rms roughness, only the thermal emittanceincreases rapidly.

Fig. 8. Effect of surface roughness on the spectral reflectance of Ru: Al2O3 graded 3-layered composites.


Fig. 9. Effect of surface roughness on the solar absorptance of graded 3-layered various composites.

Fig. 10. Effect of surface roughness on the thermal emittance of graded 3-layered various composites.

5. Summary

A theoretical study of the multilayer composite solar selective absorbers was madeand a model programme is developed to investigate the best possible design for theabsorbers. This three-layer design is quite simple and the advantage of destructiveinterference in this design makes it worth applying.

The materials have been studied for solar selective absorbers on the basis of theirrefractive indices and the results match very well with our assumption. The metalshaving a refractive index of between 3 and 3.5 are suitable for selective absorbersto create destructive interference in the visible spectrum to absorb intense portionof solar radiation. The porosity and roughness on the AR layer were optimized. Theporosity reduces the refractive index of the AR dielectric material if its refractive


index as an AR layer is higher than the underneath composite. The absorptionincreases linearly with the roughness up to 1 × 10�7m RMS and any further increaseraises the thermal emittances due to thermal radiation absorption.

Acknowledgements

The authors are grateful to Mr. Yang Sung-Ho of KAIST for his valuable sugges-tions and moral support.

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Computations of the optical properties of metal/insulator-composites for solar selective absorbers