Bio-inspired TiO2 nano-cone antireflection layer for the optical performance improvement of VO2 thermochromic smart windows

Vanadium dioxide (VO2) is a promising material for thermochromic glazing. However, VO2 thermochromic smart windows suffer from several problems that prevent commercialization: low luminous transmittance (Tlum) and low solar modulation ability (ΔTsol). The solution to these problems can be sought from nature where the evolution of various species has enabled them to survive. Investigations into the morphology of moths eyes has shown that their unique nanostructures provide an excellent antireflection optical layer that helps moths sharply capture the light in each wavelength from a wide angle. Inspired by this mechanism, a VO2 thermochromic smart window coated with a TiO2 antireflection layer with a novel nano-cone structure, is presented in this study to achieve high Tlum and ΔTsol. Optimization for the key structure parameters is summarized based on the FDTD numerical simulations. The optimized structure exhibits a Tlum of 55.4% with ΔTsol of 11.3%, an improvement of about 39% and 72% respectively compared to the VO2 window without an antireflection layer. Furthermore, wide-angle antireflection and polarization independence are also demonstrated by this nano-cone coating. This work provides an alternative method to enhance the optical performance of VO2 smart windows.

www.nature.com/scientificreports/ where n is the refractive index of the material and d is the thickness of the layers. For a double-layer film structure with two dielectric films, there are normally two commonly used planar antireflection optical structures as shown in Supplementary Fig. S1. One is a quarter-quarter-waved structure ( Supplementary Fig. S1a), and the other is a quarter-three quarter-waved structure ( Supplementary Fig. S1b). The quarter-quarter-waved structure contains two films which have equal h as the quarter wavelength (λ/4). For the quarter-three quarter-waved structures, one film has the quarter-waved optical thickness (h = λ/4), the other film has the three quarter-waved optical thickness (h = 3λ/4). Apart from the optical thickness of the antireflection layers, the refractive index of each layer also plays an important role to influence the antireflection performance. Based on the Fresnel equation, normal-incidence reflection can be minimized if the refractive index of the top layer can fulfill the condition 19 : where, n s = refractive index of the substrate, n 0 = refractive index of air, n 1 = refractive index of the top layer, n 2 = refractive index of the bottom layer.
By carefully selecting a suitable material (refractive index) and thickness of antireflection layer, a desired state of antireflection can be achieved. Based on these guidelines, researchers apply various materials as planar antireflection layers to improve the optical performance of VO 2 smart windows. TiO 2 is one of the most widely used materials due to its matching refractive index with VO 2 16,20 . P. Jin's group first designed a double-layerantireflection coating with TiO 2 /VO 2 and reported increases of the T lum from 32 to 49% and the ΔT sol from 4.4 to 7.0% 21 . Later, a three layered TiO 2 /VO 2 /TiO 2 structure was proposed by the same group 22 achieving a maximum increase in T lum of 86% (i.e. from 30.9 to 57.6%) but with an undesirable drop of ΔT sol from 3.9 to 2.9% 23 . Furthermore, N. R. Mlyuka's group proposed a TiO 2 /VO 2 /TiO 2 /VO 2 /TiO 2 five layered structure, and T lum increased from 40.5 to 43.65% while ΔT sol increased from 6.7 to 12.1% compared with the VO 2 single layer 24 . Although previous reports using antireflective coatings demonstrated some improvements in the T lum or ΔT sol , significant simultaneous improvements in the T lum and ΔT sol of VO 2 remain challenging. This is because the continuous thin film antireflection layer can only reduce the reflection at certain wavelengths, and it is hard to achieve a broadband wavelength (300 nm-2.5 µm in this study) antireflection performance 25 . While the target wavelength to improve T lum is in the visible light region, the thermochromic effect (∆T sol ) occurs primarily in the NIR (> 800 nm) region. Hence, it is difficult to design a planar antireflection structure to achieve the reflectance in both the visible light region and NIR region. Alternatively, nanostructure arrays are proposed as the antireflective coating to achieve antireflection in both the visible and NIR region owing to their refractive index gradient 25 .
Inspired by moth eyes [26][27][28] , researchers investigated the 3D nano-cone antireflection structure and found that it can dramatically suppress reflection and improve light transmission 29 . Most importantly, this 3D nanocone structure provides antireflection ability in broadband wavelength and it is insensitive to the direction and polarization of the incident light 27,28 , which helps moths capture the light in each wavelength from a wide angle (Fig. 1a). The nano-cone surface is composed of tapered arrays with dimensions less than the incident light wavelength. The nanoscale array provides a gradual refractive index change from the top of the cone where the refractive index is n air = 1 to the bottom with a higher refractive index. Because of the refractive index gradient, the incident light is insensitive to the structures and tends to bend progressively into the material (Fig. 1b,c) 19,25 . Although the angle of incidence changes, the coating still exhibits a relatively smooth change of refractive index, thereby suppressing the reflection of incidence in a broad range of wavelength. Furthermore, the super-hydrophobic property of the nanoscale array promotes the self-cleaning function which is helpful to address contamination problems on the antireflection surface 30,31 . Therefore, this kind of nanoscale coating has the perfect properties, namely, high transmittance in the broadband wavelength, polarization-insensitivity and self-cleaning. There are some reports of using a nano-cone antireflection layer on solar cells to reduce the light reflection and achieve good optical and energy harvesting performance [32][33][34] .
In 2013, Taylor et al. designed nanostructured, densely packed SiO 2 paraboloidal protrusions coated with a single thin layer of VO 2 on a smart window. Based on their Finite-difference Time-domain (FDTD) simulation results, the ΔT sol can reach 23.1% while simultaneously maintaining a high T lum of 70.3% 23 . The optimized results were achieved when the width of the cone was about 130 nm with height greater than 500 nm, and the coated VO 2 thin film was less than 10 nm. However, the large aspect ratio and the small thickness of the VO 2 layer pose great difficulties in fabrication of the structure. Following the simulation by Taylor et al., Qian et al. fabricated nanostructure VO 2 smart windows (with a periodicity of 440 nm and VO 2 film thickness of 140 nm), and reported the T lum of only 44.5%, with ΔT sol of 7.1% 5 .
This work aims to achieve high T lum and ΔT sol simultaneously for VO 2 thermochromic smart windows. A novel VO 2 -TiO 2 nano-cone structure antireflection layer for the thermochromic smart window is proposed since TiO 2 is an easily obtained and refractive matching material for the antireflection layer. Also, TiO 2 is frequently employed to treat pollutants and withstand fogging due to its photocatalytic and photo-induced hydrophilic properties, which can help the windows achieve self-cleaning functions 36 . In addition, the refractive index gradient nano-structure can improve the antireflection performance in the broadband wavelength and imprinting techniques have been widely used on TiO 2 to imprint nano-patterns [37][38][39][40] . In order to achieve the best results of T lum and ΔT sol , FDTD simulations are conducted to examine the best geometrical dimension for the thickness of VO 2 and TiO 2 as well as the height and pitch of the nano-cone array. The optimized structure shows that the nano-cone structure offers an improvement of T lum without deteriorating ΔT sol . Meanwhile, the independence of the polarization and wide-angle of the incident light is demonstrated. This opens a new approach to enhance www.nature.com/scientificreports/ optical properties for thermochromic VO 2 smart windows in real-life applications, providing high transmittance along with low energy consumption for buildings.

Methodology
Calculation of optical parameters. There are two important indices to quantify the optical performance of the VO 2 thermochromic smart windows, which are luminous transmittance (T lum ) and solar modulation ability (∆T sol ). T lum describes the amount of visible light transmitted by the windows that is useful for human vision under normal conditions, it is defined in Eq. (3), where T(λ) is the transmittance of the windows at wavelength λ. y ̅ (λ) is the CIE (International Commission on Illumination) standard for photopic luminous efficiency of the human eyes. The wavelength range used for T lum is 380 nm-780 nm, corresponding to the limits of human vision. For convenience in this study, the average luminous transmittance (T lum,ave ) which describes the average value of luminous transmittance in the cold (T lum,cold ) and hot state (T lum,hot ) is defined as, T lum,ave = T lum,cold + T lum.hot 2 , where AM 1.5 (λ) is the solar irradiance spectrum for an air mass of 1.5. The AM1.5 weighting spectrum is chosen for T sol calculations as it represents an overall annual average for mid-latitudes including diffuse light from the ground and sky on a south facing surface tilted 37° from horizontal 41 . The wavelength range for calculation is from 300 to 2,500 nm which accounts for higher than 99% of terrestrial solar energy. Apart from transmittance, the luminous reflectance (R lum ) 42 and absorption (A lum ) are calculated by integrating with photopic luminous efficiency as Eqs. (6) and (7), where R(λ) is the reflectance. In order to quantify the amount of solar thermal energy entering the house through windows, solar transmittance (T sol ) is defined as Eq. (8) and the solar modulation effect of a smart window between cold and hot state is quantified as Optimization criteria. In a preliminary design of the structure, in order to select the antireflection material with suitable refractive index and predict the thickness of the antireflection layer, one specific wavelength is chosen as the target wavelength for simplicity. Considering the highest photopic luminous efficiency and solar irradiance (green and orange regions, respectively, in Supplementary Fig. S2) 23 , the wavelength of 550 nm is designated as the target wavelength and the main purpose of the antireflection coating is to minimize the reflectance at 550 nm. It should be pointed out that the wavelength of 550 nm is only used to carry out the preliminary design to determine the suitable material as the antireflection material. In the detailed FDTD simulation, the simulated wavelength region is indeed from 300-2,500 nm which covers the whole visible light and solar irradiation range. The wavelength dependent complex refractive index of VO 2 and TiO 2 are also considered in the wavelength range of 300-2,500 nm.
Optimization design. The approximate refractive index (neglecting the extinction coefficient) of VO 2 at 550 nm is 2.79 in the cold state and 2.44 in the hot state 23 . The result calculated from Eq. (2) shows that the refractive index of the suitable antireflection material should be about 2.30 in the cold state and 2.03 in the hot state. The refractive index of TiO 2 (2.44 at 550 nm) is closer to that ideal value, justifying our choice of TiO 2 as the optical antireflection material in this work.
Nano-cone antireflection surface was first discovered on the cornea of night-flying moths in 1967 43 . The eyes of this insect are covered with nipples at a pitch ranging from 180 to 240 nm and heights varying between 0 and 230 nm. Their hexagonal arrangement is due to the high areal densities to provide a large area for antireflection 26 . So only a hexagonal nano-cone surface distribution is investigated in this study. To support the nano-cones, a planar TiO 2 layer is designed between the VO 2 and TiO 2 nano-cones. The whole structure is deposited on the quartz substrate in sequence and is schematically illustrated in Fig. 2. For the best optical performance, the thickness of VO 2 and TiO 2 planar layers, as well as the pitch (the distance between two adjacent nano-cones) and the height of the TiO 2 nano-cones are the key parameters to be optimized in the simulation. It should be noted that the main purpose of this study is to investigate the improvement of optical performance by adding nano-cones, so only one planar TiO 2 antireflection layer is adopted even though multiple layers may lead to better T lum and ΔT sol . The optimization is conducted by a cycling method to ensure the optimized structure can be selected. The detailed optimization steps can be found in Supplementary Fig. S3 and Supplementary Note S1. FDTD simulation model. As FDTD gives an excellent scaling performance of the method as the problem size grows and is widely used in the research of nanophononics 33,[44][45][46] , FDTD simulations are conducted to optimize the thickness of each layer as well as the dimensions of the nano-cones and to analyze the optical performance. The real and imaginary parts of the complex refractive indices from 300-2,500 nm of the VO 2 and TiO 2 are taken from the references 23,47 . The structure is drawn in the commercial software Lumerical FDTD Solutions as shown in Supplementary Fig. S4. For the structure optimization to determine the suitable thickness of VO 2 and TiO 2 as well as the dimensions of the nano-cones, the plane wave propagating along the Z direction is used to simulate the normal incident light. Two frequency-dependent monitors are put into the SiO 2 substrate and on the top of the plane wave source respectively to collect spectral data of transmittance and reflectance. Validation of the FDTD model is carried out using two different approaches to ensure the accuracy and reliability of our proposed simulation model. Firstly, the T lum and ∆T sol of the simulation results based on only one-layer of VO 2 are compared with the previous simulation results in different thicknesses. The comparison as shown in Supplementary Fig. S5 demonstrates that the FDTD simulation results match those previously reported by others 23 . The other validation is conducted to compare with the experimental results 48 , using a glass/ TiO 2 /VO 2 /TiO 2 /VO 2 /TiO 2 five layer structure with 40 nm VO 2 films and 80 nm TiO 2 films. The same structure is repeated in our FDTD model for validation. The results show that T lum = 29.1%, T sol = 29.7% in the hot state, and T lum = 35.2%, T sol = 43.4% in the cold state, which are almost identical to the experimental results of Nuru R. Mlyuka's study 48 as shown in Supplementary Table S1. The consistency of these validations proves that the simulation model in this study is accurate and reliable.

Results and discussion
This study starts the investigation based on normal incidence. The transmittance data from the wavelength of 300-2,500 nm are collected and analyzed to evaluate the optical performance of the smart window. To explore the T lum and ∆T sol for the TiO 2 nano-cone antireflection layer, studies have been systematically conducted by varying the four parameters, the thicknesses of VO 2 and TiO 2 as well as the pitch and height of the nano-cone, and the results are discussed. Finally, to prove polarization-insensitive anti-reflectivity of the nano-cone structure, the simulations of incidence angles up to 60° under p-and s-polarized light are conducted, and the results are demonstrated.
The effect of VO 2 layer thickness on the T lum and ∆T sol . The thickness of VO 2 is important to the T lum and ∆T sol . The simulation results shown in Fig. 3 demonstrate the trade-off between the T lum and ∆T sol with the change of VO 2 thickness (i.e. 10-200 nm) , while the other parameters are constant (TiO 2 thickness: 140 nm, pitch: 100 nm, height: 250 nm). As the VO 2 -thickness increases, ∆T sol grew while T lum decreases. For window applications, the higher T lum (e.g. > 55%) is necessary to meet the indoor lighting requirement. Meanwhile, as a thermochromic smart window, better energy saving performance can be achieved with higher ΔT sol (e.g. > 10%). Based on this criterion, VO 2 with 50 nm thickness is selected in the optimized structure since the relatively moderate T lum and ∆T sol larger than 55% and 11% are achieved, respectively.
The effect of TiO 2 layer thickness on the T lum and ∆T sol . A suitable thickness of the planar TiO 2 can improve the antireflection performance. Figure 4a summarizes the simulation results of the TiO 2 layer added on the planar VO 2 (thickness of VO 2 is 50 nm) with different thicknesses (10-200 nm). The T lum increases from 42.2% at 10 nm TiO 2 to the peak of 56.4% at 50 nm TiO 2 but drops as the thickness reached 100 nm . After that, the T lum grows again reaching 51.0% with a thickness of 160 nm. The simulation results verify the theory of the antireflection layer-thickness calculation based on Eq. (1). The optical thickness of VO 2 is 139.5 nm at 550 nm (d VO2 = 50 nm, n VO2 = 2.79). To form the quarter-quarter-waved structure, the theoretical thickness of TiO 2 (n TiO2 = 2.44 at 550 nm) is around 55 nm. Similarly, for the quarter-three-quarter waved structure, the thickness of TiO 2 is around 165 nm. The simulation results of TiO 2 thicknesses at 50 and 160 nm lead to peaks of T lum . The  (Fig. 4b), so the required TiO 2 thickness of the optimized structure is smaller after adding the nano-cone. The simulation results in Fig. 4b reveal that 30 nm and 140 nm TiO 2 after adding the nano-cone leads to the two relatively high transmittance vertexes with T lum at 58.1% and 55.4%, respectively. However, these two thicknesses show different improvements of ∆T sol . While ∆T sol can be improved from 6.6% to 9.0% (i.e. improved by 36.7%) after depositing 30 nm of TiO 2 compared with the pure planar VO 2 , it can reach 11.3% (i.e. improved by 71.6%) at 140 nm of TiO 2 . This difference can be explained by the stronger reflectance of near infrared light after adding 140 nm of TiO 2 in the hot state. The red and blue solid lines in Fig. 5 illustrate the reflection spectra of VO 2 after adding 30 nm and 140 nm of TiO 2 respectively. It is observed that regardless of the cold or hot state, after adding 30 nm and 140 nm of TiO 2 , the relative low reflectance appears in the visible light region. This is the key reason why T lum can be significantly improved due to the good antireflection performance in the visible light region. But the reflection spectrums are quite different in the NIR region (780 nm to 2,500 nm). Although the spectrum shapes of adding 30 nm and 140 nm TiO 2 are different in Fig. 5a, the reflectance of 30 nm and 140 nm TiO 2 are almost identical in the cold state, which induces a small difference of T sol,cold between the 30 nm and 140 nm TiO 2 layers (56.5% vs 55.7%). However, the reflectance of T sol,hot by adding 140 nm of TiO 2 is 44.5% which is lower than adding 30 nm TiO 2 whose T sol,hot is 47.6%. This is because the huge reflectance from 550 nm to 1,600 nm (shaded area in Fig. 5b), where there exists strong solar irradiance, leads to the decrease of T sol,hot after the addition of 140 nm of TiO 2 . The smaller T sol,hot enhances the ∆T sol on the condition that T sol,cold is almost the same when 30 nm and 140 nm of TiO 2 is added. The nano-cone can also help reduce the reflection in a broadband wavelength range: comparing the red solid line and red dashed line in Fig. 5, the reflection is significantly reduced over the whole wavelength from 300-2,500 nm. For example, in Fig. 5a, there are two reflection peaks from 370 to 500 nm and 500 nm to 1,060 nm (red dashed line). However, the reflectance in these two broad ranges is significantly suppressed after adding the nano-cone. This unique feature of nano-cone is quite competitive compared with the planar antireflection layer which can only reduce reflection at specific wavelengths. Since the addition of 140 nm TiO 2 leads to a larger ∆T sol and comparable T lum relative to 30 nm TiO 2 , 140 nm TiO 2 is chosen for the optimized structure.

The influence of TiO 2 nano-cones with different dimensions of pitch and height on the T lum and ∆T sol .
Researchers have established a comprehensive optical theory about the nano-cone antireflection structure 29,32,34,49,50 . Based on the equation introduced in these theories, to avoid the structures being resolved by the incident light, the pitch (P) should satisfy the following Eq. 51 : where n TiO2 and n air are the refractive index of TiO 2 and air, respectively; θ is the angle of the incident light, that was set to 0 (normal incident light) in the following simulations; λ is the wavelength of the incident light. The main function of depositing the nano-cone is to increase luminance transmittance, therefore, 780 nm became the targeted wavelength for the following antireflection design, and the pitch of the nano-cones should be smaller than 226 nm according to Eq. (10). The height of the nano-cones can also strongly influence the optical performance. It is found that reflectance can be dramatically reduced with higher nano-cones 29,50 .
Based on the guidelines, we investigate the pitch of 100 nm, 125 nm, 150 nm, 175 nm, 200 nm, and height of 250 nm, 400 nm, 900 nm and 1,500 nm. The simulation results are shown in Fig. 6. In Fig. 6a, the T lum of 50 nm VO 2 (structure 1) is 39.9% while the T lum adding 140 nm TiO 2 (structure 2) is 46.6%. It is found that when the (10) P ≤ n TiO2 + n air sin (θ) , www.nature.com/scientificreports/ pitch of the nano-cones is smaller than 200 nm, the highest transmittance can be achieved at 55.4%. Figure 6a illustrates the change of T lum with a pitch smaller than 200 nm; the smaller pitch and lower height can lead to higher transmittance. However, nano-cones with larger pitch and height can lead to lower transmittance because of the strong absorption (A lum ) for the larger height ( Supplementary Fig. S6a). Our simulation results also show that the R lum is reduced to less than 4.1% after adding the nano-cones ( Supplementary Fig. S6b), proving that the nano-cone structures are effective as antireflection layers. However, the absorbance is enhanced as the cone size increases. Regarding ∆T sol , the simulation results (Fig. 6b) do not reveal a significant change in the solar modulation ability when the pitch size varies. The ∆T sol varies from 11.3% with a nano-cone height of 250 nm to 12.1% with a height of 900 nm. www.nature.com/scientificreports/ Optical performance of optimized structure. Based on the simulation results, the suitable pitch size should be smaller than 200 nm, as a smaller pitch leads to higher transmittance. Besides, the transmittance decreases as the height increases. However, the higher cone can induce a slight positive effect (~ 0.7% absolute) on the solar modulation ability. For the feasibility of practical fabrication, the ratio of height to pitch has to be small. Hence, it is suggested the optimized nano-cone dimension range is 200 nm ≥ pitch ≥ 100 nm, and 400 nm ≥ height ≥ 250 nm. It is expected that a high transparency T lum > 55% with a moderately high ΔT sol > 11% could be obtained with the optimized structure. www.nature.com/scientificreports/ Figure 7a clearly demonstrates the transmittance in the visible light region is significantly enhanced by the nano-cones (structure 5-pitch: 100 nm, height: 250 nm, TiO 2 : 140 nm, VO 2 : 50 nm) compared with the planar VO 2 windows (structure 1-VO 2 : 50 nm). The optimized structure exhibits T lum of 55.4% with ΔT sol of 11.3%, an improvement of about 39% and 72%, respectively, compared with structure 1. A comparison of the reflectance spectra is shown in Fig. 7b. Based on these reflectance spectra, it is shown that R lum dropped from 39.2 to 5.2% in the cold state and from 30.2 to 1.5% in the hot state after adding the nano-cones, which contributes to the improvement of transmittance. For the VO 2 -based smart windows, the solar modulation is mainly due to the regulation in the NIR region. The calculation results based on Fig. 7a show that T IR in the cold state increases from 50.8% to 62.3%, while T IR in the hot state does not change as significantly as the cold state after adding the nano-cones, only from 33.3 to 37.9%. The reason is that the enhancement of the transmittance in the cold state is www.nature.com/scientificreports/ mainly at the 1,000-2,000 nm region, where the solar irradiance is strong, but the transmittance in the hot state is enhanced at the relatively long wavelength region (i.e. 1,500-2,500 nm) where the solar irradiance is low. The stronger transmittance of NIR in the cold state enhances the T sol,cold , benefiting the ΔT sol . Moreover, to prove the functional purpose of using TiO 2 nano-cone deposited on the planar TiO 2 , one more simulation is conducted. Three different structures, including structure 5 (here, it is re-named as Structure A), Structure B that is TiO 2 nano-cone directly deposited on the VO 2 layer, and Structure C that is VO 2 nano-cone deposited on top of the 50 nm VO 2 thin film are investigated. The results are illustrated in Supplementary Fig.  S7, and found that the optimized Structure B shows a slightly higher T lum than that of Structure A (i.e. 56.6% vs 55.4%). However, ΔT sol is extremely low (i.e. 7.6%) compared to Structure A (i.e. 11.3%). The optimized Structure C demonstrates a relatively high ΔT sol (i.e. 16.1%), and this can be explained by the VO 2 being thicker after www.nature.com/scientificreports/ depositing the VO 2 nano-cones. However, the T lum of Structure C is only 39.4% which is even lower than that of the planar VO 2 structure (i.e. 39.9%). The high absorption of VO 2 severely weakens the function of the nanocone. All in all, these comparisons indicate that the TiO 2 nano-cones deposited on the planar TiO 2 layer can achieve relatively high performance in both T lum, and ∆T sol . In addition, thanks to the self-cleaning property 52,53 and relatively mature imprinting technique of TiO 2 37-40,54 , the usage of TiO 2 on thermochromic smart window applications definitely provides the versatility and maneuverability in future studies.
It should be noted that natural light shows a random degree of polarization, including p-and s-polarizations, which have the electric field perpendicular and parallel to the incidence plane, respectively. Good optical performance for both p-and s-polarizations is required for the windows. To compare the T lum and ΔT sol of the planar TiO 2 antireflection layer and nano-cone structure under different polarization state, the simulations of incidence angles up to 60° under p-and s-polarized light are conducted. The optimized dimension of the selected nanocone structure is a pitch of 100 nm with height of 250 nm (structure 5). The simulation results are compared with the planar 50 nm VO 2 after adding 140 nm of TiO 2 (structure 2). Figure 8 shows that the nano-cone structure can function well over a wide range of angles and different polarization light compared with the planar structure. The planar TiO 2 antireflection layer shows a strong angular and polarization dependence, especially for the s-polarized light. The luminous transmittance drops from 47 to 27% from normal incidence to 60° incidence with the decrease of ΔT sol from 10.6 to 7.6% under s-polarized light. Nevertheless, the T lum and ΔT sol remain higher than 49.8% and 8.4% respectively for both p-and s-polarized light from 0° to 60° after adding the nano-cones. The simulation results confirm that the nano-cone structure is less sensitive to the direction and polarization of the optical source. This property can ensure the nano-cone structure exhibits high T lum and ΔT sol under different incident angles of natural light, which is more practical for the real application compared with planar structures.
Comparisons with other work. Table 1 compares previous reports with this work in improving VO 2 thermochromic smart window performance (T lum and ΔT sol ) using different strategies. It should be noted that only pure VO 2 and only one layer of TiO 2 is deposited as the planar antireflection layer in this study to show the optical enhancement of TiO 2 nano-cones. It is believed that with a multi-layer structure (e.g. TiO 2 /VO 2 /TiO 2 / Nano-cone) integrated with modified VO 2 (e.g. Chemical doping VO 2 or VO 2 nanoparticles), the T lum and ΔT sol

Conclusion
Inspired by moth eyes, this study proposes a novel TiO 2 nano-cone structure antireflection layer to achieve high T lum and ΔT sol for VO 2 thermochromic smart window applications. FDTD simulation is conducted to achieve the design rules and identify the optimal dimensions. The results show that high transparency (> 55%) with moderately high ΔT sol (> 11%) can be achieved by the optimized nano-cone dimensions with 100 nm pitch and 250 nm height coated on 140 nm of TiO 2 /50 nm VO 2 . The improvements of T lum and ΔT sol are about 39% and 72%, respectively, compared to the single layer VO 2 coated thermochromic smart window. The enhancement of the optical performance provides a brighter and more energy-efficient indoor environment. Furthermore, the wide-angle simulations demonstrate that the nano-cone structure exhibits better angular and polarization independence than the planar TiO 2 antireflection layer for VO 2 smart windows. This property makes VO 2 smart windows more practical under natural sunlight. The simulation of this work demonstrates that the TiO 2 nano-cone antireflection layer approach is unique for providing high T lum and ΔT sol under wide angle space and different polarization directions. It should be noted that the TiO 2 nano-cone can be fabricated by nanoimprint lithography of sol-gel derived TiO 2 layers [54][55][56] . The imprinting process is industrial friendly for roll-to-roll or large area fabrication, which makes the nanoimprint lithography process lower cost 54,57 . The nano-cone structure can also be easily integrated with modified VO 2 or other thermochromic materials to develop more efficient thermochromic smart windows. This study opens a new way to develop high performance thermochromic smart windows. The proposed TiO 2 nano-cone coating is very promising because of its high transmittance in broadband wavelength, high solar modulation, and polarization-insensitivity. It facilitates applications of VO 2 thermochromic smart windows as a sustainable envelope system for energy-efficient buildings.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.