1 Introduction

Metamaterial is an artificially engineered composite material that exhibits extraordinary electromagnetic properties and not easily available in nature (Smith et al. 2004). From past many years, metamaterial absorbers have gained considerable attention in applications such as solar energy harvesting (Ogawa and Kimata 2018; Liang et al. 2013), sensing (Cheng et al. 2016), thermal imaging (Liu et al. 2010), microstrip radiating structure (Patel et al. 2019a), etc., All these applications are achieved due to its exotic response of electromagnetic properties, such as negative refractive index, asymmetric transmission, and cross-polarization conversion. The metamaterial absorber is experimentally demonstrated and presented in Landy et al. (2008). Metamaterial absorber design is widely explored in the terahertz spectral range (Infrared, Visible and Ultraviolet region) by many researchers. Many such absorber structures are designed to work at single and multiband and thus fulfilling many practical applications such as solar harvesting and sensing. However, many application of Metamaterial is impeded by its losses and difficulties in 3D fabrication, especially in micro- and nano-scale. To develop multifunctional terahertz devices, the low cost and broadband absorber have important research value. Metasurfaces are two-dimensional (2D) or the planar version of metamaterials consisting of single-layer or few-layers. The planar structures with the thickness of subwavelength and can be readily fabricated using lithography and nano-printing methods. Due to their lightweight and ease of fabrication, they are broadly investigated and implemented in electromagnetic applications to suppress undesirable losses. Metasurface, with its exotic properties to manipulate EM waves are studied to design polarizer (Heidari and Sedighy 2018), and the multi-band (Cao and Cheng 2018; Cheng et al. 2018, 2019; Huang et al. 2018a), narrow or broadband absorbers (Niu et al. 2018; Cheng and Du 2019; Huang et al. 2018b; Chen et al. 2020; Patel et al. 2019b; Katrodiya et al. 2019).

The metasurface absorbers are mainly classified into three categories: multiband, narrowband and broadband absorbers. The structures are tailored with more than one resonators with different sizes and shapes together (Xu et al. 2018) or using multiple resonators on stacked structures to achieve multi-band and narrowband absorption(Gao et al. 2018; Zhang et al. 2019; Deng et al. 2018). These methods include the complicated process of fabrication that results in high cost. Therefore simple structures with single fabrication steps are having great importance (Yao et al. 2016; Arik et al. 2016). Major efforts have been put by researchers to achieve broadband absorption rather than a multiband and narrow band for terahertz application. To adapt the development of multifunction terahertz devices, the broadband absorbers with switchable absorptivity is important to research. It can be achieved by engineering the shape, size, thickness, and structure composed of a pattern array of metals placed above the dielectric spacer (Arik et al. 2017; Cao and Cheng 2019).

Many metasurface absorbers are works on pre-defined frequency region due to its restrict permittivity and permeability. Hence, it is necessary to find material with flexible properties to design frequency tunable absorber (Chen et al. 2017). The periodic arranged array of C-shaped metasurface in the proposed absorber helps to enhance the coupling of energy from the EM incident field on the metasurface. Also, multiple graphene strips arranged in parallel placed above the dielectric layer, which helps to further enhance the bandwidth and absorption coefficient. Graphene is a two-dimensional, one-atom-thick surface densely packed arranged in a honeycomb lattice (Sorathiya et al. 2019). Due to interesting electronics carriage and tuneable properties of graphene, it is far better to use than those metals and semiconductors. Graphene, with its high conductivity and excellent mechanical properties it is used as a good applicant in solar absorber design (Thomas et al. 2019; Dave et al. 2018; Patel et al. 2018). To make design cost-effective, we had introduced the tungsten material in the proposed solar absorber instead of gold. Due to its high melting point compared to Gold (Au), Silver (Ag), Chromium (Cr), Copper (Cu) and even Titanium Nitride (TiN), it helps tungsten-based absorber to withstand with high temperature when absorbing photons of greater energy (Rana et al. 2018). Graphene-based plus shape metasurface is designed to improve the absorption result and achieve broadband behavior presented in Patel et al. (2019c). Pyramid array is used with a graphene surface to achieve broadband behavior is presented in Charola et al. (2019).

The broadband response of the absorber depends upon the complex design of metasurface and multiple layers of stacks thus the need for new solar absorber design which gives the broadband response with low fabrication cost. It can be easily fabricated due to its simple metasurface design and less costly due to tungsten materials used in it. The proposed structure of the graphene-based metasurface absorber is shown in Fig. 1a with a total thickness of 560 nm and a total length (L) of 2000 nm, respectively. The total size of broadband metasurface solar absorber is chosen to ensure that it achieves broadband absorption at the operating wavelength. Absorption characteristic is analyzed from 100 to 1200 THz for proposed solar absorber with broadband absorption response.

Fig. 1
figure 1

The C-shaped metasurface absorber design a Three-dimensional design b Two-dimensional design c The unit cell of the last row of C-shaped metasurface. The top layer with the thickness (H) of 30 nm and the bottom layer with the thickness (W) 200 nm made up of tungsten material. The dielectric layer with the thickness (T) of 330 nm which separates the top and bottom layer made up of silicon dioxide (SiO2). The total length (L) of the structure is kept 2000 nm. The unit cell of C-shaped with length (L1) is 310 nm, length (L2) is 200 nm and length (L3) is 110 nm. The distance (D) between two adjacent C-shaped is 660 nm and the distance from C-shaped to the edge of structure is 330 nm

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2 Metasurface absorber design and modeling

The proposed metasurface absorber design is presented in Fig. 1. The design structure is divided into three main parts. The first part is the metallic resonator part consists of a C-shaped metasurface array placed on graphene strips. The second part is the dielectric layer made up of silicon dioxide (SiO2) layer which concentrates and absorbs incoming electromagnetic waves. The third part is the tungsten material used in the C-shaped metasurface and bottom layer which is used to absorb incoming electromagnetic waves. The experimental data of tungsten used in the proposed design is adopted from Palik (1998). The experimental data of silicon dioxide is set as a dielectric spacer to separate the top and bottom layer is adopted from Guo and Argyropoulos (2016). The use of tungsten material reduces the cost of the design as well as provide ease of fabrication.

The thickness (W) of the thin film at the bottom made up of tungsten has a 200 nm, opaque to incident light which prevents light transmission. The thickness (T) of the dielectric layer is 300 nm and the thickness (H) of the periodically arranged array of C-shape metasurface above dielectric layer is 30 nm as shown in Fig. 1b. An electromagnetic plane wave is inserted normally from z-direction in absorber such that periodic arranged nanostructure array is illuminated by the magnetic field parallel to the y-axis and electric field parallel to the x-axis as shown in Fig. 1a. As shown in Fig. 1c, the optimized geometric parameters of a unit cell for periodically arranged of C-shaped metasurface are L1 = 310 nm, L2 = 200 nm and L3 = L2 − L1 = 110 nm, where L1 and L2 are the length of single C in unit cell of the proposed absorber. The periodically arranged array of metallic resonators placed above the dielectric layer are equally spaced with the spacing distance of D is 660 nm and D/2 is spacing at outer the edges of the absorber as shown in Fig. 1c.

The periodically arranged three graphene strips in parallel with the size of width (G) and length (L) placed above the dielectric layer is 200 to 2000 nm respectively. The thickness of the graphene monolayer sheet to be considered as a 0.34 nm. The surface conductivity (\({\sigma }_{s}\)) equation of graphene is described as the sum of the interband and intraband electron transition contribution given by Kubo formula (Guo and Argyropoulos 2016) shown from Eqs. (1–4).

$$\varepsilon \left( \omega \right) = 1 + ~\frac{{\sigma _{s} }}{{\varepsilon _{o} \omega \vartriangle }}$$
(1)
$$\sigma_{intra} = \frac{{ - je^{2} k_{B} T}}{{\pi \eta^{2} \left( {\omega - j2{\Gamma }} \right)}}\left( {\frac{{\mu_{c} }}{{k_{B} T}} + 2\ln \left( {e^{{\frac{{ - \mu_{c} }}{{k_{B} T}}}} + 1} \right)} \right)$$
(2)
$$\sigma_{inter} = \frac{{ - je^{2} }}{{4\pi {\text{h}}}}\ln \left( {\frac{{2\left| {\mu_{c} } \right| - \left( {\omega - j2{\Gamma }} \right){\text{h}}}}{{2\left| {\mu_{c} } \right| + \left( {\omega - j2{\Gamma }} \right){\text{h}}}}} \right)$$
(3)
$$\sigma_{s} = \sigma_{inter} + \sigma_{intra}$$
(4)

The permittivity of graphene depends on the thickness of graphene monolayer sheet (\(\Delta (0.34nm)\)), angular frequency (\(\omega\)), permittivity of vacuum \(({\varepsilon }_{o})\) and surface conductivity \(({\sigma }_{s})\).Different parameters of graphene surface conductivity \(({\sigma }_{s})\) also depend upon temperature (T) in kelvin, \({k}_{B}\)(1.38e-23 J/K)is the Boltzmann constant, \({\text{h}}\)(6.62e-34 J.s) is the Planck's constant, \(e\)(1.6e-19 C) is electron charge value, electron–phonon, \(\Gamma\) (11e-3 [1/S]) is scattering rate and also \({\mu }_{C}\)(0.3 eV) is chemical potential. Graphene's chemical potential is given by \(\mu _{{C = }} {\text{h}}V_{F} \sqrt {\pi CV_{{DC}} /e}\), \({V}_{DC}\) is a gate voltage, t is dielectric layer thickness, \({\text{C}}\) is the capacitance is given by \({\text{C}} = \varepsilon _{d} \varepsilon _{0} /t\), \({\varepsilon }_{d}\) is dielectric layer static permittivity and t is dielectric layer thickness.

The effectiveness of absorption is very important and is measured over here by the following equations (Akimov and Koh 2010):

$$\begin{gathered} \vartriangle { } \times { }\vec{E} = { }i\omega \mu_{0} \vec{H} \hfill \\ \vartriangle { } \times { }\vec{H} = -\ i\omega \varepsilon_{0} \varepsilon \vec{E} \hfill \\ \end{gathered}$$
(5)
$$A\left( \omega \right) = \frac{{Q_{abs} \left( \omega \right)}}{{Q_{inc} \left( \omega \right)}}$$
(6)
$$Q_{abs} = \frac{\omega \varepsilon_{0}}{2}\int \limits_{V} {\text{Im}}[\upvarepsilon(\upomega)]|E|^{2} dV$$
(7)
$$Q_{abs}^{tot} { } = { }\smallint A\left( \omega \right)F\left( \omega \right)d\omega$$
(8)

where, \({\text{Q}}_{{{\text{abs}}}}\) is spectral power absorbed by each element, A(ω) is optical absorption, \({\text{Q}}_{{{\text{abs}}}}^{{{\text{tot}}}}\) is total power absorbed and \({\text{Q}}_{{{\text{inc}}}}\) is spectral power coming from the sun and incident on the surface. The simulated reflection (R) and absorption (A) spectra of designed absorber with the above-mentioned parameters as shown in Fig. 2a, b. The relation between reflection(R), absorption (A) and transmission (T) is

$$A\left( \omega \right) = 1 - R\left( \omega \right) - T\left( \omega \right)$$
(9)
Fig. 2
figure 2

a Absorption and b Reflection spectrum of the response of absorber with and without multiple graphene strips placed above the dielectric layer. The average absorption is 75.6% from 100 to 1200 THz is achieved by arranging multiple strips of graphene shown by the red line. The response of average absorption without the multiple graphene strips is 71.9% from 100 to 1200 THz shown by the blue line

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where, \(R\left(\omega \right)\) and \(T\left(\omega \right)\) both are frequency (ω) dependent parameters represents reflection and transmission. Besides, both \(R\left(\omega \right)\) and \(T\left(\omega \right)\) can be expressed in term of S-parameters as \(R\left(\omega \right)\)=\({\left|{S}_{11}\right|}^{2}\) and \(T\left(\omega \right)\)=\({\left|{S}_{21}\right|}^{2}\).Due to the bottom layer made of tungsten helps to reduce transmission co-efficient (T (ω) ≈ 0) as the thickness of the tungsten layer is much larger than its skin depth. The periodic array of C-shaped metasurface is tailored to reduce reflection such that to increase the absorption of the proposed solar absorber.

3 Results and discussion

The proposed absorber design is analyzed through the Finite Element Method (FEM) based numerical simulation using COMSOL 5.4 Multiphysics simulator. The proposed unit cell floquet boundary condition is applied in the X and Y direction. The transverse electric field applied from port-1 from ± Z direction and response of the design is computed at port-2. The ports to be considered as periodic for simulation for proposed design to observe the absorbtion characteristic from 100 to 1200 THz. The comparative plots of absorption (A) and reflection (R) of periodically arranged metallic resonators with and without multiple graphene strips are shown in Fig. 2a, b, respectively. From Fig. 2a, the average absorption is achieved with the multiple graphene strips is 75.6% and without the multiple graphene strips is 71.9%. The comparative analyses in terms of the infrared, visible and ultraviolet region with and without the multiple graphene strips are presented in Table 1. From Table 1, it is clear that the addition of multiple graphene strips achieves more average absorption in all three regions (Infrared, visible and ultraviolet region). The design presented here is also giving a better response compared to the previously published similar design (Rufangura and Sabah 2017; Liu et al. 2018; Sang et al. 2019).

Table 1 Comparative analysis of absorption in different terahertz region (Infrared, Visible and ultraviolet frequency range) by adding multiple graphene strips and without multiple graphene strips in the proposed design and previously published designs
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Different design parameters are varied to observe its effect on the absorption and reflectance response. The characteristic of absorption changes with change in graphene width (G), Design structure length (L), thickness (H) of metallic resonators, thickness (T) of dielectric layer, C-shape metasurface length (L1) and width (L2) are presented from Figs. 3, 4, 5, 6, 7, 8. The graphene strips width (W) is varied from 0.1 to 0.6 μm to observe its effect on the response of reflectance and absorption in the range of 100 to 1200 THz. The change in the width of graphene strips does not change the absorption much as shown in Fig. 3.

Fig. 3
figure 3

Absorption and reflectance responses for different graphene strips width (G) a Absorption with graphene b Reflection with graphene. Graphene strip width (G) is varied from 0.1 to 0.6 µm and frequency is varied from 100 to 1200THz

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Fig. 4
figure 4

Absorption and reflectance responses for structure length (L) varied from 1.5 to 2.5 µm a absorption with graphene b reflection with graphene c absorption without graphene d reflection without graphene

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Fig. 5
figure 5

Absorption and reflectance responses for different thicknesses (H) of C-shape metasurface varied from 0.02 to 0.05 µm a absorption with graphene b reflection with graphene c absorption without graphene d reflection without grapheme

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Fig. 6
figure 6

Absorption and reflectance responses for different thickness (T) is varied from 0.2 to 0.4 µm of the SiO2 layer. a absorption with graphene b reflection with graphene c absorption without graphene d reflection without grapheme

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Fig. 7
figure 7

Absorption and reflectance responses for different C-shape metasurface length (L1) is varied for from 0.21 to 0.56 µm. a absorption with graphene b reflection with graphene c absorption without graphene d reflection without graphene

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Fig. 8
figure 8

Absorption and reflectance responses for different C-shape metasurface width (L2) is varied for from 0.025 to 0.2 µm. a absorption with graphene b reflection with graphene c absorption without graphene d reflection without grapheme

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The total design structure length (L) is varied from 1.5 to 2.5 μm for both the designs (with graphene and without graphene) and the results are presented in Fig. 4. The absorption results are better for the middle range of 1.7–2.1 μm. The absorption range is more for graphene design compared to the design without graphene. The more absorption is achieved in the range of 450–1050 THz if the metallic resonators are placed above the graphene strips. The use of graphene increases the concentration of the light in the absorbing layer and thus the absorption is increased for the graphene design.

The thickness of metallic resonators is a very important part because by increasing the thickness the reflectance increases which reduces the absorption. The thickness is varied from 0.02 to 0.05 µm keeping other parameters constant to observe its effect on reflectance and absorption is presented in Fig. 5. As shown in Fig. 5a the absorption increases with increases in the thickness of metallic resonators. The metallic resonators placed above the graphene sheets show more absorption between 980 and 1100 THz compare to without graphene strips.

The thickness of the dielectric layer made up of silicon dioxide plays an important role in the absorption of the metasurface absorber. The thickness increase keeps the absorption high for a certain level and then the absorption does not increase much after that level. The increase in thickness also increases the size and affect its cost at the production level. The height of the SiO2 layer is varied from 0.2 to 0.4 μm and results are presented in Fig. 6. The absorption is achieved more in-between 0.3 and 0.4 μm. The absorption is almost the same for both designs with and without the graphene strips.

The C-Shape metasurface length and width are also varied to observe its effect on results. The absorption and reflectance results are presented in Figs. 7, 8. The change in length and width of the C-shape metasurface changes its structure and thus the metamaterial properties (permittivity and permeability) change which affects the reflectance and absorption results. The efficiency of absorption increases with an increase in the length (L1) of C-shaped design as shown in Fig. 7. There are two bands clearly shown in Fig. 7a where maximum absorbtion is achieved, the first band between 290 and 370 THz and the second band is 470 to 1100 THz. The absorption and reflectance results for different metasurface width (L2) is presented in Fig. 8. The results of absorption slightly decrease as the width of the metasurface (L2) increases. The increase in the width covers most of the dielectric layer and thus reflection increases and absorption decreases.

The graphene monolayer strips placed above dielctric layer and below C-shaped rectangular sawtooth metasurface to achieve more absorbtion. The absorbtion and reflectance respose of proposed absorber is observed by changing the chemical potential (μc) from 0.3 to 1.1 eV. As shown in Fig. 9, the change in chemical potential doen’t effect the absorbtion response in the range of 100–1200 THz.

Fig. 9
figure 9

a Absorption and b reflectance responses with different chemical potential (μc) varied from 0.3 to 1.1 eV

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The change in absorbtion characteristic is observed with change in the thickness of graphene monolayer strips placed above dielectric layer and below C-shaped rectangular sawtoooths from 0.34 to 1.14 nm as shown in Fig. 10. The increase in graphene layers thickness leads to increase in more absorbtion with less reflection as shown in Fig. 10.

Fig. 10
figure 10

a absorption and b reflectance responses with increasing thickness of graphene monolayer stips from 0.34 to 1.14 nm

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The normalized surface current density with a unit of A/m is presented in Fig. 11 for four different frequencies (a) 200 THz (b) 600 THz (c) 800 THz and (d) 1000 THz. The concentration of current shown by the arrow is observed around the C-shape metasurface and on the dielectric layer. The current distribution is increasing for the middle frequencies of 600 THz and 800 THz. A normalized electric field response is presented in Fig. 12 for four different frequencies (a) 200 THz (b) 600 THz (c) 800 THz and (d) 1000 THz. The normalized electric field response clearly shows the concentration of electric energy around the C-shape metasurface for the 200 THz frequency range. The absorption is also better for the 400 THz frequency response. As we move into the ultraviolet range the electric energy concentration around the C-Shape metasurface is decreasing.

Fig. 11
figure 11

Normalized current density response for solar absorber design. a 200 THz, b 600 THz, c 800 THz, and d 1200 THz

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Fig. 12
figure 12

Normalized electric field response for solar absorber design. a 200 THz, b 600 THz, c 800 THz, and d 1200 THz

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4 Conclusion

In summary, periodic array of C-shaped metasurface is placed above the multiple graphene strips and dielectric layer (SiO2) to achieve a broadband response. The results in the form of absorption, reflectance, electric field, and magnetic field are presented to show the broadband response. The absorption result of graphene design is compared with a simple design and previously published similar designs. From the comparison, it is clear that the multiple graphene strips design gives better results compared to other designs. The average absorption of 86.1%, 86.5%, and 92.99% is achieved for the infrared region, visible region and ultraviolet region respectively. The results are also observed by changing different design parameters. The change in width (W) of graphene strips is not having much effect on the results but the increase in C-shape metasurface length (L1) increases the absorption. The increase in width (L2) decreases the absorption. The proposed broadband and efficient solar absorber can be used as a building block for sensors, photovoltaic devices, and energy harvesting devices.