Temperature-dependent microwave properties of vanadium dioxide film across the phase transition

Summary

Vanadium dioxide (VO₂) holds promise for reconfigurable microwave devices due to its rapid phase transition and large conductivity contrast. However, the absence of research into VO₂’s microwave properties across its thermally induced phase transition within the microwave band in existing literature hinders the design and application of VO₂-based reconfigurable devices. In this paper, we investigate the switchable microwave properties of VO₂ across the phase transition through temperature-dependent S-parameter measurements in an X-band waveguide. The results reveal a non-monotonic variation in absorption, which is attributed to the dynamic interplay between impedance matching and material loss. The absorption peak appears at an intermediate conductivity state, where optimal energy coupling and dissipation are achieved. This behavior is further analyzed by comparing samples with different S-parameter variations. Our findings provide a theoretical and experimental basis for designing VO₂-based reconfigurable absorbers and modulation devices.

Graphical abstract

Highlights

• •S-parameters of VO₂ are measured in a rectangular waveguide
• •Transmission, reflection, and absorption of VO₂ evolve across the phase transition
• •Absorption exhibits a non-monotonic variation with a peak at an intermediate state
• •The non-monotonic absorption behavior requires sufficient S-parameter variation

Devices; Electromagnetic waves; Materials application

Introduction

The advancement of modern communication systems toward higher frequencies and multi-band operation necessitates high-performance reconfigurable microwave devices. Such reconfigurability is typically achieved through electrical, mechanical, or optical control, using nonlinear devices such as diodes, liquid crystals or micro-electro-mechanical systems (MEMS). However, these approaches exhibit notable constraints in practical applications. For instance, reconfigurable devices based on varactor and PIN diodes suffer from parasitic resistance at high frequencies, leading to high losses.^1,2,3,4,5,6 Materials like liquid crystals exhibit a limited dielectric constant tuning range, limiting the scope for performance manipulation.^7,8,9,10 Although MEMS technology is widely adopted in mobile communication,^11,12,13 its complex structure introduces fabrication challenges.

The metal-insulator transition property of vanadium dioxide (VO₂) offers a promising approach to address these limitations. VO₂ exhibits multi-physical-field tunability, stable magnetic susceptibility, and rapid phase transition speed.^14,15,16,17 Particularly, in the insulating state, VO₂ exhibits low conductivity and is free of undesirable parasitic structures such as PN junctions, thus enabling low-loss performance at high frequencies.^18,19 In contrast to MEMS, VO₂ features a simpler structure that can be fabricated directly as thin films, facilitating easier integration.^20,21 Furthermore, the electrical conductivity of VO₂ can be tuned by 3–5 orders of magnitude across a broad frequency range, while its magnetic susceptibility remains stable. Together, these properties provide a foundation for broadband modulation capability.^22,23,24 These characteristics render VO₂ well-suited for high-frequency reconfigurable devices requiring broad bandwidth and high integration density, including controllable antennas,^25,26 absorbers,^27,28 and metamaterials.^29,30

Existing research on VO₂ has primarily focused on static material parameters between its insulating and metallic states. Notably, the electromagnetic response of VO₂ differs across frequency bands due to the distinct physical mechanisms governing the electromagnetic response. In the THz range, where the frequency is sufficiently high to probe intraband and interband transitions, the response is dominated by free-carrier effects and is well described by the Drude model, which captures the evolution of conductivity across the phase transition.^28,29,30,31 In contrast, within the microwave band, the much longer wavelength and deeper penetration depth mean that the effective conductivity is influenced by additional mechanisms such as polarization relaxation and interfacial effects, leading to a more complex frequency-dependent behavior, and the film’s response is typically described using parameters such as electrical conductivity,¹⁸ resistance,³² and sheet resistance.³³ Despite these differences in the underlying physical mechanisms, investigations in both frequency bands share a common objective: to elucidate the evolution of VO₂’s electromagnetic properties across the metal-insulator transition. Both approaches reflect the underlying changes in carrier concentration, mobility, and scattering mechanisms, offering complementary perspectives on the phase transition dynamics. However, the temperature-dependent characteristics of VO₂ across the thermally induced phase transition remain to be investigated. The absence of temperature-dependent properties may lead to unforeseen nonlinear response process in VO₂-based microwave devices. Therefore, a detailed characterization of the temperature-dependent microwave properties across the phase transition is essential to enable the reliable design of reconfigurable components.

This paper investigates the evolution of microwave properties of VO₂ across the thermally induced phase transition. The VO₂ sample was fabricated using magnetron sputtering then microwave transmission, reflection, and absorption (T-R-A) characteristics were characterized through temperature-dependent S-parameter measurements in X-band rectangular waveguide. Interestingly, the experimental results show a non-monotonic variation in the absorption during the phase transition. Using full-wave electromagnetic simulations, this behavior is explained by the balance between impedance matching and material loss. Meanwhile, additional VO₂ samples with different S-parameter variation were fabricated to analyze the non-monotonic absorption trend. This study provides a systematic analysis of the electromagnetic response properties of VO₂ during its thermally induced phase transition, providing a theoretical and experimental basis for the design and optimization of tunable microwave devices based on VO₂.

Results

Material characterization of VO₂ films

The VO₂ samples were fabricated by reactive magnetron sputtering using a JCP350 magnetron sputtering system, as shown in Figure 1A. The VO₂ film electron micrograph (JEOL JSM-6510) reveals a uniform surface with minimal particulate contamination and indicates high film quality, as shown in Figures 1B and 1C. The characteristic Raman peak (WITEC alpha3000) was observed at 194 cm⁻¹, which corresponds to the monoclinic insulating state of VO₂. The VO₂ film thickness measured with an atomic force microscopy (WITEC alpha3000) to be 260 nm. The deposited VO₂ films on mica substrates were measured at dc to examine sheet resistance across the transition temperature. A cylindrical four-point probe (Cascade M150) on a temperature controlled heated stage (Lakeshore 335) was used for the measurement from 40 °C to 80 °C. The measured DC results are presented in Figure 1D. At least a four orders of magnitude change in the DC sheet resistance which transitions from approximately 240000 to 200 Ω/sq. The transition begins at 60 °C and finishes around 80 °C.

Figure 1.

VO₂ film fabrication and characterization

(A) JCP350 magnetron sputtering system used for VO₂ sample fabrication.

(B) Raman spectroscopy of VO₂ films in the low-temperature insulating state.

(C) Scanning electron micrograph of fractured VO₂ with uniform coating and low roughness.

(D) DC sheet resistance measurements of deposited VO₂ film on a mica substrate during heating and cooling.

Temperature-dependent S-parameters measured in microwave waveguide

VO₂ sample 1 was fabricated on a 23 mm × 10 mm mica substrate with a deposition time of 90 min. The transmission and reflection of the sample assembled in the fixture were measured in a WR-90 waveguide within the X-band using an AV3672E vector network analyzer (VNA). Before conducting measurements, the VNA was calibrated using the through, reflect, and line method with a waveguide calibration kit (Ceyear TVL103), and the “zero phase” reference planes calibrated to the waveguide flanges. When the sample was inserted, the reference planes and the sample were on the same plane. The sample’s temperature was controlled using a high-precision heating stage (V-2020T) in an ambient environment of 25 °C, as shown in Figures 2A and 2B. The waveguide was closely attached to the surface of the heating stage to ensure effective thermal contact. S-parameters were monitored in real-time using the VNA to capture the response at different temperatures. To ensure the reliability of the temperature measurement, the heating stage was stabilized at target temperatures for 30 min to mitigate a hysteresis effect caused by the different heating rates of the waveguide. The temperature uniformity of the sample area was then verified by scanning multiple points (on the left, right, and top side of the fixture) with an infrared thermal imager (FLUKE TiS55+), the averaged value from these points was used to confirm the accuracy of the measured temperature before S-parameter extraction. After completing the measurements, we quickly disassembled the waveguide and directly measured the VO₂ film surface temperature using the same infrared thermal imager, and found it to be close to the set temperature, further validating the reliability of our temperature control.

Figure 2.

Sample fixture and heating setup

(A) VO₂ sample 1 with fixture installed in the WR-90 waveguide and (B) the WR-90 waveguide placed on the heating stage, connected to vector network analyzer.

Figure 3A–3F show the S-parameter variations during heating and cooling cycles at 8 GHz, 10 GHz, and 12 GHz. The phase transition initiates at 60 °C and is nearly complete at 80 °C during heating, while cooling starts at 70 °C and completes at 50 °C, showing hysteresis behavior. A considerable electromagnetic modulation capability is demonstrated by sample 1, with the S₂₁ reduction exceeding 10 dB and S₁₁ enhancement over 14 dB across the measured temperature range from 40 °C to 80 °C. The high transmission S-parameter variation, combined with consistent performance across frequencies, indicates the sample’s suitability for broadband reconfigurable device design.

Figure 3.

Temperature-dependent S-parameters and absorption behavior

(A–C) S₁₁ and (D–F) S₂₁ at 8 GHz, 10 GHz and 12 GHz for sample 1 during thermal cycling over X-band and the (G) transmission, (H) reflection and (I) absorption of Sample 1 at different temperatures, and (J) real and (K) imaginary components of permittivity at different temperatures across the phase transition.

The T-R-A spectra of sample 1 are analyzed across the phase transition, as shown in Figures 3G–3I. The sample exhibits consistent stability within the X-band, with its transmission, reflection, and absorption showing minimal variation across the frequency at a fixed temperature. At 60 °C, the sample shows high transmission and low reflection, with transmission exceeding 0.94, reflection is below 0.02, and the absorption is less than 0.1. At this point, the sample is in the low-temperature insulating state and allows low-loss transmission of the energy. As the temperature increases to 67.5 °C, the absorption reaches its peak, exceeding 0.45 across the X-band and achieving a maximum of 0.5 at 10 GHz, the sample is in the intermediate state during the phase transition and can efficiently absorb the incident energy. At 80 °C, the sample shows high reflection, with the maximum reflection exceeding 0.72, while the transmission drops below 0.1. The absorption in this state remains between 0.20 and 0.26, the sample is in the high-temperature metallic state, and the majority of the energy is reflected.

To further analyze the electromagnetic characteristics, we extracted the complex dielectric constant of sample 1 from the S-parameters using the Nicolson-Ross-Weir (NRW) method. Figures 3J and 3K present the frequency-dependent real and imaginary components of permittivity at different temperatures across the phase transition. As the temperature increases, the real component shows a gradual increase from approximately 6.1 at 60 °C to around 7.1 at 80 °C, while the imaginary component increases from below 0.7 at 60 °C to values exceeding 250 at 80 °C.

Analysis of transmission, reflection, and absorption with varying temperatures

The T-R-A characteristics of the sample at 10 GHz are further analyzed, as shown in Figure 4A. As the temperature rises and the conductivity of VO₂ increases, the transmission decreases. Between 60 °C and 67.5 °C, it drops rapidly, while from 67.5 °C to 80 °C, the decline slows and eventually stabilizes around 80°C. Conversely, the reflection increases, it rises rapidly from 60 °C to 70 °C, and then increases slowly above 70 °C.

Figure 4.

T-R-A variation and substrate thickness effect

(A) T-R-A variation of sample 1 at different temperatures at 10 GHz. Simulated (B) transmission and (C) reflection at different conductivities of VO₂ films. The absorption at different conductivities for substrate thicknesses of (D) 0.2 mm, (E) 0.5 mm, and (F) 0.8 mm.

Interestingly, the absorption of the sample exhibits a non-monotonic variation. It increases and reaches a maximum at 67.5 °C, then begins to decrease. In the initial stage of the phase transition (60 °C–67.5 °C), the reflection is low and increases slowly, while the increase in conductivity leads to a rise in material loss, causing the transmission to decrease rapidly. During this stage, the rate of decrease in transmission exceeds the rate of increase in reflection, resulting in an increase in the absorption. At the mid-phase transition (around 67.5 °C), the increasing rate of reflection accelerates while decreasing rate of transmission slows. The two rates reach a balance, causing absorption to attain its maximum value. In the later stage of the phase transition (67.5 °C–80 °C), as the sample approaches the metallic state, transmission stabilizes near its minimum while the reflection continues to rise, leading to a decrease in absorption. It can be concluded that the non-monotonic variation of absorption arises from the dynamic interplay between the decreasing rate of transmission and the increasing rate of reflection during the phase transition.

To further analyze the non-monotonic variation in the absorption, a full-wave electromagnetic simulation model was established using CST Studio Suite, as shown in Figure 5A. A WR-90 rectangular waveguide was built, with the VO₂ film of 260 nm and its mica substrate of 0.2 mm placed at the center. The sample matches the waveguide’s inner cross-section, which is 22.86 mm × 10.16 mm. In the simulation, both ends of the waveguide are set as excitation ports with the TE₁₀ mode incident. It is worth noting that the DC sheet resistance measurement yields a conductivity of approximately 6,400 S/m at 67.5 °C (calculated from R_s ≈ 600 Ω/sq and thickness 260 nm). However, due to the influence of high-frequency mechanisms such as polarization relaxation and displacement currents, the effective microwave conductivity governing the X-band response is significantly higher. Therefore, instead of directly using the DC-derived value, we determined the appropriate conductivity through inverse extraction by fitting the simulated S-parameters to the experimental data. By sweeping the conductivity of VO₂, the T-R-A properties were extracted, and the results are shown in Figures 4B–4D. The simulations show that the transmission decreases and the reflection increases with rising conductivity. The absorption shows a trend of first increasing and then decreasing, reaching a maximum absorption of 0.5 at a conductivity of 20,000 S/m. This pattern matches the variation in absorption characteristics observed during the phase transition of Sample 1. To further analyze the influence of substrate thickness on the absorption behavior, simulations were performed for substrate thicknesses of 0.5 mm and 0.8 mm, as shown in Figures 4E and 4F. For both thicknesses, the absorption maintains the same non-monotonic trend with a peak at 20,000 S/m. However, the peak absorption value decreases with increasing thickness, this reduction is attributed to the additional phase shift and impedance transformation introduced by a thicker substrate, which degrades impedance matching and reduces energy coupling into the VO₂ film.

Figure 5.

Simulation model and energy distribution

(A) The VO₂ thin film and mica substrate structure inside the waveguide.

(B and C) (B) Electric field distribution during wave propagation and (C) energy dissipation distribution on the VO₂ film surface at different conductivities.

To provide an intuitive representation of the T-R-A characteristics under different conductivities, the energy transmission process within the waveguide and the energy dissipation in the VO₂ thin film were simulated and analyzed, as shown in Figure 5B. The simulations show that the transmitted energy through the sample decreases with increasing conductivity, reaching a minimum at 60,000 S/m, while the reflected energy increases, as shown in Figure 5B. This corroborates the trends of decreasing transmission and increasing reflection, consistent with the experimental results in Figures 3G and 3H.

The energy dissipation distribution within the VO₂ film is shown in Figure 5C. The overall dissipation intensity first increases and then decreases with conductivity. At 50 S/m, although localized areas of higher dissipation exist, the majority of the film surface exhibits low dissipation, resulting in low loss and correspondingly low absorption, matching the properties of sample 1 at 60 °C. At 20,000 S/m, large-area regions of high energy dissipation appear across the film surface, leading to high dissipation and high absorption, corresponding to sample 1 at 67.5 °C. When the conductivity further increases to 60,000 S/m, the high-dissipation area remains substantial, but the peak dissipation intensity is lower than that at 20,000 S/m. Consequently, the dissipation and absorption decrease, corresponding to the state of sample 1 at 80 °C. This explains the observed non-monotonic trend of absorption, which first increases and then decreases, aligning with the measured results in Figure 3I.

These observations show the interplay between impedance matching and material loss across the phase transition. For the sample 1, a moderately matched impedance allows substantial energy to enter the VO₂ layer. However, low material loss enables most of the incident energy to transmit through the sample, yielding high transmission, low reflection, and low absorption at 60 °C. At 80 °C, enhanced material loss is counterbalanced by impedance mismatch with space, causing most energy to reflect directly at the sample, with only a small fraction entering and being absorbed, leading to low transmission, high reflection, and moderate absorption. At 67.5 °C, an optimal balance is achieved. Effective impedance matching coexists with moderate material loss, allowing substantial energy to enter the VO₂ sample and dissipate internally through ohmic losses, leading to medium transmission, medium reflection, and high absorption.

Condition for non-monotonic absorption behavior

To further analyze the non-monotonic absorption behavior, samples 2 and 3 were fabricated with reduced magnetron sputtering deposition times of approximately 40 min and 30 min, respectively, resulting in lower S-parameter variation compared to sample 1, as shown in Figure 6. Based on the deposition rate of about 4 nm/min, the estimated film thicknesses are approximately 160 nm for sample 2 and 120 nm for sample 3. Figure 7A shows the S-parameters of samples 2 and 3 in both the insulating and metallic states. Similar to sample 1, both samples exhibit high transmission at low temperatures. However, in the high-temperature metallic state, their S₂₁ are higher than that of sample 1, the S₂₁ for sample 2 dropped to approximately −9 dB, while for sample 3 it remained around −3 dB. The T-R-A characteristics of samples 2 and 3 at 10 GHz are analyzed, as shown in Figures 7B–7D. As temperature increases, the transmission decreases and the reflection increases for both samples, following the same trend as sample 1. Sample 2 exhibits a non-monotonic behavior with a distinct peak at 77.5 °C, similar to sample 1. However, the absorption of sample 3 increases monotonically with temperature.

Figure 6.

Photograph of the prepared VO₂ samples with different S-parameter variation

Figure 7.

Comparative analysis of samples

(A) S₂₁ in the low-temperature insulating state and high-temperature metallic state.

(B–F) (B) Transmission, (C) reflection, and (D) absorption of samples 1 to 3 at different temperatures at 10 GHz. Smith chart of (E) sample 1 and (F) sample 3 at 8, 10, and 12 GHz across the phase transition.

This difference can be explained through the interplay between impedance matching and energy dissipation. During the phase transition, the impedance of VO₂ decreases with increasing conductivity. The larger S-parameter variation observed in samples 1 and 2 indicates a greater impedance variation during the phase transition. As a result, at an intermediate temperature, although impedance matching to free space continuously degrades with increasing temperature, the coupling efficiency remains substantial while the material loss has increased. At this state, the combined effect of impedance matching and material loss reaches an optimum, leading to a peak in absorption. At higher temperatures, the further decline in coupling efficiency outweighs the continued increase in material loss, causing absorption to decrease. In contrast, sample 3, with its lower S-parameter variation, exhibits a limited impedance variation. It does not reach the optimal balance between coupling efficiency and material loss, and therefore its absorption increases monotonically without exhibiting a peak. To illustrate the impedance evolution, Figures 7E and 7F present the Smith chart of samples 1 and 3 across the phase transition. It can be seen that for both samples, the impedance moves monotonically away from the center as temperature increases, indicating progressively worsening impedance matching to free space. This further confirms that the non-monotonic absorption behavior arises not from non-monotonic impedance matching, but from the dynamic balance between the monotonically decreasing coupling efficiency and the monotonically increasing material loss. Therefore, to achieve the non-monotonic absorption variation in VO₂ during the thermally induced phase transition, the S-parameter variation must be sufficiently high. This ensures that the sample’s impedance traverses and approximately matches the space impedance at an intermediate state, enabling both efficient energy coupling and effective dissipation, thereby yielding a peak in absorption.

Discussion

This paper analyzes the microwave properties of VO₂ across the thermally induced phase transition within the X-band. The research reveals that the absorption exhibits a non-monotonic variation during the transition, reaching a peak at an intermediate state. This behavior is attributed to the dynamic balance between impedance matching and material loss. Moreover, analysis of samples with different S-parameter variation indicates that achieving such a non-monotonic absorption response requires a sufficient level of variation. These findings provide a theoretical and experimental basis for the design of VO₂-based reconfigurable microwave devices and contribute to the understanding of its microwave properties during the phase transition.

Limitations of the study

The temperature measurement in the waveguide setup did not use a thermocouple placed directly on the VO₂ film to avoid perturbing the microwave field. The reported temperatures represent the fixture surface temperature rather than the absolute film temperature. Additionally, de-embedding was not performed to extract the intrinsic properties of the VO₂ film alone; the measured S-parameters reflect the combined response of the film and the mica substrate. These limitations do not affect the main conclusion of the non-monotonic absorption behavior, which is based on relative changes rather than absolute temperature values. Future work will address these limitations by employing in situ temperature sensing and de-embedding techniques.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Chenxi Liu (liuchenxi09@nudt.edu.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All data reported in this paper will be shared by the lead contact upon request.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data are available from the lead contact upon request.

Acknowledgments

This work was financially supported by the Natural Science Foundation of China under grant 62293491, Natural Science Foundation of China under grant 62571533 and the Hunan Provincial Natural Science Foundation of China under grant 2026JJ40059.

Author contributions

Sample preparation, H.M. and J.H.; experimentation and writing – original draft, Y.C., T.L., S.X., and Y.X.; writing – review and editing, C.L., Y.X., and P.L.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, peptides, and recombinant proteins
High-purity vanadium target (99.9%, φ101.6 × 5 mm)	Beijing Zhongnuo New Material Technology Co., Ltd.	http://www.znxc.cn/productShow.jsp?id=100234
N-methyl-2-pyrrolidone (NMP, AR grade, ≥99%)	Beijing Zhongnuo New Material Technology Co., Ltd.	CAS: 872-50-4
Other
JCP350 magnetron sputtering system	Beijing Technol Science Co., Ltd.	https://www.technol.cn/
WITEC alpha3000 (Raman/AFM system)	WITEC, Germany	https://www.witec.com
AV3672E vector network analyzer	Ceyear, China	https://www.ceyear.com
FLUKE TiS55+ infrared thermal imager	Fluke Corporation	https://www.fluke.com
Lakeshore 335 temperature controller	Lake Shore Cryotronics	https://www.lakeshore.com
JEOL JSM-6510 scanning electron microscope	JEOL	https://www.jeol.com
V-2020T high-precision heating stage	Vinstek, China	N/A

Method details

Materials and fabrication

The materials used included mica substrates (23×10×0.2 mm) as the deposition base; a high-purity vanadium target (99.9%, φ101.6×5 mm) as the sputtering source; N-methyl-2-pyrrolidone (NMP, AR grade, ≥99%, C5H9NO, molecular weight: 99.13, CAS: 872-50-4) and deionized water (DI water, resistivity ≥18 MΩ·cm) as cleaning solvents.

The VO₂ samples were fabricated by reactive magnetron sputtering using a JCP350 magnetron sputtering system, as shown in Figure 1A. Prior to deposition, mica substrates were ultrasonically cleaned in NMP and deionized water for 30 seconds each. The chamber was evacuated to a background vacuum below 10^-4 Pa before sputtering to ensure high film purity. A high-purity vanadium target was sputtered in an argon/oxygen mixed atmosphere with an oxygen volume ratio of 0.4%, a chamber pressure of 0.6 Pa, and a sputtering power of 55 W. The substrate was not heated during deposition, and the target-to-substrate distance was fixed at 10 cm. The deposition rate was approximately 4 nm/min. After deposition, the VOx films were annealed in a low-pressure tube furnace under a flowing oxygen atmosphere (3.5 sccm, chamber pressure 4.5 Pa). The temperature was ramped to 450 °C at a rate of 20 °C/min and held for 10 minutes to form polycrystalline VO₂. After annealing, the samples were allowed to cool naturally to room temperature.

Material characterization

Film morphology was examined by scanning electron microscopy. Raman spectroscopy and film thickness measurement were performed using a WITEC alpha3000 system (Raman mode for phase identification; AFM mode for thickness). DC sheet resistance was measured with a cylindrical four-point probe on a temperature-controlled heating stage from 40 °C to 80 °C. In the transition region (60–80°C), measurements were taken with a step size of approximately 2 °C.

Microwave S-parameter measurement

The VO₂ film on mica substrate was inserted into a WR-90 rectangular waveguide (22.86 mm × 10.16 mm inner cross-section). S-parameters were measured using an AV3672E vector network analyzer over the X-band (8–12 GHz). The VNA was calibrated with a waveguide calibration kit using the Through-Reflect-Line method. The sample temperature was controlled by a high-precision heating stage. The waveguide was stabilized at each target temperature for 30 min to ensure thermal equilibrium. Temperature uniformity was verified by scanning multiple points on the fixture surface with an infrared thermal imager. After completing the measurements, the waveguide was disassembled and the VO₂ film surface temperature was directly measured with the same thermal imager, confirming close agreement with the set temperature.

Complex permittivity extraction

The complex dielectric constant of Sample 1 was extracted from the measured S-parameters using the Nicolson-Ross-Weir (NRW) method over the X-band at six representative temperatures: 60, 65, 67.5, 70, 75 and 80 °C.

Electromagnetic simulation

Full-wave electromagnetic simulations were performed using CST Studio Suite (Dassault Systèmes). A WR-90 waveguide model was built with the VO₂ film (260 nm) and mica substrate (0.2 mm) placed at the center. The conductivity of VO₂ was swept from 50 S/m to 60,000 S/m, and the transmission, reflection, and absorption were calculated. Additional simulations were run for substrate thicknesses of 0.5 mm and 0.8 mm to assess the effect on absorption.

Quantification and statistical analysis

No statistical hypothesis testing was used in this study. All experimental data (S-parameters, sheet resistance, permittivity) were directly measured and plotted without statistical inference. The simulation results were obtained from deterministic electromagnetic solvers.

Replicates and n values

For S-parameter measurements, at least three independent heating-cooling cycles were performed (n = 3, where n represents the number of cycles). For the comparative analysis of different samples (Sample 1, Sample 2, and Sample 3), each sample was fabricated once and measured; therefore, no statistical replicate is reported. The results are presented as representative measurements.

Definition of center

For S-parameter measurements, the presented data points represent the mean values of the three cycles. For other measurements (sheet resistance, permittivity), single measurements are shown.

Dispersion measures

Error bars are not shown for S-parameters because the variations were within the symbol size in the main figures, the measurement uncertainty is within ±0.1 dB. For other data, no error bars are applicable.