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Graphene-based highly efficient and broadband solar absorber
Optical Materials 96 (2019) 109330
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Graphene-based highly efficient and broadband solar absorber a,b,∗
Shobhit K. Patel Tianjing Guob a b c
a
c
a
T c
, Shreyas Charola , Charmy Jani , Mayurkumar Ladumor , Juveriya Parmar ,
Electronics and Communication Department, Marwadi University, Rajkot, 360003, India Electrical and Computer Engineering Department, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA Physics Department, Marwadi University, Rajkot, 360003, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene Absorber Solar Broadband Efficient
We propose graphene-based solar absorber for broadband absorption response. The absorber is designed by sandwich graphene layer between the dielectric layer and resonator layer. The use of graphene layer improves the absorption in the dielectric layer. The design results in the form of absorption, reflection and normalised electric field are analysed for graphene-based design and simple design (without graphene layer). The design with the graphene layer is giving better absorption behaviour in the range of 100 THz to 1600 THz. The design results are also analysed for the different physical design parameters like gold resonator width (G_W), silver resonator width (S_W), gold dielectric layer height (G_H) and total structure width (W). The increase in the gold resonator and silver resonator width reduces the absorption and increase in height of gold dielectric layer increases the absorption. The designed structure is absorbing not only visible energy but also infrared energy and ultraviolet energy. The designed graphene-based broadband solar absorber is applicable in solar energy harvesting, light trapping and photovoltaic devices.
1. Introduction Optical materials are gaining interest in the research community due to their attractive properties, which include controlling or altering electromagnetic radiations in ultraviolet, visible and infrared regions. These materials are used as reflectors, transmitters, refractors, dispersers, polarisers, detectors, and modulators. Electromagnetic absorbers are applicable in the design of plasmonic thin-film solar cells with its broadband absorption enhancement [1]. They are applicable in sensing [2] and solar thermal photovoltaic device applications [3]. There are mainly two types of the electromagnetic absorber. The two types are resonant absorber and broadband absorber. The resonant absorber is frequency dependent and provides absorption at the resonant frequency, where as the broadband absorber which provides very large frequency absorption [4]. The electromagnetic absorber is designed for a different range of frequencies in the range of microwave [5]. infrared [6,7], visible [8–10], and terahertz [11–14]. Terahertz absorber is presented by simply staking the double layer graphene metasurface at different geometric dimensions this single frequency absorption reaches up to 99.51% at 2.71 THz [15]. Plasmonic metamaterial based on Au/SiO2 absorber is presented in Ref. [16], which has a broadband visible range
∗
of frequency. Absorption depends on the function of shape, dimension, and arrangement of materials. Perfect absorption in the visible region is also achieved using metal-dielectric-metal structured designed using Cu/Si3N4/Cu. It provides 80% average of absorption in the visible range 400–700 nm [17]. The polarization insensitive absorption in the mid-infrared wavelength is designed using a genetic algorithm with super-octave bandwidth [18]. Metamaterial has shown great potential in many scientific and technical application due to its perfect absorption characteristic. Gradient metasurface with a single layer and dual layer respectively got absorption of 50% and 95% respectively in the infrared region [19]. A narrow layer distance of dual-band terahertz absorber based on two pair of an Au strip/dielectric layer is designed [20]. Metasurface based solar absorber using circular gold resonator is presented and it is showing its absorption characteristics in the infrared region 155 THz to 428 THz. It is also further analysed in the region to 155 THz to 1595 THz in infrared, visible and ultraviolet [21]. The plasmonic biomimetic nanocomposite with spontaneous wavelength broadband absorber is designed [22]. Achieved broadband absorption by 90% of the light from the ultraviolet to the infrared part of the spectrum. Crossshaped gold nanorods based design has provided multiband absorption resonance over the entire solar spectrum [23]. The conductivity of the
Corresponding author. Electronics and Communication Department, Marwadi University, Rajkot, 360003, India. E-mail address: [email protected] (S.K. Patel).
https://doi.org/10.1016/j.optmat.2019.109330 Received 1 July 2019; Received in revised form 1 August 2019; Accepted 16 August 2019 0925-3467/ © 2019 Published by Elsevier B.V.
Optical Materials 96 (2019) 109330
S.K. Patel, et al.
bulk-Dirac-semimetal (BDS) layer is changed by applying biasing potential [24]. Graphene-metal metasurface based tunable frequency selective surface (FSS) absorber is designed using random-hill climbing (RHC) algorithm to achieve broadest bandwidth absorption [25]. Plasmonic graphene-based absorber having three geometrical variant structure is characterized to get total absorption of the unit cell [26]. Terahertz broadband absorber with eight gold nanoresonator provides a wide-angle absorption in near infrared region [27]. Metamaterial solar absorber provides up to 80–90% absorption of the solar spectrum [28]. Metamaterial absorber is designed for near infrared and visible spectrum using the silicon-chromium-silica layer to have absorption characteristics in 0.4–1.4 μm wavelength [29]. Ultra-broadband and polarization independent metamaterial are designed using circular ringshaped resonator to achieve 95.5% absorption in all solar spectrum [30]. Terahertz broadband absorber with four layers metallic gold ring is designed to have polarization insensitive characteristics [31]. Metamaterial absorber with square shape structure is investigated to provide broadband absorption [32].
ε (ω) = 1 +
σs ε 0 ω▵
(1)
σintra =
μ −je 2kB T ⎛ μc − c ⎜ + 2 ln ⎛e kB T + 1⎞ ⎞⎟ π ℏ2 (ω − j2Γ) ⎝ kB T ⎝ ⎠⎠
(2)
σinter =
−je 2 ⎛ 2 μc − (ω − j2Γ)ℏ ⎞ ln ⎜ ⎟ 4π ℏ ⎝ 2 μc + (ω − j2Γ)ℏ ⎠
(3) (4)
σs = σinter + σintra
Where different parameters are defined as, ε0 = vacuum permittivity, σs = conductivity, e = electron charge, ω = angular frequency, kB = Boltzmann's constant and ℏ = reduced Planck's constant. Graphene's optical conductivity is controlled by giving different graphene chemical potential (0.1eV–0.6 eV). Graphene's chemical potential is given by μC = ℏvF πCVDC / e , VDC -gate voltage, the capacitance is given by C = εd ε0/ t , εd - dielectric layer static permittivity, tdielectric layer thickness. The effectiveness of absorption is very important and is measured over here by the following equations [34]:
2. Design and modelling Graphene based metasurface solar absorber is presented in Fig. 1. The absorber is created by placing square and plus shape layers over graphene which is placed on SiO2 substrate. The 3D view of the design and 2D view of the design are presented in Fig. 1(A) and (B) respectively. The silver, gold and graphene layer combination helps in concentrating the light inside. The light is absorbed in the gold layer placed below SiO2 layer. This absorption of energy is used in solar energy harvesting and photovoltaic energy conversion. The graphene material is an atom layer thick sheet with the conductivity σs given by equations (1)–(4) [33].
A (ω) =
Qabs (ω) Qinc (ω)
Qabs =
ωε0 2
∫ Im [ε(ω)]
(5)
E 2 dV
V
Qinc = S F (ω) tot Qabs =
∫
A (ω) F (ω) dω
(6) (7) (8)
where A(ω) = Optical absorption, Qabs = Spectral power absorbed by each element, Qinc = Spectral power coming from sun and incident on tot the solar surface, Qabs = Total power absorbed. It is very important to add other two material layers in such a way that it minimizes reflection and transmission of incident electromagnetic radiations and increases the absorptions as absorption is
A (ω) = 1 − R (ω) − T (ω)
(9)
WhereR (ω) , T (ω) represent frequency(ω) dependent reflection and transmission. In addition R (ω) , T(ω) can be expressed as R (ω) = S11 2 and T(ω) = S21 2 . The efficiency of the metasurface absorber can be increased as reflection and transmission rate are reduced. In this work, the ground plane is thick and made of tungsten to stop the reflections of sunlight from device. It prothe duced transmission near close to zero (T (ω) ≈0) for the ground plane and the refractive index of tungsten can be obtained as given in Ref. [36]. The plus-shaped and square shape metasurface layer is added at the top of the graphene layer to improve absorption of the structure. The absorber parameters are enhanced by incorporating metasurface resonating layers [21]. 3. Results and discussions The graphene-based metasurface solar absorber design presented in Fig. 1 is analysed using COMSOL Multiphysics. Two designs (with graphene and without graphene) are analysed. The results in the form of Absorption, Reflectance, Electric field are presented in Fig. (2-6). The results in the form of reflectance and absorption are presented for the frequency range of 200 THz to 1600 THz in Fig. 2 and Table 1. The comparative analysis of absorption achieved in the different frequency ranges for proposed graphene design, simple design and design from Refs. [35–38] is presented in Table 1. The total absorption of the graphene-based design is achieved 92.72% and without graphene layer is achieved 89.9%. The highest absorption of 97.51% is achieved in the visible range for graphenebased solar absorber design. This indicates that the graphene layer placed above the SiO2 layer and gold layer keeps all the rays inside the
Fig. 1. Graphene-based metasurface solar absorber design. (A) Three-dimensional view (B) Two-dimensional view. Square Gold and plus shape silver particles are placed over a thin graphene layer with SiO2 and Gold base layer. Height and width of Silver and gold layer are H=S_W = G_W = 150 nm. Height of the SiO2 layer is S_H = 150 nm. Height of Gold layer is G_H = 150 nm. Total structure length and width W = 800 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 2
Optical Materials 96 (2019) 109330
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Fig. 2. Absorption and Reflectance results of Solar absorber design with and without graphene layer. (A) Absorption without Graphene layer (B) Absorption with the Graphene layer (C) Reflectance without Graphene layer (D) Reflectance with the Graphene layer.
Fig. 4. Graphene-based solar absorber design with variation in the width of silver material (S_W) from 100 nm to 200 nm. (A) Absorption result and (B) Reflectance result. Redcolour indicate the highest value and blue colour indicate the lowest values. It is evident that absorption is higher for the range of 400 THz to 1600 THz range with maximum values are achieved in the middle range. There is a small variation in absorption result by changing the silver material width. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 3. Graphene-based solar absorber design with variation in the width of gold material (G_W) from 150 nm to 250 nm. (A) Absorption result and (B) Reflectance result. Red colour indicate the highest value and blue colour indicate the lowest values. It is evident that absorption is higher for the range of 300 THz to 1600 THz range with maximum values are achieved in the middle range. There is a reduction in absorption by increasing the gold resonator width (G_W). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
3
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S.K. Patel, et al.
Fig. 5. Graphene-based solar absorber design with variation in the height of gold material (G_H) for the range of 150 nm–250 nm (A) Absorption result for design without Graphene material (B) Absorption result for design with Graphene material (C) Reflectance result for design without Graphene material (D) Reflectance result for design with Graphene material. Red colour indicates the highest value and blue colour indicate the lowest values. The absorption values are higher for design with graphene material. The design with graphene material has absorption values higher above 250 THz for the whole range. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
graphene-based solar absorber design. In all other regions, the graphene-based solar absorber design is showing far better absorption compared to design without graphene. The reflectance is minimum throughout the frequency range of 200 THz to 1600 THz.
substrate layer and thus absorption is enhanced. Thick gold layer blocks all the radiation inside the absorber layer and does not pass it through. In the ultraviolet region, the performance of solar absorber design without graphene is showing better absorption compared to the
Fig. 6. Graphene-based solar absorber design with variation in the total structure width (W) from 500 nm to 100 nm (A) Absorption result for design without Graphene material (B) Absorption result for design with Graphene material (C) Reflectance result for design without Graphene material (D) Reflectance result for design with Graphene material. Red colour indicates the highest value and blue colour indicate the lowest values. The absorption and reflectance values are almost similar and there is no change evident from the result. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 4
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Table 1 Comparative analysis of absorption for infrared, visible, ultraviolet and whole solar spectrum range. Design
Infrared Range Absorption (%)
Visible Range Absorption (%)
Ultraviolet Range Absorption (%)
Whole solar range (100 THz to 1600 THz) (%)
Proposed design With Graphene layer Proposed design without Graphene layer Broadband design of Ref. [35] Graphene based Design of Ref. [36] Graphene based design of Ref. [37] Graphene based design of Ref. [38]
85.48 71.84 79.67 – –
97.51 92.80 93.7 70 93 71.1
89.57 93.49 92.3 – – –
92.72 89.80 88.4 – 90 –
Table 2 Comparison of Ag resonator design, Au resonator design and our proposed design (Au and Ag both). Design
Infrared Range Absorption (%)
Visible Range Absorption (%)
Ultraviolet Range Absorption (%)
Whole solar range (100 THz to 1600 THz) (%)
Proposed design With Ag and Au resonator Ag resonator design from Ref. [39] Au resonator design from Ref. [21]
85.48 – –
97.51 80 92
89.57 – –
92.72 – 89
use of graphene increases the absorption of the design. The use of graphene also gives the ability to tune the response of the design. The wide wavelength absoprtion is very necessary in the solar absorber [42–45]. In the proposed design the wide wavelenght absorption is achieved using the gold and silver resonator based on the graphene design. The wide wavelength behaviour of solar absorber by changing different physical parameters of the design is presented in Fig. (3-6). Absorption property of the solar absorber design is changed by changing various design parameters of the design. The design parameters like the width of the gold resonator (G_W), width of the plus resonator (S_W), gold absorber layer height (G_H) and total absorber structure width (W) are varied to check the absorber behaviour. The width of the gold resonator (G_W) is varied from 150 nm to 250 nm to check the absorption behaviour of the design. Width of the gold resonator is very important because Increasing the width of the gold resonator layer will cover the substrate layer fully and absorption in the substrate layer is reduced. The results are shown in Fig. 3 clearly indicate that the higher values of width decrease the absorption of the design. The reflectance is increased by increasing the width values of gold resonator because the gold resonator layer covers most of the substrate part and thus the reflectance is increased. The results in the form of absorption and reflectance for different width size of plus metasurface silver resonator is presented in Fig. 4. The plus metasurface width is increased from 100 nm to 200 nm to check the reflectance and absorption behaviour. The increase in width makes the gap between the gold resonator and silver resonator negligible and it also overlaps at a certain point. This increase will make a rectangular sheet of gold and silver resonator. This rectangular sheet reduces the absorption of substrate layers. From the results, it is clear that over 175 nm width level, the absorption results reduce for the whole range. To observe the effect in absorption and reflectance with different height of the bottom layer (G_H) from 150 nm to 250 nm by keeping all other parameters constant is shown in Fig. 5. As shown in Fig. 5, by increasing the height of bottom layer which helps in reducing the transmission of incoming EM wave. From the results, the broadband absorption is observed more in graphene-based design absorber beyond 250 THz. As shown in Fig. 6, the width (W) of the whole design is increased from 500 nm to 1000 nm to check the effect of absorption and reflectance. The results from Fig. 6 has no effect on reflectance and absorption with a change in the width of the proposed absorber. This clearly indicates that there is no relationship of absorption with the total width of the design. The absorption result is better for graphenebased design. The normalised electric field results for the frequencies 600 THz,
Fig. 7. Normalised Electric Field for the frequency of (A) 600 THz (B) 800 THz (C) 1000 THz (D) 1200 THz (E) 1400 THz (F) 1600 THz. Red colour indicates the maximum field intensity and blue colour indicates minimum electric field intensity. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Our Proposed design is based on Au and Ag resonators. The use of Ag and Au resonators give better absorption which is given in comparative Table 2. In this table the comparison of Ag resonator design [39], Au resonator design [40] and our proposed design is presented. The proposed design is better in terms of absorption as it is giving the best absorption in Visible as well as overall spectrum. Graphene design presented in Refs. [36–41] clearly show that the 5
Optical Materials 96 (2019) 109330
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800 THz, 1000 THz, 1200 THz, 1400 THz, and 1600 THz is presented in Fig. 7. The results indicate that energy concentration in the plus shape silver resonator is clear from the results. It is very important to show how to improve the absorption further [46]. The absorption of the design can be further improved by varying the graphene chemical potential. The absorption spectrum can be tuned by changing the graphene chemical potential.
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4. Conclusion In conclusion, a graphene-based broadband solar absorber using silver and gold structure is proposed and investigated from 100 THz to 1600 THz. The average absorption is 85.48% in infrared, 97.51% in visible, 89.57% in the ultraviolet region and 92.72% absorption in the whole solar spectrum is obtained. The resonators made up of silver and gold material placed above the dielectric layer with the sandwich graphene layer. The design with the graphene layer gives more absorption compared to design without the graphene layer. The maximum absorption of 97.51% is achieved for the graphene-based solar absorber design. The variation of the absorption band is achieved by changing the different parameters of physical structure (width of gold material (G_W), the width of silver material (S_W), the height of gold material (G_H), total structure width (W)). The proposed graphene-based broadband solar absorber has the potential to become future building blocks light trapping and energy harvesting devices. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was partially supported by the Office of Research and Economic Development at University of Nebraska-Lincoln, USA, Nebraska EPSCoR, NSF Nebraska MRSEC and Marwadi Education Foundation's Group of Institutions, Rajkot. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optmat.2019.109330. References [1] R.A. Pala, J. White, E. Barnard, J. Liu, M.L. Brongersma, Design of plasmonic thinfilm solar cells with broadband absorption enhancements, Adv. Mater. 21 (34) (2009) 3504–3509. [2] V. Dave, V. Sorathiya, T. Guo, S.K. Patel, Graphene-based tunable broadband farinfrared absorber, Superlattice Microstruct. 124 (2018) 113–120. [3] A. Lenert, D.M. Bierman, Y. Nam, W.R. Chan, I. Celanović, M. Soljačić, E.N. Wang, A nanophotonic solar thermo photovoltaic device, Nat. Nanotechnol. 9 (2) (2014) 126. [4] C.M. Watts, X. Liu, W.J. Padilla, Metamaterial electromagnetic wave absorbers, Adv. Mater. 24 (23) (2012) OP98–OP120. [5] S.K. Patel, Y.P. Kosta, Metamaterial superstrate-loaded meandered microstrip-based radiating structure for bandwidth enhancement, J. Mod. Opt. 61 (11) (2014) 923–930. [6] Y. Avitzour, Y.A. Urzhumov, G. Shvets, Wide-angle infrared absorber based on a negative-index plasmonic metamaterial, Phys. Rev. B 79 (4) (2009) 045131. [7] P. Ahir, S.K. Patel, J. Parmar, D. Katrodiya, Directive and tunable graphene based optical leaky wave radiating structure, Mater. Res. Express 6 (5) (2019) 055607. [8] X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, J. Tian, Polarization-insensitive and wideangle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime, J. Opt. 16 (12) (2014) 125107. [9] M.K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V.S.K. Chakravadhanula, ... M. Elbahri, Design of a perfect black absorber at visible frequencies using plasmonic metamaterials, Adv. Mater. 23 (45) (2011) 5410–5414. [10] Q. Liang, T. Wang, Z. Lu, Q. Sun, Y. Fu, W. Yu, Metamaterial‐based two-dimensional plasmonic subwavelength structures offer the broadest waveband light harvesting,
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Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Graphene-based highly efficient and broadband solar absorber a,b,∗
Shobhit K. Patel Tianjing Guob a b c
a
c
a
T c
, Shreyas Charola , Charmy Jani , Mayurkumar Ladumor , Juveriya Parmar ,
Electronics and Communication Department, Marwadi University, Rajkot, 360003, India Electrical and Computer Engineering Department, University of Nebraska-Lincoln, Lincoln, NE, 68588, USA Physics Department, Marwadi University, Rajkot, 360003, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Graphene Absorber Solar Broadband Efficient
We propose graphene-based solar absorber for broadband absorption response. The absorber is designed by sandwich graphene layer between the dielectric layer and resonator layer. The use of graphene layer improves the absorption in the dielectric layer. The design results in the form of absorption, reflection and normalised electric field are analysed for graphene-based design and simple design (without graphene layer). The design with the graphene layer is giving better absorption behaviour in the range of 100 THz to 1600 THz. The design results are also analysed for the different physical design parameters like gold resonator width (G_W), silver resonator width (S_W), gold dielectric layer height (G_H) and total structure width (W). The increase in the gold resonator and silver resonator width reduces the absorption and increase in height of gold dielectric layer increases the absorption. The designed structure is absorbing not only visible energy but also infrared energy and ultraviolet energy. The designed graphene-based broadband solar absorber is applicable in solar energy harvesting, light trapping and photovoltaic devices.
1. Introduction Optical materials are gaining interest in the research community due to their attractive properties, which include controlling or altering electromagnetic radiations in ultraviolet, visible and infrared regions. These materials are used as reflectors, transmitters, refractors, dispersers, polarisers, detectors, and modulators. Electromagnetic absorbers are applicable in the design of plasmonic thin-film solar cells with its broadband absorption enhancement [1]. They are applicable in sensing [2] and solar thermal photovoltaic device applications [3]. There are mainly two types of the electromagnetic absorber. The two types are resonant absorber and broadband absorber. The resonant absorber is frequency dependent and provides absorption at the resonant frequency, where as the broadband absorber which provides very large frequency absorption [4]. The electromagnetic absorber is designed for a different range of frequencies in the range of microwave [5]. infrared [6,7], visible [8–10], and terahertz [11–14]. Terahertz absorber is presented by simply staking the double layer graphene metasurface at different geometric dimensions this single frequency absorption reaches up to 99.51% at 2.71 THz [15]. Plasmonic metamaterial based on Au/SiO2 absorber is presented in Ref. [16], which has a broadband visible range
∗
of frequency. Absorption depends on the function of shape, dimension, and arrangement of materials. Perfect absorption in the visible region is also achieved using metal-dielectric-metal structured designed using Cu/Si3N4/Cu. It provides 80% average of absorption in the visible range 400–700 nm [17]. The polarization insensitive absorption in the mid-infrared wavelength is designed using a genetic algorithm with super-octave bandwidth [18]. Metamaterial has shown great potential in many scientific and technical application due to its perfect absorption characteristic. Gradient metasurface with a single layer and dual layer respectively got absorption of 50% and 95% respectively in the infrared region [19]. A narrow layer distance of dual-band terahertz absorber based on two pair of an Au strip/dielectric layer is designed [20]. Metasurface based solar absorber using circular gold resonator is presented and it is showing its absorption characteristics in the infrared region 155 THz to 428 THz. It is also further analysed in the region to 155 THz to 1595 THz in infrared, visible and ultraviolet [21]. The plasmonic biomimetic nanocomposite with spontaneous wavelength broadband absorber is designed [22]. Achieved broadband absorption by 90% of the light from the ultraviolet to the infrared part of the spectrum. Crossshaped gold nanorods based design has provided multiband absorption resonance over the entire solar spectrum [23]. The conductivity of the
Corresponding author. Electronics and Communication Department, Marwadi University, Rajkot, 360003, India. E-mail address: [email protected] (S.K. Patel).
https://doi.org/10.1016/j.optmat.2019.109330 Received 1 July 2019; Received in revised form 1 August 2019; Accepted 16 August 2019 0925-3467/ © 2019 Published by Elsevier B.V.
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bulk-Dirac-semimetal (BDS) layer is changed by applying biasing potential [24]. Graphene-metal metasurface based tunable frequency selective surface (FSS) absorber is designed using random-hill climbing (RHC) algorithm to achieve broadest bandwidth absorption [25]. Plasmonic graphene-based absorber having three geometrical variant structure is characterized to get total absorption of the unit cell [26]. Terahertz broadband absorber with eight gold nanoresonator provides a wide-angle absorption in near infrared region [27]. Metamaterial solar absorber provides up to 80–90% absorption of the solar spectrum [28]. Metamaterial absorber is designed for near infrared and visible spectrum using the silicon-chromium-silica layer to have absorption characteristics in 0.4–1.4 μm wavelength [29]. Ultra-broadband and polarization independent metamaterial are designed using circular ringshaped resonator to achieve 95.5% absorption in all solar spectrum [30]. Terahertz broadband absorber with four layers metallic gold ring is designed to have polarization insensitive characteristics [31]. Metamaterial absorber with square shape structure is investigated to provide broadband absorption [32].
ε (ω) = 1 +
σs ε 0 ω▵
(1)
σintra =
μ −je 2kB T ⎛ μc − c ⎜ + 2 ln ⎛e kB T + 1⎞ ⎞⎟ π ℏ2 (ω − j2Γ) ⎝ kB T ⎝ ⎠⎠
(2)
σinter =
−je 2 ⎛ 2 μc − (ω − j2Γ)ℏ ⎞ ln ⎜ ⎟ 4π ℏ ⎝ 2 μc + (ω − j2Γ)ℏ ⎠
(3) (4)
σs = σinter + σintra
Where different parameters are defined as, ε0 = vacuum permittivity, σs = conductivity, e = electron charge, ω = angular frequency, kB = Boltzmann's constant and ℏ = reduced Planck's constant. Graphene's optical conductivity is controlled by giving different graphene chemical potential (0.1eV–0.6 eV). Graphene's chemical potential is given by μC = ℏvF πCVDC / e , VDC -gate voltage, the capacitance is given by C = εd ε0/ t , εd - dielectric layer static permittivity, tdielectric layer thickness. The effectiveness of absorption is very important and is measured over here by the following equations [34]:
2. Design and modelling Graphene based metasurface solar absorber is presented in Fig. 1. The absorber is created by placing square and plus shape layers over graphene which is placed on SiO2 substrate. The 3D view of the design and 2D view of the design are presented in Fig. 1(A) and (B) respectively. The silver, gold and graphene layer combination helps in concentrating the light inside. The light is absorbed in the gold layer placed below SiO2 layer. This absorption of energy is used in solar energy harvesting and photovoltaic energy conversion. The graphene material is an atom layer thick sheet with the conductivity σs given by equations (1)–(4) [33].
A (ω) =
Qabs (ω) Qinc (ω)
Qabs =
ωε0 2
∫ Im [ε(ω)]
(5)
E 2 dV
V
Qinc = S F (ω) tot Qabs =
∫
A (ω) F (ω) dω
(6) (7) (8)
where A(ω) = Optical absorption, Qabs = Spectral power absorbed by each element, Qinc = Spectral power coming from sun and incident on tot the solar surface, Qabs = Total power absorbed. It is very important to add other two material layers in such a way that it minimizes reflection and transmission of incident electromagnetic radiations and increases the absorptions as absorption is
A (ω) = 1 − R (ω) − T (ω)
(9)
WhereR (ω) , T (ω) represent frequency(ω) dependent reflection and transmission. In addition R (ω) , T(ω) can be expressed as R (ω) = S11 2 and T(ω) = S21 2 . The efficiency of the metasurface absorber can be increased as reflection and transmission rate are reduced. In this work, the ground plane is thick and made of tungsten to stop the reflections of sunlight from device. It prothe duced transmission near close to zero (T (ω) ≈0) for the ground plane and the refractive index of tungsten can be obtained as given in Ref. [36]. The plus-shaped and square shape metasurface layer is added at the top of the graphene layer to improve absorption of the structure. The absorber parameters are enhanced by incorporating metasurface resonating layers [21]. 3. Results and discussions The graphene-based metasurface solar absorber design presented in Fig. 1 is analysed using COMSOL Multiphysics. Two designs (with graphene and without graphene) are analysed. The results in the form of Absorption, Reflectance, Electric field are presented in Fig. (2-6). The results in the form of reflectance and absorption are presented for the frequency range of 200 THz to 1600 THz in Fig. 2 and Table 1. The comparative analysis of absorption achieved in the different frequency ranges for proposed graphene design, simple design and design from Refs. [35–38] is presented in Table 1. The total absorption of the graphene-based design is achieved 92.72% and without graphene layer is achieved 89.9%. The highest absorption of 97.51% is achieved in the visible range for graphenebased solar absorber design. This indicates that the graphene layer placed above the SiO2 layer and gold layer keeps all the rays inside the
Fig. 1. Graphene-based metasurface solar absorber design. (A) Three-dimensional view (B) Two-dimensional view. Square Gold and plus shape silver particles are placed over a thin graphene layer with SiO2 and Gold base layer. Height and width of Silver and gold layer are H=S_W = G_W = 150 nm. Height of the SiO2 layer is S_H = 150 nm. Height of Gold layer is G_H = 150 nm. Total structure length and width W = 800 nm. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 2
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Fig. 2. Absorption and Reflectance results of Solar absorber design with and without graphene layer. (A) Absorption without Graphene layer (B) Absorption with the Graphene layer (C) Reflectance without Graphene layer (D) Reflectance with the Graphene layer.
Fig. 4. Graphene-based solar absorber design with variation in the width of silver material (S_W) from 100 nm to 200 nm. (A) Absorption result and (B) Reflectance result. Redcolour indicate the highest value and blue colour indicate the lowest values. It is evident that absorption is higher for the range of 400 THz to 1600 THz range with maximum values are achieved in the middle range. There is a small variation in absorption result by changing the silver material width. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 3. Graphene-based solar absorber design with variation in the width of gold material (G_W) from 150 nm to 250 nm. (A) Absorption result and (B) Reflectance result. Red colour indicate the highest value and blue colour indicate the lowest values. It is evident that absorption is higher for the range of 300 THz to 1600 THz range with maximum values are achieved in the middle range. There is a reduction in absorption by increasing the gold resonator width (G_W). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
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Fig. 5. Graphene-based solar absorber design with variation in the height of gold material (G_H) for the range of 150 nm–250 nm (A) Absorption result for design without Graphene material (B) Absorption result for design with Graphene material (C) Reflectance result for design without Graphene material (D) Reflectance result for design with Graphene material. Red colour indicates the highest value and blue colour indicate the lowest values. The absorption values are higher for design with graphene material. The design with graphene material has absorption values higher above 250 THz for the whole range. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
graphene-based solar absorber design. In all other regions, the graphene-based solar absorber design is showing far better absorption compared to design without graphene. The reflectance is minimum throughout the frequency range of 200 THz to 1600 THz.
substrate layer and thus absorption is enhanced. Thick gold layer blocks all the radiation inside the absorber layer and does not pass it through. In the ultraviolet region, the performance of solar absorber design without graphene is showing better absorption compared to the
Fig. 6. Graphene-based solar absorber design with variation in the total structure width (W) from 500 nm to 100 nm (A) Absorption result for design without Graphene material (B) Absorption result for design with Graphene material (C) Reflectance result for design without Graphene material (D) Reflectance result for design with Graphene material. Red colour indicates the highest value and blue colour indicate the lowest values. The absorption and reflectance values are almost similar and there is no change evident from the result. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 4
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Table 1 Comparative analysis of absorption for infrared, visible, ultraviolet and whole solar spectrum range. Design
Infrared Range Absorption (%)
Visible Range Absorption (%)
Ultraviolet Range Absorption (%)
Whole solar range (100 THz to 1600 THz) (%)
Proposed design With Graphene layer Proposed design without Graphene layer Broadband design of Ref. [35] Graphene based Design of Ref. [36] Graphene based design of Ref. [37] Graphene based design of Ref. [38]
85.48 71.84 79.67 – –
97.51 92.80 93.7 70 93 71.1
89.57 93.49 92.3 – – –
92.72 89.80 88.4 – 90 –
Table 2 Comparison of Ag resonator design, Au resonator design and our proposed design (Au and Ag both). Design
Infrared Range Absorption (%)
Visible Range Absorption (%)
Ultraviolet Range Absorption (%)
Whole solar range (100 THz to 1600 THz) (%)
Proposed design With Ag and Au resonator Ag resonator design from Ref. [39] Au resonator design from Ref. [21]
85.48 – –
97.51 80 92
89.57 – –
92.72 – 89
use of graphene increases the absorption of the design. The use of graphene also gives the ability to tune the response of the design. The wide wavelength absoprtion is very necessary in the solar absorber [42–45]. In the proposed design the wide wavelenght absorption is achieved using the gold and silver resonator based on the graphene design. The wide wavelength behaviour of solar absorber by changing different physical parameters of the design is presented in Fig. (3-6). Absorption property of the solar absorber design is changed by changing various design parameters of the design. The design parameters like the width of the gold resonator (G_W), width of the plus resonator (S_W), gold absorber layer height (G_H) and total absorber structure width (W) are varied to check the absorber behaviour. The width of the gold resonator (G_W) is varied from 150 nm to 250 nm to check the absorption behaviour of the design. Width of the gold resonator is very important because Increasing the width of the gold resonator layer will cover the substrate layer fully and absorption in the substrate layer is reduced. The results are shown in Fig. 3 clearly indicate that the higher values of width decrease the absorption of the design. The reflectance is increased by increasing the width values of gold resonator because the gold resonator layer covers most of the substrate part and thus the reflectance is increased. The results in the form of absorption and reflectance for different width size of plus metasurface silver resonator is presented in Fig. 4. The plus metasurface width is increased from 100 nm to 200 nm to check the reflectance and absorption behaviour. The increase in width makes the gap between the gold resonator and silver resonator negligible and it also overlaps at a certain point. This increase will make a rectangular sheet of gold and silver resonator. This rectangular sheet reduces the absorption of substrate layers. From the results, it is clear that over 175 nm width level, the absorption results reduce for the whole range. To observe the effect in absorption and reflectance with different height of the bottom layer (G_H) from 150 nm to 250 nm by keeping all other parameters constant is shown in Fig. 5. As shown in Fig. 5, by increasing the height of bottom layer which helps in reducing the transmission of incoming EM wave. From the results, the broadband absorption is observed more in graphene-based design absorber beyond 250 THz. As shown in Fig. 6, the width (W) of the whole design is increased from 500 nm to 1000 nm to check the effect of absorption and reflectance. The results from Fig. 6 has no effect on reflectance and absorption with a change in the width of the proposed absorber. This clearly indicates that there is no relationship of absorption with the total width of the design. The absorption result is better for graphenebased design. The normalised electric field results for the frequencies 600 THz,
Fig. 7. Normalised Electric Field for the frequency of (A) 600 THz (B) 800 THz (C) 1000 THz (D) 1200 THz (E) 1400 THz (F) 1600 THz. Red colour indicates the maximum field intensity and blue colour indicates minimum electric field intensity. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Our Proposed design is based on Au and Ag resonators. The use of Ag and Au resonators give better absorption which is given in comparative Table 2. In this table the comparison of Ag resonator design [39], Au resonator design [40] and our proposed design is presented. The proposed design is better in terms of absorption as it is giving the best absorption in Visible as well as overall spectrum. Graphene design presented in Refs. [36–41] clearly show that the 5
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800 THz, 1000 THz, 1200 THz, 1400 THz, and 1600 THz is presented in Fig. 7. The results indicate that energy concentration in the plus shape silver resonator is clear from the results. It is very important to show how to improve the absorption further [46]. The absorption of the design can be further improved by varying the graphene chemical potential. The absorption spectrum can be tuned by changing the graphene chemical potential.
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4. Conclusion In conclusion, a graphene-based broadband solar absorber using silver and gold structure is proposed and investigated from 100 THz to 1600 THz. The average absorption is 85.48% in infrared, 97.51% in visible, 89.57% in the ultraviolet region and 92.72% absorption in the whole solar spectrum is obtained. The resonators made up of silver and gold material placed above the dielectric layer with the sandwich graphene layer. The design with the graphene layer gives more absorption compared to design without the graphene layer. The maximum absorption of 97.51% is achieved for the graphene-based solar absorber design. The variation of the absorption band is achieved by changing the different parameters of physical structure (width of gold material (G_W), the width of silver material (S_W), the height of gold material (G_H), total structure width (W)). The proposed graphene-based broadband solar absorber has the potential to become future building blocks light trapping and energy harvesting devices. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work was partially supported by the Office of Research and Economic Development at University of Nebraska-Lincoln, USA, Nebraska EPSCoR, NSF Nebraska MRSEC and Marwadi Education Foundation's Group of Institutions, Rajkot. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.optmat.2019.109330. References [1] R.A. Pala, J. White, E. Barnard, J. Liu, M.L. Brongersma, Design of plasmonic thinfilm solar cells with broadband absorption enhancements, Adv. Mater. 21 (34) (2009) 3504–3509. [2] V. Dave, V. Sorathiya, T. Guo, S.K. Patel, Graphene-based tunable broadband farinfrared absorber, Superlattice Microstruct. 124 (2018) 113–120. [3] A. Lenert, D.M. Bierman, Y. Nam, W.R. Chan, I. Celanović, M. Soljačić, E.N. Wang, A nanophotonic solar thermo photovoltaic device, Nat. Nanotechnol. 9 (2) (2014) 126. [4] C.M. Watts, X. Liu, W.J. Padilla, Metamaterial electromagnetic wave absorbers, Adv. Mater. 24 (23) (2012) OP98–OP120. [5] S.K. Patel, Y.P. Kosta, Metamaterial superstrate-loaded meandered microstrip-based radiating structure for bandwidth enhancement, J. Mod. Opt. 61 (11) (2014) 923–930. [6] Y. Avitzour, Y.A. Urzhumov, G. Shvets, Wide-angle infrared absorber based on a negative-index plasmonic metamaterial, Phys. Rev. B 79 (4) (2009) 045131. [7] P. Ahir, S.K. Patel, J. Parmar, D. Katrodiya, Directive and tunable graphene based optical leaky wave radiating structure, Mater. Res. Express 6 (5) (2019) 055607. [8] X. Duan, S. Chen, W. Liu, H. Cheng, Z. Li, J. Tian, Polarization-insensitive and wideangle broadband nearly perfect absorber by tunable planar metamaterials in the visible regime, J. Opt. 16 (12) (2014) 125107. [9] M.K. Hedayati, M. Javaherirahim, B. Mozooni, R. Abdelaziz, A. Tavassolizadeh, V.S.K. Chakravadhanula, ... M. Elbahri, Design of a perfect black absorber at visible frequencies using plasmonic metamaterials, Adv. Mater. 23 (45) (2011) 5410–5414. [10] Q. Liang, T. Wang, Z. Lu, Q. Sun, Y. Fu, W. Yu, Metamaterial‐based two-dimensional plasmonic subwavelength structures offer the broadest waveband light harvesting,
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