BST-silicon hybrid terahertz meta-modulator for dual-stimuli-triggered opposite transmission amplitude control

2.1 Tuning mode and performance

Figure 2 shows the experimental THz time-domain spectra of the proposed meta-atom (Figure 1) under varying external voltages (top right corner of Figure 2) and currents (bottom right corner of Figure 2). A blank sample (air) is also provided in Figure 2 as a reference for subsequently calculating the frequency-domain transmittance coefficient. All the corresponding results are measured through a THz time-domain spectroscopy (THz-TDS) system, and notably, when conducting the experiments, only the time-domain signals from 0 to 20 ps are collected to avoid the multipath effect and eliminate Fabry–Perot reflection, which can directly affect the test precision even cause obvious errors. The signal waveforms transmitted through the fabricated sample show totally different changes with increasing current and voltage amplitude. With regard to the voltage tuning mode, the amplitude of the time-domain signal increases from 7.27 ps @ 0 V to 8.63 ps @ 100 V and the time-domain peak shifts from 14.45 ps @ 0 V to 14.6 ps @ 100 V as the input voltage gradually increases. Furthermore, once the applied electric current is boosted to above 0.6 A, the transmitted THz main pulse rapidly decreases, while little pulse position shift can be observed. From the time-domain signal waveforms shown in Figure 2, the basic functionality and operation method of the proposed hybrid meta-atom can be qualitatively revealed to be as desired, but the performance parameters of the dual-mode modulation, such as the modulation depth, cannot be intuitively exhibited. Hence, the frequency-domain spectra of the transmitted THz waves need to be provided, which contain more information such as amplitude and phase.

Figure 2:

Time-domain transmittance signals of the proposed dual-mode meta-modulator and their amplitude change under different external voltage and current excitations. The signal waveform of the reference (blue dotted line) is plotted on the left side.

By performing a fast Fourier transformation (FFT) of the experimental data in Figure 2, the frequency-dependent amplitude ( T ( ω ) ) of the THz pulse transmitted through the hybrid metamaterial can be obtained, as shown in Figures 3a and 4a. Here, free space (blank sample) is considered as the reference, which can be used to normalize the electric field intensity as follows:

in which E Sample/Ref . ( ω ) is the E-field calculated from the time-domain data of the sample/reference, as illustrated in Figure 2. Figures 3a and 4a show the calculated transmission coefficient through the BST–silicon hybrid meta-modulator with different applied currents and voltages in the frequency range of 0.3 THz to 1.1 THz.

Figure 3:

Voltage tuning mode (a) Simulated and measured transmittance of the hybrid meta-modulator under different bias voltages. (b) Operating schematic illustration of the meta-modulator under the voltage tuning mode. (c) Voltage dependence of the imaginary part of the effective permittivity for our design at different frequencies. (d) Measured voltage–current relation of our design under current tuning mode and voltage tuning mode.

Figure 4:

Current tuning mode (a) Simulated and measured transmittance of the hybrid meta-modulator under different currents. (b) Operating schematic diagram of the meta-modulator under the current tuning mode. (c) Measured (circle), fitted (solid black curve) and theoretical (colored solid curve) values of the normalized transmission amplitude as a function of frequency at bias currents of 0.9, 1.2, 1.5, 1.8, and 2.1 A. (d) Current intensity dependence of the imaginary part of the effective permittivity for our design at different frequencies.

From Figure 3a, the all-band (from 0.3 THz to 1.1 THz) transmission of THz waves through the sample is obviously gradually enhanced as the input voltage applied on the Pt interdigital electrodes increases from 0 to 100 V, which is consistent with the measured time-domain results (Figure 2). In addition, the opposite phenomena can be observed in Figure 4a. Once a DC current flow greater than 0.6 A is brought into the amplitude modulation system along the Pt interdigital electrodes, the transmittance rate rapidly attenuates, as predicted in Figure 2.

To further demonstrate the dynamic modulation ability of the proposed meta-device, the amplitude modulation depth is defined as

where T V g ( ω ) and T V 0 ( ω ) are the normalized transmission at ω in terms of V ₀ (0 V) and V _g voltages, respectively. According to Eq. (2), the calculated amplitude modulation depth reaches an average value of 20.5% from 0.3 THz to 1.1 THz when the bias voltage is equal to 100 V. Similarly, the amplitude modulation depth under various applied currents can be calculated as

in which T I g ( ω ) and T I 0 ( ω ) are the normalized transmission rates for 0 and I _g currents at ω . When the input current rises to 2.1 A, the modulation depth is greater than 85.8% during the operation bandwidth, making our design an excellent THz switch. Until now, we have introduced the tuning method and the corresponding modulation performance of the proposed hybrid metamaterial in detail. In the next section, we will deeply investigate the physical mechanism of the interesting characteristics observed above.

2.2 Physical mechanism

In our design, N-type silicon with abundant free electrons is chosen as the bottom substrate, the inside carrier distribution of which can be flexibly adjusted under various external stimuli, thus making it convenient to influence the transmittance features of the incident THz waves [36]. To confine the flow of the electric charges when driven by voltage or current fields, the BST film is patterned as a circular-hole array, and the Pt electrodes are arranged on both sides [37]. Note that due to the inevitable generation of oxygen vacancies during the coating process, the BST thin film that has few free charges can be regarded as a high-resistance semiconductor.

With regard to the voltage tuning mode, to reveal its physical mechanism, the microscopic behavior of the carriers inside the meta-atom is provided in Figure 3b. An interdigital electrode is used to apply a potential difference between the adjacent electrodes. Once an external voltage field is introduced, the patterned BST layer can be polarized along the electric field line from the anode to the cathode (Figure 3b). Due to the special hole-shaped design (Figure 1) that removes the redundant BST in the central part, the induced polarization phenomena can clearly be found to mostly occur below the Pt electrodes. Near the anode, the induced electric field in the BST layer is vertical to the surface and points to the positive pole, while the opposite electric field line can be achieved below the cathode. Hence, owing to the polarized BST, an opposite potential distribution to that of the input voltage field is produced at the boundary between BST and N-type silicon, which can directly determine the behavior of the carriers inside the bottom silicon. As shown in Figure 3b, under the influence of the extra field caused by BST polarization, some of the disordered free charges and holes in the silicon can be separated and driven to the corresponding regions (Figure 3b) by the electric force, resulting in a decrease in the conductivity. Therefore, the dielectric loss of the entire meta-structure gradually decays with the regression of the dielectric nature of the adopted N-type silicon, and accordingly, the THz transmittance is improved. In the following, to uncover the effect of the dynamic bias voltage on the modulation depth, the induced electrostatic potential difference (V _EP) is calculated as [37]

where C is the capacitance between the electrodes with an area of S. P determined by the external electric voltage denotes the polarization degree of BST. In Eq. (4), S is fixed once the meta-device is fabricated. Additionally, we consider C to be a constant parameter for the thin layer BST patterns that has little effect on the capacitance between the electrodes when various external voltages are applied. Therefore, only P can be used to adjust the induced electrostatic potential difference formed at the interface between the BST-patterned layer and the N-type silicon substrate. That is, with increasing input electric voltage, the polarization degree of BST and induced V _EP can be synchronously promoted. Combined with the previous analysis, more carriers in the silicon can be confined beneath the corresponding electrodes, and their dissipation of the incident THz waves can be gradually alleviated, thereby leading to enhancement of the transmitted power. Based on this theoretical model (Figure 3b), the simulated results also have been revealed in Figure 3a, showing great consistent with the measured ones (see Supplementary Note S1 for a detailed introduction of the simulation method).

To further reveal the voltage tuning mechanism, the imaginary part of the effective dielectric constant of the meta-modulator is extracted from the THz transmittance spectra (Figure 2). Based on the classical model proposed by L. Duvillaret and T. D. Dorney [38], [39], [40], the complex refractive index of the total structure can be expressed as

in which n ( ω ) represents the real refractive index and κ ( ω ) denotes the extinction coefficient, which describes the absorption characteristics of the sample. Furthermore, according to the interaction between the sample and THz waves, the transmitted signal can be described as

where A ( ω ) and φ ( ω ) are the amplitude and phase of the transmitted signal, respectively, d is the thickness of the sample, and c is the speed of light in vacuum. Therefore, by substituting Eq. (5) into Eq. (6), n ( ω ) and κ ( ω ) can be derived as follows:

Finally, since the complex permittivity has relationships with n ( ω ) and κ ( ω ) of

the real part ( ε r ) and imaginary part ( ε i ) of the effective permittivity can be obtained by substituting Eqs. (7) and (8) into Eq. (9) and (10), respectively. In Figure 3c, the calculated ε i corresponding to different bias voltages is illustrated, and the dielectric loss of the entire structure clearly gradually decreases as the input voltage increases, which agrees well with the above qualitative analysis.

Thus far, we have comprehensively revealed the inner physical mechanism of the proposed meta-modulator under the voltage tuning mode. Next, we will perform an in-depth investigation of the physical source of the current tuning mode.

With regard to the current tuning mode, two different processes successively impact the transmission characteristics of the proposed meta-modulator. In the first process, as the bias current increases to 0.6 A from the initial condition (0 A), a similar phenomenon to that in the voltage tuning mode can be observed by comparing the transmittance spectra in Figure 4a with those in Figure 3a. Generally, a current source can provide a stable output current without considering the voltage between the electrodes. Hence, due to the high resistance property of the BST film, a relatively high voltage can be generated by the current supply even when the bias current is small, resulting in almost the same modulation effect as the voltage tuning mode. In addition, this phenomenon also can be revealed from the overlapped voltage–current curves (Figure 3d), which denote the identical physical process.

In the second process, as the applied current further increases (exceeding 0.6 A), free electrons can be injected into the boundary between the patterned BST film and the silicon layer across the hole structures etched in the BST film, leading to the generation of a thin carrier layer at the corresponding locations (Figure 4b). In the meantime, for the conductive path is successfully built, the load resistance inner our design significantly decreases, resulting in the reduction of the input voltage as the bias current is more than 0.6 A (Figure 3d).

Therefore, as the bias current increases from 0.6 to 2.1 A, the carrier concentration of the assumed conducting layer significantly increases as desired, resulting in dissipation of the incident THz power. To verify this hypothesis, we study the effect of the induced carrier layer and its carrier density on THz transmittance. Since the induced carrier layer is quite thin [41], a theoretical model is chosen to obtain the approximate transmittance | T ( ω ) | of the total structure as follows [30, 41], [42], [43]:

where N refers to the equivalent layer number of the induced carrier layer, Z ₀ is the vacuum impedance, and n _sub is the effective refractive index of the proposed meta-modulator at 0.6 A. Note that all the measured, fitted, and theoretical transmittances shown in Figure 4c are normalized to the condition in which the bias current is equal to 0.6 A. In addition, σ ( ω ) in Eq. (11) is the complex conductivity of the induced carrier layer, which can be approximately described by the Drude model [41]:

in which n is the carrier density of the induced carrier layer, and τ is the carrier relaxation time. e and m* are the charge and effective mass of an electron. Therefore, the normalized transmittance can be calculated by substituting Eq. (12) into Eq. (11). Furthermore, once the structure and the adopted materials are decided, N, Z ₀, n _sub, e, m*, and τ are fixed, and thus, only the parameter n can be optimized to force the calculated | T ( ω ) | approach to the fitted value (black lines in the left part of Figure 4c). After several rounds of optimization, the carrier density is confirmed to be 1.1 × 10¹⁷ cm⁻³ @ 0.9 A, 15 × 10¹⁷ cm⁻³ @ 1.2 A, 41 × 10¹⁷ cm⁻³ @ 1.5 A, 81 × 10¹⁷ cm⁻³ @ 1.8 A and 160 × 10¹⁷ cm⁻³ @ 2.1 A. As previously predicted, the fitted carrier density is positively associated with the applied current. The final calculated results of the normalized transmittance are illustrated in the right part of Figure 4c, which are consistent with the measured and fitted results in the left part, proving the correctness of our previous hypothesis. At the same time, we conduct the simulation of the proposed theoretical model (Figure 4b) by utilizing CST Microwave studio, and the simulated results demonstrate excellent agreement with the measured ones (Figure 4a), further verifying this analytical method (see Supplementary Note S1 for a detailed introduction of the simulation method).

Additionally, the dielectric loss of the entire meta-structure under different bias currents is calculated based on Eqs. (7)–(10) and provided in Figure 4d. When the input current increases, more incident power can clearly be dissipated by our design as a result of the promotion of the imaginary part of the permittivity (Figure 4d) of the entire structure, which further reveals the current tuning mechanism from the aspect of the equivalent medium.

4.1 Coating process

To fabricate the proposed meta-device, a three-layer substrate (Pt–BST–silicon) is first prepared for the subsequent lithography process. During the coating process, the BST film with the optimized thickness is primarily deposited on a clean N-type silicon wafer through radio frequency (RF) magnetron sputtering with a deposition speed of approximately 50 nm/h. Then, a 200 nm thick Pt film is deposited on the semi-finished sample by direct current (DC) magnetron sputtering with a sputtering rate of approximately 10 nm/min. Notably, the prepared BST film needs to be annealed in a 650 °C pure oxygen atmosphere to facilitate growth of the lattice and adequate filling of the oxygen holes.

4.2 Lithography process

Before conducting overlay lithography, the photoresist is evenly coated on the top surface of the manufactured three-layer substrate through a two-step method with the help of a spin coater (Laurell EDC-650Mz-23NPPB). Then, the sample is in turn treated with soft baking (at 100 °C for 60 s) and hard baking (after exposure) at 110 °C for 90 s to evaporate the residual solvent and release the extra stress in the photoresist film. In addition, these annealing treatments can help improve the adhesion between the photoresist and the sample and reduce the standing wave effect.

In the following, traditional semiconductor technology, as shown in Figure 5a, is adopted to fabricate the overlapping patterns. First, mask #1 for manufacturing Pt interdigital electrodes is utilized for the exposure process, which can transfer the predesigned complementary pattern to the photoresist. Then, the photosensitive region can be removed through chemical development and ion beam etching while the other part is protected and wiped away in the photoresist removal step. The fabrication process mentioned above can be observed in the blue part of Figure 5a. Next, with the help of mask #2, periodic circular holes are etched in the middle-layer BST film by utilizing a similar preparation method as before. Note that overlay technology is the key point during the second round of the photoetching process, determining the quality of the final sample. Here, to overcome this challenge, we have left several alignment marks at identical locations (always along the diagonal line) of both mask #1 and mask #2 in advance. When the marks remaining in the preliminary sample are matched with those in mask #2, the overlay operation can be finished with high precision. The procedure of the overlay lithography is provided in the brown part of Figure 5a.

Figure 5:

Fabrication process and sample display (a) Schematic diagram of the overlay lithography process. Photograph (b) and SEM image (c) of the fabricated BST–silicon hybrid meta-modulator.

As shown in Figure 5b, ports (L-shaped structures) for connection to the external voltage and current sources are reserved around the array in the fabrication process. In addition, a scanning electron microscopy (SEM) image (Figure 5c) is also given to exhibit the excellent microscopic morphology of the sample, proving the high accuracy of the adopted overlay lithography.