Metamaterials (MMs) are artificially constructed electromagnetic (EM) materials and media which have exotic EM responses that are unavailable in nature. Consequently, they have many applications, such as negative refractive index,^[1] cloaking,^[2] superlenses,^[3] optical switching,^[4] absorbers,^[5] modulators,^[6] and thermal emitters.^[7]

Recently, many THz filters based on the MMs have been proposed; for example, a modified four-split complementary structure MM was used to construct a dual-band band-pass filter with central frequencies centered at 0.315 TH and 0.48 THz,^[8] respectively. In addition, an ultra-broad THz band-pass filter based on metal–dielectric–metal sandwich structure was presented.^[9] It should be noted that neither can be actively tuned and modulated.

However, in many practical applications, tunable THz filters are greatly needed. Thus, they have become a research focus over the past decade, and many tunable THz MMs filters which utilize optical,^[10] electrical,^[11] and mechanical^[12] stimuli to reconfigure the MMs’ structures have been reported. For all these active stimuli, the optical stimulus requires an external optical source, which increases the system's complexity and alignment difficulty. The electrical stimulus method has good compatibility with the integration circuit (IC) process, but its modulation depth is not very high and sometimes shows distinct resonance frequency shift. The mechanical stimulus usually contains some movable micromechanical segments, can achieve high modulation depth, and has good compatibility with the IC process, but its fabrication is complex and expensive.

Recently, more attention has been focused on the thermal stimulus^[13–15] method, which usually uses phase-transition materials (i.e., VO₂) to reconfigure the MMs and achieves a very high modulation depth and a broad modulation bandwidth, because VO₂ shows the insulator phase at a low temperature and the metal phase above the critical temperature about T_c=340 K.^[16,17]

In a recent work,^[18] demonstrated a broadband on/off filter using frequency selection surface and VO₂. However, an external heater was required to induce the phase transition of the whole VO₂ layer, which was very difficult for integration, and the time for the phase transition of VO₂ is very long. In another work,^[19] a THz modulator with a modulation depth of 87% and a bandwidth of 0.7 THz was proposed but the maximum bias current of 0.5 A is still too high for many applications. In addition, an electrically voltage driven THz modulator based on a hybrid bowtie-antenna-VO₂ device was proposed for modulating the THz wave in a wide frequency range of 0.3 THz to 2.5 THz.^[20] However, the maximum modulation depth is smaller than 81%. Therefore, the tunable THz filters with low driven current (or voltage) and high modulation depth are very important for integration.

In this work, we propose an electrically triggered dual-band tunable THz band-pass filter based on the Si₃N₄–VO₂–Si₃N₄ sandwich-structured hybrid MMs. By introducing a closed ring and two split ring resonators (SRRs) in a unit cell, three absorption peaks are produced at the frequencies of 0.37 THz, 0.78 THz, and 1.03 THz, just by forming two pass-bands between these absorption peaks. The full width at half maximum (FWHM) of the first and that of the second pass-band are 0.29 THz and 0.2 THz, respectively. Unlike other VO₂-based tunable THz filters,^[18–20] the tunable filter proposed in this work has three advantages. First, it has good ability for resisting the thermal stress due to the use of Si₃N₄–VO₂–Si₃N₄ sandwiched structure. Second, it is fully electrically triggered and has good compatibility with the IC process. Finally, it can achieve high modulation depth at very low bias currents.

A schematic diagram of the unit cell is shown in Fig. 1(a). From bottom to top, there are thick high resistance silicon substrate, 100 nm thick Si₃N₄ layer, 125 nm thick VO₂ phase-transition layer, 500 nm thick Si₃N₄ layer, and 100 nm thick aluminum pattern layer (which is used for the frequency selection and the electrical connection). The lower layer of Si₃N₄ is used as a buffer layer, while the upper layer of Si₃N₄ has three functions. First, it is used as an electrical isolation layer between the top metal layer and the VO₂ layer. Second, it works as a heat transfer layer to lower the loss of VO₂ at room temperature. Finally, it is served as a diffusion barrier that allows crystallization of the VO₂ layer. When the external current is applied, the Joule heat produced in the metal layer could induce the insulator–metal phase transition of the VO₂ layer. Due to the good ability of Si₃N₄ to resist thermal stress, this device has good thermal stability. In addition, low current is required to produce the phase transition in the VO₂ layer, because the aluminum has good electrical conductivity and thermal conductivity.

Fig. 1.

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	Fig. 1. Schematic diagrams of the device. (a) Oblique view of a unit cell, (b) top view of a unit cell, and (c) microscopy image of the sample.

The top view of a unit cell is illustrated in Fig. 1(b), which contains a closed ring and two split-ring-resonators, and all optimized dimensions of the unit cell are listed in Table 1.

Table 1.

Table 1.

Table 1. Optimized dimensions of a unit cell ( ). . w1 w2 w3 L1 L2 px py g1 g2 2 3 3 66 48 90 90 10 6

Table 1. Optimized dimensions of a unit cell ( ). .

The sample is fabricated by a surface micromachining process. The process begins with a double-sided polished high resistance silicon wafer, and the process flow is illustrated in Fig. 2. First, in Fig. 2(a), a layer of 100 nm Si₃N₄ is deposited on the high resistance silicon wafer by using plasma enhanced chemical vapor deposition (PECVD) process; second, in Fig. 2(b), a layer of 125 nm VO₂ is deposited using magnetron sputtering method and then annealed at 450 degrees; after that, in Fig. 22(c), the second layer of Si₃N₄ with the thickness of 500 nm is deposited using the PECVD process; then, in Fig. 2(d), negative photoresist is spin-coated and lithographically patterned, and then developed; after that, in Fig. 2(e), a metal stack consisting of 10 nm chrome and 100 nm aluminum is deposited over the photoresist pattern by e-beam evaporation; finally, in Fig. 2(f), the photoresist is dissolved using lift-off process and leave behind the metal in the opened areas. The microscopy image of the fabricated sample is shown in Fig. 1(c).

Fig. 2.

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	Fig. 2. The fabrication process flow.

Microwave Studio 2016, which is a commercial software computer simulation technology (CST), is used to implement a full-wave electromagnetic simulation to compute and optimize the transmission properties of the device. In the simulation, an open boundary condition is set in the z direction, and unit cell boundary conditions are set in the x and y directions, respectively. An adaptive mesh refinement is used in the frequency solver, and a classical Drude model^[21] is introduced to define the properties of the VO₂ film, in which the relative permittivity of VO₂ in the THz region is described as 1 where the relative permittivity at high frequency , is the conductivity-dependent plasma frequency, and γ is the collision frequency. Both the conductivity σ and are proportional to the density of free carriers in the VO₂ film; thus, the plasma frequency can be expressed as 2 where , , and . These parameters agree well with the reported experimental results.^[22] The layer of Si₃N₄ is modeled as a normal dielectric with a complex permittivity of . The metal aluminum is modeled as a lossy metal with an electrical conductivity . Figure 3 presents the schematic of the bias method in the test experiment.

Fig. 3.

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	Fig. 3. A schematic diagram of the bias method in the test experiment. All closed rings are connected to the two pads on both sides and biased with a current source. The phase transition is induced by the Joule heating of the metal pattern. The red arrows represent the intensities of the THz wave under different bias currents.

In the simulation, to investigate the phase transition of the VO₂ layer, we change its conductivity and calculate the transmission spectra of the device (Fig. 4(a)). The black solid curve represents the transmission without bias current (I = 0), which shows three intensive resonance absorption peaks at 0.38 THz, 0.73 THz, and 0.96 THz, respectively. The maximum transmissions at the central frequencies of two passbands, i.e., 0.59 THz and 0.86 THz, are 84.2% and 80.6%, respectively. When the conductivity of the VO₂ layer increases from the minimum of 12 S/m to the maximum of 3×10⁵ S/m, the transmission of the device decreases gradually from the maximum to near zero, and the corresponding modulation depth achieves about 100%.

Fig. 4.

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	Fig. 4. Simulation and experiment results. (a) Simulated transmissions for different conductivity of the VO2 layer. (b) Measured transmissions for different bias currents.

In the experiment, the bias currents are supplied with a direct power supply. When the bias currents are applied, the transmissions are measured using a THz time-domain spectrum system (Z-3 model, Zomega Corp.)^[23] and plotted in Fig. 4(b). When the bias current increases from zero to 0.225 A, the transmission gradually decreases from the maximum to about 0.1. The full width at half maximum (FWHM) of the first passband and that of the second one are 0.29 THz and 0.2 THz, respectively. The experiment shows good agreement with the simulation.

To understand the modulation characteristics of the device, we have defined the modulation depth as , where T₀ and T are the transmission without current and the transmission with practical bias currents, respectively. The calculated results extracted from Fig. 4(b) are presented in Figs. 5(a) and 5(b), showing that the measured maximum transmission at the two central frequencies (i.e., 0.56 THz and 0.91 THz) of two passbands are 68.2% and 70.4%, respectively. Moreover, the maximum modulation depths of 0.56 THz and 0.91 THz are 81.7% and 81.3%, respectively. The fine tuning capability of the sample is attributed to the gradual thermal-induced phase transition of the VO₂ film. The differences between the simulation and the experiment are probably derived from the fabrication process, which results in the practical values of the material parameters being different from those used in the simulation.

Fig. 5.

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	Fig. 5. Hysteresis behavior and modulation depth. (a) Hysteresis behavior and modulation depth at the central frequency of the first band (f = 0.56 THz). (b) Hysteresis behavior and modulation depth at the central frequency of the second band (f = 0.91 THz).

In addition, as shown in Figs. 5(a) and 5(b), a distinct hysteresis behavior is observed when the applied currents go up and down.

To understand the physical mechanism of the device, the surface currents distributed on the aluminum film at three absorption frequencies are plotted in Fig. 6 .

Fig. 6.

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	Fig. 6. Surface currents distributed on the top patterned aluminum film for three absorption frequencies: (a) f = 0.38 THz, (b) f = 0.7 THz, and (c) f = 0.96 THz.

Figure 6(a) shows that the first absorption peak at the resonant frequency of f = 0.38 THz is mainly produced by the surface currents oscillating on the inner SRR, which is a typical inductive–capacitive (LC) resonance mode.^[24] As shown in Fig. 6(b), the surface currents mainly oscillate on the outer SRR and they are typical tri-pole resonance. Two of them on the upper section of the SRR have the same phase which is reverse to the phase of another one on the bottom of the SRR. Therefore, the second resonant frequency f = 0.73 THz is excited by this tri-pole resonance. Figure 6(c) indicates that the third absorption peak at f = 0.96 THz is similar to the second one, and it is produced by the tri-pole resonance on the inner SRR.

To investigate the steady-state temperature distribution and the Joule heating performance of the device, we implement an electrical–thermal simulation by using finite element analysis (FEM) software, COMSOL multiphysics 5.3a.^[25] The material parameters of Al, Si, and Si₃N₄ are taken from the default textbook,^[26] where the heat capacity, the thermal conductivity, and the density of VO₂ film are set as , and 4571 kg/m³,^[27] respectively. The Joule heating effect is simulated by coupling an electric currents (EC) physics model to a heat transfer (HT) in solid physics model. The right pad is set to ground and the left pad is set to the current terminal excitation with a parametric sweep. To simulate actual heat radiation, the boundaries of the model are set to diffuse surfaces with an initial temperature of T = 293.15 K.

Figure 7(a) presents the relationship between the peak temperature of the device at the thermal steady-state and the applied currents. The red-solid curve is obtained by the electrical–thermal FEM simulation, and the black dashed curve is obtained from the experiment. In the simulation, the temperature of the device at thermal steady-state is 342.18 K for I = 0.2 A, which shows very little difference from the experiment result of 342.05 K. Meanwhile, the phase transition temperature in the simulation is consistent with the first order phase transition temperature of T_c = 340 K. In the temperature test experiment, a thermometer with a touching point detector is used to test the temperature on the surface of the filter, as shown in Fig. 7(b).

Fig. 7.

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	Fig. 7. Electrical–thermal characteristics. (a) The relationship between peak temperature of the device and the applied currents. (b) Temperature distributions on VO2 film for I = 0.2 A. (c) Temperature distributions on four unit cells for I = 0.2 A. (d) Temperature distributions on the cross section of a unit cell for I = 0.2 A.

Figure 7(c) illustrates the temperature distribution on the VO₂ layer for I = 0.2 A, which shows that the maximum and the minimum temperatures of the VO₂ layer at the thermal steady-state are 342.15 K and 341.65 K, respectively. Meanwhile, it is evident that the temperature difference between the center and the margin of VO₂ layer is less than 0.5 degrees.

Figure 7(d) presents the steady-state temperature on the surface of the four unit cells, which shows that the maximum temperature distributes on the horizontal beam of the closed ring, because the bias currents just flow through it. Due to the driven currents flow through the sample from left to right, the temperature distribution is not symmetric about the center.

At the same time, Figure 7(e) shows the temperature distributions on the cross section of a unit cell, indicating that there is very little difference on the cross section of the device. This could be attributed to the good heat transfer ability of the Si₃N₄ layer.

We have experimentally demonstrated a fully electrically triggered THz dual-band tunable band-pass filter based on the Si₃N₄–VO₂–Si₃N₄ sandwich-structured hybrid MMs. The insulator–metal phase transition of the VO₂ film is induced by the Joule thermal effect of the top metal pattern. When the bias current is 0.225 A, the modulation depths at the central frequencies of two bands, i.e., 0.56 THz and 0.91 THz, reach 81.7% and 81.3%, respectively. In particular, the central frequency of each band can be tuned to the desired frequency by only changing the geometries of the unit cell. This design paves a new way to develop fully electrically controlled THz functional devices. Therefore, it has broad applications in the field of THz communication, imaging, sensing, and astronomy exploration.