1. Introduction

The energy usage of buildings in the US is between 20% and 40% of US primary energy demand and approximately half of this portion is actually spent on heating or cooling buildings [1]. In order to cut down the energy consumption of air conditioning, incorporation of intelligent architectural windows is considered as a green solution to improve building efficiency. Thermochromic smart windows can modulate solar thermal energy through adaptive response to weather conditions and vanadium dioxide (VO₂) is one of leading materials that could be used in the applications of thermochromic smart windows [2–4]. VO₂ has an excellent temperature-responsive behavior of switching near-infrared (NIR) transmittance upon a critical transition temperature (τ_c) of 341 K (68 °C) near room temperature, whereas maintaining luminous transmittance (T_lum) from 380 nm to 780 nm [5, 6]. The practical architectural windows requires T_lum larger than 60% [7, 8] while concurrently maintaining moderately high solar modulation (ΔT_sol). A dilemma to simultaneously improve both T_lum and ΔT_sol of inorganic VO₂ films has been tackled by a range of approaches via simulation as shown in Table 1 and the efficacy of such simulations have been proved experimentally [9–13].

Table 1. A comparison of simulated thermochromic performances presented by contemporary VO₂ smart window systems

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Introducing pores into VO₂ films [12] reduces the optical constants, thereby overcoming the physical limits of continuous films [14]. By imbedding VO₂ nanoparticles in dielectric matrix [10, 11, 14, 17] large luminous absorption of VO₂ at both high and low temperature in the continuous film can be alleviated to enhance the T_lum. Biomimetic surface [13, 15] with high aspect ratio paraboloid cones provides antireflection functionality leading to largely improved T_lum while larger volume of VO₂ contained in such structure offered enhanced ΔT_sol. However, the process of synthesizing good crystalline VO₂ nanoparticles or achieving extremely high aspect ratio nanostructures usually involves complex procedures, low reproducibility and poor durability [11, 17, 18]. The more recent pure organic [5] and hybrid thermochromic coatings [19] enjoyed unprecedented combination of high T_lum and ΔT_sol, however the loss of transparency at high temperature is not tolerated in many applications.

To maximize T_lum without the expense of ΔT_sol, this study pioneers a novel smart window design using nano-patterned VO₂-based perforated films. Since ΔT_sol of VO₂ films is largely contributed by the NIR modulation (ΔT_NIR) instead of luminous modulation (ΔT_lum) [2, 20], nanogrid structures physically allow more short-wavelength visible light to pass through the holes, while retaining the advantageous long-wavelength NIR modulating abilities of VO₂. Meanwhile, the abundant ridge area is capable of holding a high volume of VO₂, which could possibly intend to facilitate strong ΔT_sol. The dimension and shape of nanogrid design, as well as cell periodicity and film thickness were investigated by using Finite Difference Time Domain (FDTD) simulations. The calculated data demonstrate that nano-patterned films offer significant improvement of T_lum without deteriorating ΔT_sol, which open up a new approach to enhance thermochromic properties for smart windows in the real-life applications.

2. Optical design for VO₂-based nanogrid films

2.1 Structural models

In order for the perforated nanogrid not to diffract visible light or be resolved by incident light, the cell periodicity (see Fig. 1), which is defined as the distance between two adjacent holes, should be smaller than the wavelength of the visible light in the medium [21, 22]. The coating thickness should not be too large to degrade window transmittance due to light absorption [15]. Three structural models used in current optical simulation work are schematically illustrated in Fig. 1, namely square cells with square holes (Fig. 1(a)) [21, 23], square cells with circular holes (Fig. 1(b)) [24–26] and hexagonal cells with circular holes (the most densely packed) (Fig. 1(c)) [15, 27, 28].

 

Fig. 1 Three different 3-dimensional models of VO₂-based perforated thin films, (a) square holes in square lattices, (b) circular holes in square lattices and (c) circular holes in hexagonal lattices are densely packed with defined periodicity and hole length/radius as labeled.

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2.2 FDTD simulation

We performed 3D finite difference time domain (FDTD) simulations using commercial software (FDTD solution, Lumerical Inc. Vancouver, Canada). A uniform mesh size of 3 nm (x, y, and z directions) was chosen. The optical constants of materials were taken in the spectrum range from 300 nm to 2500 nm [29]. The dielectric dispersion profiles of the materials were fitted by the multi-coefficient model that relies on an extensive set of basis functions. To calculate the frequency dependent transmittance, PML (perfectly matched layer) boundary conditions were set for the z direction, and Bloch boundary conditions were applied to x and y directions of the simulation region. The VO₂ nanogrid films were supported by a glass substrate, the entire system was suspended in air/vacuum, and the incident beam was modeled as a plane wave traveling along the z-axis. Field monitors were placed at fixed z position below the surface of the VO₂ nanogrid film to detect the intensity of the transmitted beam.

2.3 Optical calculations of thermochromic properties

In order to quantify the amount of visible light useful for human vision under normal conditions, a photopically averaged transmittance has been defined as the integrated luminous transmittance T_lum. Similarly, the terms named as “integrated NIR transmittance T_NIR” and “integrated solar transmittance T_sol” are to define the NIR light and solar averaged transmittance respectively, as to quantify the amount of NIR or solar thermal energy entering a building. Upon these determinations, the modulations of transmitted luminous, NIR and solar energy are characterized as ΔT_lum, ΔT_NIR and ∆T_sol and they can be integrated by using the mathematical relationships stated below as Eq. (1) and Eq. (2).

Where T(λ) represents the measured film transmittance. The CIE (represents “Commission Internationale de I’eclairage”) photopic luminous efðciency of the human eye [30], Φ_lum, and the air mass (AM) 1.5 solar irradiance spectrum distribution [31] are used as weighting functions for the wavelength dependent transmittance coefðcients. The dimming effect of a smart window between cold and hot state is quantified as ∆T_lum. The wavelength range used for T_lum is 380 nm - 780 nm corresponding to the limits of human vision. The AM1.5 weighting spectrum is chosen for T_NIR and T_sol calculations as it represents an overall yearly average for mid-latitudes including diffuse light from the ground and sky on a south facing surface tilted 37° from horizontal. The wavelength range used for these calculations is 300 nm - 2500 nm which accounts for 99.2% of terrestrial solar energy.

3. Computed optical data and discussion

3.1 Square holes in square cells

The contour (see Fig. 2(a)) suggests that with fixed periodicity, larger holes lead to increased T_lum and depressed ΔT_sol, which is consistent with other observations [10, 20]. The table in Fig. 2(b) shows three selected samples and it suggested that T_lum could be enhanced without much sacrifice on ΔT_sol compared with continuous thin films. For unknown reason, the sample with the period size of 180 nm and hole size of 80 nm as highlighted gives both enhanced T_lum(avg) (29.0 v.s. 26.0%) and ΔT_sol (14.7 v.s 11.1%) compared with continuous films. This proves the efficiencies of nanogrid VO₂ nanostructures, which has the great potential to enhance both T_lum and ΔT_sol.

 

Fig. 2 Thermochroimc properteis for square holes perforated in VO₂ square cells at different values of periodicity and square hole length. (a) Contour lines (red dashed) of ΔT_sol are overlaid upon a coutour map of T_lum, (b) thermochomic properties of selected samples in table form.

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3.2 Structure design for nanogrid

Different nanostructures may induce different optical performance due to light interaction with different shapes of holes and cells. To exploit the shape and size effects, the nanogrid films are fixed at 110 nm thickness and 180 nm period. The computational results for each system are schematically displayed in Figs. 3(a)-3(d) respectively.

 

Fig. 3 Relationship between nanogrid parameters and thermochromic properties in terms of (a) square holes (length varied from 30 nm to 150 nm) in square cells; (b) circular holes (radius varied from 20 nm to 80 nm) in square cells; (c) circular holes (radius varied from 20 nm to 80 nm) in hexagonal cells; (d) four different structural systems with similar fill factor; (e) solar transmittance and (f) light modulation ability as a function of fill factor ( = $\frac{A(hole)}{A(cell)}$) of perforated films.

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According to Fig. 3(a), by inserting square holes into square cells with increasing hole length, the T_lum at both low and high temperature (black and red bar) are increased dramatically when the fill factor (FF) reaches to ~70% at the sacrifice of the ΔT_sol (blue bar). T_lum(low) elevates dramatically from hole length of 30 nm to hole length of 150 nm, whereas the value is surpassed by T_lum(high) once hole length is greater than 90 nm, leading to a undesirable spectra overlap in the visible range (i.e., negative ∆T_lum). Since the short-wavelength visible light carries half of energy in the entire solar spectra [19], the negative ∆T_lum induces an observable degradation in ∆T_sol, which is undesirable for a good thermochromic performance.

The large increments of T_lum with increasing hole size also occur in the circular hole design systems either in square cells or in hexagonal cells as illustrated in Figs. 3(b) and 3(c). By comparing with square holes, the circular one reveals better thermochromic behaviors, because T_lum is doubled without jeopardizing ΔT_sol appreciably. The highest averaged T_lum has been enhanced to ~63%, together with securely maintained ΔT_sol at 9.22%, when 80 nm radius circular holes arrange in 180 nm period hexagonal cells.

By summarizing the relationship between FF and the transmission, it suggested that the T_lum, T_NIR and T_sol at both low and high temperature are dominantly controlled by FF instead of the hole size or shape. This gives a general guideline for enhancing T_lum. In contrast, increasing the FF has much more complicated effects on the transmission difference between high and low temperatures as shown in Fig. 3(f), which is to the advantage of the possibility to enhance both T_lum and ΔT_sol simultaneously via increasing the FF. It is of interest to observe that the ΔT_NIR, ΔT_sol and ΔT_sol relate with the FF in a parallel way.

3.3 Circular holes in hexagonal cells

3.3.1 Thickness effect

As T_lum could be largely enhanced by increasing the FF, circular holes in hexagonal cells are chosen for further study due to the closest packed characteristics of such structure. In order to achieve ΔT_sol much higher than that of continuous VO₂ thin film, thickening the perforated nano-patterned film could be a feasible solution to raise VO₂ content and compensate the slightly sacrificed ΔT_sol when the FF is increased (Fig. 3(c)). With fixed periodicity and hole size, ΔT_sol and T_lum were studied by increasing film thickness. The highest ΔT_sol achievable is 16.7% if the film thickness is as thick as 400 nm (see Fig. 4(a)). T_lum keeps decreasing as the thickness increases. It is of great interest that as compared to continuous thin films (see Fig. 4(b)), the turning point (defined by the point where thickening loses its effect on increasing ΔT_sol) of the perforated sample can be much thicker (400 nm) than that of the continuous film (160 nm).

 

Fig. 4 Computed (a) thickness effect on ΔT_sol (black) and T_lum(avg) (blue) for nanogrid films with period = 180 nm and hole radius = 80 nm, (b) thickness effect on continuous thin films (dashed black) and perforated films (solid red).

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3.3.2 Periodicity and fill factor

The influences of periodicity and FF on the optical behaviors are presented in Fig. 5(a) with fixed 120 nm hole radius and 300 nm film thickness. An obvious blue shift of the transmission peaks could be observed with reducing periodicity and increasing FF; meanwhile both transmission at high and low temperature increases dramatically. This is indicated in the Fig. 5(b) and transmission at both visible and NIR ranges could be enhanced significantly. Compared with continuous film, T_lum increases from 4.3 to 12.6% when the FF increases to 0.666. As the hole is touching the edge of cell with corresponding FF of 0.907, T_lum can be abruptly enhanced to nearly three times as compared with the sample where the FF is 0.773. Similar trends can be observed in both NIR transmission and solar transmission which suggests that with touching holes, the whole solar transmission could be boosted enormously. The periodicity effects on modulation (Fig. 5(c)) are more complicated. ΔT_lum/ΔT_NIR can be increased from 0.3%/18.8% (continuous film) to 5.0%/24.3% (the touching holes sample with corresponding largest FF). This, to large extent, favors the largely enhanced ΔT_sol (8.6 v.s 14.0%) compared with continuous films.

 

Fig. 5 (a) Computed spectra of transmittance for perforated VO₂ films with different periodicity and FF as compared to continuous thin films. (All film thickness = 300 nm) (b) solar transmittance and (c) light modulation ability as a function of periodicity.

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3.4 Summary of parameter optimizations

The thermochromic properties of best performing samples are listed in Table 2. As hexagonal cells/circular holes provide the largest possible FF, good combinations of high transparency (> 70%) with moderately high ΔT_sol (>10%) could be obtained with touching holes design. This finding surpasses the best reported simulation results such as nanoporous thin film and nanothermochromic coatings (Table 1). Although the ΔT_sol is slightly lower (14.0% v.s.15.5%) than the moth-eye nanostructuring, the averaged T_lum is higher (76.5% v.s 68.5%). It should be noted that such biomimetic moth-eye structure with 500 nm height and 135 nm base-width nanostructures is of great technical challenge to achieve in practice.

Table 2. Typical thermochromic properties for the samples with optimized nano-patterning parameters

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Finally it should be mentioned that diffraction effects from the periodic structures were considered and found to be negligible. For window applications it is essential that the light transmittance will be direct, i.e. the window should not be diffractive. In order to evaluate possible diffraction effects in VO₂ perforated film, the transmitted diffraction efficiencies at different orders were calculated using Rigorous Coupled Wave Analysis (RCWA) [22]. In the simulation, the circular holes were replaced with rectangular holes of the same surface area to reduce computation time. The calculations were performed for the optimum structure with the largest period. The diffraction depends on the ratio of the period to the wavelength and hence the highest effect is supposed to occur in the largest period and the shortest wavelengths. Therefore, the sample tested was with the period size of 240 nm, square hole size 212 nm, and thickness 300 nm. The transmission contribution is found mainly due to the zeroth order whereas the higher diffraction order efficiencies are up to 5% in the 500-600 nm range while it is less than 0.5% throughout the wavelength range 550-2500 nm.

4. Conclusion

Numerical optimizations using parameter search algorithms were implemented through a series of FDTD simulations with taking account of film thickness, geometrical design of nano-holes and cells as well as periodicity and FF. This study presents a novel approach towards achieving high T_lum for thermochromic smart window applications via VO₂-based nanogrid perforated films whilst maintaining moderate ΔT_sol as required for smart architectural window applications. Increasing the FF could tremendously enhance T_lum and the largest possible T_lum (~80%) could be acquired via touching holes configuration in hexagonal cells with circular hole design. Thickness effects on enhancing ΔT_sol is limited to less than 200 nm in continuous films, whereas it is extended up to 400 nm by adopting periodic perforating structure. This opens up a new concept for thermochromic VO₂-based films to satisfy the real-life requirements for smart window applications.