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Abstract
We optimize planar, passive thermal-regulation devices that use the phase-change properties of VO2. We calculate the tunable total emittance, defined as the difference in normalized radiated power in the insulator and metallic states of VO2 at the phase transition temperature. A single-layer VO2/ZnSe/Au device achieves a tunable total emittance of 0.574 in simulation. An optimized multilayer device using the same materials achieves a value of 0.69 in simulation, which outperforms all planar devices found in the literature. We present an analysis showing that an increase in tunable total emittance reduces the temperature fluctuations experienced by the device within a fluctuating environment.
© 2022 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Thermal regulation has been a wide area of interest for many applications. Active thermal regulation approaches based on electrical or mechanical tuning have been widely studied [1] but require power. More recently, passive thermal regulation, or “thermal homeostasis,” utilizing the phase-change properties of materials has been growing in interest [2]. Solid-state phase change materials, such as Vanadium Dioxide (VO2), change their crystalline structure at the critical temperature, thereby changing their optical properties [3]. Changes in the VO2 absorptivity at the phase transition can result in large changes in emittance.
Previous work has incorporated VO2 in the design of passive, thermal homeostasis devices based on planar [4–10], flexible planar [11], microsphere [12], and metamaterial [13–15] geometries. A common figure of merit is the tunable emittance Δε. The tunable emittance is defined as the difference in total emittance between the high- and low-temperature states of VO2, where the total emittance is defined as the wavelength-integrated radiated power divided by the blackbody reference value. Values from the literature are given in Table 1. The best experimental device is a planar design consisting of a VO2 layer on top, HfO2 middle layer, and Ag back reflector, with a Δε of 0.55 [7]. The best-performing simulated device achieves a higher Δε of 0.8, based on an array of microstructured Si cones coated in a layer of VO2 [14]. However, this requires a special structure that is difficult to fabricate and may be impractical for widescale implementation.
Table 1. List of devices found in literature
Here, we propose and optimize a planar design to achieve high performance. The device is based on a multilayer stack of VO2, ZnSe (an infrared transmissive material), and gold. We optimize the device dimensions for a single-layered stack to obtain Δε of 0.574. Using the same materials, we then optimize a multilayered stack to obtain a Δε of 0.69. This predicted value is significantly higher than experimentally measured values for planar structures.
We further analyze how the figure of merit Δε relates to temperature-regulation performance. We define the environment in terms of the power levels absorbed by the device in a hot and cold state, assuming the device makes a complete phase transition between the two states. We quantify the temperature-regulation performance by the magnitude of temperature fluctuations experienced by the device within the environment; smaller fluctuations correspond to better regulation. Under these assumptions, we find that for a particular environment, higher Δε corresponds to better device performance. We then compare our device to a constant emissivity material over a range of environments. We find that the reduction in temperature fluctuations relative to a constant emissivity material is largest when the device is “well matched” to the environment. That is, the absorbed power in the hot state is just large enough for the device to transition to the metallic state, while the absorbed power in the cold state is just small enough for the device to transition to the insulator state. To this end, the high-Δε planar designs studied here will allow optimal performance in environments with widely varying heat input levels, without the need for micropatterning.
2. Optimization of planar homeostasis devices
Figure 1(a) shows three planar device structures studied in this work. Device 1 is the planar homeostasis device studied in Ref. [10]. It consists of 62nm of VO2 coated on a 200µm silicon layer. The device has a 100nm gold back reflector. Figure 1(b) shows the normal-incidence total emittance in the metallic and insulating states of VO2, calculated as in Ref. [10]. Here, the total emittance is defined as the thermal radiated power at 330 K divided by the blackbody radiated power at 330 K. The optical constants of VO2 were taken from [10], which obtained values through ellipsometry performed on an ALD-fabricated thin film for the metallic and insulating states. The optical constants for Si and gold were taken from [17] (see Supplement 1). The difference in total emittance between the two states is approximately 0.3.
Fig. 1. (a) Device structures; (b) Total emittance in metallic and insulating states for devices shown in (a).
We next investigate the effect of tuning the thickness of the dielectric spacer layer. For this purpose, we use ZnSe as the spacer material, which has good transparency in the infrared. Figure 2(a) shows a planar structure with a ZnSe intermediate layer, which we refer to as a single-layer device. We used the built-in Matlab function fminsearch and the Transfer Matrix Method (TMM) to determine the optimal layer thicknesses for the VO2 and ZnSe, while keeping the gold layer constant at 100 nm. The optimal result was 68 nm and 650 nm for the VO2 and ZnSe layers, respectively. The largest difference in total emittance comes from a εmet of 0.631 and εins of 0.057, leading to a total emittance tunability (Δε) of 0.574.
Fig. 2. (a) Single-layer ZnSe device schematic; (b) Absorption spectrum for optimized device with ZnSe thickness of 650.7 nm.
Comparing the optimal ZnSe single-layer device (Device 2) to our previous Si design (Device 1) in Fig. 1, we see that it has a higher total emittance in the metallic state and a lower total emittance in the insulating state. This increases the total emittance tunability Δε to 0.574, nearly double that of the Si design. The absorption spectrum for the optimal single-layer ZnSe device can be seen in Fig. 2(b). The metallic absorption is higher than the insulator state absorption over the 2–30 µm range. The peaks seen in the insulating state from 12–25 µm can be attributed to the wavelength-dependent absorptivity of VO2, as observed in [10]. The prominent dip observed at 4 µm is due to the Fabry-Perot effect in the cavity formed by the metal-insulator-metal layer structure.
To further improve performance, we consider the multilayer device shown in Fig. 3(a). To determine the optimal layer thicknesses, we used the same optimization process described previously. The initial layer thicknesses were set to 17 nm, 750 nm, 55 nm, and 715 nm, from top to bottom of the stack. The result of the optimization is shown in Fig. 3(a). The optimal layer thicknesses were found to be 3.5 nm, 672 nm, 145 nm, and 365 nm, from top to bottom. The maximized Δε corresponding to these thicknesses was calculated to be 0.69, with εmet = 0.772 and εins = 0.082. With an emissive tunability greater than 0.6, this device theoretically outperforms all but one device found in the literature, including metamaterials and microstructured devices (Table 1).
Fig. 3. (a) Multilayer ZnSe device; (b) Absorption spectrum for insulating and metallic states of vanadium dioxide.
This increase in Δε from the single-layer device can be better understood looking at the absorption spectrum in Fig. 3(b). Comparing this spectrum to the one in 2(c), the absorption in the metallic state is increased significantly. This is particularly true near 4um, where the pronounced Fabry-Perot dip of the single-layer structure has been smoothed. The additional cavity in the multilayer structure also gives rise to an additional absorption peak between 5 and 10μm. Although the absorption in the insulating state also increases somewhat, there is an overall improvement in the difference between the two. We have further verified that the performance at off-normal angles represents an improvement over both the single layer Si device and the single-layer ZnSe device (see Supplement 1).
3. Discussion of performance metrics
We next examine how an increase in Δε improves the performance of a thermal homeostasis device. Such devices are designed to passively regulate temperature in a fluctuating environment. We assume that the environment we are discussing oscillates between a “hot” and a “cold” state. In Fig. 4(a), we assume that the fluctuating environment produces an absorbed power (Pabs) of 680W/m2 in the hot state, and 55W/m2 in the cold state, with a time period of 1 hour. We calculated the resulting temperature fluctuations in the device using the time-dependent heat equation, following the method of Ref. [10].
Fig. 4. (a) Absorbed power as a function of time; (b) Temperature of ZnSe Multilayer Device (solid red), Si Single-Layer Device (dashed blue), and a 0.35 Constant Emissivity Device (dotted green); (c) Colormap of temperature difference as a function of hot and cold state emissivities. Values listed next to each device correspond to their respective cold and hot state emissivities.
Figure 4(b) illustrates the performance of the VO2/ZnSe multilayer device, the VO2/Si single-layer device, and a constant emissivity material with ε = 0.35. The multilayer device yields the best performance, reducing the temperature fluctuations to ∼25 K. This value is significantly smaller than the temperature fluctuations of the Si single-layer device and the constant emissivity device, which are ∼140 K and ∼200 K, respectively.
To compare the performance of the multilayer device to an ideal device, we define a generalized performance space. Consider a thermal homeostasis device in an environment that toggles between a hot state and a cold state. We assume that each state persists long enough for the temperature to reach steady state. The device takes on steady-state emissivity values εhot and εcold, which lie between 0 and 1. In steady state, the absorbed and radiated powers are equal (Pabs = Prad), and we can use Stefan-Boltzman Law to calculate the temperature in each state.
Figure 4(c) plots the temperature difference as a function of εhot and εcold. We assume that εhot > εcold, which restricts our attention to the portion of Fig. 4(c) above the dashed line. The white region at εcold < 0.08 is excluded from the graph, since the steady-state temperature in the cold state is too high for the device to undergo a complete phase transition. Looking at the colormap in Fig. 4(c), we see that the difference in temperature decreases greatly as we increase εhot and decreases as we decrease εcold. The best-performing devices have the large difference in emissivity between the hot and cold states.
For each of the devices shown in Fig. 4(b), we can determine the corresponding values of εhot and εcold. The two emissive states of the VO2 devices can be approximated as two constant emissivity states with a switch at the critical temperature, Tc = 330 K. The three devices are shown by colored dots in 4(c). The temperature difference for the VO2/ZnSe multilayer device is nearly optimal, while the Tdiff of the Si single-layer device and the constant emissivity material are much larger.
Depending on the environment in which a device is operated, the values of absorbed power will change. Figure 4 was plotted for a particular choice of absorbed power in the hot and cold states, shown in Fig. 4(a). To understand how our multilayer device performs in various environments, we calculated the temperature fluctuations that result from different choices of absorbed power levels.
Figure 5(a) plots the temperature difference ratio as a function of the absorbed power in the hot and cold states. The temperature difference ratio is defined as the temperature difference for the multilayer device divided by the temperature difference for a constant-emissivity value material with ε = 0.35. Values less than one indicate that the multilayer device reduces temperature fluctuations better than a constant-emissivity reference. Smaller values indicate improved performance.
Fig. 5. (a) Ratio of temperature difference between the Multilayer ZnSe device and a 0.35 constant emissivity device as a function of Pabs,high and Pabs,low; (b) Modeled hysteresis loop of Multilayer ZnSe device. The blue and red curves correspond to the device’s cooling and heating cycles, respectively. The dashed black lines mark constant emissivity curves denoted by their labels. The greyed-out area was excluded from the prediction in (a).
Figure 5(a) shows that the multilayer device outperforms the constant emissivity device over the entire range of potential heat states simulated. Even at the device’s worst performance (high Pabs,high and low Pabs,low, or top, left corner of colormap), the temperature difference ratio is 0.71, corresponding to a 29% reduction in temperature fluctuations relative to a constant emissivity device. For low Pabs,high and high Pabs,low (bottom right corner of colormap), the performance of the multilayer device improves greatly. At about 657 and 55 W/m2, the multilayer device’s temperature fluctuations are about 90% smaller than that of the constant emissivity device. The white regions in Fig. 5(a) indicate parameter values outside the range of our quantitative model.
4. Discussion
To gain insight into the trends in Fig. 5(a), we can consider the hysteresis curve for our multilayer film, plotted in Fig. 5(b). The curve is plotted using the model from Ref. [18]. Within this model, the hot and cold states of the device are approximated as constant emissivity curves, with emissivity values calculated from the electromagnetic simulations (Fig. 3). Here, the values correspond to 0.690 and 0.085, respectively. The constant emissivity curve corresponding to our ε = 0.35 material is also shown for comparison. The red line indicates the multilayer device response as it is heated, and the blue line as it is cooled.
From Fig. 5(b), we observe that the absorbed power values yielding the best performance in Fig. 5(a), 657 and 55 W/m2, correspond to values just above and below the hysteresis loop. For these values, temperature fluctuations are most strongly reduced relative to a constant-emissivity reference device. We conclude that a device operates optimally when the heat states of its environment line up closely to the upper and lower radiative power limits of its hysteresis loop. This leads us to believe that the best PCM-based temperature regulation device for a specific environment will be tailored specifically for that environment’s heating cycle.
For hot and cold state absorbed powers that fall inside the hysteresis loop (grey region in Fig. 5(b); white regions in Fig. 5(a)), the device will not make a complete phase transition. From the literature [19–21], we expect minor loops to form within the major hysteresis loop [4]. While outside the range of our mathematical model, it is interesting to speculate what may occur in this region. If the device behavior along the minor loop is qualitatively similar to that of the major loop, it may also perform better than a constant emissivity reference.
In the analysis above, we have analyzed the performance of various devices assuming given values of absorbed power. This allows a straightforward comparison between devices with different cold and hot state emissivities, as well as the illustration of certain general trends. In real applications, the absorbed power may depend both on the presence of nearby heat sources and absorption of sunlight. In the latter case, the change in optical properties across the phase transition will also change the solar absorption of the device. The absorbed power in the “cold” and “hot” states will thus depend both on the incident solar flux and the state of the device (insulator or metallic). For the devices presented in this paper, we have found that the solar absorption increases somewhat across the transition. For use in a dynamically fluctuating solar environment, solar absorption should ideally decrease across the transition, in order to damp temperature fluctuations in the device. Future work could incorporate a more complex, multi-band objective function to achieve this goal.
5. Conclusion
In this paper we improved the design of planar, thermal homeostasis devices based on VO2. We found that replacing the Si device layer with ZnSe, which has higher transparency in the infrared, strongly increased the total emissive tunability. This quantity, Δε, increased from 0.3 for our previously published Si device to 0.574 for a ZnSe device, making it comparable to most of the best microstructured and metamaterial designs in the literature. Adding a second pair of VO2 and ZnSe layers to form a multilayer device further improves Δε to a predicted value of 0.69. This value is higher than all previous experimental values in the literature, making the multilayer structure a promising candidate for experimental fabrication and testing. Both VO2 and ZnSe [22–23] are compatible with ALD growth methods, allowing precise control over layer thickness.
We further investigated how the difference in emissivities across the transition affects device performance. The intuitive notion that a larger switch between εhot and εcold results in better performance was found to be correct: larger Δε corresponds to smaller temperature fluctuations in the device. We also found that a device performs optimally when the environment is “matched” to its hysteresis loop. That is, when the absorbed power levels in the hot / cold states are just large / small enough for the device to experience a complete phase transition in each cycle, the reduction in temperature fluctuations relative to a constant-emissivity device is strongest. For larger fluctuations in the environment, and more widely separated values of absorbed power, the device will still damp temperature fluctuations, but less strongly than when the environment is matched to the hysteresis loop. For environmental fluctuations that are too small to result in a complete phase transition, direct experimental measurements should shed further insight on behavior in this region and are a fruitful area for future study.
Funding
National Science Foundation (ECCS-1711268).
Acknowledgements
The authors acknowledge Vladan Jankovic, Philip Hon, and Luke Sweatlock for useful conversations and Michael Barako for suggesting the analysis framework used in Fig. 4(c).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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