Active tunable THz metamaterial array implemented in CMOS technology

Terahertz (THz) modulators offer multifaceted capabilities for various practical applications such as THz imaging, wireless communications, sensing, etc. However, compared to the modulation devices used for other electromagnetic bands, the ubiquitous proliferation of THz applications is severely impeded by the tremendous lack of complementary metal-oxide-semiconductor (CMOS)-compatible technology. Here we demonstrated a CMOS-based active tunable THz metamaterial array (C-ATTMA) with split-ring resonators (SRRs). The THz metamaterial can be externally controlled with an electrically controlled dynamic. The C-ATTMA fabricated by the 180 nm CMOS technology featuring a resonant frequency of 0.30 THz was connected to the source and drain of a bottom metal-oxide-semiconductor field-effect transistor (MOSFET) through the vias. By delicately controlling the MOSFET gate voltage, the equivalent circuit response of the C-ATTMA was actively engineered, enabling tailoring THz resonance frequencies. Under a gate voltage of 1.8 V, we successfully realized a resonant frequency shift of ∼35 GHz and 3° phase shift. The equivalent circuit successfully explained the principle of the change. Inductor–capacitor (LC) resonance and electric dipole resonance of single-layer and double-layer SRRs have also been studied. The exhibited CMOS-compatible electrically regulated THz metamaterials provided a potential method for voltage regulation of THz, which may contribute to THz wireless communications, information encryption, THz compressed sensing and imaging, etc.

Currently, most metamaterials have demonstrated powerful performance [31][32][33]. However, static metamaterials face the disadvantage that, once fabricated, their performance is statically decided. In order to solve this problem, various materials and devices have been applied to metamaterial structures for active tuning of the metamaterial devices [34][35][36][37][38][39][40]. Photosensitive metamaterial planar arrays have been fabricated on light-sensitive material substrates and their response can be controlled by external light pumping and the free carriers in the substrate, such as GaAs [41] and photoactive silicon [19]. Such methods are very promising for alloptical -controlled THz devices and applications. Electrically controlled active metamaterials have their own indispensable potentials and numerous electrically enabled metamaterials have been successfully demonstrated in microwave and millimeter wavebands [42][43][44]. However, in the THz frequency range, straightforward copying of such technologies is limited by device size and fabrication resolution. Therefore, most reported electrically active THz metamaterials are combined with two-dimensional materials, borrowing their capabilities as transparent electrodes and electrical regulation of conductivity. Exemplified by graphene-based metamaterials, the position of the transparency peak can be tuned when the Fermi energy increases [45][46][47][48]. Another method is based on Schottky diodes. Double-channel heterostructures are inset into metamaterial unit gaps and the charge carrier concentration in the gaps is tuned by applying gate voltage to the two-dimensional electron gas [49]. However, these voltagecontrolled metamaterials are limited either by non-standard material systems or low feasibilities for large-scale fabrication.
Embedding transistors [42,43,50] and other conventional integrated circuit process technologies [51] into metamaterials has been implemented in the microwave frequency band and is beginning to expand to the THz region. Meanwhile, advanced complementary metal-oxide-semiconductor (CMOS) technology has been used above 400 GHz for the oscillator [52] and imaging applications [9]. The CMOS process is highly accurate and can fully meet the design requirements of metamaterials. The CMOS process allows the use of a multi-layer metal structure, giving CMOS devices many advantages over other processes in the field of 3D metamaterials [53]. The critical dimensions of the advanced CMOS back-end-of-line interconnections also fulfil the more complex metamaterial geometry requirements of THz applications. The front-end-of-line transistors and the back-end-of-line interconnections of the CMOS technology offer a path to control each unit of the metamaterial, which is of great significance for the realization of THz band-coding metamaterials. Designing and fabricating active metamaterials with controlling transistors monolithically with single CMOS technology is a potential solution for large-scale THz modulators. The back-end-of-line metamaterial array and sub-arrays can be grouped for a variety of THz sub-bands with differnt geometries and can be actively controlled with the underlying CMOS transistors.
In this work, we demonstrated a CMOS-based active tunable THz metamaterial array (C-ATTMA) with its source and drain of a metal-oxide-semiconductor field effect transistor (MOSFET) connected to the gap of split-ring resonator (SRR). By electrically controlling the voltage applied to the transistor gate, the resonant frequency and phase could be adjusted by changing the equivalent circuit performance of the C-ATTMA. As the applied voltage increased from 0 V to 1.8 V, the resonance peak was red shifted by 35 GHz. The phase transition was also realized by electrically controlling the THz metamaterials. Our C-ATTMA may provide a new approach to realize active THz modulation for multi-band THz wireless communications, sensing and imaging applications, as well as active phase-shift devices for THz beam-forming and beam-steering applications.

Device design and fabrication
The schematic diagram of the C-ATTMA is shown in figure 1. The whole system was divided into multiple regions, as shown in the top left inset of the figure. Different regions with different parameters enable the expanded tuning bandwidth. Here, the effect of one region was assessed in detail and the principle of the remaining regions was equivalent. The SRR array was fabricated on high-resistance silicon based on the CMOS process and the operating range was limited to the THz band by strict parameter design. When the electric field of the plane wave was incident perpendicularly to the gap, the inductorcapacitor (LC) resonance response appeared in the transmittance spectrum. The inset on the bottom left illustrates the details of each unit. A transistor was embedded into the SRR by connecting the source and drain to the gap of the SRR. A DC control voltage was applied to the gate. When the transistor was turned off, the entire device exhibited passive metamaterial properties. As the control voltage increased from 0 V to 1.8 V, the variation of the resonant frequency f x occurred due to the effect of the MOSFET. The idea was achieved in a 180 nm six-layer metal process from Semiconductor Manufacturing International Corporation and the cross section of the process is exhibited in figure 2(a). The metamaterial array was made on the top metal layer, which was connected to the bottom transistor by applying vias from the top metal to the bottom metal. The thickness of the metal layer was ∼200 nm and the thickness of each dielectric layer was 4 µm. The width of the gate was 180 nm. The transistor was fabricated by heavily doping two high-concentration n-zones on a p-type silicon substrate and the size of n + doping region was 1.58 µm × 0.92 µm. The width of the channel was 380 nm and the geometric dimensions of each via was 380 nm × 380 nm. The metamaterial contained a 23 × 23 periodic array of closely placed SRRs. The scanning electron microscope image of one unit with the size of 100 µm × 100 µm is exhibited in figure 2(b). The control principle of the metamaterial array is depicted in figure 2(c). The whole system was supported by an external voltage V cc of 3.3 V. A control voltage V control was applied to all of the transistors by connecting the gates to the external electrode. The whole metamaterial array can reach an area of 2.35 mm × 2.35 mm. In order to apply the control voltage effectively, it is necessary to package the device. In this case, the electrode was bonded to the printed circuit board (model: FR-4) with gold wire. The surface of the printed circuit board was applied by a gold deposition process to ensure the success of the bonding and silica gel (Loctite Ablestik 2025D) was applied to cover the gold wire and protect it, as shown in figure 2(d).

Regulation theoretical analysis
The finite-element analysis software integration package CST Microwave Studio was employed to simulate the THz wave. The magnetic boundary was along the x-direction and the electric boundary was along the y-direction, which were adopted to simulate the plane wave polarized along the y-direction. When the electric field direction of the electromagnetic wave was perpendicular to the gap of the SRRs, it caused a highfrequency current in the loops. The inset of figure 3(a) depicts a complete circulating current, which proves that the SRRs were operating in the LC resonant state at this frequency. The equivalent circuit model of the SRR-embedded transistor is given in the inset of figure 3(b), on which the accurate circuit parameters and relevant mathematical relations are determined. The intrinsic resistance and equivalent inductance of the SRR loop can be expressed as R m and L m , respectively. Loop resistance R m can be calculated by the size of SRR and aluminum resistivity. The equivalent inductance L m can be obtained by equation (1) [54]: where λ 0 can be obtained by the dimension of the SRRs, λ0 = 80 µm × 10 and the final equivalent inductance L m is ∼2 × 10 −9 H. When the current passed through the gap, it flowed between the source and drain in the transistor. The transistor can be seen as a parallel combination of total drainto-source capacitance (C ds ) and equivalent resistance (R t ) between source and drain. In the transistors, C ds can be calculated from the known structural capacitance of the transistor as shown in equation (2), and would not be significantly varied when the gate-to-source voltage (V gs ) is adjusted: As the gate-to-source capacitance (C gs ) and gate-to-bulk capacitance (C gd ) were negligible, the drain-to-bulk capacitance (C db ) described the equivalent capacitance of the MOS-FET, which was ∼10 −16 F. R t was a variable resistor in the gap, which originated from the equivalent channel resistance between the source and drain that varied dynamically with gate voltage V control . As V control increased, the equivalent resistance R t decreased. When V control reached 1.8 V, the equivalent resistance was minimum. As the equivalent impedance of C t ((jωC t ) −1 ) in the THz range was close to R t , either one of them was not negligible in the calculation. On the other hand, since the RF current was a small alternating current, the alternating voltage between the source and drain (v ds ) was so small that the conducting channel could not become 'pinched-off'. Based on the above conditions, the construction of equivalent circuit was considered to be feasible.
Based on the constructed equivalent circuit model, the resonant frequency was firstly analyzed. As R t changed dynamically with V control , the resonant frequency also changed accordingly. Through the circuit model and known parameters, the resonant frequency ω 0 of the LC resonance system can be found from the basic definition of circuit resonance. Firstly, the total impedance Z of the circuit can be obtained easily by the circuit model in equation (3). From this equation, the resonance frequency expression was obtained under the condition that the imaginary part of Z was zero as shown in equation (4): The curve of resonance frequency f 0 changing with resistance R t was obtained from equation (4), as shown in figure 3(a), we found that when R t exceeded 20 kΩ, the slope was nearly flat. It is known that when the channel reaches its maximum width, the minimum R t can be achieved close to several thousand ohms. Here, we took R t from 5 kΩ to 30 kΩ to explore. The quality factor Q of the loop is defined as the The Q factor as a function of the SRR unit gap resistance; the inset shows the equivalent circuit model. ratio of energy stored to energy consumed. The inductance L m stores the magnetic energy in the resonant frequency and the impedance R m describes the resistance of the SRR. In fact, capacitance and inductance store the same energy in resonance, the expression can be further simplified according to this principle in equation (5): IL m is the current flowing through the L m , VC t is the voltage applied to the C t , IR m and IR t are currents flowing through R m and R t . In the final solution of the Q factor, the working conditions for the transistor under different voltages should be considered. When the transistor is off and the value for R t is high, the transistor is equivalent to a capacitive reactance and the Q factor of the circuit is high. When the resistance decreases and the current flowing through R t increases, the circuit loss increases while the Q factor decreases. On the other hand, when the transistor is on, and R t is lower than the capacitance impedance, the loss will be reduced, and the Q factor will increase again [50]. The curve of the Q changing with the resistance R t is illustrated in figure 3(b). The Q value first decreases and then increases along with the increase of the resistance, reaching the minimum value at ∼8.6 kΩ, which is consistent with the working principle of transistors. The ability to achieve negative permeability was considered an important property of SRRs. When LC resonance occurs, the permeability can be negative. Here, the expression of the permeability µ r changing with resonance frequency is given in equation (6): F is the geometric factor of the unit cell, µ 0 is the vacuum permeability, A loop is the area contained in the SRR ring and V cell is the volume of the cell. Here, the R t in the range of 5 kΩ to 30 kΩ was taken and the corresponding permeability was calculated. The curves of the real and imaginary parts of the permeability varying with resistance were obtained indirectly in figures 4(a) and (b). According to equation (6), the influence on the permeability can be attributed to ω 0 and the Q, both of which are decided by R t . Then the transmittance coefficient can be further calculated in equation (7) according to the above parameters [55].
where n is the refractive index (n = √ µ r ε r ), z is the impedance (z = √ µr/ εr), and the dielectric constant of LC resonance is a positive number assumed to be 1, d is the length of each cell and k = ω/c is the wavenumber of the incident wave. The variation of the calculated transmittance parameters with the transistor resistance R t is plotted in figure 4(c). According to equation (7), the transmittance is decided by the permeability µ r . According to equation (6), the µ r is decided by both ω 0 and the Q. With the increase of R t , ω 0 will increase, leading to an increase of the resonance frequency of LC resonance. On the other hand, the variation of the transmittance can be attributed to the change of Q which is caused by R t . With the increase of R t , the Q first decreases and then increases, and finally leads to the corresponding variation for the transmittance.

Results and discussion
The THz experiments were performed on a home-built THz time-domain spectrometer ( figure 5(a)) driven by a commercial Ti:sapphire laser oscillator, which was consistent with the system used in reference [14]. The center wavelength of the femtosecond laser pulses was 800 nm, the pulse duration was 70 fs and the repetition frequency was 80 MHz. The laser beam was divided into two beams. One beam was used to excite a GaAs photoconductive antenna (Z-omega) with a 50 µm gap and the other beam was used to detect THz signal in a 1 mm thick ZnTe detector. Our C-ATTMA was placed in the center of the optical path, as shown in figure 5(a). The direction of the device satisfied that the gap was perpendicular to the THz polarization direction. The device was connected to the external signal source through the pin of the printed circuit board. The THz radiation generated by the antenna was focused into the metamaterial array through two parabolic mirrors. Two other parabolic mirrors were then used to collimate and focus the transmitted THz waves onto the ZnTe crystal. The THz electric field can induce the variation of the refractive index of the detected crystal, which was coherently recorded by the electro-optic sampling method through the ZnTe crystal, a λ/4 wave-plate, a Wollaston prism and a pair of photodiodes [14]. All the measurements were carried out under a dry nitrogen gas environment to eliminate the fluence from water vapor.
First, to describe the effect of 180 nm CMOS process on the metamaterial, a single-layer SRR array without an embedded transistor was designed as a control sample. In order to study its transmittance performance, a THz plane wave with an electric field perpendicular to the gap was applied. Figure 5(b) illustrates the experimental and simulation results of the single-layer SRR. It was found that LC resonance and the dipole resonance were generated ∼0.3 THz and 0.9 THz, manifesting that the THz metamaterials were successfully realized by using the CMOS process. Figure 5(c) shows the experimental and simulation results of a doublelayer SRR structure, which adopted the same structure parameters as those from the single-layer SRR. The two openings above were staggered and connected by a via, which is extremely difficult to achieve when just using lithography and evaporation procedures. The device had no transistors. The experimental and simulation results showed that the LC resonance strength in the double-layer ring structures was obviously weakened. It was speculated that the interaction between the two layers at this time affected the LC resonance of the metamaterials. The discrepancies between the simulation and the experiment were due to the difference in the dielectric environment. In the simulation, SiO 2 was used as the dielectric layer, and the actual dielectric layer may include SiO 2 , Si 3 N 4 and other materials. Then the SRR array embedded with transistors was repeatedly tested to obtain the frequency domain waveform affected by different voltage. Figure 6(a) depicts the test results with varying resonance frequencies from 0.25 THz to 0.36 THz when applied various control voltage V control . Unfortunately, there was no significant LC resonance in the expected range, for the external conditions such as the effects of the printed circuit board and the silica gel may have interfered with the results. To verify this speculation, a bare sample without packaging was tested and the results are shown in the inset of figure 6(a). The apparent LC resonance was obtained at 0.32 THz. In order to reflect the effect of applied V control on the experimental results, the measured data under different V control was normalized, which is plotted in figure 6(b). The data were obtained from dividing the experimental results with different V control values by the result from 0 V, respectively. It was found that the waveform changes significantly with the V control , indicating the reliability of this measurement.
To intuitively extract the electrically induced phenomenon, an equivalent transformation was introduced. The measured data of the unpackaged bare chip in the inset of figure 6(a) can be considered as the result for 0 V applied V control . Figure 6(c) is the processed results obtained by multiplying the test data of the unpackaged bare chip with the normalized value of figure 6(b). The resonance frequency variation was obtained by multiplying the two signals together to amplify the trend. This method overcomes the influence of packaging interference and the final signal shows an obvious redshift along with the gradual increasing of the applied voltages. Transmittance increases and then decreases as the voltage increases, our experimental results have already been quantitatively reproduced by the calculated results. Figure  6(d) illustrates the relative frequency variation as a function of the external applied voltages, further visually corroborating the redshift phenomenon. When the V control exceeded 0.6 V, the redshift trend was found to be slowed down. This behavior can be attributed to the intrinsic characteristics of channel resistances under gate voltages. Since the V control was ultimately applied to the gate, the increase of voltage meant the decrease of R t . When the V control was below the threshold voltage V T , the transistor was working in the cutoff region and the resistance dropped rapidly with the increase of the voltage. However, when the applied voltage exceeded the V t , the conductive channel was almost formed. In this case, the transistor was working in the linear region and the resistance no longer promptly decreased with the increase of the voltage. The tuning range is only 35 GHz, but CMOS technology is still seen as a potential method of regulation.
The effect of gate voltage on phase variation was also comprehensively evaluated and the phase difference from 0.25 THz to 0.36 THz is plotted in figure 6(e). As can be seen from this figure, the phase differences were varied for different voltages. The summarized results are exhibited in figure 6(f). It can be found that the phase difference decreases with the increase of the applied voltage and the maximum absolute phase difference reached up to 3 • . Although the phase tunability was weak in these principle verification experiments, our preliminary results open the door for CMOScompatible electrically controlled phase devices and systems. The performance of the C-ATTMA can also be improved. For example, the size of the transistor we use is small, which limits its impact on the whole structure. On the other hand, the metamaterials were made in the top metal layer, far away from the transistors, which also reduces the impact of transistors. By modifying the metal layer and increasing the size of the transistor, the transistor would fit into the SRR perfectly, which might greatly improve the performance of the device. We believe that with more delicate design and manufacturing, THz metamaterials regulated by electricity can be fabricated in the future. The proposed design can make use of the CMOS multi-layer metal process effectively and produce more complex three-dimensional metamaterials. We demonstrated the double-layer SRRs to prove it. As far as we know, this is very difficult to achieve with other processes such as lift-off. Furthermore, compared to other materials, such as GaAs and Schottky diodes, the CMOS has a standardized process, which provides a huge advantage in terms of large-scale fabrication and cost reduction. Finally, by configuring a separate circuit for each SRR, it will be possible to control each unit, which is difficult for other processes. The proposed structure has the potential to achieve coding metamaterials and will play an important role in large-scale applications.

Conclusion
In summary, C-ATTMAs with SRRs have been successfully demonstrated and they performed as tunable devices at 0.3 THz. The experimental results show that the resonance frequency can be redshifted by 35 GHz and the phase can be engineered along with the increase of the applied bias voltage from 0 V to 1.8 V. The preliminary experimental results can be well interpreted by an equivalent circuit model. We believe that the CMOS technology has great potential in making controllable THz metamaterials, which can be easily applied at frequencies above 200 GHz through scaling in size. This work can be further extended to programmable and encrypted intelligent THz metamaterials, enabled by the proposed electrically active THz units. The C-ATTMA paves the way to a range of applications in the imaging, sensing and wireless communication fields.

Acknowledgments
This study is also supported by the 'Zhuoyue Program' of Beihang University (ZG216S18B5), Qingdao Innovation and Entrepreneurship Leadership Program (18-1-2-21-zhc), and the VR innovation platform from Qingdao Science and Technology Commission and Magnetic Sensor innovation platform from LaoShan District.

Authors' contributions
Professor L G Wen, Professor T X Nie and Professor X J Wu conceived original idea of combining CMOS technology with metamaterials. Y S Liu and Z Y Bai presented the operation mode of metamaterials. T Sun designed and made the external circuit. Y S Liu and T Sun conducted experiments. Y Sun and H L Li played an important role in experiment and simulation. Professor X J Wu, Professor T X Nie and Professor Y Hu provided theoretical guidance and technical support. Professor C J Ruan, H Y Zhang, K L Chen, Y X, Professor W S Zhao and Y Z Sun provided valuable advice and all the authors contributed to the writing. Professor T X Nie and Professor X J Wu supervised the project. The authors read and approved the final manuscript.

Conflicts of interest
The authors declare that there are no conflicts of interest related to this article.

Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.