1. Introduction

Thermochromic coatings have attracted significant interest from researchers due to their important applications in energy-efficient smart windows [1–8]. A stimuli-sensitive nanoparticle that resonates with light can control light flow in these coatings [9–13]. The external stimuli alter the optical refractive index of the particle, which changes the light-scattering properties. As a result, reflection and transmission from the coating can be manipulated by controlling the stimuli. Thermochromic materials can be classified into three types, including inorganic, organic, and liquid crystal types [14]. Inorganic thermochromic materials such as VO₂, ZnO, TiO₂, Cu₂HgI₄, etc., exhibit thermochromic behavior ranging from 70-500°C [15]. Among them, vanadium dioxide (VO₂), with attractive optical and electrical properties around its transition temperature (around 68°C), is known as the most suitable inorganic thermochromic material in the near IR region [16]. Also, VO₂ has been employed as a primary material for thermochromic composites in which temperature variation alternates the optical index in the material [17,18]. Due to these reasons, VO₂ was chosen as the phase change material in this study. The temperature dependence of the optical properties of vanadium dioxide has led researchers to investigate this material's morphology [19–21]. VO₂-based thermochromic composites can be classified into VO₂-based layered structures and VO₂ nanoparticles [22]. The research focused on controlling and optimizing the optical properties of VO₂ thin films and doping with various elements [23–25], multilayer structures [26], and manufacturing using various techniques such as sputtering [27]. In addition, the transmittance and absorbance of these coatings has been investigated extensively in the literature [28,29].

VO₂ core-shell nanoparticles offer more flexibility for tailoring the optical properties through the geometry and materials of the core or shell structures [30–34]. Adding shells to resonant nanoparticles can allow nano-scale control of energy [35,36] and tuning of the localized surface plasmons [37]. The insulator of a resonant localized surface plasmon shell in solar cells enhances the photon absorption rate of the particle and governs its reflectivity to improve light harvesting [38]. Using this method, the reflectivity of the core nanoparticles can be improved.

This paper proposes a VO₂/Si core-shell structure to boost the composite reflection response switching. Implementing the proposed structure further reduces the losses in the nanoparticle at room temperature (T =30°C), which shows that 67% of the incident power dynamically can be controlled by switching the composite temperature from 85°C to 30°C. In general, metals are reflective above their plasma wavelength [39]. The metallic VO₂ plasma wavelength is around 900 nm [40]; therefore, this work studies VO₂ plasmonic resonance above 900 nm. On the other hand, VO₂ refractive index switching is not significant in the mid-far infrared regime [40]. Therefore, we focus on the near-infrared regime, where VO₂ particles support plasmonic resonances in this wavelength range. VO₂ is a lossy metal that absorbs incident light with a core-shell structure; however, high reflectivity is obtained by dielectric resonance. Optical dielectric resonators can be engineered to provide high reflectivity like their radio frequency counterparts [41–43]. Switching VO₂ core temperature helps switching the quality of this dielectric resonance. When the VO₂ core is metal, the resonance quality of the dielectric shell drops. As a result, the reflectivity of the core-shell structure drops when VO₂ is metal. In general, the metallic form of VO₂ has higher reflectivity in comparison with the dielectric form. The results of the current work demonstrate that the opposite of this situation can be obtained under certain conditions using the dielectric particle resonances and the lossy nature of VO₂. Another important contribution of this work is the demonstration of a random distribution of VO₂/Si core-shell particles and a comparison of the spectral results of the random distribution with those of the deterministic counterpart. This random distribution can account for possible fabrication imperfections. After studying the structure in a lattice form, randomly distributed core-shells are studied to illustrate that a composite may have behavior similar to its lattice counterpart.

2. Reflectivity of VO₂ nano-spheres

Reflection from the surface of a particle array is directly related to the ability of each particle to scatter light. On the other hand, a small particle with dimensions comparable to wavelength can have remarkable scattering properties [44]. A mathematical formulation has been developed for spherical particles [45,46]. This method analyzes isolated dielectric spheres by calculating the particle's electric and magnetic resonance modes and studying their interference's scattering characteristics in the far-field region. Hence, sub micro-meter semiconductors in the infrared regime can be modeled by their first-order mode electric and magnetic polarizabilities neglecting the small contribution from higher-order modes. The back-scattering cross-section of the low-loss dielectric nanosphere particle normalized to its physical cross-section is given as [45]:

In this equation, a₁ and b₁ are Mie scattering coefficients corresponding to the transverse magnetic and transverse electric modes, k₀ is the wavenumber in the ambient medium, and r is the particle's radius. Equation (1) is valid for an isolated spherical nanoparticle. Coatings involving phase change materials can provide an adaptive response to infrared radiation, which can play an important role in thermal management for problems involving significant radiative thermal load. This is particularly crucial for aerospace applications and extreme environments where the temperatures can be in the 1000 K – 2500 K range, for which the peak of black body radiation corresponds to (1.0 - 3.0 µm) spectral range. If absorbed, the incident radiation can create high levels of heating, which can create structural and stability problems in materials. Therefore, it is essential to achieve surfaces and surface coatings that can reduce the IR radiation load through adaptive reflective surfaces. In this study, we focus on adaptive coatings involving phase change materials VO₂ to control the reflectivity of the surfaces in the (1.0 - 3.0 µm) spectral range. To achieve this, VO₂ particles must have a considerable back-scattering coefficient at the lower temperature at this wavelength. The inherent VO₂ losses at high temperatures will reduce the back-scattering, and therefore, the reflection will decrease. To obtain an optimum particle size for higher back-scattering, Eq. (1) is utilized here. The host material is a polymer with a dispersion-less index of 1.5, and the VO₂ index is 3:2 + 0:17j for λ =2000nm. Extracting the scattering coefficients from [47] and applying them to Eq. (1) for various r gives an overview of the Q_b dependence on particle radius. Figure 1(a). illustrates this dependency for a range of radius r. Hence Eq. (1) is not valid for metallic VO₂ nanoparticles due to higher losses of VO₂ at high temperatures starting from T =50°C.

 

Fig. 1. (a) Normalized back-scattering cross-section of insulator VO₂ at λ =2000nm as a function of particle radius. (b) The reflectivity of VO₂ arrays for the lattice sizes of a =1000, 2000, and 3000 nm in 1000 <λ< 2500 nm.

Download Full Size | PDF

Figure 1(a) shows that for a small radius, Q_b is very small. When the particle size is much smaller than the wavelength, the back-scattering cross-section of the particle is a negligible fraction of its physical cross-section. However, for insulator VO₂ this amount increases smoothly up to 64% of the physical cross-section around r =320 nm, then decreases until r =400 nm. Q_b goes larger than 0.64 for larger particle sizes, but after the first local minimum at r =400 nm, the higher-order modes get excited, but their scattering is not significant compared to the main mode in r =320 nm. Therefore, an r =320 nm particle can give the maximum backward scattering.

When the nanoparticles are placed in arrays, in addition to the particle size, array lattice size plays an important role in the resonance wavelength. To find out the lattice size effect, reflection from a two-dimensional array is examined in Fig. 1(b) for the spectrum ranging from 1400 to 2500 nm. Array lattice a is selected so that the particle covers a considerable physical cross-section of the array, and the effect of different lattice sizes has been analyzed numerically using a commercial-grade simulator [48] based on the finite-difference time-domain (FDTD) method [49]. The dispersive optical index of VO₂ is taken from [50], and the silicon optical index is extracted from the experiment data by Palik [51]. The results are depicted in Fig. 1 (b) for lattice sizes of a =1000, 2000, and 3000 nm. The results in Fig. 1(b) indicate that increasing the lattice size shifts the resonance wavelengths. The collective coupling of the structure has a strong dependency on the lattice size [52]. With a smaller lattice, the electric dipole looks dominant in reflectance; nonetheless, as the lattice size grows, the sharp magnetic resonance impact increases and might exceed the electric dipole as in the case of the 2000nm lattice (red). However, with a bigger lattice size, the incident wave can pass through the particles without interacting with them. As a result, the total reflectance drops significantly. Therefore, the small lattice sizes are more desirable to achieve higher reflectivity levels. Furthermore, shrinking the lattice size to smaller sizes is not viable because VO₂ particles may overlap, and overlapped particles do not support Mie scattering.

In Fig. 2, normalized reflected power is given at both T =30°C and T =85°C for the lattice size a =1000 nm, in which the particle takes 32% of the array surface. This figure shows that by switching the temperature from T =30°C to T =85°C, the reflectivity of the array changes due to the insulator to metal phase change in VO₂. The difference in reflectivity at two temperatures maximizes around 1900nm, which the insulator VO₂ particle resonates by the incident wave. At this wavelength, the VO₂ phase transition switches the reflectivity from 0.33 to 0.05. For longer wavelengths starting from 2140 nm, the reflectivity of metallic VO₂ at T =85°C exceeds the reflectivity of insulator VO₂ at T =30°C.

 

Fig. 2. Power reflection by a 2-D array of VO₂ spheres with r =320 nm and a lattice period of a =1000 nm upon a normal light incident at mid-infrared wavelengths. Increasing ambient temperature from T =30°C to T =85°C changes the optical index of VO₂; consequently, the reflectivity of the array switches.

Download Full Size | PDF

Fundamentally, the phase transition of VO₂ changes both resonance wavelength and loss factor. At the metallic phase, the particle resonates at longer wavelengths with a relatively higher absorption rate. Therefore, the reflectivity of metallic VO₂ particles at longer wavelengths is greater than the insulator state. Basically, in an insulator state, resonance is weaker. Maximum switching in reflectivity response is around 25% of the incident power. This amount is comparable with the reported thermal reflectivity controls in the literature [10]. Note that the resonance of reflection at T =30°C has slightly shifted from the designed wavelength. This shift occurs because of the resonance mode interaction in closely packed coupled particles. The maximum reflection wavelength can be set to the designed value by tuning (in this case, increasing) the particle's radius. As shown in Fig. 2, the maximum normalized reflected power difference at two temperatures occurs around 1900nm, which manipulates approximately 25% of the incident power in this structure. Lattice dimensions shifted the resonance wavelength slightly, and the particle dimensions can be adjusted to fine-tune the resonance wavelength. This amount of reflection control is promising; however, a higher switching capability is needed in applications where controlling power is desired.

3. Reflectivity of VO₂/Si core-shells

Even though decreasing the lattice size can increase the reflected power at the low-loss resonances, controlling inter-particle distance is a challenging task [44]. Here an alternative method based on spherical core-shell structures is employed. In this technique, a lower-loss material is utilized as the shell of the VO₂ spherical core to diminish the absorbed power in the structure at resonances. Due to the high reflectivity of a pure Si nanosphere and its closer optical index to the insulator form of VO₂, Si is selected as the shell material. The combination of the VO₂ core and Si shell led to stronger scattering peak resonances and, therefore, higher reflection. Keeping the outer radius of the structure constant and increasing the thickness of the shell, the effect of a low-loss shell can be studied on the ability of the structure to control the power reflectivity. Figure 3 illustrates the power reflectivity for different shell thicknesses at T =30°C and T =85°C. The optical properties of Si are taken from [51].

 

Fig. 3. Power reflection by a 2-D array of VO₂/Si core-shells with r =320 nm and lattice period of a =1000 nm upon a normal light incident at mid-infrared wavelengths for T =30°C to T =85°C and different Si thicknesses.

Download Full Size | PDF

Figure 3 shows that the reflectivity of the core-shell is enhanced by increasing the silicon thickness at room temperature. Although the overall diameter of the core-shell remains constant, the peak of reflectivity response shifts to higher wavelength as the shell thickness grows. The index of silicon, which is slightly bigger than the index of VO₂ at T =30°C, causes this shift. At T =85°C, by increasing the thickness of the Si shell up to 0.4r, the reflectivity of the core-shell array increases. By further increasing the shell thickness at T = 85°C, the structure resonates around 2000nm. This resonance increases because the metallic VO₂ losses diminish as the volume of VO₂ decreases in the structure. As a result, the reflectivity around the resonance increases. It can be understood from the figure that the difference between power reflectivity at T = 30°C and T = 85°C maximizes at Si = 0.4r. The maximum power reflection controllability core-shell reaches 70% of the incident wave, which is bigger than the VO₂ spheres of the same size.

Generally, having an array with precise lattice is difficult, and implementing such a structure is expensive. Rather than that, composites with the same core-shell sizes but with random distribution over space can be more affordable. Here core-shells are randomly relocated in a three-layer array of VO₂/Si to study the effect of irregular composites. To form the random arrays, Gaussian random points with a median of zero and the standard deviation of 100 nm, which is almost 30% of the nanoparticle radius, are built-in 3D space using MATLAB. The numerical analysis here is limited to a 3*3 array with random relocations. The reflectivity of this composite in T =30°C and T =85°C is shown in Fig. 4 (a). This figure shows the ability of randomly distributed VO₂/Si core shells to manipulate the reflected power by shifting the temperature. In addition, Fig. 4 (b) compares the normalized reflected power for some deviation from the curve of Fig. 3 for the same Si thickness for the specific case with the randomly distributed arrays. The results indicate that the overall trend of both curves matches except for small differences around 1600 nm for T =30°C. It can be concluded that this resonance is not an inherent resonance of the core-shell, but it comes from the regular lattice of the structure. By disordering the lattice and switching it to the random array, this resonance disappears too. If the standard deviation of the nanoparticle distribution further increases, the reflection curve can have more fluctuation than in Fig. 4. We anticipate the spectral response will get smoother as the area of the structure expands. We can expect the randomly distributed core-shells of VO₂/Si to switch the reflection up to 67% by temperature switching in the structure.

 

Fig. 4. (a) Power reflectivity by a 3-D array of randomly distributed VO₂/Si core-shells at T =30°C and T =85°C. The nanoparticle radius is 320 nm, and Si has 40% of the overall thickness. (b) The comparison of the periodic lattice (a =1000 nm, r =320 nm, t_Si =0.4r) with the randomly distributed array of VO₂/Si at T =30°C and T =85°C.

Download Full Size | PDF

4. Conclusion

In summary, a core-shell structure of VO₂/Si was proposed to manage a more considerable portion of the incident light. To achieve this, first, the metal to insulator phase change of vanadium dioxide was employed to control the back-scattering from nano-spheres by adjusting their temperature. The resonance of the incident light with VO₂ nano-spheres causes bigger back-scattering at room temperature, while VO₂ has an insulator form. However, when the temperature rises to T =85°C, VO₂ reversibly transforms to a lossy metal, resonance quality degrades, and its frequency shifts to larger wavelengths. This switching in back-scattering is used to control reflection from an array of VO₂ nano-spheres. It is shown that a quarter of incident light energy can be switched around in the main resonance by reflection control via temperature switching. Then, the optical properties of the proposed VO₂/Si core-shells structure were studied numerically for a deterministic and randomly distributed set of particles embedded in a polymer host. The core-shells could switch up to two-thirds of incident light power in reflection form by controlling the resonance via temperature switching. That proves the capability of the proposed structure in implementing switchable mirrors in smart reflector applications.