High-precision digital terahertz phase manipulation within a multichannel eld perturbation coding 2DEG meta-chip

Hongxin Zeng University of Electronic Science and Technology of China https://orcid.org/0000-0002-4404-9485 Huajie Liang University of Electronic Science and Technology of China Yaxin Zhang (  zhangyaxin@uestc.edu.cn ) University of Electronic Science and Technology of China Ziqiang Yang University of Electronic Science and Technology of China Feng Lan University of Electronic Science and Technology of China Shixiong Liang Hebei Semiconductor Research Institute Zheng Li University of Electronic Science and Technology of China Lan Wang University of Electronic Science and Technology of China Xilin Zhang University of Electronic Science and Technology of China Sen Gong University of Electronic Science and Technology of China Yubin Gong University of Electronic Science and Technology of China Ziqiang Yang University of Electronic Science and Technology of China


Introduction
Terahertz (THz) technology has potentially transformative applications in high-rate communication, biomedical imaging, holography, spectroscopy, radar and security [1][2][3][4][5][6][7][8][9][10][11][12][13] . As the demand for the wireless bandwidth increases, wireless communication systems applying terahertz waves as carriers provide ultrahigh transmission rates and low delays, which are expected to exceed those of 5G communication systems. The demand for terahertz systems is driving the development of high-performance integrated terahertz devices. As one of the key techniques, the e cient and dynamic manipulation of the phase and amplitude of THz waves has to become the subject of in-depth research worldwide. The dynamic metamaterials composed of a metamaterial and an active material have led to remarkable achievements in terahertz amplitude and phase dynamic manipulation devices 4,14-21 . The resonance mode and intensity of such metamaterials are affected by the distribution of electrons in the metamaterial structure.
Different transport paths of electrons generate various resonance modes, such as LC resonance 14 , dipole resonance 21 , and Fano resonance 16 . Metamaterials containing active materials can transform the electrical characteristics under external excitation, altering the resonance mode and intensity to manipulate terahertz waves.
As early as 2006, the combination of metamaterials and doped semiconductors realized the modulation of the terahertz wave transmission amplitude for the rst time 14 . Since then, various THz dynamic or tunable metamaterials have emerged to achieve effective manipulation of the THz wave amplitude and phase [22][23][24][25][26][27][28][29][30][31] . In 2009, a composite metamaterial based on an n-doped GaAs layer was reported 22 , which achieved a phase modulation of 0.56 rad. Subsequently, doped silicon 24 , vanadium oxide 29 , graphene 25,32 , high electron mobility transistors (HEMTs) 30 , liquid crystals 33 , and other dynamic materials were used to manipulate the terahertz wave phase, promoting the development of terahertz phase manipulation devices. However, almost all terahertz phase manipulation devices with dynamic metamaterials are based on the direct interaction between terahertz waves and metamaterials, which results in sensitivity of the phase to the resonant mode and intensity and affects the linearity and accuracy of the phase manipulation. Furthermore, general dynamic metamaterial phase-controlling devices work in free space, which is not the case for integrated systems.
To overcome the above issues, the development of THz phase dynamic manipulation requires a completely new mechanism. Instead of coupling all of the terahertz wave with the metamaterial, coupling a minority of the energy of the terahertz wave with the metamaterial may improve the phase manipulation accuracy and reduce system losses. Interacting with on-chip terahertz waves, instead of with free space terahertz waves, may enable convenient integration of the system.
Recently, an information metamaterial [34][35][36][37][38][39][40][41] , as a special digital metamaterial, consisting of coding metaatoms digitalized as "0" or "1" was introduced. The binary codes produce different effects on electromagnetic waves by varying the electromagnetic characteristics of the meta-atoms. In this way, digital metamaterials can be programmed to realize numerous functions, such as communication 40 , imaging 35,36 and holography 34 . These works suggest that phase manipulation can be programmed with different coding sequences to achieve a precise degree of phase shifting. This approach also possesses great advantages in high-rate and real-time systems. Based on these considerations, in this paper, a multichannel eld perturbation coding 2DEG meta-chip (MPCM) combining nanometer 2DEG meta-atoms and on-chip transmission lines is proposed. Different from the general dynamic metamaterial structure, the meta-atom is not directly coupled with all of the terahertz wave in free space but with a minority of the terahertz wave on the chip to form a local resonance perturbing the quasi-TEM terahertz wave on the chip. By controlling the electronic transport in 2DEG nanostructures, the perturbation intensity is altered to shift the phase. In addition, coding the perturbation intensity generated by different meta-atoms results in diverse perturbations with different orders to nely manipulate the THz phase.
The MPCM that we propose, as shown in g. 1, combines an on-chip microstrip transmission line with meta-atoms. As a main transmission line, the on-chip microstrip line divides the surface of the substrate into two sides: on one side is placed 2DEG nanostructures, and the other side has a grounded metal pad. All of the metal layers are 1 µm thick gold, which are fabricated on a 50 µm thick SiC substrate. The metaatom consists of one metal pad, one gaped thin metal line, and two metal electrodes located on both sides of the gap. The 2DEG, which use the same manufacturing processes as HEMTs, is nested in the gap, providing active properties to the device. A terahertz wave propagates along the main transmission line, wherein the energy is concentrated in the dielectric substrate. The electric elds of the on-line propagating terahertz wave can induce weak resonant modes in the unilaterally located meta-atoms; meanwhile, the change in the transport of the 2DEG in the meta-atom causes a variation in the carrier concentration, which leads to a further change in the electronic stacking in both metal electrodes. Such a change in the electronic stacking can generate different perturbations of the electromagnetic eld distributed on the surface of the substrate and cause a phase shift of the terahertz wave transmitting along the main transmission line. With this mechanism, we can consider that in the case of a high carrier concentration of the 2DEG, named the "0" state, a slight electronic stacking occurs in both metal electrodes of the meta-atoms, which brings about a high concentration 2DEG resonance (HCR) for the terahertz wave. The HCR leads to a faint perturbation of the electromagnetic eld. In the contrary case, named the "1" state, the low carrier concentration of the 2DEG allows more electronic stacking in both metal electrodes, which means a depleted 2DEG resonance (DR) can be produced, which slightly enhances the perturbation to a mild perturbation. The change in the perturbation of the propagating THz wave could lead to a de nite phase shift. Thus, by applying different bias voltages to the 2DEG with a metal pad, we can control the carrier concentration of the 2DEG to achieve conversion between the 0 and 1 states, realizing a change in the phase manipulation of the transmitting terahertz wave.
Based on this mechanism, we set up a meta-atom array with multiple meta-atoms. Each meta-atom at a certain distance can individually exhibit the perturbation states through different bias voltages, and the perturbations can superimpose on each other. More importantly, perturbations with different intensities are distributed at different positions of the transmission line, bringing about a nonlinear superposition. As depicted in g. 1, each meta-atom of the meta-atom array is coded with binary code sequences to convert it between the 0 and 1 states; thus, various combinations of the states of all meta-atoms will cause precise phase shifting of the terahertz wave. Hence, we demonstrate a multichannel eld perturbation coding 2DEG meta-chip controlled by programing binary codes. Bene ting from this phase manipulation mechanism of local resonant coding perturbation, phase manipulation with different precisions from 2°t o 5° is observed from 0.26 to 0.27 THz. Compared with the traditional terahertz metamaterial phase manipulation device, our MPCM demonstrates high-precision phase manipulation with high transmission e ciency and low amplitude uctuations. Moreover, it has excellent scalability and compatibility for terahertz integrated communications, imaging and radar systems.

Results
Perturbation of the electromagnetic eld by single 2DEG meta-atoms.
The perturbation of the electromagnetic eld within 2DEG meta-atoms can be demonstrated by the surface current and electromagnetic eld distributions. Therefore, to extract persuasive information regarding the phase manipulation characteristics of the MPCM, we rst analyzed a single meta-atom eld perturbation coding 2DEG meta-chip (SPCM), as shown in g. 2. Its schematic diagram is shown in g. 2a, where the blue is the SiC substrate, the yellow is the gold, and the red area in the center is the 2DEG. For comparison, three conditions are included: the bare on-chip microstrip line structure without any meta-atoms (see g. 2b, 2e, 2h); the meta-chip with a single meta-atom accompanied by a high carrier concentration of the 2DEG (see g. 2c, 2f, 2i); and the meta-chip with a single meta-atom accompanied by a low carrier concentration of the 2DEG (see g. 2d, 2g, 2j).
The distributions of the transient surface current in these three conditions are shown in g. 2b, g. 2c and g. 2d, and the corresponding distributions of the electric eld are shown in g. 2e, g. 2f and g. 2g, respectively. In these gures, the color of the current indicates different amplitudes of the current, where a redder color means a larger amplitude and a bluer color means a smaller amplitude. In the case of the rst condition, the surface current on the on-chip microstrip line ows from both sides to the middle in a local area, which is just a quasi-TEM transmission mode (see g. 2b). After a meta-atom is introduced, the surface current on the on-chip microstrip line ows towards the meta-atom (see g. 2c, 2d). Then, electrons accumulate in both metal electrodes on both sides of the gap, forming an electronic stacking with a local resonance. In the case of a high carrier concentration of the 2DEG in the meta-atom, the electron transport capability is strong, so less electronic stacking occurs in both metal electrodes on both sides of the gap ( g. 2c), which leads to the formation of a local electric eld between the gap with HCR (see g. 2f). When the 2DEG is depleted, the carrier concentration of the 2DEG in the meta-atom is lower, and the electron transport capability is weaker. More electrons accumulate in both metal electrodes ( g. 2d), resulting in the local electric eld between the gap becoming stronger, which can enhance the local resonance to be a DR (see g. 2g). We plotted a normalized surface electric eld intensity map along the y-axis with the meta-atom as the center ( g. 2k) to more intuitively demonstrate the variation in the local resonance strength at different carrier concentrations of the 2DEG after the introduction of a meta-atom (the maximum surface electric eld intensity of the microstrip transmission line was taken as a reference). In the gure, the electric eld on the surface of the microstrip transmission line is symmetrically distributed about the y-axis (gray part). After introducing the meta-atom, the original electron distribution is broken. Under the conditions of a high carrier concentration and a low carrier concentration, the local electric eld intensity formed at the gap of the meta-atom is approximately 5.2 times and 8 times the maximum electric eld intensity in the microstrip transmission line, respectively.
Resonances of different intensities can be formed by meta-atoms with different carrier concentrations.
The local resonances have three remarkable characteristics. First, these local resonances do not directly impact the major eld of the terahertz wave in the substrate because the propagation mode of the terahertz wave in the microstrip transmission line is the quasi-TEM mode. Thus, most of the energy is concentrated in the GaN substrate between the microstrip line and the grounded metal plate, and the electric eld direction is parallel to the z direction (see g. 2h), while the meta-atom is fabricated on the surface of the GaN substrate, which does not impact the major eld of the terahertz wave. Second, although these local resonances do not directly impact the major eld of the terahertz wave, the electric eld generated by resonance will provide an electric eld component Ez ( g. 2i, 2j) in the z direction, thus causing perturbation of the major electric eld of the terahertz wave. Moreover, different local resonances, HCR and DR, mean different electric eld components Ez, so the perturbation of the major electric eld will change with switching between HCR and DR.
This perturbation not only increases the intensity of the Ez component of the electric eld but also increases the area of the electric eld distribution in the cross section. According to the relation between the relative equivalent permittivity and the electromagnetic eld of a microstrip transmission line 42 , the relative equivalent permittivity of the microstrip transmission line will be augmented as the intensity of the Ez component and the area of the electric eld distribution in the cross section increase. Thus, the phase velocity will decrease as the relative equivalent permittivity of the microstrip transmission line increases. As a consequence, the phase of the terahertz wave will change when perturbation occurs. Moreover, various perturbations can cause different phase shifts.
We compare the perturbation of the main eld for high and low carrier concentrations in g. 2l. The green and red lines represent the average Ez along the propagation direction of the single meta-atom chip under a high carrier concentration and a low carrier concentration, respectively. The black line shows the average Ez along the propagation direction of the microstrip transmission line, which is taken as the normalized standard. The intensity of the HCR to that of the major electric eld at a high carrier concentration is slightly smaller than that of the DR at a low carrier concentration. The perturbation of the major electric eld shifts the phase of the THz wave. As shown in g. 2m, where we take the phase of the THz wave in the microstrip transmission line as a reference, in the case of a high carrier concentration of the 2DEG, the HCR brings about a smaller perturbation such that the phase shift from the reference is 7 degrees. When the carrier concentration of the 2DEG decreases, the DR causes a phase shift of approximately 10 degrees.
High-precision phase manipulation of the MPCM.
The above analysis indicates that the local resonance of the meta-atom will perturb the major eld of the terahertz wave in the traditional microstrip line, so phase manipulation can be realized by varying the carrier concentration of the 2DEG to tune the strength of the local resonance. After introducing multiple meta-atoms, we can control the local resonance strength generated by different meta-atoms; thus, the superposition of the perturbations will provide more abundant and more precise phase manipulation.
Here, we coded the high concentration 2DEG resonance (HCR) perturbation as "0" and the depleted 2DEG resonance (DR) perturbation as "1". As a demonstration, we designed a coding 2DEG meta-chip containing 6 meta-atoms with a total of 64 coding states. The state with the code of 000000 is set to the initial state as a reference. Figure 3 (a-c) depicts the electrical eld distributions of each meta-atom under three representative coding sequences of "100000", "111000" and "101111". The black pattern in the gure represents the electric eld distribution in the case of coding sequence "000000", and all values of the local resonant electric eld intensity have been normalized by an arbitrary preset value. Under coding sequence "100000", the DR perturbation of the rst meta-atom leads to a slight electric eld intensity enhancement, while the eld intensities of the other ve meta-atoms remain the same as the initial state, as shown in g. 3a. With this analysis, coding sequence "111000" can be found to result in electric eld intensity variations of the 1st-3rd meta-atoms, while the last three meta-atoms remain unchanged. Similarly, in the case of coding sequence "101111", the resonance state of the second meta-atom belongs to HCR perturbation, so the eld is the same as that of the initial state; the other meta-atoms have their own slight eld changes. Thus, different coding sequences can lead to various electric eld intensity distributions, which makes the superposition of the phase shifts of different meta-atoms perform nonlinearly. Therefore, by applying the nonlinearity of the phase superposition, we can obtain different phase shift degrees and phase shift precisions. As shown in g. 3d, the phase perturbations in the propagation process under the four coding sequences are different. The black line represents the phase perturbation with code "000000" as a reference. Furthermore, the red, blue and green curves represent the perturbations of the phase for the coding sequences of "100000", "111000" and "101111", respectively. The gure shows that the three curves have 1, 3 and 5 perturbations, respectively, which correspond to 1, 3 and 5 DRs in the coding sequence. At the same time, every perturbation caused by a DR will have a certain phase shift, and the more perturbations there are, the larger the phase shift will be. The relationship between the number of DRs and the phase shift of the meta-atom in the meta-chip is shown in g. 3e-f. When the number of DRs is 0, the coding sequences only include "000000", for which the phase is indicated by a red point. As the number of DRs increases to 1, the number of coding sequences increases to 6: "100000", "010000", "001000", "000100", "000010" and "000001", for which the phase is represented by orange points. We can clearly observe that the phases of the 6 coding sequences are different, which indicates the nonlinear relation of the phase shift with different meta-atoms. Similarly, an increase in the number of DRs to 2 leads to 15 coding sequences. In this case, the phases of the 15 coding sequences exhibit different values, indicated by purple points. Based on the above principle, the total six bits of the code correspond to 64 coding sequences, which provide us with plentiful selections of different phase shifts similar to a coding-phase database. We can determine all high-precision phase shift data under different frequencies from this coding-phase database.
Based on the above results, we designed a low-loss and high-precision multichannel eld perturbation coding 2DEG meta-chip (MPCM). The simulation results are shown in g. 3f-j. At a frequency of 0.265 THz, a continuous phase shift with a minimum phase accuracy of 2° and a maximum phase shift of 50°c an be realized, and the insertion loss of the chip is less than 4 dB. At 0.260 THz, the continuous phase shift has a maximum of 35°, where the insertion loss is less than 6 dB. At 0.270 THz, the phase shift can reach 60°. According to the results, different working frequencies can have their own phase distribution relation. Therefore, by applying the coding phase, such a single device can work at different frequencies.
Experimental results of the MPCM.
A prototype of the multichannel eld perturbation coding 2DEG meta-chip (MPCM) was obtained by following the processing of a GaN-HEMT. As shown in g. 4, an epitaxial layer of AlGaN/GaN was grown on a SiC substrate by metal organic chemical vapor deposition (MOCVD) in the rst step. After removing oil stains and other impurities, such as metal ions, by the standard cleaning process for HEMTs, a process combining photolithography with excessive etching was used to etch away the zones that did not include the active regions (2DEG regions). Next, several processes, such as photolithography and electron-beam evaporation, were used to fabricate a complex metal layer of Ti/Al/Ni/Au on one side of the active regions. Then, after a high-temperature rapid annealing process at 900°C in nitrogen, the complex metal layer was lifted off to form an ohmic contact with the 2DEG for negative electrodes. Next, a Ni/Au layer was fabricated on the other side of the active regions by precise electron-beam lithography, forming a Schottky contact for positive electrodes after the lift-off process. Finally, through photolithography, electron-beam evaporation and lift-off processes, a Ni/Au layer was fabricated for accurate connection of the ohmic contact and Schottky contact, forming the whole structure of the 2DEG meta-atom.
As a demonstration, the manufactured 6-channel 2DEG meta-chip is shown in g. 5e and f. Next, a metallic cavity composed of an input/output rectangular waveguide chip loading area and a control circuit was designed to package this meta-chip, as shown in g. 5a-c. The control circuit is based on the Rogers 5880, which provides the coding external bias voltage input. Each meta-atom is connected to the pads on the Rogers 5880 by gold bond wires. The external coding control voltage can be loaded on the meta-atom through the Rogers 5880 to realize different coding sequences for the meta-array. Figure 5d demonstrates the whole inner structure. The whole physical process can be described as 3 phases: In the 1 st phase, after inputting a terahertz wave to the rectangular waveguide, the E-plane waveguide-microstrip probe can couple the terahertz wave from the rectangular waveguide to the microstrip line. In the 2 nd phase, the terahertz wave propagates through the meta-atoms while the external coding voltages are loaded, and a phase shift is induced. In the last phase, the terahertz wave is coupled to the rectangular waveguide and output to the THz detector. A vector network analyzer was utilized to test the packaged device.
The results of the experiment are shown in g. 6, where g. 6a, b and c shows the relation diagram between the number of DRs and the phase shift of the meta-atoms at 0.265 THz, 0.260 THz and 0.270 THz, respectively. The phase shift increases with increasing number of DRs of the meta-atoms, consistent with the simulation. Figure 6d, e and f shows the phase shift and insertion loss for different coding sequences at 0.265 THz, 0.260 THz, and 0.270 THz, respectively. At 0.265 THz, we can obtain a total phase shift of over 50° with an insertion loss of approximately 6 dB. In the same way, at 0.260 THz, a total phase shift of over 30° and an insertion loss of less than 7 dB can be achieved. Moreover, at 0.270 THz, we realize a total phase shift of up to 55° with an insertion loss of approximately 8dB.
Further, by applying the principle that different coding sequences correspond to different phase shifts, we can select appropriate coding sequences to design what kind of chip we need. As shown in g. 6g, the designed multichannel eld perturbation coding 2DEG meta-chip possesses a high phase shift precision of 5°, in which the total phase shift can reach 50 degrees with a low insertion loss of approximately 6 dB. In addition, the chip phase shift precision can reach 2° at 0.260 THz, and a phase shift precision of 4° is provided at 0.270 THz. Tables 1-3 show the coding sequences at (Table 1) 265 GHz, (Table 2) 260 GHz, and (Table 3) 270 GHz, which include the phase shift error and insertion loss in each coding state. We nally determine that the average phase shift error is only 0.35° and the average insertion loss is as low as 6.14 dB at 265 GHz. In addition, an average phase shift error of 0.23° and an average insertion loss of 6.04 dB are achieved at 260 GHz; the values obtained at 270 GHz are 0.46° and 8.08 dB. As a consequence, the chip that we designed not only has a high phase shift precision but also ensures su ciently low phase shift error and insertion loss.
In summary, based on combining meta-atom perturbation resonance and the electronic transport characteristics of a 2DEG, we have designed a multichannel eld perturbation coding 2DEG meta-chip, wherein, by digitally controlling the external coding voltages, high-accuracy phase manipulation of a THz wave can be achieved. Both the simulation and experimental results show that phase manipulation with different precisions from 2° to 5° is obtained from 0.26 to 0.27 THz. The average phase error is only 0.36°, the average transmittance is -6.75 dB, and the maximum root mean square of the transmittance is 0.36 dB, demonstrating high-precision phase manipulation with high transmission e ciency and low amplitude uctuations. Furthermore, previous contributions inform us that the 2DEG-based magnitude modulator possesses a high modulation rate. Therefore, this on-chip digital coding control has excellent scalability and compatibility for terahertz integrated systems.