Tunable absorber embedded with GST mediums and trilayer graphene strip microheaters

Investigation was made of the optical response of metal-dielectric stacks-based cavity structures embedded with graphene microheaters for the purpose of perfect absorption. The absorber configuration exploits the Ge2Sb2Te5 (GST) phase changing medium, and the effects of different parametric and operational conditions on the absorption spectra were explored. The refractive indices of GST layers can be manipulated by the external electrical pulses applied to microheaters. The amplitude and duration of electrical pulses define the crystallinity ratio of the used GST mediums. The results revealed achieving perfect absorption (> 99%) in the visible and infrared (IR) regimes of the electromagnetic spectrum upon incorporating two thin GST layers of different thicknesses (in the stack) in the amorphous state. The proposed configuration showed the capability of introducing independent transition state (amorphous and/or crystalline) for each GST layer—the visible regime could be extended to the IR regime, and the perfect absorption peak in the IR regime could be broadened and red-shifted. It is expected that the structure would find potential applications in active photonic devices, infrared imaging, detectors and tunable absorbers.


Design and analysis
exhibits the schematic of the proposed multilayered planar structure comprised of 08 layers altogether; Fig. 1a, b, respectively, show the 2D and 3D versions of the configuration. Here the bottom is a silver (Ag) layer having a thickness of 50 nm. Also, it has 02 top-up stacks of GST-graphene-SiO 2 mediums as space layers, and finally, a thin layer of SiO 2 on top to serve the purpose of capping. This protects the upper planar GST medium from evaporation as well as provides more heat confinement within the structure. We use the SiO 2 medium because of its stable interaction with graphene sheets, and also, low amount of loss in the IR regime 44 . The bottom silver layer acts as a reflective mirror which introduces critical coupling conditions.
The proposed multilayered structure can be fabricated exploiting the chemical vapor deposition (CVD) technique without undergoing complex lithography process. Multilayered graphene medium can be deposited over a thin layer of SiO 2 23,25,37 . A graphene medium having 1 nm thickness normally corresponds to trilayer graphene structure, which can be synthesized on a ceramic substrate by the CVD method, and then transferred on the SiO 2 layer 42 . We consider the trilayer graphene sheets as microheaters for the used GST layers. The bottom Ag layer can be deposited over the Si substrate by thermal evaporation. The same process can be exploited to deposit the GST layers on the SiO 2 mediums 38,41,42 . It has been reported before that 100 nm thick Ti/Au metal pads on graphene layers can be used as metal connectors to induce the required electrical current for heating the GST layers 37,41 .
Using the optical constants of mediums 23,26,45 , Fig. 2a exhibits the variations of the real ( ǫ r ) and imaginary ( ǫ i ) parts of the permittivity of GST in the amorphous ( α ) and crystalline (c) states with wavelength. These components of permittivity are, respectively, shown by ℜ(ǫ) and ℑ(ǫ) . It is clear from this figure that the permittivity of both the phases of GST greatly depends on the operating wavelength. However, the dependence on wavelength is more prominent up to 2.5 µm in the case of c-phase, whereas the α-phase exhibits it up to 1.5 µm only. Beyond these operating points, the permittivity values of the c-and α-phases of GST become almost independent of wavelength. Though in both the phases the real part of permittivity is always larger than the imaginary part, the values of those become very close in the c-phase above 2.5 µm wavelength.
On the other hand, the conductivity σ (ω) of N-layer graphene can be determined as 46,47 Scientific Reports | (2021) 11:3603 | https://doi.org/10.1038/s41598-021-83304-y www.nature.com/scientificreports/ where ( = h/2π ) is the reduced Planck's constant, k B is Boltzmann's constant, T is the absolute temperature, e is the electronic charge, γ is the rate of scattering (which is inversely proportioned to the relaxation time τ ), N is the number of graphene layers and α 1 (= 217 meV) is the interaction energy of misoriented graphene layers 47 .
In the present work, we take γ = 1.32 meV. It has been reported before that, in the case of N-layer graphene, a higher carrier density can be obtained, thereby demanding a lower external electrical potential 48 . Figure 2b exhibits the wavelength dependence of ǫ r and ǫ i in the case of monolayer graphene (i.e., N = 1 ). We observe in this figure that the real part shows the positive and negative dependence on the operating wavelength,   www.nature.com/scientificreports/ whereas the imaginary part remains positive-valued only. The increase in chemical potential µ c causes red-shifts in the peaks of the real and imaginary parts, thereby determining µ c to be the tuning parameter to alter the optical characteristics of graphene layer. We study the propagation of electromagnetic waves through the proposed structure using a TMM-based numerical approach 30,48 . In the treatment, we consider plane waves of either transverse electric (TE) polarization with E = 0, E y , 0 and H = (H x , 0, H z ) or transverse magnetic (TM) polarization with E = (E x , 0, E z ) and H = 0, H y , 0 impinge on the top surface of the proposed structure at an angle θ (Fig. 1). We consider the multilayer stack as a uniaxial homogeneous medium, which has the optical axis perpendicular to the plane of interface, i.e., the x-y plane. Now, the wavenumbers corresponding to the TE-and TM-polarized waves propagating in the i th layer of the structure can be determined as 49 In these equations, k 0 is the free-space wavenumber,k iz is the wavenumber of the normal components, k ix = k 0 sin θ , and the subscripts t , ⊥ represent the transverse and normal (directions) permittivity values, respectively.
We now exploit Maxwell's equations to satisfy the boundary conditions at the two interfaces of each layer. Then the equations are reorganized in the form of a 2 × 2 matrix, i.e., the transfer matrix M i describing the propagation characteristics corresponding to the TE-and TM-polarizations, as follows 48 : In Eq. (4), d i is the thickness of each layer, µ 0 , ǫ 0 , are the respective free-space values of permittivity and permeability, ǫ i is the permittivity of the i th layer, and p i is determined by the wave polarizations so that it assumes the values equal to either (k iz /ωµ 0 ) or (k iz /ωµ 0 ǫ 0 ǫ i ) , respectively, corresponding to the cases of TE-or TM-polarizations.
For an N-layer model, the total transfer matrix ( M T ) of the structure (of Fig. 1) is evaluated as a serial product of transfer matrices where N is the total number of component layers and m ij represents the transfer matrix components.
The absorbance (or the absorption coefficient) A for both the polarizations can be obtained in the form ; T( ) and R( ) being the wavelength-dependent transmission and reflection coefficients, respectively. In the case of critical coupling, the transmission coefficient is eliminated, thereby the absorbance to assume the form as A( ) = 1 − R( ) . The critical coupling occurs when the rate of reflection becomes equal to the rate of absorption. In this view, the perfect absorption can be attained at the resonance frequencies.
Many investigations have been performed to enhance the perfect absorption in the optical regime by using the Fabry-Perot cavity structures and lossy dielectric mediums 1,3,29,42 . Within the context, one may think of the effects due to the cross-polarized component, which may alter the total absorptivity 50 . However, we neglect the cross-polarization effect because the medium is considered as uniaxial homogeneous, as stated before.

Results and discussion
We now investigate the tunable absorption characteristics of the proposed structure under various operating conditions. In this stream, we first take up the influence of the upper GST layer thickness d GST1 in the amorphous phase, and vary this in a range of 90-150 nm at a step of 10 nm, keeping the value of the thickness d GST2 of the lower GST layer fixed (to a value of 90 nm). Also, we take the other parametric values as d s1 = 100 nm  (Fig. 1). We use trilayer graphene at this stage having a thickness of 1 nm and a chemical potential of µ c = 0.1 eV. Figure 3 exhibits the variation of absorbance A (and also, the reflectance R ) with wavelength considering the TM-polarized incidence excitation impinging on the top SiO 2 surface normally (i.e., θ = 0 • ). Figure 3 shows that the absorption (and reflection) characteristics of the proposed structure have two spans of resonances, viz. the visible (600-1000 nm) and IR (1300-1570 nm) regimes. This figure exhibits that the increase in the thickness of the upper GST layer (i.e., d GST1 ), as shown by the dashed arrow in the figure (the direction of arrow represents increase in d GST1 ), results in significant broadening of the resonance absorption in the visible regime with a perfect absorption (> 99%). Moreover, we observe red-shifts in the absorption peak upon increasing the value of d GST1 -the feature that remains more prominent in the visible regime than the IR span.
We now consider the effect of varying the value of d GST2 in a range of 50-110 nm, keeping d GST1 fixed (130 nm), on the absorbance and reflectance. The other parametric/operational conditions are left unchanged as before. We suppose that, due to shorter optical length of the lower cavity, the thickness of the lower GST layer (i.e., d GST2 ) would be shorter than that of the upper cavity. Figure 4 depicts the results of this study.
We clearly observe in Fig. 4 that the alterations in the thickness of the lower GST layer (i.e., d GST2 ) has significant impact on the absorption peaks in the IR regime, whereas those in the visible range remain almost intact, so far as the broadening of absorption spectra is concerned. We observe that, in the IR regime, the increase in d GST2 (as shown by the dashed arrow in the figure) causes the peak absorption to decrease a little, and also, the absorption peaks undergo strong red-shifts from 1295 to 1696 nm. Following Fig. 4, in order to maintain strong absorption, we keep d GST2 = 70 nm, in order to achieve the maximum absorption at the desirable wavelength of about 1.45 μm. Within the context, it is worth mentioning that the red-shifts in absorption peak are linearly scaled for a larger GST layer thickness. Since most of the environmental gas sensors operate in the mid-IR regime, this property remains desirable for designing tunable optical gas sensors 51 .
Next, we attempt to study the effect of SiO 2 layer thicknesses. To perform this, we first sweep the value of the upper SiO 2 layer thickness d s2 in the range of 50-150 nm, keeping the upper and lower GST layer thicknesses as d GST1 = 130 nm and d GST2 = 70 nm, respectively; the other parametric and operational conditions are used as before. Figure 5 exhibits the results of this investigation, which essentially reveals the linear relationship between d s2 and the obtained red-shifts in the absorption peaks (with increasing d s2 , as shown by the dashed arrow in Fig. 5). Interestingly, the absorption spectra in the visible and IR regimes exhibit very small increase in the absorption peaks, and reach perfect absorption condition corresponding to the largest chosen value of d s2 (i.e., 150 nm). We also observe that, in the visible regime, the increase in d s2 results in wider absorption band,   We now focus on the effect of the lower SiO 2 layer thickness d s3 on the absorption spectra. To investigate this, we vary d s3 in a range of 50-150 nm, while keeping the other parametric/operating conditions fixed, as considered before. We take the values of d GST1 , d GST2 and d s2 as 130 nm, 70 nm and 120 nm, respectively. Figure 6 illustrates the results of this investigation, wherein we notice that the increase in d s3 causes significant impact on the absorption characteristics in the IR regime; the effect in the visible regime remains the least. This is attributed to the fact that the absorption in cavities is mostly caused by the GST layers. As the thickness of the upper SiO 2 layer increases, the optical length of cavity also undergoes increase, thereby resulting in red-shifts of the absorption peaks. However, the thicker the SiO 2 layer is, the thinner the GST layer becomes in a cavity, which results in lower absorption property. We also observe that the absorption span gradually increases with increasing thicknesses of the SiO 2 layer-the feature that the inset of Fig. 6 depicts. Based on the obtained results, we choose d s3 = 60 nm in further investigations as the respective absorption peak exists close to 1.5 μm wavelength.
We now examine the effect of the capping layer thickness d s1 on the absorption characteristics. This thickness can be kept in a range of 70-130 nm. However, the afore discussed results use d s1 = 100 nm as a default value, as stated before. Figure 7 shows the wavelength-dependence of absorption (and reflection) by the structure under varying d s1 . We observe in this figure that the increase in capping layer thickness causes enhancement in absorption in the visible regime. The figure exhibits perfect absorption, while the span is decreased upon increasing d s1 .
In the IR regime, however, the spectral characteristics are not appreciably affected, thereby almost eliminating red-shifts in the absorption peaks-the feature in contrast to what noticed before. As such, in the 70-130 nm range of d s1 , we observe trivial effect on the absorption properties, and the peak absorption decreases from the perfect condition (100% absorption) to 99% (with increasing d s1 ). In the above discussed results, we chose the capping layer thickness as 100 nm, in order to balance the absorption peaks in the visible and IR regimes.
At this point, one would be interested to observe the effect on the absorption characteristics when all the three SiO 2 layers in the structure are the same. That is, the parameters d s1 , d s2 and d s3 assume equal values. It has been comprehensively explained above that the parameter d s1 remains useful mostly in tuning the absorption in the UV and visible regimes, whereas the values of d s2 and d s3 affect the absorption in the visible and mid-IR regimes. Furthermore, the parameter d s3 is used to fine-tune the absorption peak in the mid-IR range. By making all the three parameters equal, the perfect absorption characteristic is lost, as becomes evident from Fig. 8. This figure illustrates the results in respect of three different designs. We notice that, in the case of d s1 = d s2 = d s3 = 120 nm, the absorption is decreased in the visible regime, while the peak in the mid-IR range is blue-shifted to 1.4 µm.  www.nature.com/scientificreports/ On the other hand, the case of d s1 = d s2 = d s3 = 60 nm yields reduced absorption in the UV regime, and also, the same happens in the mid-IR span, where the absorbance dropped from the perfect absorption condition, and it is further red-shifted. Figure 8 clearly shows that the use of parametric values as d s1 = 90 nm, d s2 = 120 nm, and d s3 = 60 nm yields the best absorption performance. The efficiency of graphene microheaters can be enhanced by reducing the contact resistance between the electrodes and graphene sheets. This ultimately reduces the total voltage required, and also, avoid the current saturation to reach high temperatures 42 . Several approaches can be exploited to reduce the contact resistance, such as patterning the electrodes and implementing the one-dimensional (1D) edge coupling 37,41 . Furthermore, the hexagonal boron nitride encapsulated graphene devices or multilayer graphene structures can be used to increase the carrier density of graphene 42 . In the present work, however, we use multilayer graphene sheets (i.e., the trilayer graphene) to increase the carrier density as well as to avoid the high voltage requirement.
Since we are exploiting the trilayer graphene sheets as microheaters, it would be interesting to study the effect of graphene on the optical properties of the structure. In such an attempt, we now increase the number of graphene sheets from 1 to 10 layers-the situations that correspond to the use of monolayer graphene to graphite; Fig. 9 illustrates the obtained results. We observe from this figure that gradual increase in the number of graphene layers hardly leaves significant impact on the absorption spectra in either of the two wavelength regimes (i.e., visible or IR), apart from introducing small red-shifts in the absorption peaks. This is attributed to the nearly transparent nature of graphene with very low-loss property in the stated span of wavelength.
To further study the effect of graphene layers on the absorption spectra, we now observe the impact of chemical potential µ c , which we vary in a range of 0.2-0.9 eV; Fig. 10 exhibits the obtained results. This figure clearly indicates that the absorption spectra in both the visible and IR regimes are not much affected due to alterations in µ c . However, the absorption peak at 4.4 µm wavelength (in the mid-IR regime) decreases fast from 0.7 to until it stays steady at 0.4. As such, we find that the absorption properties of the proposed structure are not enough affected by either changing the number of layers or the chemical potential. This confirms that the use of trilayer graphene mediums in the structure can serve as microheaters without imposing any disruptive effect on the optical characteristics. In other words, the proposed structure would accept applied potentials or any extra layers to generate more heat while maintaining the optical properties of the same.
So far, we discussed the results in respect of the absorption/reflection spectra of the structure under the normal incidence (i.e., θ = 0 • ) of waves impinging on the top surface (Fig. 1). We now move to the cases of oblique incidence when the obliquity varies from 0° to 90° (the grazing condition). Using µ c = 0.1 eV, Fig. 11 shows the    www.nature.com/scientificreports/ obtained results; the other parametric/operational conditions are kept unchanged, as used before. We observe in this figure that, as the incidence angle increases, the absorption peaks in the visible regime are obtained corresponding to the angles < 80°, whereas the peaks in the IR regime undergo small shifts toward smaller wavelengths, as the obliquity becomes almost grazing. We also observe in Fig. 11 that the absorption peak at 4.4 µm disappears at the angles larger than 67° and another peak begins to appear from this angle onward. This clearly indicates that the absorption properties in the visible and IR regimes are not enough dependent on the incidence angle, while the absorption wavelengths can be slightly tuned. We finally study the thermal tunability of the structure, which provides multi-level adjustments of the absorption wavelength by manipulating the refractive index (RI) of GST layer(s) in both the α -and c-phases. In fact, the reversible switching between the two phases of GST mediums requires a strict control over the heating process. The permittivity of GST layer for different ratios of crystallinity can be stated by the effective permittivity theory and Lorentz-Lorenz relations 37-39 : Here m is the ratio of crystallinity which can take values from 0 to 1 corresponding to the pure amorphous (i.e., m = 0 ) and completely crystalline (i.e., m = 1 ) states, respectively. Also, ǫ eff ( ) , ǫ c ( ) , and ǫ a ( ) are, respectively, the wavelength-dependent effective permittivity of GST medium, and its permittivity values in c-and α -states.
The wavelength dependence of the real ( n eff ( )) and imaginary ( k eff ( )) parts of RI of a heated GST layer can be obtained by exploiting Eq. (9); Fig. 12 exhibits the obtained results. This figure shows the RIs and extinction ratios for the amorphous ( m = 0 ; solid red lines), crystalline ( m = 1 ; solid blue lines), and the intermediate states (of GST) corresponding to different values of m with 0 < m < 1 (gray dashed lines). As can be seen, by increasing the value of m (as indicated by the dashed arrows in Fig. 12; the direction of arrows being the indication of increasing m ), the RI gradually moves from the α-state (i.e., m = 0 ) toward the c-state (i.e., m = 1 ). This determines that, as far as the exhibited changes of GST layer is nonvolatile, the effect of Joule heating can be approximated by the level of crystalline-to-amorphous ratio.
The afore discussed results correspond to the cases when the design/geometry of the proposed structure is fixed. We now attempt to introduce further tunability by independently altering the RI of GST layers in the presence of graphene microheaters. In this stream, we first consider varying the RI of the upper GST layer by sweeping the ratio m from 0 to 1, and evaluate the wavelength dependence of absorption spectra in the range of visible to the mid-IR regime; Fig. 13 exhibits the obtained results when the lower GST layer remains in the α-state.
We clearly observe in Fig. 13 that m = 0 results in absorption peaks in the visible and IR (~ 1520 nm) regimes. Another absorption peak with relatively less amplitude forms in the mid-IR regime around 4.67 µm. By increasing the crystallinity ratio, say for m = 0.5 , absorption spectra shift a little toward the IR regime, whereas in the visible span, these become more expanded (as compared to the IR regime). The heating of the upper GST layer would increase m , which causes ultimately splitting of the absorption peaks in two parts positioned at 770 nm and 1340 nm (for m > 0.8 ; Fig. 13). The peak absorption at ~ 1520 nm, as observed before, now undergoes redshift to 1750 nm, while maintaining the perfect absorption. In the mid-IR regime, we notice broad-band perfect absorption at ~ 6500 nm. As such, we see that the heating of the upper GST layer results in shifting the absorption www.nature.com/scientificreports/ peaks from the IR to the mid-IR regime without significantly affecting the magnitude of absorption. However, such an operation causes expansion of absorption spectra in the visible regime, as long as m < 0.7. Figure 14 illustrates the effect of heating (i.e., varying m from 0 to 1) the lower GST layer, considering the upper GST layer in the α-state. We notice that the absorption spectra in the visible wavelength span remain unchanged including the peak absorption values, whereas those in the IR span experience red-shifts in resonance wavelengths from 1520 to 2184 nm along with slight broadening in the absorption bandwidth. This determines that the lower GST layer remains more responsible to alter the spectral characteristics in the IR regime. However, the presence of weak absorption peak in the mid-IR region is attributed to the RI of the upper GST layer in the structure. As such, the investigation reveals that the absorption spectra in the visible regime are better controlled by the upper GST layer, whereas those in the IR (or the mid-IR) span are governed more by the lower GST layer. Table 1 presents the comparative aspects (in terms of performance characteristics and the other operational and/or geometrical features) of the proposed GST-graphene-based absorber structure with some of the previously reported works [52][53][54][55][56] . We clearly observe that the proposed structure offers a broad absorption bandwidth with simultaneously maintaining the stability (in absorption characteristics) against the incidence obliquity of waves. A wide range of absorption in either the visible or mid-IR regime can be governed by controlling the crystallinity ratio of GST layers, while the thickness of the structure is comparable with other multilayer kind of absorbers.

Conclusion
The investigation is pivoted to the optical response of specially designed multilayered structure comprised of dielectric, GST alloys in amorphous and crystalline states and trilayer graphene sheets. The results reveal the presence of absorption spectra in the visible and IR regimes. Under different parametric and operational conditions,  www.nature.com/scientificreports/ the incorporation of two GST layers in the structure results in perfect absorption. The width and position of absorption bands can be governed by suitably controlling the layer thicknesses of different mediums and incidence obliquity. The embedded graphene microheaters can be utilized to achieve phase transition of GST layers, thereby introducing additional tunability feature of the structure. It has been found that the graphene layer has no disruptive effect on the optical properties as the relevant functional parameters, namely the number of sheets (in the structure) and chemical potential, do not affect the spectral performance. The results demonstrate that the use of 10 graphene layers and 0.9 eV chemical potential slightly improves absorption. The GST crystallization process has been simulated by introducing the crystalline-to-amorphous ratio-the feature that adds more tunability of the absorption spectra. The obtained results indicate the usefulness of the structure in various photonic applications, such as bolometry, label-free biosensors, IR detectors, and tunable wide-band absorbers.
Received: 16 September 2020; Accepted: 1 February 2021 License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.