Dynamic tuning of optical absorbance and structural color of VO₂-based metasurface

2.1 Structural design

The VO₂/Au/Si hierarchical structure was fabricated by the magnetron sputtering method as shown in Figure 1a. Real photographic images of the hierarchical structure before and after the phase transition are presented. The structure appears lime green at room temperature and yellowish brown after the phase transition. The sample was characterized by XRD (Rigaku SmartLab 3 kW) with Cu K1 irradiation at a scanning rate of 3°/min with 2θ ranging from 25° to 70°. In the test, the grazing incidence was chosen at an incidence angle of 0.5° because that the high energy of normal incident light easily penetrates the film and reaches the substrate, thus causing a large disturbance to the final result. The peaks at 28.03°, 44.5°, 55.5°, and 64.8° in Figure 1b correspond to the (011) [35], (012) [36], (211) [37], and (013) [36] planes of VO₂, respectively, confirming the existence of monoclinic (M₁) phase transition of VO₂. It is worth noting that there is a 38.5° peak, which is not strictly an Au diffraction peak ((111), 37.9° [35]) nor a VO₂ diffraction peak ((020), 39.9° [37]). This is a mixed peak of the two elements caused by the energy breakdown through the VO₂ film to the Au surface due to the excessive intensity of the light source and the thin thickness of the VO₂ film. The diffraction peaks of other impurities or phases were not detected except for the diffraction peaks of M₁-VO₂ films. The surface morphology (Figure S1) and energy dispersion (Figure 1c) of the samples were also investigated by scanning electron microscope (SEM) – energy dispersive spectroscopy (EDS) model SU8220. The results confirm the presence of V and O elements in the sample. Figure 1c also shows the Au peak caused by the energy breakdown through the VO₂ film.

Figure 1:

Characterization of the prepared samples and model parameters for calculation. (a) The real optical photograph images of the fabricated VO₂/Au/Si multilayer structure at 27 °C, 80 °C, and 100 °C, respectively. (b) XRD results of VO₂/Au/Si multilayer structure at grazing incidence. (c) EDS spectrum of VO₂/Au/Si multilayer structure. (d) Optical schematic of the hierarchical structure. (e) Parametric diagram and (f) global schematic diagram of MoS₂/VO₂/Au/Si metasurface.

Figure 1d depicts the experimentally prepared schematic diagram of multilayer VO₂/Au/Si. The total thickness is 1 mm, and the thickness of Au and VO₂ is 150 nm and 123 nm, respectively. In the FEM simulation, the periodic tetragonal structure with a period P of 250 nm × 250 nm is used. The total thickness is set to 700 nm, ensuring that the electromagnetic waves do not penetrate the structure, so the absorption is A = 1−R. Figure 1e and f shows the MoS₂/VO₂/Au/Si metasurface, where the MoS₂ shape is square with default side length and height of L = 125 nm and h = 50 nm, respectively. The main polarization directions of the light source are transverse electric (TE) and transverse magnetic (TM) directions.

2.2 Experiments and simulations

The reflectivity and temperature-dependent dielectric function of the VO₂/Au/Si hierarchical structure was measured with the RC2 ellipsometer purchased from J.A. Woollam Company. In the high-temperature test, the Linkam heat cell heated the system. The measured angle of incidence was set to 70°. Nitrogen gas was continuously introduced during heating to remove oxygen from the heating chamber to prevent oxidation. The ellipsometric parameters of ψ and Δ were first obtained by RC2 ellipsometer. Each layer was modeled separately for the hierarchical structure to extract its dielectric function and thickness. The silicon substrate layer was modeled first, followed by an intermediate layer of thin-film gold with a thickness of 150 nm. Finally, the VO₂ layer was modeled with the optical model B-spline [38] to improve the fitting accuracy of this layer, and the thickness fitting option was turned on. The dielectric functions of Si, Au, and VO₂ at temperatures ranging from 30 °C to 300 °C in the spectral range of 300 nm–1600 nm were obtained and the thickness of VO₂ obtained by fitting was 123 nm. A more detailed ellipsometric working principle can be found in our previous study [39].

With the SE-measured dielectric function as input, FEM simulations on radiative properties of multilayer structures were performed. Floquet periodic boundary conditions were used in the X and Y directions to mimic the composite structures, and perfect matching layers (PML) boundary conditions were used in the Z direction to truncate the simulation volume. The thickness of PML was set to 1/4 wavelength and the convergence mesh to 1/5 wavelength, respectively.

The impedance transformation method can be applied to analyze the absorption properties of the structure, and the impedance Z of the absorber and impedance Z ₀ of free space are calculated following [40, 41]

where S ₁₁ and S ₂₁ are the reflection and transmission coefficients, μ(λ) and ε(λ) are the magnetic permeability and dielectric function of the structure at the wavelength, respectively. The closer the impedance of the absorber is to Z ₀ = 1, the stronger its absorption capacity.

3.1 VO₂/Au/Si hierarchical structure

We first investigate the dielectric function of VO₂ films in the VO₂/Au/Si hierarchical structure. According to previous studies [42, 43], VO₂ undergoes tetragonal rutile (R) phase to M₁ phase transition as the undimerized vanadium atoms undergo classical Mott transition, and the crystal symmetry is broken (Figure S2). This process inherently changes the dielectric function of VO₂, which is closely related to the atomistic and electronic structure, and Figure 2a and Figure S3 illustrate the differences. The onset of the absorption peaks of the absorption coefficient spectrum (α) reflects the optical band gap and can be obtained from the intersection of the tangent line of the absorption edge of the spectral absorption peak with the energy axis (x-axis) [44], as shown in Figure 2b. In VO₂, the absorption onset O of main peak K₁ (Figure 2b) is related to the indirect transition process involving O-2p and V-3d states near the Fermi energy level. And the onset O′ of peak K₂ is contributed by the transition process of O-2p states to higher energy levels (see S4 for more details in Supplementary Information). The temperature dependence of onsets for different absorption peaks is thoroughly investigated. As seen in the inset of Figure 2c, high temperature induces a red-shift of the onset O due to Mott physics [42], i.e., the band gap energy decreases with increasing temperature. In the R phase, the onset O disappears due to the vanishing of the interband transitions between V-3d and O-2p states. On the other hand, the onset O′ of peak K₂ blueshifts with increasing temperature in the M₁ phase indicates an increase in the transition energy of O-2p states. However, after the phase transition occurs, there is a significant red-shift in the absorption onset O′ due to the reduced band gap and lower transition energy of O-2p states to higher energy states (Figure S4a–b). Also, there is an overall decreasing pattern of onset O′ with increasing temperature, which indicates that high temperature causes a decrease in the O-2p states transition energy in the R phase. More relevant details of DFT calculations and discussions are given in Supplementary Information S4.

Figure 2:

Ellipsometric measurements: (a) VO₂ dielectric function under two phases, (b) VO₂ absorption coefficients under two phases and the location of the marked of absorption onset, (c) absorption onset at different temperatures, (d) absorptance under s (TE) and p (TM) polarization, and (e) the comparison between experimental measurements and FEM calculations.

Next, the radiation characteristics of the multilayer structure are studied using FEM simulations. Since fewer metallic features are involved [45], we call the dielectric states before and after the phase transition high-ε and low-ε, respectively. Figure 2d shows a considerable polarization sensitivity in the absorption of the hierarchical structure at oblique incidence, so all the absorption mentioned in this paper is total A _total = (A _TE + A _TM)/2. As seen in Figure 2e, the FEM simulation results agree well with experimental results regarding absorption peak positions, which provides favorable conditions for the peak coupling study below. However, the absolute value of the simulated absorption is lower than that of the experimental results, possibly due to the deviation of the VO₂ thickness (confirmed by Figure 3b) chosen in the simulation from the actual experiment and errors from the material parameters.

Figure 3:

Absorption characteristics of VO₂/Au/Si hierarchical structure. (a) The absorption at 60° incidence, including the VO₂/Au/Si hierarchy (including simulation and experiment), the individual contribution from its components (including Au layer and VO₂ layer), and VO₂/Si bilayer reference structure. (b) Calculation of the thickness dependence of VO₂ at vertical incidence. (c) Absorption of the hierarchy structure at 30 °C and 100 °C at 60° incidence. The positions of absorption peaks A, B, and C at 30 °C and 100 °C are 0.588 nm, 0.504 nm, 0.460 nm and 0.561 nm, 0.489 nm, 0.444 nm, respectively. Dotted lines plots indicate ∂ 2 A ∂ λ 2 at the corresponding temperatures. (d) Impedance ((Z _TE + Z _TM)/2) of the hierarchy structure at 30 °C and 100 °C at 60° incidence. Magnetic fields of absorption peaks A, B, and C at (e) 30 °C and (f) 100 °C.

Then, the absorption contribution of each layer in the hierarchical structure is investigated. Figure 3a shows that the VO₂/Au/Si structure has three absorption peaks in the visible range, and they are all contributed by the VO₂ layer, which can be confirmed by comparing the absorption of the VO₂/Si bilayer structure. The Au layer mainly contributes to the 0.46–0.56 μm range absorption. To better distinguish the absorption features, we fit the second derivative of the absorption spectra concerning wavelength ∂ 2 A ∂ λ 2 referring to the previous treatment of enhanced dielectric function spectral line shapes [46, 47] (see S5 for more details in Supplementary Information). Then, the formation conditions of the F–P resonance [20] in VO₂ and its contribution to peak A are studied. The magnetic field (Figure S6) at peak A is localized inside the VO₂, confirming the formation of F–P resonance. Figure 3b shows that as the thickness of VO₂ decreases, the absorption peak A blueshifts and weakens until peak A disappears at the height h ≈ 50 nm. It is due to the reduction of the effective cavity length and the gradual disappearance of the F–P resonance. The low thickness exhibits a narrower bandwidth, which has lower energy dissipation, as evidenced by the more muscular magnetic field strength (Figure S6).

When VO₂ shifts from high-ε state to low-ε state, peak A blueshifts and decreases in value (Figure 3c). It is due to the weakened F–P resonance, and the magnetic field exhibits a weaker and nonuniform character, as shown in Figure 3e and f. Since A _TE is similar to A _total, this paper’s magnetic and electric fields are considered under the TE wave. In the near-infrared (NIR) range, a plasmonic resonance (peak P) appears attributed to the more active surface electrons in metallic VO₂ [31]. The solid optical interference [30] enhances the total absorption within the spectrum (Vis-NIR region), as shown in Table S1. The impedance transformation method can also be used to analyze the absorption changes of the hierarchical structure caused by the phase transition of VO₂ [48]. As shown in Figure 3d, the low-ε state makes the impedance lower and closer to 1, thus increasing the absorption of the structure. The peak A related to F–P resonance of the low-ε state is blue-shifted concerning the high-ε state, while the impedance value of the low-ε at the dip is higher than that of the high-ε state, indicating a lower absorption capacity. The impedance curve is smoother in the range below 561 nm, which is shown in the absorption curve as the disappearance of the remaining peaks except peak A (Figure 3c). In addition, an impedance dip at the wavelength of 880 nm indicates the appearance of a new absorption.

3.2 MoS₂/VO₂/Au/Si metasurface

The bulk MoS₂ has excellent excitonic polarization that can realize light–matter solid interactions [49], which helps improve the spectral tuning of the VO₂ system. A MoS₂/VO₂/Au/Si simulation model is developed using the default parameter values in Figure 1c and d and studied for the radiation performance. The dielectric function of bulk MoS₂ is available in the literature [27]. Figure 4a shows that the introduction of the bulk MoS₂ broadens the strong absorption range and increases the absorption features, which is attributed to the high-ε property (see Equation (S2) in Supplementary Information) and abundant exciton absorption of MoS₂ (Figure S3e). Peak A red-shifts, and peaks B, C, and E related to MoS₂ excitons emerge, suggesting the enhanced average optical absorption (from 0.54 up to 0.65 in the 400 nm–1000 nm range). Peak D contributed by MoS₂ blueshifts slightly and increases in amplitude. Figure 4b–d demonstrates the specific physical mechanism. The magnetic fields at peaks A, B, and C show a longer optical path and are located in the middle region between the lower MoS₂ layer and the upper VO₂ layer, demonstrating that a new F–P resonance is generated in MoS₂ [20], where the Au layer and the top MoS₂ act as two reflectors. The optical field at peak D is strongly localized at the MoS₂ surface edge, and the internal field strength is also more extensive than that of the pure VO₂ structure (Figure 4c and d), explaining the high value (see Equation (S2) in Supplementary Information) and the narrow bandwidth of peak D.

Figure 4:

Absorption characteristics of MoS₂/VO₂/Au/Si metasurface. (a) Comparison of absorption of structures with and without MoS₂ at an oblique incidence angle of 60°. The size of MoS₂ is the default structural parameter. Dotted lines plots indicate ∂ 2 A ∂ λ 2 at the corresponding structure. (b) The magnetic fields at different peaks of the structure with MoS₂. (c) Optical field of peak D (λ = 495 nm) under MoS₂ nanostructure. (d) Optical field of D under VO₂/Au/Si structure.

Furthermore, the effect of the polarization and incidence angles on the MoS₂ metasurface is investigated. The sensitivity of the metasurface to the polarization angle is first studied, as shown in Figure S7a–d. When averaging the absorption of the TE and TM directions at an oblique incidence angle of 60°, it is found that in the 0°–80° polarization range, the absorption shows a symmetric distribution with the polarization angle of 40° as the dividing line, i.e., the closer to 40° polarization angle, the larger the absorption of the metasurface. Then, the sensitivity of the metasurface to the incidence angle is investigated. As shown in Figure 5a and e, peak A decreases with increasing angle, while the absorption in the range from peak E to peak B position shows the first increase and then decreases with increasing angle, and the turning point of the change is near 30°. It is evidenced by the weaker optical field of peak B at a larger angle (>30°), as shown in Figure S7e. The contour plot of total absorption (contour plots of absorption in the TE and TM directions are shown in Figure S8a and S8b in Supplementary Information) shows that the dip X becomes apparent around 35°, which derives from the blueshift and decreases in the bandwidth of peaks E and D with increasing angle. The peak X (at λ = 544 nm) is smoothed to annihilation at an increasing angle of 50°, which the more divergent magnetic field can explain at a higher angle (Figure S7f). In a word, the incidence angles can improve the spectral modulation performance of the metasurface and realize the free transition between multiple peaks and dips.

Figure 5:

Contour map of absorption A _total  dependent on structural morphology. (a) Calculated A _total contour map at different angles. (b) Calculated height-dependent absorption A _total contour map of MoS₂ at vertical incidence. (c) Calculated length-dependent absorption A _total contour map of MoS₂ at vertical incidence, P = 250 nm. (d) Calculated period-dependent absorption A _total contour map of metasurface at vertical incidence, L = 125 nm. (e) A _total of metasurfaces at different angles. The inset shows the ∂ 2 A ∂ λ 2 at the corresponding angles. (f) Calculated absorption at different MoS₂ heights at vertical incidence. (g) Calculated absorption at different MoS₂ lengths at vertical incidence, P = 250 nm. (h) Calculated absorption at different metasurface periods at vertical incidence, L = 125 nm.

The excitonic features of MoS₂ determine the absorption of the metasurface, and the height affects the performance of the excitonic mode, so the optical absorption related to the height of MoS₂ is further investigated. The finite-thickness MoS₂ weakly increases the absorption and optical fields of the structure (Figure S9a–b). However, as the bulk MoS₂ thickness increases to about 35 nm, peak A keeps red shifting and splitting, and its slight dip feature at λ = 660 nm turns into a peak (B) feature (Figure 5b and f). This is due to increased excitonic mode coupling specific gravity [50], which induces the Fano resonance. In this process, the quality of peak C (λ = 612 nm) also becomes apparent and no longer varies with height. The ∂ 2 A ∂ λ 2 shows more information on the displacement of the absorption peaks with height (Figure S9c). In addition, the absorption increases with height, and the average absorption in the visible region (380–760 nm) reaches 0.9 when h = 70 nm (angle = 0°). A nearly perfect absorption of 0.9992 can be achieved at λ = 735 nm. This is due to the increased effective cavity length and the enhancement of the optical interference [30]. The magnetic fields are more localized at the higher height in the MoS₂ nanostructure (Figure S10), where the excitons coupling is enhanced. It proves that the F–P resonance is also generated in MoS₂ at long wavelengths at a certain height.

The length of MoS₂ (L) determines the responsiveness of the nanostructure to light. Therefore, maintaining the period P = 250 nm unchanged, the effect of MoS₂ size on the metasurface’s optical absorption is investigated. Figure 5c–g show that the dominant peak A exhibits a significant red-shift and decreases in amplitude as L increases. When L increases to 140 nm, a new absorption peak N appears near λ = 680 nm and shows a trend of feature enhancement followed by weakening as L increases. This feature can be interpreted with the help of the optical field, as shown in Figure S11. At this time, the strong magnetic field is contributed by the upper surface and lower surface (MoS₂/VO₂ intersection) of MoS₂. The optical field is mainly localized around the MoS₂ bottom corner between adjacent cells, and the MoS₂ interior also contributes a part of the field strength. In addition, when L increases to 142 nm, the absorption peak D′ at λ = 520 nm becomes gradually apparent. By observing its optical and magnetic field distribution, one can find that the peak D′ is very similar to D contributed by MoS₂ mentioned above (see S13 for more details in Supplementary Information). Then, keeping the MoS₂ size L = 125 nm unchanged, the period (P) variation on the metasurface absorption properties is investigated. First, the changes in the period do not produce new absorption features (peaks or dips). As the period increases, the prominent peak A blue shifts, and its broadening decreases. The peaks of exciton peaks B and C increase, and their broadening increases. By defining the filling factor FF = (L/P)² [51] for the metasurface, it is observed that the absorption peak A red-shifts markedly and the exciton peaks B and C decrease with increasing filling factor.

The effect of VO₂ phase transition on absorption is further investigated, as shown in Figure 6a. When VO₂ changes from high-ε state to low-ε state, the absorption peaks blueshift, and peak A couples with peak B to produce a blue-shifted peak B′ with a higher value. The quality factors Q (see Equation (S3) in Supplementary Information) [50] before and after coupling are 9.39 and 52.57, respectively, with a ratio of 5.60. It proves the occurrence of stronger coupling (see S14 for more details in Supplementary Information). The F–P resonances in peaks A, B, and C move from the VO₂ layer to the MoS₂ layer, where the VO₂ layer mainly acts as a reflector (Figure S14a). Also, the mean value of the metasurface’s absorption in the visible range decreases from 0.75 to 0.74, opposite to the temperature dependence of the VO₂/Au/Si structure’s absorption. The impedance analysis shows that the Z of low-ε state increases in the wavelength range of 646–756 nm and further away from 1, which is the main reason for the lower average absorption in the visible range (Figure 6b). In the low-ε state, a plasmon resonance peak P is formed in the NIR region, and the relationship between the plasmon resonance and the bulk MoS₂ side length L is investigated, as shown in Figure 6c. The peak P red-shifts and increases bandwidth with increasing L of MoS₂. It can be explained by the expansion of the magnetic field from the MoS₂ layer to the VO₂ layer (raised optical path) and by the diverging magnetic field (Figure S14b). As L increases, the peak P value increases and then decreases, reaching a maximum at L = 140 nm, which can be verified by the average optical field value trend (Figure S14c).

Figure 6:

Absorption of MoS₂/VO₂/Au/Si metasurface effected by VO₂ phases transition. (a) Comparison of calculated absorption in the high-ε state and the low-ε state at an oblique incidence angle of 60°. Dotted lines plots indicate ∂ 2 A ∂ λ 2 at the corresponding structure. (b) Impedance ((Z _TE + Z _TM)/2) of the MoS₂ metasurface at 30 °C and 100 °C at 60° incidence. (c) Variation of plasmonic resonance peaks with MoS₂ side length L.

3.3 Modulation of structural color

The above results suggest that the temperature, oblique incidence angle, and morphology improve the metasurface system’s light–matter interactions and that structural color’s dynamic regulation potential is accordingly stimulated [34]. First, the effects of temperature and VO₂ thickness on the structural color are investigated. Based on the temperature-dependent dielectric function, the reflectance spectra of the VO₂/Au/Si structure in the visible range at different temperatures are obtained by dispersion relations [52]. The phase transition caused a blue shift in the spectrum with decreased absorption amplitude (Figure S15a). The data in the CIE chromaticity diagram intuitively represent the variations of color coordinates from (0.2281, 0.2128) to (0.3199, 0.2710) with increasing temperature from 30 °C to 100 °C (Figure 7a). Then, the color coordinates do not change with temperature. During this process, the brightness decreases from 0.9078 to 0.8784, with a change of 0.0294. The saturation decreases from 0.8724 to 0.3459, with a change of 0.5175. The color changes from aquamarine (Hue:8.7804°) to pink (Hue:128.185°). Figure 7b shows the color comparison between the FEM calculation and experiment, with an average error of 0.02415 in the coordinate positions, which is suitable for subsequent variable analyses. Next, we compared the difference in the effect of structural color on VO₂ thickness due to phase transition by numerical calculation. More details of the calculations and analysis are shown in Supplementary Information S16. The results indicate that with increasing VO₂ thickness at the normal incidence, the maximum variations of brightness and hue in the high-ε state are more prominent than that in the low-ε state, while the maximum variation of saturation is the opposite.

Figure 7:

Structural color characteristics of the MoS₂/VO₂/Au/Si metasurface. (a) Data points in the CIE chromaticity diagram at different temperatures. The data in Figure S12a provide the raw spectral information. (b) Comparison of experimental data with FEM simulation data in x–y coordinates. The color palette of the reflective colors as a function of the thicknesses of MoS₂ layers and oblique incidence angles at (c) 30 °C and (d) 100 °C.

The sensitivities of the structural color of MoS₂/VO₂/Au/Si metasurfaces to the oblique incidence angles and heights of the MoS₂ are investigated. Figure 7c shows that as the MoS₂ height increases from h = 0 nm to h = 60 nm at an oblique incidence angle of 15°, the brightness increases from 0.32 to 0.4863 (h = 45 nm) and then decreases to 0.409 (h = 60 nm), with a maximum variation of 0.164. The hue falls from 183.5955° to 87.6893°, with a maximum variation of 96.206°. The saturation decreases from 1 to 0.1866, with a maximum variation of 0.8134. When the oblique incidence angle is 60°, the maximum variation values of brightness, hue, and saturation are 0.045, 49.5°, and 0.155, respectively. It indicates that the three attributes of color are all more sensitive to heights at low incidence angles. Fixed the height h = 15 nm, as the oblique incidence angle increases from 0° to 60°, the brightness first decreases from 0.4412 to 0.3863 (Angle = 30°) and then increases to 0.5686 (Angle = 60°), with a maximum variation of 0.1823. The hue increases from 176.5048° to 180° (Angle = 30°) and then decreases to 160.5°, with a maximum variation of 19.5°, corresponding to the turning trend of the variable angle spectra (Figure 5a–e). The saturation increases from 0.4578 to 0.4882 (Angle = 15°) and then decreases to 0.1818 with a maximum variation of 0.3064. When the height h = 60 nm, the maximum variation of brightness, hue, and saturation are 0.1647, 34.29°, and 0.1648, respectively. It indicates that the angular sensitivities of brightness and saturation are more significant at low heights, while the hue is the opposite. On the other hand, Figure 7 shows that the sensitivities of brightness and hue to height are more significant at low incidence angles in the low-ε state, while the trend for saturation is reversed. In addition, brightness and saturation are more sensitive to angle at low heights, while hue has the opposite direction. Furthermore, the sensitivities of structural color’ attributes to the temperature are consistent with the above findings (see S16 for more details in Supplementary Information). For example, the hue caused by the height of MoS₂ in the low-ε state has a more pronounced change than the high-ε state, which can be visualized by comparing the color changes in the bottom two rows of Figure 7c and d, respectively. Table S2 in the Supplementary Information gives the RGB values under each structure with the corresponding detailed brightness, hue, and saturation values for the reader’s reference.