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Abstract
A near-field multistage radiative thermal rectifier is proposed based on two different phase-change materials, which can achieve multistage thermal rectification with different rectification ratios. The phase-change materials vanadium dioxide (VO2) and Ge2Sb2Te5 (GST), with different metal-insulator transition temperatures, are utilized within the active terminal of thermal rectifier. Four types of active terminal structures, including multi-film and composite nanograting structures, are introduced to explore to multistage thermal rectification. Our calculations find that the active terminal composed of a one-dimensional VO2 grating atop a GST thin film is the most suitable for multistage thermal rectification due to its realization of well-distributed and flexible thermal rectification. Furthermore, it is found that the passive terminal temperature of thermal rectifier can significantly affect the multistage radiative thermal rectification by modifying the rectification ratio and adjusting the stage number of multistage thermal rectification. This work sheds light on the role of different phase-change materials within the design of promising radiative thermal rectifiers boasting multistage thermal rectification.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Thermal rectification based on radiative heat transfer, which can facilitate heat flux along a specific direction larger than that along the opposite direction under the same temperature difference, has recently garnered much attention [1–6]. Differing from conduction-based thermal rectifiers, radiative thermal rectification devices are immune to the influences of the phonon speed and the presence of Kapitza resistances [7–10]. Furthermore, the near-field radiative heat transfer (NFRHT) between the two terminals of a thermal rectification device that can exceed that of corresponding blackbody radiation limit by several orders of magnitude [11–16]. Thus, near-field radiative thermal rectifiers can further enhance the thermal rectification performance, offering promising applications for nanoscale heat control and thermal modulation, such as thermal rectifiers [17], thermal switches [18], radiative thermal diodes [6,19–22], radiative thermal transistors [8], thermal memristors [23] and electronics cooling devices [24].
Most thermal rectification devices exploit phase-change materials (PCMs) to achieve thermal rectification. The thermal and optical properties of PCMs significantly change with temperature due to the correlated interactions of phonons and electrons within the materials. Non-contact radiative thermal rectification devices utilize the change in the dielectric properties of PCMs including vanadium dioxide (VO2), Ge2Sb2Te5 (GST), La0.7Ca0.15Sr0.15MnO3 (LCSMO). These PCMs have recently garnered significant attention in theoretical and experimental research due to their valuable metal-insulator transition (MIT) temperatures. For example, when the temperature of VO2 is lower than 341 K, VO2 is in the anisotropic insulator state, while it exists in the isotropic metallic state when its temperature is above 341 K [25–27]. GST is another PCM with amorphous and crystalline phases [28–32]. The amorphous-phase GST (referred to as ‘aGST’) transforms into the crystalline-phase GST (referred to as ‘cGST’) when it is annealed above 160 °C [32,33].
Ben-Abdallah et al. designed an efficient near-field thermal diode by means of using two semi-infinite plane bodies made of VO2 and silicon dioxide (SiO2), respectively, whose rectification factor can be as high as 90% [34]. Yang et al. also investigated the near-field radiative thermal rectification between a SiO2 thin film and VO2 bulk material, which can achieve a thermal rectification ratio of almost 3 when two terminals are separated by a 100 nm gap [35]. Ghanekar et al. utilized one-dimensional rectangular and triangular VO2 gratings to significantly improve the thermal rectification ratio as high as 16 for the near-field thermal diode [20]. Chen et al. theoretically demonstrated that a near-field thermal rectifier made of a polydimethylsiloxane (PDMS) thin film and a VO2 grating can obtain an ultrahigh rectification ratio of 23.7 [19]. Some studies have also combined two PCMs to develop radiative thermal rectification devices. For example, Huang et al. investigated a near-field thermal rectification structure made up of terminals of bulk VO2 and bulk LCSMO, which can improve the rectification ratio to 8.7 when a vacuum gap between the two terminals is 10 nm [17]. Kasali et al. studied plane, cylindrical and spherical radiative thermal diodes consisting of terminals of VO2 and GST. These three types of diodes can achieve optimal rectification factors of 82%, 86% and 90.5%, respectively, indicating that compared with single one PCM, a combination of two PCMs can further promote the rectification factor of radiative thermal diodes [36]. Taking into account that two different PCMs provide more degrees of freedom than a single PCM to modulate the radiative heat transfer between two terminals of radiative thermal rectification devices, the rectification ratio of thermal rectification devices is expected to be tailored by the combination of two PCMs in one terminal of a thermal rectification device, rather than two PCMs in two different terminals.
In this paper, we propose a near-field multistage radiative thermal rectifier based on VO2 and GST, which comprise one of two terminals of thermal rectifier. This is done by considering the temperature dependence of the thermal and optical properties of each PCM within their MITs. Differing from previous studies that mainly focus on the improvement of thermal rectification ratio, this study concentrates on the multistage thermal rectification of rectifier, which can offer different thermal rectification ratios in a certain operation temperature range without changing any structural parameters. Thus, our multistage thermal rectifier can provide more flexible modulation of heat transfer in different temperature conditions. Furthermore, our work investigates the effects of the passive terminal temperature on the multistage thermal rectification of devices. Our calculations show that the passive terminal temperature can affect the value of the rectification ratio and adjust the stage number of multistage thermal rectification of rectifier. This work verifies the possibility of increasing the number of stages of thermal rectification through the composite nanostructures utilizing different phase-change metamaterials. It sheds light on the high-performance and multifunctional radiative thermal rectifier and motivates promising applications in dynamic and flexible thermal modulation in nanoscale devices.
2. Theoretical model
Here, a composite design of the multistage radiative thermal rectifier is shown in Fig. 1(a). The device consists of two terminals separated by a nanoscale gap L = 100 nm (less than the thermal wavelength $2.6\mu \textrm{m} \le \lambda \le 15\mu \textrm{m}$). The passive terminal is composed of a 1 μm gold layer on the top of a Si substrate. The active terminal has a 1D PCM-1 nanostructure of height h1 = 100 nm atop the PCM-2 thin film. The PCM-2 thin film is then placed on top of a 1 μm thick gold layer deposited on a Si substrate. The materials of PCM-1 and PCM-2 are varied to simulate different structures, utilizing the two PCMs (VO2 and GST). In Fig. 1(b), we show four structural cases for the active terminal while the passive terminal remains unchanged: (I) 100 nm VO2 film atop 500 nm thick GST layer. (II) 100 nm GST film atop 500 nm thick VO2 layer. (III) 1D VO2 grating of height h1 = 100 nm, grating period Λ = 50 nm, and filling ratio ϕ = 0.5 atop 500 nm thick GST layer. (IV) 1D GST grating of height h1 = 100 nm, grating period Λ = 50 nm, and filling ratio ϕ = 0.5 atop 500 nm thick VO2 layer. There have been several experimental works reported on the fabrication of VO2-based nanostructures [37–41]. In this calculation, GST possesses dramatically different optical properties between the aGST and the cGST due to changes in the dielectric function. The corresponding refractive index n and extinction coefficient k of the aGST and the cGST obtained from the Ref. [32] are shown in Fig. 1(c).
Fig. 1. (a) Schematic of a near-field multistage radiative thermal rectifier based on two different PCMs. (b) Four structural cases for the active terminal. Au film thickness h3 = 1 μm for these four cases. (I) 100 nm VO2 film atop 500 nm thick GST layer. (II) 100 nm GST film atop 500 nm thick VO2 layer. (III) 100 nm VO2 grating atop 500 nm thick GST layer. (IV) 100 nm GST grating atop 500 nm thick VO2 layer. (c) The refractive index n and the extinction coefficient k of aGST and cGST.
To calculate radiative heat fluxes across the near-field multistage radiative thermal rectifier, we utilize the formula for NFRHT based on the dyadic Green’s function formalism [42–45]. The NFRHT formula is as follows:
3. Results and discussion
To demonstrate the multistage thermal rectification for the proposed designs shown in Fig. 1, the heat flux is calculated based on the temperature difference between the active and passive terminals of the thermal rectifier for the four structural cases and plotted in Fig. 2(a). The phase changes of VO2 and GST are not instantaneous, and occur gradually along temperature. Here, we assume the MITs of VO2 and GST occur in a minimum temperature interval (e.g, 1 K) near 341 K and 433 K, respectively, to simplify the calculation of heat flux between two terminals of thermal rectifier. To obtain the rectification efficiency of a thermal rectifier, the rectification ratio is defined as $R = ({Q_\textrm{F}} - {Q_\textrm{R}})/{Q_\textrm{R}}$, where QF and QR refer to the forward and reverse heat fluxes, respectively [50]. Here, the temperature of the active terminal TA increases from 141 K to 541 K, while the passive terminal temperature remains the same TP = 341 K based on the MIT temperature of VO2 near 341 K. When TA > TP, the state of thermal rectifier is a forward bias, and VO2 is in the metallic phase. As for the change of GST phase with the increase of TA in the forward bias, GST is in the crystalline phase when TA > 433 K, and in the amorphous phase below this temperature. When TA < TP, the thermal rectifier is in the reverse bias state, VO2 is in insulator phase and GST is always in amorphous phase. It can be clearly seen in Fig. 2(a) that the slopes of QF are much larger than those of QR for all four cases, indicating apparent rectifier-like characteristics. Meanwhile, different from previous studies about radiative thermal rectification, each case of QF possesses two different slopes within different temperature ranges, while QR has only one slope. Thus, our thermal rectifier has two rectification ratios in the temperature range 141 K < TA < 541 K, achieving two-stage thermal rectification. More specifically, for Case I, the rectification ratio is 3.77 when ΔT = |TA - TP| < 92 K (433 K - 341 K = 92 K), while the rectification ratio increases to 4.49 when ΔT = |TA - TP| > 92 K. Similarly, the rectification ratio increases from 2.75 to 3.48 when the temperature difference between the active and passive terminals exceeds 92 K for Case II. As for the composite nanostructure of VO2 grating on the GST thin film (Case III), the rectification ratio sharply increases from 2.71 to 3.93 when the temperature difference between two terminals exceeds 92 K. However, the rectification ratio in Case IV changes less obviously than those of the other three cases, which increases from 3.27 to 3.61. Based on the comparison of four cases, it is obvious that Case III has well-distributed rectification ratios in the same operation temperature range of the thermal rectifier because the difference between two rectification ratios in Case III is larger than that in other three cases.
Fig. 2. Forward and reverse radiative heat fluxes (QF and QR) versus the temperature difference between active and passive terminals of thermal rectifier for Cases I, II, III and IV, with different passive terminal temperatures TP. (a) TP = 341 K and (b) TP = 433 K.
Due to the VO2 and GST materials having different MIT temperatures, the passive terminal temperature is set to 433 K near the MIT temperature of GST to explore the effect of the passive terminal temperature on the multistage thermal rectification. The heat flux dependent on the temperature difference between two terminals for Cases I, II, III and IV is plotted in Fig. 2(b) with the passive terminal temperature 433 K. The temperature of the active terminal TA is in the range of 233 K to 633 K. When TA > TP, the state of rectifier is the forward bias, VO2 is in the metallic phase and GST is in the crystalline phase. When TA < TP, GST is in only one amorphous phase. VO2 transforms from the metallic state into the insulating state with the decrease of TA when the thermal rectifier is in reverse bias. In contrast with the above calculation results when TP = 341 K, QR experiences two different slopes while QF has only one slope when TP= 433 K. For Case I, the rectification ratio is 0.24 when ΔT = |TA - TP| < 92 K, while the rectification ratio sharply increases to 4.49 when ΔT = |TA - TP| > 92 K. For Case II, the rectification ratio increases from 0.28 to 3.48 when the temperature difference between two terminals is greater than 92 K. For the composite nanostructure of PCM grating on another PCM thin film, two rectification ratios are 0.43 and 3.93 in Case III, and 0.14 and 3.61 in Case IV, respectively. It can be clearly seen that although all four cases can produce two different rectification ratios in the same temperature range when TP = 433 K, one of the rectification ratios is very small compared to another one in each case. Furthermore, compared with other three cases, the rectification ratio in Case III is the largest when ΔT = |TA - TP| < 92 K, which proves Case III is more suitable for multistage thermal rectification.
To further study the effect of passive terminal temperature on the multistage thermal rectification of rectifier, we also consider other five different passive terminal temperatures by setting TP = 301 K, 361 K, 387 K, 413 K and 473 K, respectively. Figures 3 and 4 display the radiative heat flux and the rectification ratio as a function of temperature difference for Case III studied with varying passive terminal temperatures, respectively. When TP = 361 K, 387 K and 413 K (between the two MIT temperatures of VO2 and GST), it can be clearly seen that both of QF and QR have two different slopes, which is attributed to the phase changes of VO2 and GST. This occurs regardless of the bias direction of the thermal rectifier. The rectification ratios of multistage radiative thermal rectifier under different passive terminal temperatures for Case III shown in the Table 1. When TP = (433 K + 341 K)/2 = 387 K, there are two rectification ratios: 0 and 3.93, respectively. In other words, the multistage thermal rectifier can achieve a rectification effect only in a certain range of temperature differences (ΔT = |TA - TP| > 46 K). However, when TP = 361 K, there are three rectification ratios: 0, 2.71, and 3.93, respectively, leading to a three-stage thermal rectification due to the asymmetry of the passive terminal temperatures. Similarly, when TP = 413 K, three rectification ratios are 0, 0.43, and 3.93, respectively. In addition, we also consider two TP not between two MIT temperatures of VO2 and GST, such as 301 K and 473 K. When TP = 301 K, less than the MIT temperatures of VO2 and GST, QF possesses two different slopes while QR has only one slope, because VO2 and GST experience a phase change with the increase of the active terminal temperature when the rectifier is in forward bias. In this case, the three rectification ratios are: 0, 2.71, and 3.93, respectively. This situation is reversed when TP = 473 K, because QF has only one slope, while QR has two different slopes. There are also three rectification ratios are: 0, 0.43, and 3.93, respectively. Interestingly, coupled with the two calculation results in Fig. 2 (TP = 341 K and 433 K), the rectification ratios start to change when TA approaches the two MITs of VO2 and GST for all cases with different passive terminal temperatures. Besides, by comparing the calculation results for Case III with seven different passive terminal temperatures, we find that the higher rectification ratios R3 remain the same (R3 = 3.93). This indicates that the rectification ratio is not affected by the passive terminal temperature when both phases of VO2 and GST have been identified. However, the smaller rectification ratio (R2) in each calculation case occurs the change with the passive terminal temperature. Specifically, when TP < 387 K = (341 K +433 K)/2, R2 = 2.71, but decreases to R2 = 0.43 when TP > 387 K. Furthermore, the set of passive terminal temperatures can actively adjust the of stage number of multistage thermal rectification of rectifier. This is exemplified by the two-stage thermal rectifier when TP = 341 K, 387 K or 433 K, and the three-stage thermal rectifier when TP = 301 K, 361 K, 413 K or 473 K. This proves that the passive terminal temperature significantly affects the dynamic modulation of small-scale thermal transfer of the multistage thermal rectifier.
Fig. 3. The effects of passive terminal temperature TP on the multistage thermal rectification for Case III.
Fig. 4. Rectification ratios of multistage radiative thermal rectifier as a function of the temperature difference under different passive terminal temperatures for Case III.
Table 1. The rectification ratios of multistage radiative thermal rectifier under different passive terminal temperatures for Case III.
4. Conclusion
In summary, we propose a near-field multistage radiative thermal rectifier with the active terminal made up of two phase-change materials, VO2 and Ge2Sb2Te5. Due to their different metal-insulator transition temperatures, a multistage radiative thermal rectifier can obtain different rectification ratios within a range of temperature differences between the active and the passive terminals. Compared with the multi-film structure of active terminal, the composite nanostructure of the one-dimensional VO2 grating on the GST thin film is more suitable for multistage thermal rectification due to its realization of well-distributed and flexible thermal rectification. Additionally, our calculations indicate that the temperature of the passive terminal can change the value of the rectification ratio and adjust the stage number of multistage thermal rectification, proving that the passive terminal temperature significantly affects the multistage radiative thermal rectification. This work verifies that employing two dissimilar phase-change materials in the active terminal of thermal rectifier plays a significant role in the multistage modulation of heat flux across the radiative thermal rectifier. This work has considerable potential for practical applications in micro/nanoscale thermal harvesting, conversion, and management.
Funding
National Science Foundation (CBET-1941743).
Acknowledgements
This project is supported by the National Science Foundation through grant number CBET-1941743.
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.
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