Abstract

Active control of terahertz waves is a critical application for terahertz devices. Silicon is widely used in large-scale integrated circuit and optoelectronic devices, and also shows great potential in the terahertz field. In this paper, a p-Si hybrid metasurface device is proposed and its terahertz characteristics under avalanche breakdown effect is investigated. In the study, a plasmon-induced transparency (PIT) effect caused by the near-field coupling of the bright mode and the dark mode is observed in the transmission spectrum. Due to avalanche breakdown effect, the resonance of the PIT metamaterial disappears as the current increased. Carriers existed in the interface between the metasurface and substrate result to a dipole resonance suppression. When the current continues increasing, the maximal modulation depth can reach up to 99.9%, caused by the avalanche effect of p-Si. Experimental results demonstrate that the avalanche breakdown p-Si can achieve a performance modulation depth, bringing much more possibilities for terahertz devices.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Metasurface is engineered electromagnetic materials, which offers enormous opportunities and unprecedented functionalities to manipulate electromagnetic waves [13]. Therefore, the potential applications of metasurface have attracted attention such as biosensing, compression imaging and so on [410]. Various devices based on metasurface including modulators, switches and absorbers have been extensively studied. Chen H.T. demonstrated an active metamaterial device capable of efficient real-time control and manipulation of THz radiation, leading to terahertz metamaterials attracting widespread attention all over the world [11]. In 2015, Seongsin M. Kim proposed a plasma-induced transparency (PIT) metasurface which gave rise to a sharp transparency window in the original absorption trough [12]. The PIT phenomenon is always accompanied by a drastic modification of the dispersion properties and thus useful in optical devices potentially [1315]. Studies shows that metasurface characteristics are mainly affected by the electromagnetic response of the subwavelength structure [1622]. In addition, when the optical parameters of metasurface gradually change from positive to negative, the local electric or magnetic field is intensively enhanced near the point of zero refractive index. By introducing active media for dynamic control, the singular electromagnetic behavior of metamaterials is significantly enhanced. Therefore, metamaterials could be dynamically controlled by electrical, optical methods or thermal through optoelectronic materials including graphene, silicon and VO2 [2332]. Thus, the change of conductivity of optoelectronic materials is the key to realize terahertz active modulation.

With the development of terahertz devices, novel materials have received widespread attention due to their excellent physical properties such as graphene, MoS2, VO2 and etc [2834]. Owing to the fascinating electronic, mechanical and thermal sensitivity properties, novel materials have been widely investigated and applied. However, considering the shortcomings such as complex processing, easily damaged and low modulation depth, there are still many difficulties in the large-scale application of novel materials in the future. Silicon is widely used in large-scale integrated circuits due to its easy availability and mature processing technologies. However, the main role of silicon is as a substrate rather than as a dielectric layer to study its characteristics in electronically controlled devices in the terahertz field. Therefore, it is necessary to study its electrical control characteristics in the terahertz range, such as avalanche characteristics. Compared with other metamaterials based on mechanical reconfiguration and incorporation with active materials such as varactor diodes, liquid crystals, phase change materials, superconductors, and two-dimensional materials under various external stimuli, metasurface based on avalanche effect is a novel idea to achieve dynamic modulation of metamaterials with great modulation depth [35].

In this paper, we proposed a p-Si hybrid metasurface device with performance modulation depth. A power supply was utilized to regulate avalanche breakdown p-Si, and effective switching and modulation of terahertz waves is achieved by the p-Si hybrid metasurface device. The transmission characteristics of p-Si hybrid metasurface device were characterized by terahertz time-domain spectroscopy.

2. Experimental setup and method

The metasurface structure fabricated on a 300 μm low-resistivity (ρ = 15 Ω·cm, Carrier density N=2×1013 cm-3, Carrier mobility μ=1000 cm2 V-1 s-1) p-Si is displayed in Fig.  1(a). They are prepared by photo-lithography technique. Mask pattern is transferred to a AZ5214 photoresist layer (3500 rpm, 35 s; dehydrated slightly for 90 s at 110°C) on p-Si by the MJB4 mask aligner. The development process is conducted in 400 K AZ remover/H2O mixture at the ratio of 1:4. 20 nm chromium (Cr) and 100 nm gold (Au) films is deposited by electron beam evaporation. Finally, the sample is soaked in acetone for 2 h to peel off the remaining photoresist and the metallization layer covering it by a lift-off process. At the same time, p-Si remove the native oxide layer by soaking hydrofluoric acid before photo-lithography technique in order to reduce contact resistance between the metal electrode and the p-Si. The geometric structure of the unit cell is shown in the inset of Fig.  1(a). Unit cell of the metasurface consists of a cut wire (CW) and a pair of identical but oppositely oriented split ring resonators (SRRs), and the structure parameters of the metasurface are displayed at the same time [13]. As shown in Fig.  1(b), the optical microscope image of the metasurface and interdigital electrodes can be observed with very high accuracy. Interdigital electrodes include 12 pairs of gold stripes with 5 μm wide and 14 mm length, and the distance between the two interdigital electrodes is 100 μm.

 figure: Fig. 1.

Fig. 1. Diagram of the p-Si hybrid metasurface device. (a) The normal incident THz wave propagates along the z-direction, with its electric field polarized along the y-direction. The unit cell of the metasurface is depicted in the inset, where px = 80 µm, py=105 µm, L = 86 µm, s = 10 µm, l = 30 µm, d = 20 µm, and the size of the gaps is g = 7 µm. (b) The optical microscope image of the sample. (c) The I–V characteristic curve of sample in experiments. (d-e) The corresponding I-G curve and I-R curve, showing the sudden change of p-Si conductance and resistance.

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Figure  1(c) shows the avalanche breakdown process of the device. The avalanche breakdown of silicon refers to the phenomenon that the current as well as the total power increases exponentially at a critical voltage [3638]. As the voltage continue to increase, the current in the device gradually increases. At the same time, the resistance of the device is constantly decreasing. This indicates that the carrier concentration of the device changed greatly. As shown in Fig.  1(c), with voltage increasing, the current slowly increases in the linear mode. When the voltage increases to about 20 V, the current suddenly increase to 0.5 A which is preset on the power supply and the voltage decrease rapidly. The phenomena indicate that the device enter the avalanche mode. The corresponding conductance and resistance results are shown in Fig.  1(d) and (e). The results reveal that the conductance and resistance of p-Si change suddenly when avalanche breakdown effect occurs in p-Si. In the experiment, the power supply is a purchased product, the model is Aim-tti EX752M which has a protection value of the total output power. In the linear mode, the power supply is used as a constant voltage mode. When the device is converted to avalanche mode, the voltage drops sharply and the current reach a balanced value. In the meantime, the power supply acts as a constant current mode.

In the linear mode, the current of the device increases slightly with the increasing of the applied gate voltage. In this mode, the total resistance of the device is quite large. In the mode of avalanche breakdown, some conductive channels are formed in the p-Si. For bulk materials, the carrier density near the conductive channel is higher, which is conducive to electron conduction. As the current increases, the flux of the conductive channel increases and the temperature within the channel is higher, causing the carriers to more easily collide with the electron-hole pair [3638]. Therefore, when the current increases, the carrier concentration gradually increases. In the avalanche breakdown mode, the modulation mechanism of the p-Si is to adjust the current to adjust the carrier concentration injected into the p-Si, thereby realizing the modulation of the terahertz waves. The injected carriers increase as the current increases. Conversely, when the current decreases, the injected carriers decrease. The dynamic modulation can be done by changing the current. Thus, the current of the device is turned to electrically manipulate its performance. Next, when the current is carefully turned from the avalanche-breakdown-point back to about 0.2 A, it still works at the avalanche mode. Then, the current gradually increases from 0.2 A to 1.4 A, the corresponding gate voltage decreases.

3. Experimental results and discussion

To reveal the underlying physical mechanism for the electromagnetic response of the metasurface, numerical simulations are performed using the commercial software CST, a full-wave electromagnetic simulation software based on a finite integration technique. For the numerical simulation, an electromagnetic field excitation propagating normally to the xy plane and polarized along the y direction is assumed. The periodic boundary conditions along the x and y directions are employed to the unit cell and the meshgrid type is set as hexahedral. Figure  2 displays the simulated transmission spectra and the simulated electric field distribution of the sample based on metasurface. In the simulation process, the propagation wave vector (k) is perpendicular to the structure plane whereas the electric field (E) and magnetic field (H) are parallel to the incident plane. In addition, we chose the Au with electric conductivity σ = 4.50 ×107 S / m as lossy metallic pattern. The simulated parameters of the p-Si are calculated by the Drude model:

$$\mathrm{\varepsilon} = {\mathrm{\varepsilon} _\infty } - \frac{{\omega _\textrm{p}^2}}{{{\omega ^2} + i\omega \gamma }}$$
where high frequency dielectric constant ε∞ = 12.5, the damping rate γ = 5×1012 rad / s and the plasma frequency ωp = 3.57×1012 rad / s [39]. Figure  2(a)-(c) show the transmission spectrum of the complete metasurface structure, CW and a pair of SRRs, respectively. The near field coupling between CW and a pair of SRRs leads to an indirect excitation and the classical destructive interference between them giving rise to a PIT analogue. When the unit cell of CW and SRRs are simultaneously arranged, a narrow transparency window is clearly observed within a broad absorption profile at dip of CW. In this configuration, the CW acts as a bright mode resonator which can be directly excited by the incident plane wave, and the SRRs act as a dark mode resonator which cannot be directly excited by this excitation. The electric field at the resonance frequency further illuminate the underlying physics behind the PIT analogue. As shown in Fig.  2(d) and (f), the CW and SRRs are excited by the incident plane wave with a very strong enhancement of the electric field concentrating on the edges and corners at the resonance frequency points dip A and dip B, correspondingly. The near-field coupling between the two discrete modes leads to coherent superposition, which suppresses the bright mode and its electric field, as shown in Fig.  2(e). Therefore, a transparency window of PIT appears.

 figure: Fig. 2.

Fig. 2. Simulated transmission spectra and the electric field at the resonance frequency of terahertz metasurface. (a), (b) and (c) The simulated transmission spectrum for the unit cell, CW and a pair of SRRs, respectively. (d-f) The simulated electric field at the resonance frequency at the resonance frequency points dip A, peak and dip B, respectively.

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Figure  3(a) shows the typical experimental results of terahertz time-domain waveforms passing through the device, which have been measured by a home-made terahertz time-domain spectroscopy (THz-TDS). The signal-to-noise ratio (SNR) of THz-TDS system is larger than 1000:1, which is detected and recorded using a lock-in amplifier and the bandwidth of THz-TDS is from 0.2 THz to 1.0 THz [32]. The size of focal spot is approximately 2 mm. The signal waveforms transmitting through the p-Si hybrid metasurface change appreciably with the increasing current. When the current is 1.4 A, the THz pulse decreases to almost disappear, which indicating the change of transmission is significant. In order to further investigate the refined variation of transmission characteristics under the avalanche mode, Fig.  3(b) displays the transmission properties of the p-Si hybrid metasurface with increasing gate current. The transmission of our device is obtained using the formula $t(\omega ) = |{E_s}(\omega )/{E_r}(\omega )|$, where ${E_s}(\omega )$ and ${E_r}(\omega )$ are Fourier transformed electric fields from the time-domain signal transmitted through the sample and air, respectively. With the increasing of gate current, the transmission amplitude spectrum of the p-Si hybrid metasurface gradually decreases. Hence, when terahertz waves irradiate the p-Si hybrid metasurface, the phenomenon of PIT will disappear with the increasing of gate current. From the transmission spectrum, it can be observed red-shift of the PIT frequency for that the increasing conductivity of the p-Si affects the coupling of metasurface. When the current is 0.5 A, the transparent window basically disappears. This is attributed to more carriers existed in the interface between the metasurface and substrate, which hinders the near-field coupling between the bright and dark modes. As for the PIT effects of the device, carriers play an important role in modulating plasmonic resonance, such as the value of Q [31]. As the current continues to increase, the resonance peak of the metasurface disappears and the transmission continue to decline to near zero. With the increasing of gate current, the conductivity of the surface of substrate in contact with metasurface will increase. The corresponding increase of the conductivity leads to the increase of the carriers in the substrate. When the gate current is applied to the substrate, large numbers of carriers are excited, leading to the transmission decrease. Moreover, Fig.  3(c)-(d) display the transmission and the modulation depth (MD) of the p-Si hybrid metasurface with different current corresponding to each resonance frequency points. Here, the MD is defined as $MD = ({t_g} - {t_{trf}})\textrm{/}{t_{trf}}$, where ${t_g}$ and ${t_{trf}}$ are the transmission under the different current and maximum transmission at different resonance frequency point on the terahertz spectrum, respectively. It can be observed that the transmission of resonance peak decrease with the increasing of gate current. In the avalanche mode, the maximum difference of MD at resonance points is 41% at the current 0.4 A, which show that the role of metasurface is significant when the current is small. When the current is 0.6 A, the PIT resonance basically disappears, and the modulation depth at the peak point is 72.3%. The transmission of resonance points basically coincides, indicating that the role of metasurface disappears. At this stage, the increasing of conductivity and carriers of the substrate play a decisive role in the transmission of THz [39,40]. Meanwhile, the MD is gradually approaching 1. The resonance at dip A 0.58 THz and dip B 0.67 THz basically unchanged when the current is small in avalanche mode. When the current is 1.4 A, the MD of the resonance frequency points at peak, dip A and dip B are 99.9%, 99.7% and 99.8%, respectively, which is caused by the absorption and reflection of terahertz waves with the increase of conductivity and excited carriers. This indicates that the conductivity of the substrate in contact with the metasurface is already extremely large.

 figure: Fig. 3.

Fig. 3. (a) Time domain THz signals of the p-Si hybrid metasurface and its amplitude change under various external electric excitation. (b) Measured transmission amplitude spectrum of the p-Si hybrid metasurface at various gate currents. (c) The measured transmission and the modulation depth of the p-Si hybrid metasurface at the resonance frequency corresponding to (b). (d) The measured modulation depth of the p-Si hybrid metasurface at the resonance frequency.

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In order to further research the characteristics of the surface of the metasurface/p-Si substrate, we use the simulation software CST with the Poisson equation to calculate the trend of electric energy density with thickness in Fig.  4(a). The interdigital electrodes are added to the surface of the metasurface/p-Si substrate at the voltage 20 V. Figure  4(a) shows the electric energy density distribution at the voltage 20 V, which represents the energy distribution of the electric field. Considering that the applied voltage acted on the surface, the gate current of device decreases with the increasing of substrate thickness. The electric energy density ratio between the depth dependent accumulation from surface and the total at the voltage 20 V is shown in the Fig.  4(b), and the distance d represents the distance between the detection point and the sample’s upper surface [41,42]. We have compared the field confinement at different voltages 10 V, 15 V and 20 V, finding that the electric energy densities have a similar thickness change trend. With the distance increasing, the change in electric energy density gradually slows down. To achieve the purpose of studying the physical properties of the p-Si surface layer, which is contacted with the matesurface, we fit the curve to the exponential function $(1 - {e^{ - \alpha L}})$ to obtain the penetration depth δ of the electric energy density p, which is defined as the electric energy density p decays to 1/e of that at the surface of p-Si and we obtained δ=1/α=14.06 μm [43]. According to Ohm’s law [44], the relationship between the electric energy density p and the current density ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over J} _s}$ can be written as:

$$p = \frac{1}{2}\mathrm{\varepsilon} {\left|{{{\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over J} }_s}} \right|^2}{\mathrm{\rho} ^2}$$
in which, ε and ρ are the permittivity and resistivity of p-Si respectively. Since there is a square relationship between the electric energy density p and the current density ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over J} _s}$, so the equivalent decay thickness of the current density is twice as that of the electric energy densities.

 figure: Fig. 4.

Fig. 4. (a) The electric energy density distribution at the voltage 20 V. (b) Percentage of electric energy density confined within a volume extending the depth distance of the sample from the surface at the voltage 20 V.

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To obtain the conductivity of the p-Si surface layer under the effect of avalanche breakdown in the terahertz range, we perform the same experiment the p-Si without metasurface but with same interdigital electrodes. The differential transmission (-ΔT/T) data of the terahertz waves through the p-Si under avalanche breakdown effect are used to extract the conductivity of the surface layer of p-Si for various currents. For a thin film sample on a nonconducting, semi-infinite and non-absorbing substrate, the complex transmission is given by [43,45]:

$$T(\omega ) = \frac{{{T_s}(\omega )}}{{{T_{Re f}}(\omega )}} = \frac{{1 + {n_{sub}}}}{{1 + {n_{sub}} + {Z_0}\varDelta \tilde{\sigma }(\omega ){d_f}}}$$

where ${T_s}(\omega ) = {T_{\textrm{Re} f}}(\omega ) - \Delta T(\omega )$ is the THz waves passing through the sample under the gate current, TRef (ω) is the substrate transmission spectrum without the gate current, nsub is the complex refractive index of p-Si, Z0 is the impedance of free space, and df is the equivalent decay thickness of the current density. Figure  5(a) shows the conductivity of the p-Si surface layer under the effect of avalanche in the current 0.2 A to 1.4 A. With the increase of current, the conductivity of the p-Si surface layer under the effect of avalanche continue increasing. According to Drude model, the conductivity is expressed as follow: $\Delta \sigma = \frac{{\Gamma \omega _p^2}}{{\pi ({\omega ^2} + {\Gamma ^2})}}$, $\Gamma$ is the scattering rate of the free carriers and ωp is the plasma frequency. Because the fitted scattering rate of free carriers $\Gamma$ is larger than our highest measurement frequency, the scattering rate of free carriers $\Gamma$ is set to a fixed value 2π×2 THz [46,47]. The plasma frequency ωp can be further expressed as $\omega _\textrm{p}^2 = {{N{e^2}} / {{\mathrm{\varepsilon} _0}{m^\ast }}}$, where N denotes the carrier density, e is the electronic charge, ɛ0 is the free-space permittivity, and m* is the effective carrier mass [39]. As shown in the Fig.  5(a), the results show that the fixed scattering rate of free carriers $\Gamma$ does not affect the fitting effect and all fitted values of confidence is levels above 95%, indicating that this method is feasible. After fitting the conductivity of the p-Si surface layer under the effect of avalanche breakdown, the carrier density N can be calculated in Fig.  5(b). When current is 0.2 A, the carrier density N is 6.68×1015 cm-3. Once the gate current 1.4 A is applied on the sample, the carrier density N increases to 1.01×1019 cm-3, indicating that there is a dramatic increase in excited carriers under the effect of current.

 figure: Fig. 5.

Fig. 5. (a) The Measured (circle) and theoretical (solid curve) values of the conductivity for the surface layer of p-Si at the gate currents 0.2 A, 0.4 A, 0.6 A, 0.8 A, 1.1 A, 1.4 A in the avalanche mode. (b) The density of carriers for the surface layer of p-Si at the current.

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4. Conclusions

We characterized the transmission properties of metasurface/p-Si under the effect of avalanche breakdown with the gate current. The phenomenon of the PIT effect is observed in the transmission spectrum of the hybrid sample, resulting from near-field coupling of bright and dark modes. Experimental results show that the avalanche breakdown of p-Si affects the interaction of terahertz wave and the structural units, thus the transparency window changes with the different current. The phenomenon of the PIT effect disappears when the current further increases. The phenomenon is caused by the excited carriers in surface of the metasurface/p-Si substrate block the terahertz waves. The carriers generated by the avalanche breakdown effect short-circuited the capacitance gap of the resonator, resulting in the suppression of the dipole resonance and the strong modulation of transmission. When the current continues to increase, the MD gradually approaches 1 and meaning the p-Si rather than the matesurface has a main effect on the terahertz wave. The conductivity of the p-Si surface layer without metasurface is investigated under avalanche breakdown effect, applying gate current from 0.2 A to 1.4 A. Because more carriers existed on the surface of the p-Si substrate, the conductivity of the p-Si surface layer increases with the current increasing. Owing to the excellent electrical properties, the effect of avalanche breakdown on the p-Si is considered as a potential candidate for applications in the THz range, such as THz modulators and detectors. The results of the present experiment provide a reference for further development of tunable structures controlled by an external electrical field.

Appendix

To simulate the influence of the conductivity of the p-Si surface layer under the effect of avalanche breakdown on PIT resonance, we place a p-Si surface layer under the effect of avalanche breakdown on the substrate by defining the experimentally obtained conductivity values of p-Si surface layer. we plot the electric field distributions at the resonance frequency to further substantiate the physical mechanism of the active modulation of the PIT analogue. The conductivity of the device settings in Fig.  6(a), (b) and (c) are 50 S/m, 1000 S/m and 8×104 S/m, respectively. And the corresponding currents are 0.2 A, 0.6 A and 1.4 A. As shown in Fig.  6, as the current increases, the resonance of the metasurface gradually weakens. When the current gradually increases to 0.6 A, the electric field is redistributed, where the enhancement in the SRRs significantly declines while that in the CW obviously increases in Fig.  6(b). When the current was 1.4 A, the metasurface no longer played a resonance role [13]. As shown in Fig.  6(c), there is no obvious electric field distribution at 1.4 A. At this stage, the increasing of conductivity of the substrate plays a decisive role in the modulation of THz.

 figure: Fig. 6.

Fig. 6. The simulated electric field distributions of the PIT metasurface at the peak resonance frequency point 0.614 THz. The corresponding current of device are (a) 0.2 A, (b) 0.6 A, (c) 1.4 A.

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Funding

Foundation of President of China Academy of Engineering Physics (YZJJLX2018001); National Natural Science Foundation of China (11604316, 11704358, 61427814, 61771327, U1730138, U1730246, U1930123); National Key Research and Development Program of China (2015CB755403, 2017YFC1200400); National Safety Academic Fund (U1930117); the Distinguished Young Scholars of Sichuan Province (2020JDJQ0008); the Key Project of the Education Department of Guizhou Province (KY2021045); the Construction Project of Characteristic Key Laboratory in Guizhou Colleges and Universities (KY2021003); the National Science Foundation of Guizhou Province (ZK[2021]YB301).

Disclosures

The authors declare no conflict of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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26. R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014). [CrossRef]  

27. H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020). [CrossRef]  

28. W. Liang, Y. Jiang, J. Guo, N. Li, and S. Luo, “Van der Waals Heteroepitaxial VO2/Mica Films with Extremely Low Optical Trigger Threshold and Large THz Field Modulation Depth,” Adv. Opt. Mater. 7(20), 1900647 (2019). [CrossRef]  

29. K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric Huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018). [CrossRef]  

30. J. S. T. Smalley, F. Vallini, X. Zhang, and Y. Fainman, “Dynamically tunable and active hyperbolic metamaterials,” Adv. Opt. Photonics 10(2), 354 (2018). [CrossRef]  

31. J. Ji, S. Zhou, W. Wang, F. Ling, and J. Yao, “Active control of terahertz plasmon-induced transparency in the hybrid metamaterial/monolayer MoS2/Si structure,” Nanoscale 11(19), 9429–9435 (2019). [CrossRef]  

32. H. Zhu, J. Li, S. Zhong, L. Du, Q. W. Shi, B. Peng, H. K. Yuan, W. Huang, and L. G. Zhu, “Continuously tuning the impedance matching at the broadband terahertz frequency range in VO2 thin film,” Opt. Mater. Express 9(1), 315–329 (2019). [CrossRef]  

33. P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(1), 8969 (2015). [CrossRef]  

34. P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012). [CrossRef]  

35. S. Xiao, T. Wang, T. Liu, C. Zhou, X. Jiang, and J. Zhang, “Active metamaterials and metadevices: a review,” J. Phys. D: Appl. Phys. 53(50), 503002 (2020). [CrossRef]  

36. W. Kaiser and G. H. Wheatley, “Hot electrons and carrier multiplication in silicon at low temperature,” Phys. Rev. Lett. 3(7), 334–336 (1959). [CrossRef]  

37. K. G. McKay, “Avalanche breakdown in silicon,” Phys. Rev. 94(4), 877–884 (1954). [CrossRef]  

38. C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017). [CrossRef]  

39. J. Ji, S. Zhou, W. Wang, C. Luo, Y. Liu, F. Ling, and J. Yao, “Active multifunctional terahertz modulator based on plasmonic metasurface,” Opt. Express 27(3), 2363 (2019). [CrossRef]  

40. H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018). [CrossRef]  

41. P. Bendt and A. Zunger, “Simultaneous Relaxation of Nuclear Geometries and Electric Charge Densities in Electronic Structure Theories,” Phys. Rev. Lett. 50(21), 1684–1688 (1983). [CrossRef]  

42. L. Liu, T. Li, Y. Liu, and J. Leng, “Electromechanical Stability of Dielectric Elastomer Using Electric Energy Density Function With Variable Dielectric Constant,” Asme Conference on Smart Materials. 2010.

43. C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016). [CrossRef]  

44. M.F. Iskander, Electromagnetic fields and waves, 2th ed. (Waveland Press, 2013).

45. H. Tang, L.-G. Zhu, L. Zhao, X. Zhang, J. Shan, and S.-T. Lee, “Carrier Dynamics in Si Nanowires Fabricated by Metal-Assisted Chemical Etching,” ACS Nano 6(9), 7814–7819 (2012). [CrossRef]  

46. W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021). [CrossRef]  

47. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997). [CrossRef]  

References

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    [Crossref]
  25. L. Wu, T. Du, N. Xu, C. Ding, H. Li, Q. Sheng, M. Liu, J. Yao, Z. Wang, X. Lou, and W. Zhang, “A New Ba0.6Sr0.4TiO3–Silicon Hybrid Metamaterial Device in Terahertz Regime,” Small 12(19), 2610–2615 (2016).
    [Crossref]
  26. R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
    [Crossref]
  27. H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020).
    [Crossref]
  28. W. Liang, Y. Jiang, J. Guo, N. Li, and S. Luo, “Van der Waals Heteroepitaxial VO2/Mica Films with Extremely Low Optical Trigger Threshold and Large THz Field Modulation Depth,” Adv. Opt. Mater. 7(20), 1900647 (2019).
    [Crossref]
  29. K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric Huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
  32. H. Zhu, J. Li, S. Zhong, L. Du, Q. W. Shi, B. Peng, H. K. Yuan, W. Huang, and L. G. Zhu, “Continuously tuning the impedance matching at the broadband terahertz frequency range in VO2 thin film,” Opt. Mater. Express 9(1), 315–329 (2019).
    [Crossref]
  33. P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(1), 8969 (2015).
    [Crossref]
  34. P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
    [Crossref]
  35. S. Xiao, T. Wang, T. Liu, C. Zhou, X. Jiang, and J. Zhang, “Active metamaterials and metadevices: a review,” J. Phys. D: Appl. Phys. 53(50), 503002 (2020).
    [Crossref]
  36. W. Kaiser and G. H. Wheatley, “Hot electrons and carrier multiplication in silicon at low temperature,” Phys. Rev. Lett. 3(7), 334–336 (1959).
    [Crossref]
  37. K. G. McKay, “Avalanche breakdown in silicon,” Phys. Rev. 94(4), 877–884 (1954).
    [Crossref]
  38. C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017).
    [Crossref]
  39. J. Ji, S. Zhou, W. Wang, C. Luo, Y. Liu, F. Ling, and J. Yao, “Active multifunctional terahertz modulator based on plasmonic metasurface,” Opt. Express 27(3), 2363 (2019).
    [Crossref]
  40. H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
    [Crossref]
  41. P. Bendt and A. Zunger, “Simultaneous Relaxation of Nuclear Geometries and Electric Charge Densities in Electronic Structure Theories,” Phys. Rev. Lett. 50(21), 1684–1688 (1983).
    [Crossref]
  42. L. Liu, T. Li, Y. Liu, and J. Leng, “Electromechanical Stability of Dielectric Elastomer Using Electric Energy Density Function With Variable Dielectric Constant,” Asme Conference on Smart Materials. 2010.
  43. C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
    [Crossref]
  44. M.F. Iskander, Electromagnetic fields and waves, 2th ed. (Waveland Press, 2013).
  45. H. Tang, L.-G. Zhu, L. Zhao, X. Zhang, J. Shan, and S.-T. Lee, “Carrier Dynamics in Si Nanowires Fabricated by Metal-Assisted Chemical Etching,” ACS Nano 6(9), 7814–7819 (2012).
    [Crossref]
  46. W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021).
    [Crossref]
  47. T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
    [Crossref]

2021 (1)

W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021).
[Crossref]

2020 (3)

S. Xiao, T. Wang, T. Liu, C. Zhou, X. Jiang, and J. Zhang, “Active metamaterials and metadevices: a review,” J. Phys. D: Appl. Phys. 53(50), 503002 (2020).
[Crossref]

Z. Zhao, H. Zhao, R. T. Ako, S. Nickl, and S. Sriram, “Polarization-insensitive terahertz spoof localized surface plasmon-induced transparency based on lattice rotational symmetry,” Appl. Phys. Lett. 117(1), 011105 (2020).
[Crossref]

H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020).
[Crossref]

2019 (8)

W. Liang, Y. Jiang, J. Guo, N. Li, and S. Luo, “Van der Waals Heteroepitaxial VO2/Mica Films with Extremely Low Optical Trigger Threshold and Large THz Field Modulation Depth,” Adv. Opt. Mater. 7(20), 1900647 (2019).
[Crossref]

J. Ji, S. Zhou, W. Wang, F. Ling, and J. Yao, “Active control of terahertz plasmon-induced transparency in the hybrid metamaterial/monolayer MoS2/Si structure,” Nanoscale 11(19), 9429–9435 (2019).
[Crossref]

H. Zhu, J. Li, S. Zhong, L. Du, Q. W. Shi, B. Peng, H. K. Yuan, W. Huang, and L. G. Zhu, “Continuously tuning the impedance matching at the broadband terahertz frequency range in VO2 thin film,” Opt. Mater. Express 9(1), 315–329 (2019).
[Crossref]

Z. Zhao, X. Zheng, W. Peng, J. Zhang, H. Zhao, and W. Shi, “Terahertz electromagnetically-induced transparency of self-complementary meta-molecules on Croatian checkerboard,” Sci. Rep. 9(1), 6205 (2019).
[Crossref]

P. R. Tang, J. Li, S. C. Zhong, Z. H. Zhai, B. Zhu, L. H. Du, Z. R. Li, and L. G. Zhu, “Giant dual-mode graphene-based terahertz modulator enabled by Fabry–Perot assisted multiple reflection,” Opt. Lett. 44(7), 1630–1633 (2019).
[Crossref]

Z. Zhao, H. Zhao, R. T. Ako, J. Zhang, H. Zhao, and S. Sriram, “Demonstration of group delay above 40 ps at terahertz plasmon-induced transparency windows,” Opt. Express 27(19), 26459–26470 (2019).
[Crossref]

S.-C. Chen, L.-H. Du, K. Meng, J. Li, Z.-H. Zhai, Q.-W. Shi, Z.-R. Li, and L.-G. Zhu, “Terahertz wave near-field compressive imaging with a spatial resolution of over λ/100,” Opt. Lett. 44(1), 21 (2019).
[Crossref]

J. Ji, S. Zhou, W. Wang, C. Luo, Y. Liu, F. Ling, and J. Yao, “Active multifunctional terahertz modulator based on plasmonic metasurface,” Opt. Express 27(3), 2363 (2019).
[Crossref]

2018 (7)

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

R. Won, “Metasurface mixer,” Nat. Photonics 12(8), 443 (2018).
[Crossref]

P. Tang, L. Ren, L. Guo, L. Du, and J. Jiang, “Ultrasensitive specific terahertz sensor based on tunable plasmon induced transparency of a graphene micro-ribbon array structure,” Opt. Express 26(23), 30655–30666 (2018).
[Crossref]

G. D. Bai, Q. Ma, S. Iqbal, L. Bao, H. B. Jing, L. Zhang, H. T. Wu, R. Y. Wu, H. C. Zhang, C. Yang, and T. J. Cui, “Multitasking shared aperture enabled with multiband digital coding metasurface,” Adv. Opt. Mater. 6(21), 1800657 (2018).
[Crossref]

S. Xiao, T. Wang, T. Liu, X. Yan, Z. Li, and C. Xue, “Active modulation of electromagnetically induced transparency analogue in terahertz hybrid metal-graphene metamaterials,” Carbon 126, 271–278 (2018).
[Crossref]

K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric Huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

J. S. T. Smalley, F. Vallini, X. Zhang, and Y. Fainman, “Dynamically tunable and active hyperbolic metamaterials,” Adv. Opt. Photonics 10(2), 354 (2018).
[Crossref]

2017 (3)

B. Wells, Z. A. Kudyshev, N. Litchinitser, and V. A. Podolskiy, “Nonlocal Effects In Transition Hyperbolic Metamaterials,” ACS Photonics 4(10), 2470–2478 (2017).
[Crossref]

Z. Zhao, X. Zheng, W. Peng, J. Zhang, H. Zhao, Z. Luo, and W. Shi, “Localized terahertz electromagnetically-induced transparency-like phenomenon in a conductively coupled trimer metamolecule,” Opt. Express 25(20), 24410–24424 (2017).
[Crossref]

C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017).
[Crossref]

2016 (4)

C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
[Crossref]

Z. Zhao, Z. Song, W. Shi, and W. Peng, “Plasmon-induced transparency-like behavior at terahertz region via dipole oscillation detuning in a hybrid planar metamaterial,” Opt. Mater. Express 6(7), 2190–2200 (2016).
[Crossref]

G. Yao, F. Ling, J. Yue, Q. Luo, and J. Yao, “Dynamically tunable graphene plasmon-induced transparency in the terahertz region,” J. Lightwave Technol. 34(16), 3937–3942 (2016).
[Crossref]

L. Wu, T. Du, N. Xu, C. Ding, H. Li, Q. Sheng, M. Liu, J. Yao, Z. Wang, X. Lou, and W. Zhang, “A New Ba0.6Sr0.4TiO3–Silicon Hybrid Metamaterial Device in Terahertz Regime,” Small 12(19), 2610–2615 (2016).
[Crossref]

2015 (5)

M. P. Hokmabadi, E. Philip, E. Rivera, P. Kung, and S. M. Kim, “Plasmon-Induced Transparency by Hybridizing Concentric-Twisted Double Split Ring Resonators,” Sci. Rep. 5(1), 15735 (2015).
[Crossref]

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6(1), 7082 (2015).
[Crossref]

P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(1), 8969 (2015).
[Crossref]

N. Dabidian, I. Kholmanov, A. B. Khanikaev, K. Tatar, S. Trendafilov, S. H. Mousavi, C. Magnuson, R. S. Ruoff, and G. Shvets, “Electrical switching of infrared light using graphene integration with plasmonic Fano resonant metasurfaces,” ACS Photonics 2(2), 216–227 (2015).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators, A 231, 74–80 (2015).
[Crossref]

2014 (2)

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2(12), 1221–1226 (2014).
[Crossref]

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

2013 (1)

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area CVD graphene to a terahertz metamaterial,” Nano Lett. 13(7), 3193–3198 (2013).
[Crossref]

2012 (5)

P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching teraherz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
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H. Tang, L.-G. Zhu, L. Zhao, X. Zhang, J. Shan, and S.-T. Lee, “Carrier Dynamics in Si Nanowires Fabricated by Metal-Assisted Chemical Etching,” ACS Nano 6(9), 7814–7819 (2012).
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2010 (1)

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the Resonance in High Temperature Superconducting Terahertz Metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[Crossref]

2006 (1)

H. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref]

1997 (1)

T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
[Crossref]

1983 (1)

P. Bendt and A. Zunger, “Simultaneous Relaxation of Nuclear Geometries and Electric Charge Densities in Electronic Structure Theories,” Phys. Rev. Lett. 50(21), 1684–1688 (1983).
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1959 (1)

W. Kaiser and G. H. Wheatley, “Hot electrons and carrier multiplication in silicon at low temperature,” Phys. Rev. Lett. 3(7), 334–336 (1959).
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1954 (1)

K. G. McKay, “Avalanche breakdown in silicon,” Phys. Rev. 94(4), 877–884 (1954).
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Ako, R. T.

Z. Zhao, H. Zhao, R. T. Ako, S. Nickl, and S. Sriram, “Polarization-insensitive terahertz spoof localized surface plasmon-induced transparency based on lattice rotational symmetry,” Appl. Phys. Lett. 117(1), 011105 (2020).
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Z. Zhao, H. Zhao, R. T. Ako, J. Zhang, H. Zhao, and S. Sriram, “Demonstration of group delay above 40 ps at terahertz plasmon-induced transparency windows,” Opt. Express 27(19), 26459–26470 (2019).
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Al-Naib, I.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Averitt, R. D.

K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric Huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators, A 231, 74–80 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2(12), 1221–1226 (2014).
[Crossref]

H. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref]

Azad, A. K.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
[Crossref]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the Resonance in High Temperature Superconducting Terahertz Metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[Crossref]

Bai, G. D.

G. D. Bai, Q. Ma, S. Iqbal, L. Bao, H. B. Jing, L. Zhang, H. T. Wu, R. Y. Wu, H. C. Zhang, C. Yang, and T. J. Cui, “Multitasking shared aperture enabled with multiband digital coding metasurface,” Adv. Opt. Mater. 6(21), 1800657 (2018).
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Bao, L.

G. D. Bai, Q. Ma, S. Iqbal, L. Bao, H. B. Jing, L. Zhang, H. T. Wu, R. Y. Wu, H. C. Zhang, C. Yang, and T. J. Cui, “Multitasking shared aperture enabled with multiband digital coding metasurface,” Adv. Opt. Mater. 6(21), 1800657 (2018).
[Crossref]

Beck, M.

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area CVD graphene to a terahertz metamaterial,” Nano Lett. 13(7), 3193–3198 (2013).
[Crossref]

Bendt, P.

P. Bendt and A. Zunger, “Simultaneous Relaxation of Nuclear Geometries and Electric Charge Densities in Electronic Structure Theories,” Phys. Rev. Lett. 50(21), 1684–1688 (1983).
[Crossref]

Brodyanski, A.

P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref]

Cai, H.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Cao, L.

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2(12), 1221–1226 (2014).
[Crossref]

Cao, W.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Chen, H.

H. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref]

Chen, H. T.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
[Crossref]

H. T. Chen, H. Yang, R. Singh, J. F. O’Hara, A. K. Azad, S. A. Trugman, Q. X. Jia, and A. J. Taylor, “Tuning the Resonance in High Temperature Superconducting Terahertz Metamaterials,” Phys. Rev. Lett. 105(24), 247402 (2010).
[Crossref]

Chen, L.

C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017).
[Crossref]

Chen, S.

W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021).
[Crossref]

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Chen, S.-C.

Chen, Y.

H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020).
[Crossref]

Cheng, L.

C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
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Chiac, E. E. M.

C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
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Choi, C. G.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching teraherz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref]

Choi, H. K.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching teraherz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref]

Choi, J. W.

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area CVD graphene to a terahertz metamaterial,” Nano Lett. 13(7), 3193–3198 (2013).
[Crossref]

Choi, M.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching teraherz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref]

Choi, S. Y.

S. H. Lee, M. Choi, T. T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C. G. Choi, S. Y. Choi, X. Zhang, and B. Min, “Switching teraherz waves with gate-controlled active graphene metamaterials,” Nat. Mater. 11(11), 936–941 (2012).
[Crossref]

Cong, L.

R. Singh, W. Cao, I. Al-Naib, L. Cong, W. Withayachumnankul, and W. Zhang, “Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces,” Appl. Phys. Lett. 105(17), 171101 (2014).
[Crossref]

Cui, T. J.

G. D. Bai, Q. Ma, S. Iqbal, L. Bao, H. B. Jing, L. Zhang, H. T. Wu, R. Y. Wu, H. C. Zhang, C. Yang, and T. J. Cui, “Multitasking shared aperture enabled with multiband digital coding metasurface,” Adv. Opt. Mater. 6(21), 1800657 (2018).
[Crossref]

Dabidian, N.

N. Dabidian, I. Kholmanov, A. B. Khanikaev, K. Tatar, S. Trendafilov, S. H. Mousavi, C. Magnuson, R. S. Ruoff, and G. Shvets, “Electrical switching of infrared light using graphene integration with plasmonic Fano resonant metasurfaces,” ACS Photonics 2(2), 216–227 (2015).
[Crossref]

Das, S.

H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020).
[Crossref]

Ding, C.

L. Wu, T. Du, N. Xu, C. Ding, H. Li, Q. Sheng, M. Liu, J. Yao, Z. Wang, X. Lou, and W. Zhang, “A New Ba0.6Sr0.4TiO3–Silicon Hybrid Metamaterial Device in Terahertz Regime,” Small 12(19), 2610–2615 (2016).
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Du, L.

H. Zhu, J. Li, L. Du, W. Huang, J. Liu, J. Zhou, Y. Chen, S. Das, Q. Shi, L. Zhu, and C. Liu, “A phase transition oxide/graphene interface for incident-angle-agile, ultrabroadband, and deep THz modulation,” Adv. Mater. Interfaces 7(24), 2001297 (2020).
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H. Zhu, J. Li, S. Zhong, L. Du, Q. W. Shi, B. Peng, H. K. Yuan, W. Huang, and L. G. Zhu, “Continuously tuning the impedance matching at the broadband terahertz frequency range in VO2 thin film,” Opt. Mater. Express 9(1), 315–329 (2019).
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P. Tang, L. Ren, L. Guo, L. Du, and J. Jiang, “Ultrasensitive specific terahertz sensor based on tunable plasmon induced transparency of a graphene micro-ribbon array structure,” Opt. Express 26(23), 30655–30666 (2018).
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Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6(1), 7082 (2015).
[Crossref]

Du, L. H.

Du, L.-H.

W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021).
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S.-C. Chen, L.-H. Du, K. Meng, J. Li, Z.-H. Zhai, Q.-W. Shi, Z.-R. Li, and L.-G. Zhu, “Terahertz wave near-field compressive imaging with a spatial resolution of over λ/100,” Opt. Lett. 44(1), 21 (2019).
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Du, T.

L. Wu, T. Du, N. Xu, C. Ding, H. Li, Q. Sheng, M. Liu, J. Yao, Z. Wang, X. Lou, and W. Zhang, “A New Ba0.6Sr0.4TiO3–Silicon Hybrid Metamaterial Device in Terahertz Regime,” Small 12(19), 2610–2615 (2016).
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Fainman, Y.

J. S. T. Smalley, F. Vallini, X. Zhang, and Y. Fainman, “Dynamically tunable and active hyperbolic metamaterials,” Adv. Opt. Photonics 10(2), 354 (2018).
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Faist, J.

P. Q. Liu, I. J. Luxmoore, S. A. Mikhailov, N. A. Savostianova, F. Valmorra, J. Faist, and G. R. Nash, “Highly tunable hybrid metamaterials employing split-ring resonators strongly coupled to graphene surface plasmons,” Nat. Commun. 6(1), 8969 (2015).
[Crossref]

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area CVD graphene to a terahertz metamaterial,” Nano Lett. 13(7), 3193–3198 (2013).
[Crossref]

Fan, K.

K. Fan, J. Zhang, X. Liu, G. F. Zhang, R. D. Averitt, and W. J. Padilla, “Phototunable dielectric Huygens’ metasurfaces,” Adv. Mater. 30(22), 1800278 (2018).
[Crossref]

X. Zhao, K. Fan, J. Zhang, H. R. Seren, G. D. Metcalfe, M. Wraback, R. D. Averitt, and X. Zhang, “Optically tunable metamaterial perfect absorber on highly flexible substrate,” Sens. Actuators, A 231, 74–80 (2015).
[Crossref]

H. R. Seren, G. R. Keiser, L. Cao, J. Zhang, A. C. Strikwerda, K. Fan, G. D. Metcalfe, M. Wraback, X. Zhang, and R. D. Averitt, “Optically modulated multiband terahertz perfect absorber,” Adv. Opt. Mater. 2(12), 1221–1226 (2014).
[Crossref]

Fang, T.

B. Sensale-Rodriguez, R. Yan, M. M. Kelly, T. Fang, K. Tahy, W. S. Hwang, D. Jena, L. Liu, and H. G. Xing, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nat. Commun. 3(1), 780 (2012).
[Crossref]

Fu, W.

F. Valmorra, G. Scalari, C. Maissen, W. Fu, C. Schönenberger, J. W. Choi, H. G. Park, M. Beck, and J. Faist, “Low-bias active control of terahertz waves by coupling large-area CVD graphene to a terahertz metamaterial,” Nano Lett. 13(7), 3193–3198 (2013).
[Crossref]

Fu, Z.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Gao, Z.

W. Wang, L.-H. Du, J. Li, P.-R. Tang, C. Sun, S. Chen, J. Wang, Z.-H. Zha, Z. Gao, Z.-R. Li, J. Yao, F. Ling, and L.-G. Zhu, “Terahertz wave avalanche breakdown transistor for high-performance switching,” Photonics Res. 9(3), 370–378 (2021).
[Crossref]

Garcia-Pomar, J. L.

P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref]

Gossard, A. C.

H. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[Crossref]

Grischkowsky, D.

T. Jeon and D. Grischkowsky, “Nature of conduction in doped silicon,” Phys. Rev. Lett. 78(6), 1106–1109 (1997).
[Crossref]

Gu, J.

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6(1), 7082 (2015).
[Crossref]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
[Crossref]

Guo, J.

W. Liang, Y. Jiang, J. Guo, N. Li, and S. Luo, “Van der Waals Heteroepitaxial VO2/Mica Films with Extremely Low Optical Trigger Threshold and Large THz Field Modulation Depth,” Adv. Opt. Mater. 7(20), 1900647 (2019).
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Guo, L.

Gurzadyan, G. G.

C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
[Crossref]

Han, J.

Q. Li, Z. Tian, X. Zhang, R. Singh, L. Du, J. Gu, J. Han, and W. Zhang, “Active graphene–silicon hybrid diode for terahertz waves,” Nat. Commun. 6(1), 7082 (2015).
[Crossref]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun. 3(1), 1151 (2012).
[Crossref]

Haselsberger, R.

C. La-o-vorakiat, T. Salim, J. Kadro, M.-T. Khuc, R. Haselsberger, L. Cheng, H. Xia, G. G. Gurzadyan, H. Su, Y. M. Lam, R. A. Marcus, M.-E. Michel-Beyerle, and E. E. M. Chiac, “Elucidating the role of disorder and free-carrier recombination kinetics in CH3NH3PbI3 perovskite films,” Nat. Commun. 7(1), 11054 (2016).
[Crossref]

He, H.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Hoh, M.

P. Weis, J. L. Garcia-Pomar, M. Hoh, B. Reinhard, A. Brodyanski, and M. Rahm, “Spectrally wide-band terahertz wave modulator based on optically tuned graphene,” ACS Nano 6(10), 9118–9124 (2012).
[Crossref]

Hokmabadi, M. P.

M. P. Hokmabadi, E. Philip, E. Rivera, P. Kung, and S. M. Kim, “Plasmon-Induced Transparency by Hybridizing Concentric-Twisted Double Split Ring Resonators,” Sci. Rep. 5(1), 15735 (2015).
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Hsieh, P.

C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017).
[Crossref]

Hu, X.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
[Crossref]

Huang, M. H.

C. Tan, P. Hsieh, L. Chen, and M. H. Huang, “Silicon Wafers with Facet-Dependent Electrical Conductivity Properties,” Angew. Chem. Int. Ed. 56(48), 15339–15343 (2017).
[Crossref]

Huang, Q.

H. Cai, S. Chen, C. Zou, Q. Huang, Y. Liu, X. Hu, Z. Fu, Y. Zhao, H. He, and Y. Lu, “Multifunctional Hybrid Metasurfaces for Dynamic Tuning of Terahertz Waves,” Adv. Opt. Mater. 6(14), 1800257 (2018).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Diagram of the p-Si hybrid metasurface device. (a) The normal incident THz wave propagates along the z-direction, with its electric field polarized along the y-direction. The unit cell of the metasurface is depicted in the inset, where px = 80 µm, py=105 µm, L = 86 µm, s = 10 µm, l = 30 µm, d = 20 µm, and the size of the gaps is g = 7 µm. (b) The optical microscope image of the sample. (c) The I–V characteristic curve of sample in experiments. (d-e) The corresponding I-G curve and I-R curve, showing the sudden change of p-Si conductance and resistance.
Fig. 2.
Fig. 2. Simulated transmission spectra and the electric field at the resonance frequency of terahertz metasurface. (a), (b) and (c) The simulated transmission spectrum for the unit cell, CW and a pair of SRRs, respectively. (d-f) The simulated electric field at the resonance frequency at the resonance frequency points dip A, peak and dip B, respectively.
Fig. 3.
Fig. 3. (a) Time domain THz signals of the p-Si hybrid metasurface and its amplitude change under various external electric excitation. (b) Measured transmission amplitude spectrum of the p-Si hybrid metasurface at various gate currents. (c) The measured transmission and the modulation depth of the p-Si hybrid metasurface at the resonance frequency corresponding to (b). (d) The measured modulation depth of the p-Si hybrid metasurface at the resonance frequency.
Fig. 4.
Fig. 4. (a) The electric energy density distribution at the voltage 20 V. (b) Percentage of electric energy density confined within a volume extending the depth distance of the sample from the surface at the voltage 20 V.
Fig. 5.
Fig. 5. (a) The Measured (circle) and theoretical (solid curve) values of the conductivity for the surface layer of p-Si at the gate currents 0.2 A, 0.4 A, 0.6 A, 0.8 A, 1.1 A, 1.4 A in the avalanche mode. (b) The density of carriers for the surface layer of p-Si at the current.
Fig. 6.
Fig. 6. The simulated electric field distributions of the PIT metasurface at the peak resonance frequency point 0.614 THz. The corresponding current of device are (a) 0.2 A, (b) 0.6 A, (c) 1.4 A.

Equations (3)

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ε = ε ω p 2 ω 2 + i ω γ
p = 1 2 ε | J s | 2 ρ 2
T ( ω ) = T s ( ω ) T R e f ( ω ) = 1 + n s u b 1 + n s u b + Z 0 Δ σ ~ ( ω ) d f

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