**4. Applications**

depending on the sliding direction [65]. Meanwhile, the self-retracting motion of graphite, when the probe is removed away after loading, has been observed (shown in **Figure 7(a)** and **(b)**). Moreover, a set of lock-in states has been observed at certain rotation angles with 60° intervals, which requires an external force to unlock a lock-in state [66], as shown in **Figure 7(c)** and **(d)**. The interlayer shear strength of graphite where the lock-in appears is measured

**Figure 6.** (a) Schematic of the in situ TEM shearing test. (b) Low-magnification TEM image of the indenter tip pointing to the test sample. Inset: High-magnification TEM image of the test sample. (c) Force versus distance plot recorded

**Figure 7.** (a, b) Motion of a graphite flake that self-retracts after unloading. (c, d) Motion of a graphite that is in a lock-

Furthermore, the interlayer interaction of 2D materials can be investigated using Raman spectroscopy. By probing the interlayer phonons modes, both the parallel-to-plane (shear) and perpendicular-to-plane (breathing) interlayer force constants can be extracted from the Raman spectrum. Since interlayer vibrational modes are usually in the low-frequency regime, due to the weak interlayer van der Waals restoring force, a special filter in Raman spectroscopy needs

during the test. Inset: Top-view SEM image of the sheared surface. Adapted from Oviedo et al. [61].

to be approximately 0.14 GPa [67].

232 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

in state [66].

*3.2.2. Raman spectroscopy*

#### **4.1. Flexible transistor**

The combination of high breaking strain, low thickness, and versatile electronic properties of 2D materials make them competitive contenders for flexible electronics applications. Because of the semiconducting properties, certain TMDCs (such as MoS2, WS2, and WSe2) and BP can be used as channel materials in flexible transistors, while pristine graphene with relative high conductivity is suitable as an electrode material. Mica and h-BN with large bandgaps can be used for 2D gate dielectrics [74, 75]. **Figure 8(a)** shows a flexible and transparent thin film transistor (TFT) fabricated from all 2D materials on a polyethylene terephthalate (PET)-flexible substrate [76]. The structure of the TFT is depicted in the inset of **Figure 8(b)**. As shown in **Figure 8(b)**, the current On/Off ratio has been found to be about 7.5 × 103 , exhibiting p-type FET characteristics, and the device characteristics have been unaltered within a mechanical strain of 2%. **Figure 8(c)** shows the output characteristics of the flexible TFT with the charac‐ teristic of current saturation similar to conventional Si transistors, uncovering the great potential application of 2D materials in flexible transistors.

**Figure 8.** (a) All 2D materials-based TFTs on a flexible PET substrate. (b) Transfer characteristics of the TFT with and without 2% strain. Inset: Side-view schematic of the flexible TFT. (c) Output characteristics of the TFT. Adapted from Das et al. [76].

#### **4.2. Strain sensor**

The 2D materials [77, 78] have been found to undergo band structure change under applied strain. In addition, the distortion of the 2D films may result in additional scattering, thus reducing the carrier mobility [79]. The above factors contribute to a piezoresistive effect, in which the resistivity of 2D materials is modulated by mechanical deformation. Thus, 2D materials can be used as strain or pressure sensor [80, 81], by taking advantage of the piezor‐ esistive effects. The sensitivity of a strain sensor is characterized usually by its gauge factor (GF), defined as Δ*R*(*ε*) / *R*<sup>0</sup> / *ε*, where *R*0 is the total resistance of the unstrained device and Δ*R*(*ε*) is the resistance change under strain *ε*. The GF of pristine graphene has been character‐ ized to be about 2 [81–85] due to the zero bandgap and the large strain required to open the bandgap, which can be a disadvantage for strain sensors. On the other hand, the GF of MoS2 can reach approximately −200 [17, 29], resulting from the higher sensitivity of the decreasing bandgap and the direct–indirect bandgap transition under tensile strain, making MoS2 more suitable for strain-sensing systems. The sensing performance of the 2D strain sensor can be enhanced by optimizing the structure design, such as the piezopotential-gated graphene matrix sensor arrays (GF = 389, as shown in **Figure 9(a)**) [16], quasi-continuous nanographene film sensor (GF = 507, as shown in **Figure 9(b)**) [86, 87], and graphene-woven fabric sensor (GF = 1000) [88, 89].

**Figure 9.** Sensing characteristics of the (a) piezopotential-gated graphene matrix strain sensor (Adapted from Sun et al. [16]) and (b) quasi-continuous nanographene film strain sensor (Adapted from Zhao et al. [86]).

Moreover, the piezoresistive effect, combined with the high breaking strain of 2D materials enable the design of wearable strain sensors for human motion detection. **Figure 10(a)** shows a prototype of tactile sensor fabricated with graphene films on a PDMS substrate attached on the human wrist. As shown in **Figure 10(b)**, the test subject's motions can be captured clearly with the strain sensor by outputting varying current response under different motions [16].

**Figure 10.** (a) A graphene tactile strain sensor attached on the wrist detecting the hand motion. (b) The electrical re‐ sponse of the tactile strain sensor in different hand motions shown in (a) [16].

#### **4.3. Nanogenerator**

conductivity is suitable as an electrode material. Mica and h-BN with large bandgaps can be used for 2D gate dielectrics [74, 75]. **Figure 8(a)** shows a flexible and transparent thin film transistor (TFT) fabricated from all 2D materials on a polyethylene terephthalate (PET)-flexible substrate [76]. The structure of the TFT is depicted in the inset of **Figure 8(b)**. As shown in

FET characteristics, and the device characteristics have been unaltered within a mechanical strain of 2%. **Figure 8(c)** shows the output characteristics of the flexible TFT with the charac‐ teristic of current saturation similar to conventional Si transistors, uncovering the great

**Figure 8.** (a) All 2D materials-based TFTs on a flexible PET substrate. (b) Transfer characteristics of the TFT with and without 2% strain. Inset: Side-view schematic of the flexible TFT. (c) Output characteristics of the TFT. Adapted from

The 2D materials [77, 78] have been found to undergo band structure change under applied strain. In addition, the distortion of the 2D films may result in additional scattering, thus reducing the carrier mobility [79]. The above factors contribute to a piezoresistive effect, in which the resistivity of 2D materials is modulated by mechanical deformation. Thus, 2D materials can be used as strain or pressure sensor [80, 81], by taking advantage of the piezor‐ esistive effects. The sensitivity of a strain sensor is characterized usually by its gauge factor (GF), defined as Δ*R*(*ε*) / *R*<sup>0</sup> / *ε*, where *R*0 is the total resistance of the unstrained device and Δ*R*(*ε*) is the resistance change under strain *ε*. The GF of pristine graphene has been character‐ ized to be about 2 [81–85] due to the zero bandgap and the large strain required to open the bandgap, which can be a disadvantage for strain sensors. On the other hand, the GF of MoS2 can reach approximately −200 [17, 29], resulting from the higher sensitivity of the decreasing bandgap and the direct–indirect bandgap transition under tensile strain, making MoS2 more suitable for strain-sensing systems. The sensing performance of the 2D strain sensor can be enhanced by optimizing the structure design, such as the piezopotential-gated graphene matrix sensor arrays (GF = 389, as shown in **Figure 9(a)**) [16], quasi-continuous nanographene film sensor (GF = 507, as shown in **Figure 9(b)**) [86, 87], and graphene-woven fabric sensor (GF

, exhibiting p-type

**Figure 8(b)**, the current On/Off ratio has been found to be about 7.5 × 103

potential application of 2D materials in flexible transistors.

234 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

Das et al. [76].

**4.2. Strain sensor**

= 1000) [88, 89].

Research has shown that odd-layer TMDCs possess piezoelectric property due to the absence of inversion symmetry [17, 34]. **Figure 11(a)** shows a flexible device with the monolayer MoS2 flake outlined with black dashed line. When the substrate is bent from the two ends mechanically, the MoS2 flake will be stretched, and piezoelectric polarization charges will be induced at the zigzag edges of the MoS2 flake which can drive the flow of electrons in an external circuit as depicted in **Figure 11(e)**. When the substrate is released, electrons flow back in the opposite direction as shown in **Figure 11(f)**. **Figure 11(b)** and **(c)** show that periodic stretching and releasing of the substrate can generate piezoelectric outputs in the external circuit with alternating polarity, which converts mechanical energy into electricity. A maxi‐ mum mechanical-to-electrical energy conversion efficiency of 5.08% can be achieved from the device [17]. The existence of piezoelectricity, coupled with the mechanical flexibility of some 2D materials, demonstrates their potential applications in wearable power-generated nano‐ devices.

**Figure 11.** (a) A flexible device with a monolayer MoS2 flake and metal electrodes at its zigzag edges. (b) Applied peri‐ odic strain as a function of time. (c) Corresponding piezoelectric outputs when strain is applied along the armchair direction. Operation of the MoS2-based piezoelectric device in initial state (d), stretched state (e), and released state (f) [17].

#### **4.4. Resonator**

in the opposite direction as shown in **Figure 11(f)**. **Figure 11(b)** and **(c)** show that periodic stretching and releasing of the substrate can generate piezoelectric outputs in the external circuit with alternating polarity, which converts mechanical energy into electricity. A maxi‐ mum mechanical-to-electrical energy conversion efficiency of 5.08% can be achieved from the device [17]. The existence of piezoelectricity, coupled with the mechanical flexibility of some 2D materials, demonstrates their potential applications in wearable power-generated nano‐

236 Two-dimensional Materials - Synthesis, Characterization and Potential Applications

**Figure 11.** (a) A flexible device with a monolayer MoS2 flake and metal electrodes at its zigzag edges. (b) Applied peri‐ odic strain as a function of time. (c) Corresponding piezoelectric outputs when strain is applied along the armchair direction. Operation of the MoS2-based piezoelectric device in initial state (d), stretched state (e), and released state (f)

devices.

[17].

Nanoelectromechanical systems (NEMS) resonator, offering the potential for extreme mass and force sensitivity [25, 90], has triggered intense interest in recent years. The resonant frequency of the resonators depends greatly on their geometry and the mechanical properties of the vibrational materials (such as Young's modulus and mass density) [91]. As the sensitivity of resonators improves with increase in resonant frequency, 2D materials are prospective materials for highly sensitive NEMS due to their extraordinary mechanical properties and low mass. Among the family of 2D materials, graphene resonator has been studied most so far. **Figure 12(a)** shows a schematic and a SEM image of a graphene resonator. **Figure 12(b)** shows a schematic of the electrical actuation and detection of mechanical vibrations of the graphene resonator. A dc voltage *V*g applied to the gate causes static deflection of the graphene toward the gate. The resonant motion is actuated by ac voltage with an amplitude of *V*a and frequency of ω<sup>a</sup> applied to the drain electrode, and read out by the current mixing method [25] using a lock-in amplifier. As shown in **Figure 12(c)**, when *V*g = 0 V and *V*a = 250 mV, the fundamental resonance frequency (Peak A) is approximately 1 MHz, and the second vibration mode (Peak B) is measured to be approximately 2 MHz. The amplitude of vibrational modes increases with increasing *V*a. However, the resonant frequency decreases as *V*<sup>a</sup> increases due to nonlinear damping effects at higher resonance amplitudes [92]. By operating the graphene resonant sensors in the second mode regime, the detection sensitivity can be improved significantly [93].

**Figure 12.** (a) Schematic and SEM image of a graphene resonator. (b) Circuit diagram of current-mixing characteriza‐ tion setup. (c) The mixed current versus driving frequency for different amplitudes of actuation voltages. Adapted from Chen et al. [93].

NEMS with low resonant frequency can be used for acoustic electronics, such as acoustic sensor [94] and loudspeakers [95]. Since the resonant frequencies of resonators can be tuned inversely by increasing the dimensions of vibrational parts, resonators with lower resonant frequencies can be fabricated on 2D membranes with larger dimensions. **Figure 13** shows the response of a graphene resonator working in the low-frequency regime [94]. The resonator has been ac‐ tuated with a piezoelectric disk driven with a sinusoidal signal and detected using a Laser Doppler Vibrometer (LDV). The fundamental resonant frequency has been measured to be approximately 16 kHz for a 3 × 3 mm2 graphene membrane.

**Figure 13.** Measured resonant frequency for a 3 × 3 mm2 membrane over the cavity using LDV. Adapted from Grady et al. [94].
