1. Introduction

Plasmonic materials have been attracting a long-lasting research interest due to their great potential in diverse applications [1–3]. Active control of the plasmon resonance is a burgeoning subfield and relatively challenging [1,4,5]. Vanadium dioxide (VO₂) has emerged as a unique active plasmonic material due to its reversibly temperature-dependent crystal phase transition between the low-temperature monoclinic (M) state and the high-temperature rutile (R) state [6–13]. To the best of our knowledge, VO₂ is the only material that has been revealed with such crystal phase transition among the huge library of plasmonic materials. Our previous work has proven that the localized surface plasmon resonance (LSPR) on VO₂ nanoparticles (NPs) is quenched on its M state and arises on its R state [14–16]. Besides, the LSPR position is strongly related to the NP size, [14] the surrounding dielectrics, [14,15] and the distance between two NPs [15].

The unique LSPR on VO₂ also broadens the applications of plasmonic materials to the thermochromic energy-efficient smart windows [10,17–21]. It is demonstrated that the LSPR VO₂ can enhance the performance of thermochromic windows through shifting the thermal-induced transmittance contrast to shorter wavelength, [14] which possesses dense solar energy [19]. Also, the free-standing VO₂ NPs with LSPR can be incorporated into soft or elastomer matrixes for the integration with other cutting-edge technologies, such as with the kirigami or the bio-inspired reconfigurable mechanical metamaterials [15,22].

With the progress achieved, the investigation of plasmonic VO₂ is still in an early stage. Here, we investigate the plasmonic coupling effect of VO₂, compare it with one of the most-studied plasmonic material Ag, and further explore its application in thermochromic windows via a 3D finite-difference time-domain (FDTD) method. Different from Ag, the plasmonic coupling in VO₂ is characterized by strong absorbance in the NIR region and displays relatively lower sensitivity to the distance among crystals. We further optimize the cylinder arrays for thermochromic windows, which exhibits a 160% increment of luminous transmittance (T_lum) with the same solar modulation (ΔT_sol) of ∼10%, comparing to unstructured flat VO₂ films.

2. Method

A three-dimensional finite difference time domain (3D FDTD) method was performed using Lumerical FDTD Solutions to simulate the optical property in the plasmonic VO₂ nanocylinder arrays. A total-field scattered-field (TFSF) source was applied in the simulation with a simulation region of 500 nm × 500 nm × 500 nm. The perfectly matched layers were defined as boundary conditions. A fine mesh size of 0.5 nm × 0.5 nm × 0.5 nm was used. For the far-field spectra, the scattering and absorption spectra of a single VO₂ NP (M/R) with a diameter of 100 nm in PDMS medium was simulated. For the near-field responses, the electric field distribution of the single NP (M/R) at the resonance wavelength was simulated. The optical dielectric constant of VO₂ is taken from previous reports [23].

3. Result and discussion

Hexagonal VO₂ nano-cylinder arrays on quartz substrates are applied in the 3D FDTD method, as shown in Fig. 1(a). The model is characterized by three parameters, the diameter (d) and height (h) of each cylinder as well as the periodicity (p) of the arrays, described as the distance of two adjacent nano-cylinders. These parameters are deliberately adjusted in the simulation. To burst the on-off plasmonic resonance behavior of the VO₂ nano-cylinder arrays, it is natural to use the VO₂ nano-cylinder arrays with a high packing density (high filling ratio, d/h). However, for plasmonic resonators with noble metals, the high packing density may introduce strong plasmonic coupling between nano-cylinders and shift the resonance peak position significantly [24]. In this case, we first checked the plasmonic coupling behavior between VO₂ nano-cylinders to gain knowledge of whether they are suitable to be densely arranged.

 

Fig. 1. (a) Schematic of the hexagonal VO₂ cylinder arrays on quartz substrates. The structure is characterized by cylinder diameter (d), periodicity (p), and height (h), illustrating in the top- (x-y) and side-views (x-z). (b) Calculated E-field (x-y) of two adjacent high-temperature VO₂ (R) cylinders with a gap of 10 nm. (c) The E/E_o intensity analysis of VO₂ (R) alone the cylinder-gap-cylinder direction, indicating as the dashed line in (b). Analysis of the same configuration based on Ag is presented as a reference.

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The plasmonic coupling effect is investigated using two adjacent cylinders. Under a gap of 10 nm, it is observed in Fig. 1(b) a strong electric field (E-field) in the gap of two VO₂ (R) cylinders, while the intensity is relatively weak in VO₂ (M) (Supplement 1, Fig. S1). The temperature-dependent on-off phenomenon is similar to the LSPR on VO₂ reported in previous work [14,15]. The intensity in the gap is much higher than that on the surface of the cylinder, which indicates a strong plasmonic coupling effect in the 10-nm gap. To further understand the coupling effect, the Ag is applied to the same 10-nm gap model (Supplement 1, Fig. S2) and the E-field is compared with that of VO₂ (R) in Fig. 1(c). The E-field intensity is analyzed alone in the cylinder-gap-cylinder direction, indicated as the blue line in Fig. 1(b). Comparing to Ag, the VO₂ (R) shows a much weaker E-field intensity in both the gap and the cylinder surface. The result indicates the plasmonic coupling on VO₂ (R) is significantly weak than the typical plasmonic material Ag, while is nearly negligible on VO₂ (M).

To further understand the coupling effect, the scattering and absorbance spectra are calculated with a gradual increment of a gap from 10 to 40 nm. As shown in Fig. 2(a), it is observed that the plasmonic coupling of VO₂ (R) mainly represents the absorbance but is dominated by scattering for Ag (Supplement 1, Fig. S3). Besides, the plasmonic coupling is observed as the red-shift in VO₂ (R) absorbance and Ag scattering spectra as the gap decreases. However, the peak position of VO₂ (R) is only observed with a shift of 0.06 eV (from ∼0.94 to ∼1.0 eV) that is smaller than the Ag case, ∼0.28 eV from ∼1.75 to ∼2.03 eV as shown in Fig. 2(b). The result suggests that the plasmon coupling in VO₂ (R) exhibits relatively less sensitivity to the gap change, which also indicates the weak plasmonic coupling for VO₂ (R). Such a weak plasmonic coupling makes the high packing density of VO₂ nano-cylinder arrays possible.

 

Fig. 2. (a) Absorbance (abs.) and scattering (scat.) spectra of two adjacent VO₂ cylinders with gaps of 10, 20, 30, and 40 nm. (b) Analysis of gap-dependent plasmonic shifts of VO₂ (R) and Ag. (c) Transmittance spectra of cylinder arrays of the high-temperature VO₂ (R) (solid lines) and the low-temperature VO₂ (M) (dash lines). The d varies from 100 to 180 nm and the p and h are fixed at 200 and 50 nm, respectively. (d) Analysis of the T_lum and ΔT_sol based on the spectra in (c).

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The VO₂ cylinder array with a high packing density is a promising candidate for energy-efficient smart window application. The basic principle fulfills the energy-saving function is to reduce the indoor solar irradiation only on hot days with elevated temperature [17,19]. Thus two parameters T_lum and ΔT_sol are used to assess the performance and can be calculated by

We investigate the effect of the filling factor by changing d while fixing the p at 200 nm and h at 50 nm. Transmittance spectra of the cylinder arrays are presented with d changing from 100 to 180 nm, as shown in Fig. 2(c). The transmittance valley of VO₂ (R) shifts gradually to a longer wavelength under an increasing d, which is aligned with the red-shift of LSPR observed on NPs with bigger sizes [14]. The T_lum and ΔT_sol are analyzed based on these spectra, showing in Fig. 2(d). The analysis suggests under an increasing d, the T_lum decreases from ∼91% to ∼57%, while the ΔT_sol increases under an increasing d from ∼5% to ∼13% on a 180-nm array.

Under the same filling factor, the change of p also affects the performance. The h is fixed at 50 nm, the ratio of d/p is fixed for a fixing fill factor, and the p is tuned from 40 to 200 nm. The transmittance spectra of cylinder arrays with d/p = 0.9 are calculated for both high-temperature VO₂ (R) and low-temperature VO₂ (R) in Supplement 1, Fig. S4, respectively. It is observed similar transmittance before ∼750 nm (UV-Visible region), while displays distinct contrast after ∼750 nm (NIR region), which is the typical modulation region of VO₂ as reported previously [14,15]. Strong transmittance valley is observed on VO₂ (R) in NIR region due to its plasmonic-induced strong absorbance. Transmittance spectra of the arrays are further calculated with d/p = 0.8/0.7/0.6 (Supplement 1, Fig. S4) and the analysis of T_lum and ΔT_sol is plotted in Fig. 3(a) and (b), respectively. It shows under different ration of d/p, all arrays display a similar trend that is a decreased T_lum and an increased ΔT_sol for arrays with larger p. Besides, the decreased ratio of d/p (filling factor) leads to enhanced T_lum and a decreased ΔT_sol. Thus, the highest T_lum of ∼92% is observed on the array (d/p = 0.6 and p = 40 nm), accompanying with the lowest ΔT_sol of ∼3.5%. It is known that there is a trade-off between the T_lum and ΔT_sol for VO₂-based thermochromic windows [19]. The trade-off behavior is mostly attributed to the quantity changes of VO₂ crystals. Increasing VO₂ quantity promotes the ΔT_sol, while reduces the T_lum in most cases due to the strong absorbance of VO₂ in the visible region. For example, it is observed that the sample with d/p ratio of 0.9 displays a lower T_lum (Fig. 3(a)) and a higher ΔT_sol (Fig. 3(b)) than the sample with d/p ratio of 0.6.

 

Fig. 3. (a-b) Analysis of the (a) T_lum and (b) ΔT_sol of the cylinder arrays with variable p from 40-200 nm and d/p from 0.6-0.9, based on the transmittance results in Supplement 1, Fig. S4. The d/p is fixed at 0.9 and h is 50 nm. (c-d) Analysis of the (c) T_lum and (d) ΔT_sol of the cylinder arrays with variable h from 50-200 nm and d from 24-36 nm, based on the transmittance results in Supplement 1, Fig. S5. The p and d are fixed at 40 and 36 nm, respectively.

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The effect of h is further investigated, where the p and d are fixed at 40 and 36 nm, respectively. The height is tuned from 50 to 200 nm and the corresponding transmittance spectra are recorded in Supplement 1, Fig. S5a for high-temperature VO₂ (M) and Supplement 1, Fig. S5b for low-temperature VO₂ (R). Similar to the result of the filling factor effect, transmittance valley shows in the NIR region due to the plasmon-induced strong absorbance, and there is negligible change in the UV-visible region but huge contrast in the NIR spectrum. Transmittance spectra of the arrays are further calculated with d = 32/28/24 nm (Supplement 1, Fig. S5) and the analysis of T_lum and ΔT_sol is plotted in Fig. 3(c) and (d), respectively. It is observed that the increasing h leads to decreasing T_lum and increasing ΔT_sol in all arrays. The decreased p leads to a decreased filling factor, thus promoting the T_lum and reducing the ΔT_sol. The array with the highest ΔT_sol of ∼20% is observed with a low T_lum of ∼40%.

The VO₂ preparation condition is relatively harsh due to the existence of various polymorphs and several oxidization states of vanadium. [25] To our knowledge, it is extremely challenging to experimentally produce the VO₂ arrays with well-controlled morphology on such a small scale (24-36 nm) through conventional sol-gel or wet-chemistry methods [3,6,9]. Nanoscale lithography is a potential method to achieve such uniform nanostructures, while further improvement is necessary to reduce the defects, such as the domain boundaries, for large-scale production [14,20]. Other methods such as precise nanoscale assembly are also promising, [26] while have rarely been reported for VO₂ nanocrystals.

The array structure is demonstrated to significantly promote the performance of smart window applications. The T_lum and ΔT_sol of flat VO₂ films are analyzed based on their transmittance spectra of film thickness from 50 to 250 nm (Supplement 1, Fig. S6). Increasing the thickness is observed with a decreasing T_lum. The results of flat films are plotted as reference together with the performance of T_lum and ΔT_sol of cylinder array structures (Fig. 4). The results are obtained from Fig. 3 and indicated as the trend line of an increasing d/p from 0.6 to 0.9, as well as trend lines of the heigh effects on samples with a fixed d of 24, 28, 32, and 36 nm. It is observed the array structure exhibits simultaneously much higher T_lum and ΔT_sol than those of the flat films. At the same ΔT_sol of, for example, ∼10%, the array structure exhibits a T_lum of ∼79% that is 160% higher than the T_lum (∼30%) of the flat film.

 

Fig. 4. Comparison of the cylinder arrays with the flat VO₂ films in respective of the thermochromic performance of T_lum and ΔT_sol. The flat VO₂ films are calculated with thickness from 50-250 nm showing in Supplement 1, Fig. S6. The dash lines and shadow areas are guides for illustrations.

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The critical transition temperature (τ_c) of pristine VO₂ is ∼65 °C, which is slightly higher than the demand in practical energy-saving windows (∼40-50 °C). Methods to decreasing the τ_c are variable through the introduction of dopants, [27–30] size-effect, [31,32] lattice strain, [33,34] and so on [35,36]. These methods commonly accompany the electronic properties change, leading to the change of optical properties of VO₂. Thus, the performance of T_lum and ΔT_sol may vary when to lower the τ_c, and the study here may serve as general guidance for the performance of VO₂ cylinder arrays.

Besides, the hysteresis affects the thermochromic and the energy-saving performances for VO₂-based windows in a real application. This is because the VO₂ has two stable states with different transmittances at an intermediate transition temperature when the hysteresis exists: one state on the heating process and the other one on the cooling process, which usually displays a relative higher transmittance than the heating-process state. These intermediate states affect the energy-saving performance of VO₂-based smart windows in practical applications, while studies on the point are rare and extremely complex. The investigations have to consider the temperature variation of the local environment in practical, which are different from cases to cases and determined by numerous parameters, such as the climates, the building/windows orientations, the window constructions, and so on. In general, it is preferred to have a narrow hysteresis and a low τ_c for most cases. One of the promising methods is the introduction of tungsten dopants that is reported to achieve a narrower hysteresis and a lower τ_c simultaneously [29].

4. Conclusion

In summary, we investigate the plasmonic coupling effect of VO₂ and optimize the performance of VO₂ cylinder arrays for energy-efficient thermochromic windows via the 3D FDTD method. The plasmonic coupling effect displays an “on” state on VO₂ (R) and an “off” state on VO₂ (M). Compared with the Ag, the plasmonic coupling in VO₂ is characterized as strong absorbance in the NIR region with relatively weak intensity insensitive to the gap change. We further demonstrate the cylinder array is a promising candidate for thermochromic windows, which exhibits a 160% enhancement of T_lum under the same ΔT_sol of ∼10%, comparing to unstructured flat VO₂ films. The work provides a better understanding of the plasmonic properties in the phase transition of VO₂ and an efficient method for performance-enhanced thermochromic windows.