Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

High efficiency of photon-to-heat conversion with a 6-layered metal/dielectric film structure in the 250-1200 nm wavelength region

Open Access Open Access

Abstract

The optical properties and thermal stability of a 6-layered metal/dielectric film structure are investigated in this work. A high optical absorption average of > 98% is achieved in the broad spectral range of 250-1200 nm with experiment results, in good agreement with our simulated results. The samples have a typical layered structure of: SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51.4 nm)/Cu(>100 nm), deposited on optically polished Si or K9-glass substrates by magnetron sputtering. The sample of the 6-layered metal/dielectric film structure has an AM1.5G solar absorptance of 95.5% with the features of low thermal emittance of 0.136 at 700K and good thermal stability, and will be potentially suitable for practical application in high-efficiency solar absorber devices in many fields.

© 2014 Optical Society of America

1. Introduction

The technologies to more efficiently convert sunlight into heat are getting great attention with intensive studies recently, due to their potential for significant applications in many fields, such as solar heating, solar-thermal electricity generation, solar thermoelectrics, solar thermo-photovoltaic devices, and so on [1, 2]. An up-to-date summary [1, 3] describes six types of selective solar absorbers: (1) intrinsic absorbers; (2) semiconductor–metal tandems; (3) multilayer absorbers; (4) cermets, (5) textured absorbers; and (6) photonic crystals [1, 4–15]. Among them the cermet-based solar absorbers were studied most intensively in past 50 years to fulfill the goal of commercial application. The spectrally non-uniform absorptance of a cermet-based layer in the solar spectral region, however, is sensitive to chemical reactions processes which will affect profoundly the metal and dielectric particle size, composition, thickness, complex refractive index of the layer material, and so on, to make it hard to achieve the best spectral performance of the solar absorber [1, 2]. Alternatively, multilayer film structures show the unique advantage of high and uniform absorption in a broad solar spectral range with low thermal emittance and excellent thermal stability to make them particularly suitable for the photon-to-heat energy-conversion applications under medium and high temperature conditions [4–7]. In a typical sputtering layered-structure process, only pure and proper metal and dielectric media with one type of inert gas are used to control precisely the thickness of each layer, resulting in the best spectral absorption feature to be more feasibly tuned and achieved.

A four-layered metal/dielectric film structure has been studied, showing high optical absorption of > 95% in the 400-1000 nm spectral range with low thermal emittance and a simpler structure [6, 7]. For the four-layered structure, however, there is a lack of natural materials with proper optical constants which can be used to get the best matching of the optical phase and amplitude of the light propagated in the layered structure in the near ultraviolet region, resulting in a significant decrease of optical absorption down to about only 10% in the 250-400 nm wavelength region which still can be a very usable spectral window to absorb a considerable amount, about 8% of solar radiation, especially for devices to work in space conditions [1].

To improve the absorption properties of the device, especially in the short wavelength region, in this work we have studied a metal-based multilayer structure by adding two additional layers to form a six-layered metal/dielectric film structure. By optimal matching of the optical constants and thickness of each layer in the device structure, both simulated and measured results show that the optical absorption in the short wavelength region of 250-400 nm can be enhanced significantly without any reduction of absorption in the long wavelength range. Therefore a high absorption, averaging > 98% in the broad 250-1200 nm spectral region, has been achieved, and this will stimulate more studies on high efficiency solar selective absorber devices which can be put into wider applications in the future.

2. Numerical simulation

Under ideal conditions, highly efficient selective solar absorbers should be designed to have the optical properties of absorbing most of the solar radiation in a broad spectral region, and of maintaining low re-radiation in the infrared region induced by the working temperature of the selective absorber. With respect to the solar radiation spectrum and thermal emittance characteristics of black body radiation at 500K [1], the requirement is that the solar absorber device has high optical absorption in the 250-2500 nm wavelength region and low absorption with high optical reflection in the infrared region above the 2500 nm wavelength.

In previous work [6, 7], a solar absorber device with a simpler 4-layered metal/dielectric film structure was studied which achieved high absorption, > 95%, and good thermal stability in the 400-1000 nm wavelength range. Due to the lack of natural materials with proper optical constants, the mismatching of the optical phase and amplitude of the light in the near ultraviolet region occurs, resulting in a sharp decrease of optical absorption down to about only 10% in the 250-400 nm spectral region. To improve the optical absorption in the short ultraviolet wavelength region without a reduction of absorption in the 400-2500 nm wavelength region, therefore, a 6-layered metal/dielectric structure has been studied with the device structure shown in Fig. 1.

 figure: Fig. 1

Fig. 1 Schematic structure of the six-layered metal/dielectric device consisting of SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51. 4 nm)/Cu(>100 nm).

Download Full Size | PDF

In simulations, the thick Cu layer(> 100 nm) was chosen as the optical reflection layer deposited on a Si or K9-glass substrate. To achieve the best optical constant matching of the materials, the transition metal Ti and the dielectric SiO2 were chosen as the optical absorption and interference layers [16], respectively, as seen in Fig. 1. The optimized parameters for layer thickness in the structure were given in simulations as: SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51.4 nm)/Cu(>100 nm). Under the physical law of photon energy conservation, the general condition T + R + A = 1 should be satisfied, where T, R and A represent the transmittance, reflectance and absorptance of the light entering the material and structure, respectively, implying that under ideal conditions, the solar absorber device should have T = 0, R = 0 and A = 1. In the study, the absorptance A can be deduced from the calculation of T and R in the simulations. In terms of the rigorous transfer matrix approach based on Maxwell’s equations and at normal incidence, the calculated spectra of the optical absorptance A of the 6-layered structure with a comparison to that of the 4-layered structure [6] are shown in Fig. 2, indicating that the absorption in the near ultraviolet 250-400 nm wavelength region is significantly enhanced for the 6-layered structure. The calculated spectra of T, R and A for the 6-layered structure are shown in Fig. 3, indicating that both the transmittance T and reflectance R are very low, satisfying energy conservation with a very high optical absorption, averaging about 98.4%, achieved in the 250-1200 nm wavelength region according to the definition of the average absorption Aaverage which is not dependant on the intensity of the incident light in this work as:

 figure: Fig. 2

Fig. 2 The calculated spectrum of the optical absorption of the 6-layered structure: SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51.4 nm)/Cu(>100 nm) (black), compared to that of the 4-layered structure [7] (red).

Download Full Size | PDF

 figure: Fig. 3

Fig. 3 Calculated spectra of transmittance T, reflectance R and absorptance A of the 6-layered structure at normal incidence. The inset shows the zoomed spectrum of absorptance A.

Download Full Size | PDF

Aaverage=1Nn=1NA(λn)

The calculated spectrum of reflectance R in the region extending to a wavelength of 25000 nm, with comparison to the ideal reflectance spectrum is shown in Fig. 4, indicates that the reflection is very low in the 250-1200 nm wavelength region, and then increases rapidly in the 2000-3000 nm wavelength region, reaching about 96% at a wavelength of about 9000 nm. This spectral feature will be helpful for a selective solar absorber device having the property of low thermal emittance in practical applications.

 figure: Fig. 4

Fig. 4 Calculated spectrum of reflectance R of the 6-layered metal/dielectric film structure in the 250-250000 nm wavelength region at normal incidence with a comparison to the ideal reflectance spectrum of the selective solar absorber device.

Download Full Size | PDF

3. Experimental details

The samples, consisting of a 6-layered metal/dielectric film structure, were fabricated by sputtering in a Leybold LAB600SP chamber at room temperature. The metal and dielectric films were deposited by DC and RF magnetron sputtering, with a background pressure of 6.0 × 10−6 mbar, onto optically polished Si or K9-glass substrates, respectively, from targets of 99.99% purity. To control and adjust the layer thickness, the sputtering rate of each material was calibrated in advance under the condition in which the fixed sputtering power is 60 W for SiO2 and 50 W for Cu and Ti with a fixed Argon gas flow rate (70 sccm) to keep the sputtering rate stable. The sputtering rate for the SiO2 layer was calibrated by using an ellipsometer to measure precisely its thickness, and that for the thin Ti layer was calibrated by measuring the transmittance spectrum in the visible region.

Based on energy conservation, i.e., A + R + T = 1, the spectrum of absorptance A can be reliably determined by measuring the spectra of transmittance T and reflectance R. Due to the thick Cu layer’s acting as the optical reflector in the structure, the light intensity transmitted through the sample is very low, implying that T ≈0 in the measurement. The intensity of the light reflected under nearly normal incidence was measured by using a spectrometer (UV-VIS-NIR spectrometer, Shimadzu 3600) and a Fourier-transform infrared spectrometer (Nicolet Nexus 470 FT-IR spectrometer) in the 250-2500 nm and 1.0-25 μm wavelength regions, respectively. In terms of the spectra of the reflectance R, therefore, the spectra of the absorptance A were obtained from A ≈1 - R. The incidence-angle-dependent reflectance spectra were measured by using a VASE ellipsometer (Woollam VB-400).

The thermal stability of absorptance of the sample was also analyzed by annealing the sample up to the temperature 723K in the Leybold LAB600SP chamber with a background pressure of 6.0 × 10−6 mbar for 6 hours. The spectra of absorptance before and after annealing process were measured under the same nearly normal incidence condition.

4. Results and discussions

The experimental results of the optical transmittance T, reflectance R and absorptance A of the sample are shown in Fig. 5, indicating that the sample with the 6-layered metal/dielectric film structure has high optical absorption, averaging about 98.3% in the 250-1200 nm wavelength region. As seen in the inset of Fig. 6, the sample deposited on the optically polished Si substrate, with a size of about 10 × 20 mm2, shows a deep black color on the surface, implying high optical absorption characteristics of the sample in the entire visible region. The experiment results are in good agreement with the simulated absorption (98.4%) as seen in the data comparison in Fig. 6.

 figure: Fig. 5

Fig. 5 The measured spectra of the transmittance T, reflectance R and absorptance A for the 6-layered metal/dielectric film sample in the 250-1200 nm wavelength region. The inset shows the zoomed spectrum of reflectance R.

Download Full Size | PDF

 figure: Fig. 6

Fig. 6 The experimental optical absorptance is in good agreement with the simulated one in the 250-1200 nm wavelength region. The sample deposited on the Si substrate, with a size of about 10 × 20mm2, shows a deep black color on the surface, agreeing with the high optical absorption characteristics of the sample in the entire visible region. The inset shows the zoomed spectra of absorptance A.

Download Full Size | PDF

The reflectance spectrum of the sample was measured at near-normal incidence in the 250-25000 nm wavelength region with the results shown in Fig. 7.As seen, and in agreement with the simulation data, the reflectance R is very low in the 250-1200 nm wavelength region, and increases rapidly near the cut-off wavelength at about 2500 nm.

 figure: Fig. 7

Fig. 7 Data comparison between the measured and simulated spectra of reflectance R in the 250-25000 nm wavelength region indicates that the optical reflection of the sample is very low in the 250-1200 nm wavelength region and high in the infrared region, especially as the wavelength increases to the value above 3000 nm.

Download Full Size | PDF

The absorptance α of the solar absorber device also can be evaluated by taking the weight of the solar radiation into consideration under the normal incidence angle condition as [1, 2]:

α=λ1λnA(λ)Lsun(λ)dλλ1λnLsun(λ)dλ,
where Lsun is the solar radiation incident on the device. If the absorptance A is uniformly distributed in the certain wavelength region, then AaverageAα, otherwise, the absorptance α reduced by using Eq. (2) will have different values, depending on the spectral pattern of solar radiation. The evaluated absorptance α by taking integral in the certain and entire 250-3000 nm wavelength region is shown in Table 1, in which λ1 = 250nm, λn = 400nm, 1200nm, 3000nm, respectively.

Tables Icon

Table 1. Evaluated Absorptance α in Different Spectral Regions for AM0 and AM1.5 Spectra, Respectively, by Using Eq. (2)

It is clear to see that, though there are some differences, the value of α integrated by taking the weight of solar radiation into consideration is closely equal to Aaverage in the 250-400 nm and 250-1200nm region, respectively, since the absorptance A is quite uniformly distributed and not significantly dependent on the spectral pattern of solar radiation in those regions. However, the absorption α integrated in the 250-3000nm region is reduced by about 2-3%, arising from the higher and non-uniformly distributed reflectance R in the 1200-3000nm wavelength region as shown in Fig. 7, indicating that there is a room for further improvement of optical performance of the device in the 1200-3000nm region in the future.

The angle-dependent characteristics of the reflectance R(θ, λ) are also simulated and measured under the non-polarized condition. As shown in Fig. 8, the measured reflectance spectra of R(θ, λ) are in good agreement with the simulated ones in the 250-1200 nm wavelength region by changing the incidence angle from 20° to 75° . In terms of the spectra of R(θ, λ),it can be seen that the absorptance is higher at the small incidence angle condition and decreases with the increasing of the incident angle. Although the absorptance decreases with the incidence angle, it still can achieve a higher value > 50% in the entire spectral region even at the higher incidence angle of 75°.

 figure: Fig. 8

Fig. 8 The simulated (a) and measured (b) reflectance spectra of R(θ, λ) are compared in the 250-1200 nm wavelength region by changing the incidence angle from 20° to 75°, and show good agreement with each other.

Download Full Size | PDF

The thermal emittance ε is also a critical parameter used to evaluate the performance of solar absorber devices, since a device with high emittance at its normal working temperature will have low efficiency in the photon-to-heat conversion process by re-radiation of the thermal energy, especially in the infrared region [12]. The emittance parameter, ε(θ, T), is a function of the incident angle θ and temperature T, especially in the long wavelength (λ) region, and can be evaluated based on the reflection spectrum R and Planck’s black-body radiation E(T, λ) spectrum [8]:

ε(θ,T)=0E(T,λ)[1R(θ,λ)]dλ0E(T,λ)dλ,
where

E(T,λ)=8πhcλ5[exp(hc/λkBT)1]1.

In terms of Eqs. (3) and (4), by using the measured reflectance R(0, λ) and under the assumption that the optical properties of the pure metals Ti and Cu and dielectric material SiO2 are not changed significantly in the temperature range which is much lower than the melting point [17], the emittance ε(0, T) is found with the results shown in Table 2, and is equal to about 0.063 at T = 500K, indicating that the energy loss due to thermal radiation will be very low in the photon-to-heat conversion process.

Tables Icon

Table 2. Thermal Emittance ε(0, T) as a Function of Temperature Based on Near-normal Reflectance Measurements

The total hemispherical thermal emittance εthermal is defined as [4]:

εthermal(T)=0π/2ε(θ,T)sin(2θ)dθ.

In terms of the calculated R(θ, λ) and Eqs. (3)-(5), both thermal emittance ε(0, T) and εthermal(T) are calculated with the results shown in Table 3.

Tables Icon

Table 3. Calculated Emittance ε(0, T) and εthermal(T) of the 6-layered Metal/Dielectric Film Structure

The characteristic of thermal stability also should be evaluated for any solar absorber device in practical applications. The sample was annealed at temperatures up to 723K (450° C) in vacuum of 1 × 10−6 mbar for 6 hours. After the heat-treatment process, no remarkable change has been found on the sample surfaces through macroscopic observation. The spectra of reflectance measured before and after annealing in the 250-25000 nm wavelength region are almost identical as shown in Fig. 9, indicating that the sample consisting of the 6-layered metal/dielectric film structure has good thermal stability and can be applied as a selective solar absorber device under higher temperature conditions.

 figure: Fig. 9

Fig. 9 The reflectance spectra of the sample measured in the 250-25000 nm wavelength region before and after annealing at temperature 723K (450° C) are almost identical, indicating good thermal stability for the sample to work under higher temperature condition.

Download Full Size | PDF

Finally, the sensitivity of the absorptance to the layer thickness of the 6-layered structure is analyzed. The absorptance is not very sensitive to the thickness of the thicker Cu layer which acts as an optical reflector deposited on the substrate, but is sensitive to the optically absorbing Ti layer, especially for the thinner Ti layer with optimal thickness of 5.7 nm in calculation. It can be seen in Fig. 10 that about 0.5-1% of absorptance change will happen by varying the thickness of about 1nm for the thinner Ti layer. By using the Leybold sputtering system with calibration procedure, the layer thickness was controlled with a precision of about 0.1nm to make the average absorptance uncertainty be controlled within about 0.1%. This is confirmed by the data in good agreement between the simulated and measured absorptance as shown in Fig. 6.

 figure: Fig. 10

Fig. 10 The layer thickness of the thinner Ti layer is changed by about 1nm in data simulation, resulting in the absorptance variation of about 0.5-1%.

Download Full Size | PDF

5. Conclusion

In order to achieve significant enhancement of solar absorption, especially in the ultraviolet 250-400 nm wavelength region where about 8% of the solar radiation can be effectively absorbed, in this work a six-layered metal/dielectric film structure has been proposed and studied. The sample has the typical layered structure: SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51.4 nm)/Cu(>100 nm), deposited on optically polished Si or K9 glass substrates. The simulated and experimental data are in good agreement with each other, showing that the sample has high and uniform optical absorption, an average of > 98% in the 250-1200 nm wavelength region. The sample of the 6-layered metal/dielectric film structure has an AM1.5G solar absorptance of 95.5% with the features of low thermal emittance of 0.136 at 700K and good thermal stability, and will be potentially suitable for practical application as a highly efficient solar absorber device in many fields.

Acknowledgment

We thank Wei Shi and Juan-Juan Wang for support of the reflectance measurement. This work was supported by the National Science Foundation (NSF) project of China under contract numbers: #60938004 and #61427815.

References and links

1. P. Bermel, J. Lee, J. D. Joannopoulos, I. Celanovic, and M. Soljačie, “Selective solar absorbers,” in Annual review of the heat transfer, Ch. 7, P. 231 (2012).

2. F. Cao, K. McEnaney, G. Chen, and Z. Ren, “A review of cermet-based spectrally selective solar absorbers,” Energy and Environment Science 7(5), 1615 (2014). [CrossRef]  

3. C. E. Kennedy, “Review of mid- to high-temperature solar selective absorber materials,” Report, National Renewable Energy Laboratory, Golden, Colorado (2002).

4. N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express 17(25), 22800–22812 (2009). [CrossRef]   [PubMed]  

5. N. P. Sergeant, M. Agrawal, and P. Peumans, “High performance solar-selective absorbers using coated sub-wavelength gratings,” Opt. Express 18(6), 5525–5540 (2010). [CrossRef]   [PubMed]  

6. W. X. Zhou, Y. Shen, E. T. Hu, Y. Zhao, M. Y. Sheng, Y. X. Zheng, S. Y. Wang, Y. P. Lee, C. Z. Wang, D. W. Lynch, and L. Y. Chen, “Nano-Cr-film-based solar selective absorber with high photo-thermal conversion efficiency and good thermal stability,” Opt. Express 20(27), 28953–28962 (2012). [CrossRef]   [PubMed]  

7. X. F. Li, Y. R. Chen, J. Miao, P. Zhou, Y. X. Zheng, L. Y. Chen, and Y. P. Lee, “High solar absorption of a multilayered thin film structure,” Opt. Express 15(4), 1907–1912 (2007). [CrossRef]   [PubMed]  

8. D. M. Trotter Jr and A. J. Sievers, “Spectral selectivity of high-temperature solar absorbers,” Appl. Opt. 19(5), 711–728 (1980). [CrossRef]   [PubMed]  

9. D. R. Mills, “Limits of solar selective surface performance,” Appl. Opt. 24(20), 3374–3380 (1985). [CrossRef]   [PubMed]  

10. Q. C. Zhang and D. R. Mills, “New cermet film structures with much improved selectivity for solar thermal applications,” Appl. Phys. Lett. 60(5), 545–547 (1992). [CrossRef]  

11. J. Meiss, M. Furno, S. Pfuetzner, K. Leo, and M. Riede, “Selective absorption enhancement in organic solar cells using light incoupling layers,” J. Appl. Phys. 107(5), 053117 (2010). [CrossRef]  

12. P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, S. G. Johnson, and I. Celanovic, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18(S3Suppl 3), A314–A334 (2010). [CrossRef]   [PubMed]  

13. C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express 19(S5Suppl 5), A1148–A1154 (2011). [CrossRef]   [PubMed]  

14. C. H. Lin, R. L. Chern, and H. Y. Lin, “Polarization-independent broad-band nearly perfect absorbers in the visible regime,” Opt. Express 19(2), 415–424 (2011). [CrossRef]   [PubMed]  

15. K. D. Olson and J. J. Talghader, “Absorption to reflection transition in selective solar coatings,” Opt. Express 20(S4Suppl 4), A554–A559 (2012). [CrossRef]   [PubMed]  

16. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

17. D. X. Zhang, B. Shen, Y. X. Zheng, S. Y. Wang, J. B. Zhang, S. D. Yang, R. J. Zhang, L. Y. Chen, C. Z. Wang, and K. M. Ho, “Evolution of optical properties of tin film from solid to liquid studied by spectroscopic ellipsometry and ab initio calculation,” Appl. Phys. Lett. 104(12), 121907 (2014). [CrossRef]  

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1 Schematic structure of the six-layered metal/dielectric device consisting of SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51. 4 nm)/Cu(>100 nm).
Fig. 2
Fig. 2 The calculated spectrum of the optical absorption of the 6-layered structure: SiO2(57.3 nm)/Ti(5.7 nm)/SiO2(67.1 nm)/Ti(11.6 nm)/SiO2(51.4 nm)/Cu(>100 nm) (black), compared to that of the 4-layered structure [7] (red).
Fig. 3
Fig. 3 Calculated spectra of transmittance T, reflectance R and absorptance A of the 6-layered structure at normal incidence. The inset shows the zoomed spectrum of absorptance A.
Fig. 4
Fig. 4 Calculated spectrum of reflectance R of the 6-layered metal/dielectric film structure in the 250-250000 nm wavelength region at normal incidence with a comparison to the ideal reflectance spectrum of the selective solar absorber device.
Fig. 5
Fig. 5 The measured spectra of the transmittance T, reflectance R and absorptance A for the 6-layered metal/dielectric film sample in the 250-1200 nm wavelength region. The inset shows the zoomed spectrum of reflectance R.
Fig. 6
Fig. 6 The experimental optical absorptance is in good agreement with the simulated one in the 250-1200 nm wavelength region. The sample deposited on the Si substrate, with a size of about 10 × 20mm2, shows a deep black color on the surface, agreeing with the high optical absorption characteristics of the sample in the entire visible region. The inset shows the zoomed spectra of absorptance A.
Fig. 7
Fig. 7 Data comparison between the measured and simulated spectra of reflectance R in the 250-25000 nm wavelength region indicates that the optical reflection of the sample is very low in the 250-1200 nm wavelength region and high in the infrared region, especially as the wavelength increases to the value above 3000 nm.
Fig. 8
Fig. 8 The simulated (a) and measured (b) reflectance spectra of R(θ, λ) are compared in the 250-1200 nm wavelength region by changing the incidence angle from 20° to 75°, and show good agreement with each other.
Fig. 9
Fig. 9 The reflectance spectra of the sample measured in the 250-25000 nm wavelength region before and after annealing at temperature 723K (450° C) are almost identical, indicating good thermal stability for the sample to work under higher temperature condition.
Fig. 10
Fig. 10 The layer thickness of the thinner Ti layer is changed by about 1nm in data simulation, resulting in the absorptance variation of about 0.5-1%.

Tables (3)

Tables Icon

Table 1 Evaluated Absorptance α in Different Spectral Regions for AM0 and AM1.5 Spectra, Respectively, by Using Eq. (2)

Tables Icon

Table 2 Thermal Emittance ε(0, T) as a Function of Temperature Based on Near-normal Reflectance Measurements

Tables Icon

Table 3 Calculated Emittance ε(0, T) and εthermal(T) of the 6-layered Metal/Dielectric Film Structure

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

A average = 1 N n=1 N A( λ n )
α= λ 1 λ n A(λ) L sun (λ)dλ λ 1 λ n L sun (λ)dλ ,
ε(θ,T)= 0 E(T,λ)[1R(θ,λ)] dλ 0 E(T,λ)dλ ,
E(T,λ)= 8πhc λ 5 [ exp( hc / λ k B T )1 ] 1 .
ε thermal (T)= 0 π/2 ε(θ,T)sin(2θ)dθ .
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.