As an important device to manipulate the THz wave for the applications in nondestructive imaging, bio-sensing, and high-speed wireless communication [1–5], high-performance THz modulator has attracted lots of research interest in recent years [6–10]. Graphene, a single-atom layer material, has been considered as a suitable candidate to realize THz modulators due to its unique electromagnetic property in THz region [11–25]. Meanwhile, graphene-based modulator also has the advantage to be engineered into integrated devices.

Various graphene-based THz modulator approaches have been put forward by applying biased gate voltage to tune the Fermi level of graphene. Using ion-gel as an efficient high-capacitance gate dielectric and graphene-based THz modulator has been used to realize a near perfect MD with several configurations [12–15]. However, the utilization of ion-gel as the electrode inevitably limits its modulation speed due to the relatively small mobility of ions [16]. Metallic electrodes with traditional insulator (${\mathrm{SiO}}_2$ and ${\mathrm{Al}}_2{\mathrm{O}}_3$) structure is more preferred to demonstrate the high-speed graphene-based THz modulators [18,19]. For the THz modulator in the transmission configuration using monolayer [17,18] and multilayer graphene [19], a small MD about 20% with operational bandwidth around 1 THz was obtained. By integrating metamaterials to enhance the interaction between graphene and THz wave, the significant improvement of MD have been reported [20–23]. However, the operational bandwidth of these hybrid graphene-metamaterial devices is only about 0.25 THz due to the intrinsic limited bandwidth resonance property of metamaterial. Other routes to achieve high MD devices is using the optically tuned graphene on semiconductor substrate [24,25]. For these types of modulators, the MD performances are favorable, however the additional light source used to excite the sample acts as the major obstacle for its practical application [25]. Furthermore, for application in the THz communication system, a high-speed coherent modulation at a single frequency is preferred [1]. As a consequence, the MD of a single reflection or transmission THz pulse cannot represent that of a coherent THz wave due to the inevitably F-P interference of the device. While, the previous works mainly focus on THz pulse modulation situations [12–15,17–25], the F-P interference influence on MD has rarely been investigated in detail in previous works.

In this Letter, we proposed a giant dual operation mode THz modulator consisting of a graphene-insulator-silicon structure with metallic electrodes topped on an Al substrate. For the pulse operation mode, the MD of THz wave under different gate voltages is investigated in detail for all orders of echoes reflected from the Al substrate. We have experimentally achieved giant $E$-field intensity MD larger than 90% for the fifth order echo at 0.8 THz due to enhanced interaction of the F-P assisted multiple reflection. The MD retains larger than 75% within a broadband frequency range over 1 THz, which outperforms previous works with similar structure [18,19]. For the coherent single frequency operation mode, we investigated the coherent F-P interference effect on THz modulation. In this case, a MD larger than 75% has been demonstrated at frequency 0.76 THz with full width at half maximum (FWHM) about 34 GHz.

The cross-section view of our proposed THz modulator is illustrated in Fig. 1(a). The graphene sheet with area over $1{\mathrm{cm}}^2$ was grown by standard chemical vapor deposition (CVD) process and then transferred onto ${\mathrm{SiO}}_2/\mathrm{Si}$wafer [19]. The thickness of ${\mathrm{SiO}}_2$ is 100 nm, and the thickness of low-resistivity Si substrate ($p$-type, resistivity $\rho =10–15\mathrm{\Omega }·\mathrm{cm}$) is 320 μm. To electrostatically tune the Fermi level of graphene, TiAu electrodes were deposited on the graphene and p-Si as the contact and gate electrodes, respectively. Finally, the graphene/${\mathrm{SiO}}_2$/Si device is placed on the top of an Al substrate (the bottom of Si is polished and joints closely with the Al substrate). The Raman spectrum shown in Fig. 1(b) proves that the transferred graphene is a high-quality monolayer. In our experimental set-up, we used a homemade THz time-domain spectroscopy system which employed a femtosecond fiber laser that delivered 120 mW, 63 fs de-chirped pulses (after 3 m of panda-type polarization-maintaining fiber) to drive a pair of InGaAs photoconductive antennas, for generation and detection of the terahertz pulses [Fig. 1(c)]. The incidence angle of the $p$-polarized THz pulse $E_{\mathrm{in}}$ is set to 35˚. The first order echo of the incident THz pulse denoted as $E_{r1}$ is reflected from the air/graphene interface. The subsequent higher order echo pulses reflected from the Al substrate are denoted as $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$ as shown in Fig. 1(a).

 

Fig. 1. (a) Cross-section view of our proposed THz modulator; (b) Raman spectra of the monolayer graphene on the 100 nm ${\mathrm{SiO}}_2$/p-Si substrate; (c) The scheme of our THz time-domain system.

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Figure 2(a) shows the measured reflective time-domain THz signals of the device under different biased gate voltages. Six reflected pulses, well separated from each other, can be observed in the time domain window. The zoom-in THz waveforms near the peaks of pulses $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$, marked as the square areas in Fig. 2(a), are presented in Figs. 2(c)–2(f). From the THz time-domain data, obvious attenuations of the THz signal are observed for echoes $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$, under different biased gate voltages $V_g$, as a result of the increasing of charge carriers in the graphene layer. The reflected time-domain THz signals are strongly dependent on the gate voltage of our device. The baseline voltage $V_{\mathrm{bl}}$ for the MD of our devices is 16V with the highest reflection electric field intensity $I_{\mathrm{bl}}$. Figure 2(b) shows the extracted MD for echo $E_{r5}$ from 0.4 to 1.4 THz at different applied gate voltages. Here, the calculated MD is defined as $\mathrm{MD}(V)=(I_{\mathrm{bl}}-I_V)/I_{\mathrm{bl}}\times 100\%$. At the largest applied biased gated voltage of 29 V to prevent the breakdown of our modulator, the electric field amplitudes of THz signal for echoes $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$, reach their minimum, indicating the highest MD performance. It is clear that a MD around 80% is achieved across a frequency range from 0.4 THz to 1.4 THz. The maximum MD of 90.93% occurs at 0.8 THz for the fifth order echo at $V_g=29\mathrm{V}$. The maximum MD (insertion loss) for echoes $E_{r1}$, $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$ are 16.24%, 25.78%, 54.8%, 73.93%, and 90.93% (6.02 dB, 3.48 dB, 11.54 dB, 20 dB, and 27.96 dB). The insertion loss is defined as $-10\log (I_{rj}/I_{\mathrm{in}})=-20\log (E_{rj}/E_{\mathrm{in}})$ ($j=1$, 2, 3, 4, 5; $I_{rj}$ and $I_{\mathrm{in}}$ are the intensity of reflected echoes and incident wave). As the order of reflected echo increases, the maximum MD as well as the insertion loss of the THz modulator become larger. Considering the intensity signal to noise ratio of a typical THz-time domain spectroscopy instrument is larger than 60 dB [5], the insertion loss smaller than 30 dB is tolerable. As a comparison, the maximum MD and the modulation frequency range for previous graphene based metallic electrode with traditional insulator structure THz modulator are also listed. i.e., 40% and 0.6 THz [12], 15% and 0.1 THz [17], 50% and 0.25 THz [20], 72% and 0.3 THz [22], 64% and 0.06 THz [23].

 

Fig. 2. (a) Reflected time domain waveforms at six various biased gate voltages; (c)–(f) Zoomed-in THz waveforms for four reflected echoes $E_{r2}$, $E_{r3}$, $E_{r4}$ and $E_{r5}$ from (a) reflected through the THz modulator. The legends for (c)–(f) are the same as (a); (b) MD of the fifth order reflected echo under different biased gate voltages.

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To theoretically understand the behavior of our THz modulator, the conductivity of the graphene layer under different biased gate voltage is needed. Here, a verification structure similar to the device in Fig. 1 [inset of Fig. 3(a)] but without the Al substrate is used to derive the electrostatic property of graphene for different $V_g$.

 

Fig. 3. (a) Measured THz conductivity of graphene (red triangle), fitting line (red solid line), and conductance ${\sigma }_{\mathrm{total}}$ (blue dash line) at 0.8 THz as a function of the gate voltage ($V_g$). The inset shows diagrams of the graphene/${\mathrm{SiO}}_2$ device, which is used to calculate the conductivity of graphene; (b) Comparison of the experimental and simulated THz MD values versus conductivities of graphene for all the first five echoes.

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The method to derive conductivity of graphene is presented in this part. For graphene layer on the interface of two dielectric media with refractive indices $n_i$ and $n_j$, the reflection coefficient and transmission coefficient for the $p$-polarized incident THz wave at a certain incident angle ${\theta }_i$ can be given as a function of graphene’s conductivity [26,27],

The subscript $igj$ ($ij$) represents THz wave is incident from medium $i$ to medium $j$ with (without) the graphene layer on the interface. From the above analysis, the reflectance of the first order THz echo is $R_{ags}$. The reflectance for the $n$th order of THz echo is $R_n=T_{ags}{R}_{sa}^{n-1}{R}_{sga}^{n-2}{T}_{sga}$ ($n=2$, 3, 4, …, $a$ stands for air, $g$ for graphene and $s$ for Si). In verification structure, the insertion loss is larger than that of the modulator structure in Fig. 1. As a result, only three orders of echo pulse were observed. For two different values of graphene THz conductivities ${\sigma }_g(V_{\mathrm{bl}})$ and ${\sigma }_g(V_g)$, the intensity MD of the $n$th order THz echo can be expressed as $\mathrm{MD}(V_g)=[R_n({\sigma }_g(V_{\mathrm{bl}}))-R_n({\sigma }_g(V_g))]/R_n({\sigma }_g(V_{\mathrm{bl}}))$. The conductivities of graphene are obtained by fitting the MD of the verification structure without the Al substrate. Figure 3(a) shows the calculated graphene THz conductivity as a function of the gate voltage from 0 to 29 V. The data for biased gate voltage lager than $V_{\mathrm{bl}}$ is fitted with polynomial function to predict the behavior for our THz modulator under various gate voltages.

At the baseline biased gate voltage of 16 V, the intensity of reflected THz signal reaches its maximum value, which corresponds to the minimum conductance of graphene. It implies the Fermi level reaches the Dirac point of this device at $V_{\mathrm{bl}}$ and the graphene is initially $p$-doped. For the biased gate voltage smaller than $V_{\mathrm{bl}}$, the Fermi level is below the Dirac point. Thus, the increase of biased gate voltage accompanies with the decrease hole concentration and therefore the conductivity of graphene becomes smaller, resulting in larger reflectance. While, for the biased gate voltage larger than $V_{\mathrm{bl}}$, the Fermi level is above the Dirac point, the increase of biased gate voltage leads to the increase electron concentration and therefore the conductivity of graphene increases, resulting in smaller reflectance. Furthermore, the total conductance (${\sigma }_{\text{total}}$) measured by voltage ($V_{\mathrm{DS}}$) and current ($I_{\mathrm{DS}}$) between source and drain as a function of $V_g$ is also depicted [Fig. 3(a)], which shows a similar asymmetry $V$-shaped behavior to THz conductivity of the graphene as the increase of $V_g$. This asymmetry behavior of the $p$− and $n$−region has been reported in other works [28,29].

After calculating the conductivities of the graphene layer under different biased gate voltages using the verification structure, we predict the MD performance of our THz modulator device for $V_g$ larger than $V_{\mathrm{bl}}$. As shown in Fig. 3(b), the theoretical results match well with the experimental measured results. In this case, the highest reflectance corresponding to conductivity ${\sigma }_g=0.179\mathrm{mS}$ under the baseline biased gate voltage of 16 V. For all orders of the THz echoes, the MDs increase as the conductivity of graphene increases, until reach the maximum conductivity 1.09 mS of our structure. The higher order of the echoes always produces larger MD for a fixed conductivity as a result of the enhanced interaction between graphene and THz wave due to multi-time modulation. The maximum MDs for echoes $E_{r2}$, $E_{r3}$, $E_{r4}$, and $E_{r5}$ are 25.78%, 54.8%, 73.93%, and 90.93%, respectively. The absence of echoes higher than the fifth order is because their poor signal to noise ratio due to the rapid decrease of the THz signal’s amplitudes.

Considering the application in the THz communication system, a coherent modulation at a single frequency is preferred. As a result, the MD of a single reflection or transmission THz pulse cannot represent that of coherent THz wave due to the inevitably FP interference of the device. Thus, all orders of reflected echoes are needed to be taken into consideration in order to calculate the MD of coherent incident THz wave. As depicted in Fig. 4(a), a typical FP interference phenomenon of MD was observed. There exist serval maximal values of MD locating at the F-P interference peaks. Six separated peaks were well observed at 0.48 THz, 0.62 THz, 0.76 THz, 0.89 THz, 1.03 THz, and 1.17 THz with MD of 69.54%, 74.8%, 75.78%, 74.84%, 73.73%, and 71.78%, respectively. The MDs increase while the biased gate voltage increases from 24V to 29 V for all of the peaks. The FWHM of our proposed structure for single frequency modulation maintain around 34 GHz for all the peaks.

 

Fig. 4. (a) Measured MD as a function of frequency for biased gate voltages of 24 V (red solid line), 27 V (black dash dot line), and 29 V (orange solid line); (b) Measured (symbol) and simulated (dash line) MD values versus biased gate voltage for frequency at 0.76 THz.

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To theoretically investigate the MD performance in the coherent mode of our THz modulator devices, we use the similar formula as described before but take all the reflected wave information into consideration. The experimental (symbol) and simulated (line) MDs for interference peak at 0.76 THz versus biased gate voltage are illustrated in Fig. 4(b). The theoretical values of MD are well consistent with the measured values. It is well known that the F-P interference peaks $f_{\mathrm{FP}}=m·c/(2n_{S}d\cos (a\sin (\sin ({\theta }_{in})/n_S))$, with $c$ the velocity of light in vacuum, $n_S=3.42$ the refractive index of silicon, ${\theta }_{\mathrm{in}}$ the incident angle, and $m$ an integer) are strongly dependent on the refractive index and the thickness of substrate $d$ as well as the incident angle [30]. The maximum MD are slightly dependent on the thickness of the substrate considering the main mechanism of our modulator structure are the multi-interaction between graphene and THz wave. On the other hand, the FWHM is strongly rely on the substrate thickness. The thinner substrate results in wider FWHM. Thus, besides the frequencies discussed in our results, the modulation for other frequencies can be realized by varying the related geometric parameters and electromagnetic property of the substrate.

In summary, we demonstrated a dual-operation mode high performance THz modulator. In the pulse operation mode, the gate voltage dependence of MD for all orders of reflected echoes was theoretically and experimentally investigated in detail. The MDs for the fifth order echoes are large than 75% in a broadband frequency range larger than 1 THz. A maximum MD of 90.93% are realized at 0.8 THz. While for the coherent operation mode, a MD larger than 75% at 0.76 THz was achieved. Benefiting from the electrically tunable amplitude modulation of graphene, our proposed structure provides a promising way for applications in several fields of terahertz technology.