**4.2. Modulation properties of the flexible THz modulator**

The intensity modulation performance of flexible THz modulator has been investigated by using a homemade fiber-coupled THz-time domain spectroscopy (TDS). A pair of photoconductive antenna made on LT-InGaAs/InAlAs is used as both the emitter and detector, which prove a bandwidth of 2 THz approximately. The THz wave from the emitter is focused onto the center of the sample with a beam diameter of 3 mm, covering the active area of the modulator. In order to study the flexible performance of our THz modulator, the device has been measured in the flat, convex, and concave conditions, respectively. The bending strain is ~1%, which is defined as strain ≈ (*t* s –*t* <sup>p</sup>)/2r<sup>c</sup> (*t* s , *t* p> > *t* f ) [51]. *t* s is the thickness of the flexible PET substrate (~125 μm), *t* <sup>p</sup> the thickness of the ion-gel (~10 μm), *t* f the thickness of the graphene film (~0.34 nm), and *r*<sup>c</sup> the curvature radius. In addition, it is noted that, in this work, all transmittances of THz wave through the flexible modulator have been normalized to the reference signal of air.

in the fat condition. The performances of modulation under flat case, convex, and concave conditions are compared, as shown in **Figure 6(d)**. It can be observed that the three curves of transmittance-dependent gate bias at 0.8 THz are almost coincident. It indicates that the flexible modulator has excellent flexible performance, as the THz intensity modulation per-

**Figure 6.** Normalized THz transmittance from the flexible graphene modulator as a function of frequency in the (a) flat, (b) convex, and (c) concave conditions at the fixed gate voltages ranging from −3 to 3 V, with 1 V increment. (d) Normalized THz transmittances as a function of gate voltage from −3 to 5 V at 0.8 THz in the flat, convex, and

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Further demonstrating the flexible performance of our THz graphene modulator, the repeatability has been studied by performing 1000 bending times. It shows that the THz intensity can still be effectively modulated by electrical gating. The modulation depths are 21.7, 21.1, and 20.5% at 0.8 THz in the flat, convex, and concave conditions, respectively, which are very close to that of the graphene modulator before bending. The curves of transmittances as a function of gate voltage at 0.8 THz before and after bending the graphene modulator 1000 times are nearly coincident, showing its high repeatability. We can conclude that the THz intensity modulation can be maintained not only in the bending condition but also after the long bending times, indicating superior flexible performance of the THz graphene modulator. More importantly, a low insertion loss of THz wave was observed in our flexible THz modulator. By using air as the reference, the transmittance of the flexible modulator at 1 V gate voltage was measured and normalized, as plotted in **Figure 7**. It shows a broadband transmittance with the insertion loss less than 1.2 dB in the range of 0–1 THz, which is much smaller

formances are steady under different bending deformations.

concave conditions.

The modulation performance of flexible THz modulator was studied in detail. The normalized intensities of THz wave through the modulator are plotted in **Figure 6(a)**–**(c)** in the flat, convex, and concave conditions, respectively. As shown in **Figure 6(a)**, significant modulation changes in THz transmission can be obtained by applying gate bias between −3 and +3 V when the modulator is in the flat condition. From **Figure 6(a)**, it can be observed that the transmittance has a maximum value of 81.3% at 1 V and a minimum value of 63.1% at −3 V. Therefore, the MD of the modulator is calculated to be 22.4%. Importantly, when the graphene modulator is in the convex and concave conditions, the modulation depths estimated from **Figures 6(b)** and **(c)** are 21.3 and 21.4%, respectively, which are very close to that

1 cm, respectively. The ion-gel, which is a mixture of lithium perchlorate, polyethylene oxide (PEO), and carbinol, was spin coated on the surface of the graphene as the gate dielectric. The work principle of this coplanar-gate FET structure is: when a positive voltage to the device is applied, as shown in **Figure 5(a)**, negative and positive ions in the ion-gel accumulate onto the gate electrode and graphene channel, respectively. A strong electric field is thus imposed to the graphene to modulate the carrier concentration and as a result a modulation to the THz

**Figure 5.** (a) Schematic structure of the flexible THz modulator based on graphene coplanar-gate FET. (b) Photograph of the flexible THz modulator in the bending condition, where the boundary of graphene channel is marked with dotted lines.

The intensity modulation performance of flexible THz modulator has been investigated by using a homemade fiber-coupled THz-time domain spectroscopy (TDS). A pair of photoconductive antenna made on LT-InGaAs/InAlAs is used as both the emitter and detector, which prove a bandwidth of 2 THz approximately. The THz wave from the emitter is focused onto the center of the sample with a beam diameter of 3 mm, covering the active area of the modulator. In order to study the flexible performance of our THz modulator, the device has been measured in the flat, convex, and concave conditions, respectively. The bending strain is ~1%, which is defined

the curvature radius. In addition, it is noted that, in this work, all transmittances of THz wave

The modulation performance of flexible THz modulator was studied in detail. The normalized intensities of THz wave through the modulator are plotted in **Figure 6(a)**–**(c)** in the flat, convex, and concave conditions, respectively. As shown in **Figure 6(a)**, significant modulation changes in THz transmission can be obtained by applying gate bias between −3 and +3 V when the modulator is in the flat condition. From **Figure 6(a)**, it can be observed that the transmittance has a maximum value of 81.3% at 1 V and a minimum value of 63.1% at −3 V. Therefore, the MD of the modulator is calculated to be 22.4%. Importantly, when the graphene modulator is in the convex and concave conditions, the modulation depths estimated from **Figures 6(b)** and **(c)** are 21.3 and 21.4%, respectively, which are very close to that

f

through the flexible modulator have been normalized to the reference signal of air.

is the thickness of the flexible PET substrate (~125 μm),

the thickness of the graphene film (~0.34 nm), and *r*<sup>c</sup>

radiation is realized.

as strain ≈ (*t*

*t*

s –*t* <sup>p</sup>)/2r<sup>c</sup> (*t* s , *t* p> > *t* f ) [51]. *t* s

<sup>p</sup> the thickness of the ion-gel (~10 μm), *t*

126 Design, Simulation and Construction of Field Effect Transistors

**4.2. Modulation properties of the flexible THz modulator**

**Figure 6.** Normalized THz transmittance from the flexible graphene modulator as a function of frequency in the (a) flat, (b) convex, and (c) concave conditions at the fixed gate voltages ranging from −3 to 3 V, with 1 V increment. (d) Normalized THz transmittances as a function of gate voltage from −3 to 5 V at 0.8 THz in the flat, convex, and concave conditions.

in the fat condition. The performances of modulation under flat case, convex, and concave conditions are compared, as shown in **Figure 6(d)**. It can be observed that the three curves of transmittance-dependent gate bias at 0.8 THz are almost coincident. It indicates that the flexible modulator has excellent flexible performance, as the THz intensity modulation performances are steady under different bending deformations.

Further demonstrating the flexible performance of our THz graphene modulator, the repeatability has been studied by performing 1000 bending times. It shows that the THz intensity can still be effectively modulated by electrical gating. The modulation depths are 21.7, 21.1, and 20.5% at 0.8 THz in the flat, convex, and concave conditions, respectively, which are very close to that of the graphene modulator before bending. The curves of transmittances as a function of gate voltage at 0.8 THz before and after bending the graphene modulator 1000 times are nearly coincident, showing its high repeatability. We can conclude that the THz intensity modulation can be maintained not only in the bending condition but also after the long bending times, indicating superior flexible performance of the THz graphene modulator.

More importantly, a low insertion loss of THz wave was observed in our flexible THz modulator. By using air as the reference, the transmittance of the flexible modulator at 1 V gate voltage was measured and normalized, as plotted in **Figure 7**. It shows a broadband transmittance with the insertion loss less than 1.2 dB in the range of 0–1 THz, which is much smaller

**Figure 7.** Transmittance and attenuation as a function of frequency for flexible graphene modulator at the gate voltage of 1 V (Dirac point) and PET.

(QCL), despite the intrinsic MD of GFET is only 11% [53]. Inspired by the flexible and lowloss PET-GFET we developed previously, here, we propose an effective method to enhance the modulation depth by cascading multiple PET-GFET modulators with little sacrifice of insertion loss. Two GFETs were simultaneously fabricated on both sides of PET substrate to form a cascaded THz modulator, as shown in **Figure 8(a)**. The obtained devices are optically

**Figure 9.** Normalized THz transmittance spectra of cascaded modulators under different gating schemes. Gate voltage

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Modulation depth and insertion loss, two critical parameters of THz modulators are investigated. To investigate the modulation of the cascaded device, the THz transmittance was measured with an optimized gating scheme. **Figure 9** shows the transmission intensity of the THz waves through the graphene modulators at the frequency from 0.2 to 1.0 THz, which is normalized to the spectrum of air. Broadband modulation is obtained across the whole spectrum. When gate voltage is only applied to one modulator (**Figure 9(a)**), the transmittance at 0.6 THz reaches the maximum of 77.56% at 0.5 V and minimum of 61.41% at −3.0 V, respectively, leading to an MD of 20.8%. Maximum modulation depth was obtained when gate electrodes of both modulators were simultaneously driven. An enhanced MD of ~51% is achieved with an IL of only 1.4 dB. To our best knowledge, this is the largest MD reported for flexible and broadband THz modulators and can be further improved by stacking more

Field-effect transistors are one of the most widely discussed applications of graphene in microelectronics and opto-electronics. However, graphene is intrinsically a zero-band-gap semiconductor, which is believed to be unsuitable for use in an electronic transistor. Fortunately, graphene FET finds its potential usage as THz modulators since THz wave is highly sensitive to the free carrier concentration, which can be effectively tuned by electrical gating in a graphene FET. In this chapter, the physics principle, device structure, and the modulation characteristics of GFET-based THz modulators, both rigid and flexible, are discussed

transparent and highly flexible, as shown in **Figure 8(b)** and **(c)**.

applied to (a) single modulator and (b) dual modulators.

similar structures.

**5. Conclusion**

than that of the Si substrate-based rigid graphene modulators (~5 dB) [52]. The extremely low loss can be attributed to the small refractive index of PET (1.65) as compared to that of Si (3.42). Our results indicate that employing a substrate with low refractive index is beneficial for obtaining a THz modulator with low insertion loss.

Modulation depth is one of the crucial parameters that determine the real applications of THz modulators. The typical MD of existing GFET modulators is only 20%. High MD has been achieved by a complex and exquisite integration of GFET with THz quantum cascade lasers

**Figure 8.** Overview of the cascaded THz modulators. (a) Schematic illustration of the device with cascaded two GFETs on a single PET substrate. (b) Photograph of the devices. The boundaries of graphene channel and ion-gel layer are marked with dark dotted lines and red solid lines, respectively. (c) Optical image showing the flexible nature of the device.

**Figure 9.** Normalized THz transmittance spectra of cascaded modulators under different gating schemes. Gate voltage applied to (a) single modulator and (b) dual modulators.

(QCL), despite the intrinsic MD of GFET is only 11% [53]. Inspired by the flexible and lowloss PET-GFET we developed previously, here, we propose an effective method to enhance the modulation depth by cascading multiple PET-GFET modulators with little sacrifice of insertion loss. Two GFETs were simultaneously fabricated on both sides of PET substrate to form a cascaded THz modulator, as shown in **Figure 8(a)**. The obtained devices are optically transparent and highly flexible, as shown in **Figure 8(b)** and **(c)**.

Modulation depth and insertion loss, two critical parameters of THz modulators are investigated. To investigate the modulation of the cascaded device, the THz transmittance was measured with an optimized gating scheme. **Figure 9** shows the transmission intensity of the THz waves through the graphene modulators at the frequency from 0.2 to 1.0 THz, which is normalized to the spectrum of air. Broadband modulation is obtained across the whole spectrum. When gate voltage is only applied to one modulator (**Figure 9(a)**), the transmittance at 0.6 THz reaches the maximum of 77.56% at 0.5 V and minimum of 61.41% at −3.0 V, respectively, leading to an MD of 20.8%. Maximum modulation depth was obtained when gate electrodes of both modulators were simultaneously driven. An enhanced MD of ~51% is achieved with an IL of only 1.4 dB. To our best knowledge, this is the largest MD reported for flexible and broadband THz modulators and can be further improved by stacking more similar structures.
