Novel Flexible Pressure Sensor with Symmetrical Structure Based on 2-D MoS₂ Material on Polydimethylsiloxane Substrate

Abstract

Flexible pressure sensors can be widely utilized in healthcare, human–computer interaction, and the Internet of Things (IoT). There is an increasing demand for high-precision and high-sensitivity flexible pressure sensors. In response to this demand, a novel flexible pressure sensor with a symmetrical structure composed of MoS₂ and PDMS is designed in this paper. Simulation is conducted on the designed flexible pressure sensor. Its piezoresistive effect is analyzed, and the influence of the cavity structure on its sensitivity is investigated. Additionally, a fully symmetrical Wheatstone bridge composed of the flexible pressure sensor is designed and simulated. Its symmetrical structure improves the temperature stability and the sensitivity of the sensor. The structure can be used to convert pressure changes into voltage changes conveniently. It indicates that the sensor achieves a sensitivity of 1.13 kPa⁻¹ in the micro-pressure range of 0–20 kPa, with an output voltage sensitivity of 3.729 V/kPa. The designed flexible pressure sensor exhibits promising potential for applications in wearable devices and related fields, owing to its high sensitivity and precision.

1. Introduction

Since various smart devices are applied deeply in our daily lives, various types of sensors for signal acquisition are highly required. A pressure sensor is an important de-device for front-end signal input with the merits of a simple structure, good stability, and high precision [1,2].

Unlike traditional pressure sensors based on rigid materials, novel flexible pressure sensors can be conformed to various surfaces owing to the applied flexible materials for both conductive components and substrates. This characteristic enhances the convenience of the testing process and provides an advantage in measuring pressure on non-planar surfaces. Moreover, flexible pressure sensors find extensive applications across diverse fields due to their unique properties, including ultra-thinness, a low modulus, light weight, high sensitivity, and scalability. The reported applications include wearable electronics [1], electronic skin [3], and human–computer interaction [2], among others.

During the development process of flexible pressure sensors, the main performance of the sensors has been continuously improved in terms of sensitivity, response time, relaxation time, stability, etc.

In 2014, Zhu et al. [4] introduced a flexible resistive tactile sensor utilizing microstructured graphene arrays. The sensor exhibits a high sensitivity of −5.5 kPa⁻¹ in the low-pressure range (<100 Pa), an ultra-low detection limit of 1.5 Pa, and an ultra-fast response time (0.2 ms). Importantly, the sensitivity of the flexible sensor can be adjusted by selecting microstructures with different parameters to suit various sensing purposes.

In 2017, Kim et al. [5] presented a fabrication process for VACNT/PDMS composite materials, leading to a flexible resistive pressure sensor composed of a VACNT/PDMS composite conductor with irregular surface morphology. The sensor shows high sensitivity (~0.3 kPa⁻¹ to 0.7 kPa⁻¹), a stable steady-state response across various pressures (20 Pa to 5 kPa), and relatively fast response (162 ms), and relaxation times (~108 ms), along with mechanical durability (5000 cycles) and reversible on/off behavior.

In 2017, Luo et al. developed a material processing strategy to produce hollow structured graphene-PDMS composites, ensuring an excellent piezoresistive response. This unique structure enables independent adjustment of the resistance and mechanical modulus, thereby varying the sensitivity and linear range, with the highest sensitivity reaching 15.9 kPa⁻¹ in the range of 0–60 kPa [6].

In 2018, Ma et al. prepared MX/rGO hybrid aerogels using ice-template freezing technology and applied them in piezoresistive sensors. The 3D aerogels demonstrate superior sensor performance due to the synergistic effect between MXene and rGO, featuring high sensitivity (22.56 kPa⁻¹), a rapid response (<200 ms), and excellent stability over more than 10,000 cycles [7].

In 2018, Zhang, YP, et al. designed a MXene/black phosphorus (BP)-based self-powered smart sensor system. With MXene/BP as the sensitive layer in a flexible pressure sensor, the pressure sensitivity of the device can be improved to 77.61 kPa⁻¹ at an optimized elastic modulus of 0.45 MPa, with a fast response time of 10.9 ms [8].

There are numerous options for the conductive components of flexible sensors. Carbon materials (including graphene, GO, rGO, and carbon nanotubes (CNT)), metal nanomaterials, and flexible organic-based piezoelectric materials by supramolecular packing, bestowing macroscopic dipole-driven electro-mechanical and optical functions [9,10], and conductive polymers are all viable choices. Carbon-based polymer composites, in particular, have gained significant attention in research due to their superior electrical and mechanical properties, as well as their unique two-dimensional (2-D) structure [11]. However, challenges such as high hysteresis and poor repeatability still exist [12]. The strong van der Waals interactions between graphene sheets and the high junction contact significantly inhibit the high conductivity and mechanical strength of graphene sheets [11]. In this study, MoS₂, which is a two-dimensional transition metal dichalcogenide (TMDC) material, is selected as the flexible pressure-sensitive material.

Bulk MoS₂ exhibits a hexagonal layered structure with weak van der Waals forces between the adjacent layers. MoS₂ is in a “sandwich” structure, comprising two layers of sulfur atoms enclosing a central layer of molybdenum atoms [13]. Each molybdenum atom is surrounded by six sulfur atoms, forming strong covalent bonds, while each sulfur atom is bonded to three molybdenum atoms. 2D MoS₂ can offer several advantages. Firstly, its 2-D electron confinement, especially in monolayer form, makes it an ideal channel material for high-performance electronic and optoelectronic devices, resulting in competitive electron mobility. Secondly, its strong in-plane covalent bonds and atomic thickness contribute to excellent mechanical strength (fracture strain > 2.2%), flexibility, and optical transparency [14]. Compared to graphene, MoS₂ possesses a wider band gap of 1.8 eV, chemical inertness, and superior temperature stability. Lastly, MoS₂ exhibits stable operation and excellent sensitivity due to its tunable band gap and high gauge factor [12]. These attributes make MoS₂ particularly suitable for flexible piezoresistive sensors.

In 2018, Kim et al. reported on a cracked paddy-shaped MoS₂/graphene porous network (GPN) infiltrated into an Ecoflex hybrid nanostructure for a wearable strain pressure sensor. This MoS₂/GPN/Ecoflex sensor demonstrates stable characteristics, maintaining device performance even after 4000 cycles of repeated pressing and release. Additionally, it exhibits a high gauge factor (GF) of 24.1 and excellent elasticity in bending and tensile tests [11].

In 2021, Xing Pang et al. designed and fabricated a flexible piezoresistive pressure sensor combining molybdenum disulfide with PDMS. The sensor, with 1510 μm thick PDMS film, shows high sensitivity up to 22.62 MPa⁻¹ in the pressure range of 0–0.23 MPa and even 866.9 MPa⁻¹ above 0.4 MPa pressure [15]. It was successfully employed as a wearable pressure sensor for measuring plantar pressure, demonstrating good repeatability.

In 2022, X.Y. Chen et al. proposed a soaking method to fabricate an MoS₂/HEC/PU sponge pressure sensor. The porous structure imparted excellent performance to the sensor, including high sensitivity (0.746 kPa⁻¹ in the 50–250 kPa pressure range), a wide pressure detection range (up to 250 kPa), a fast response/release time (120 ms), and excellent repeatability over 2000 cycles [16].

In 2022, D.D. Xu et al. introduced a novel flexible ionic electronic pressure sensor based on MoS₂ material. The sensor exhibits ultra-high sensitivity (S = 89.75 kPa⁻¹) and a wide sensing range (722.2 kPa). Additionally, it shows rapid response and relaxation times (<3 ms), indicating its quick response speed to external pressure stimuli. Long-term cycling stability is also demonstrated, enduring over 5000 cycles without obvious degradation under pressure of 138.9 kPa [17].

In this paper, the integration of a fully symmetrical Wheatstone bridge structure with a flexible piezoresistive pressure sensor based on MoS₂ and PDMS substrate is proposed, showing superior sensitivity. The paper is organized as follows: In the first section, the research background and the significance of the PDMS + MoS₂ flexible sensor are introduced, along with an overview of current research trends. In the second part, the piezoresistive effect of the designed flexible sensor is analyzed. The sensor’s manufacturing process is reported. In the third section, the piezoresistive effect of the MoS₂ film on PDMS is simulated. The impact of the cavity structure on the sensor’s sensitivity is investigated. A circuit-level simulation model of the fully symmetrical Wheatstone bridge structure is developed to verify the zero offset effect resulting from the resistance asymmetry caused by process deviations during preparation. In the fourth part, the conclusions are summarized.

2. Design of a Novel Flexible Pressure Sensor Structure

2.1. Working Principle of a Piezoresistive Pressure Sensor

The operation principle of the piezoresistive pressure sensor is shown in Figure 1. With changing pressure, the resistance and the output voltage can be changed.

The value of the resistance is:

$$R=\rho {\displaystyle \frac{L}{A}}$$

(1)

It can be seen that the resistance is influenced by the resistivity (ρ), the contact area (A), and the electrical path length (L). When the pressure is applied, the pressure-sensitive membrane undergoes deformation, altering the values of ρ, L, and A, thus changing the resistance (R) and resulting in a corresponding change in voltage (V). The voltage change can be used to quantify the stress variation.

Figure 1a shows the diagram with rigid material, while Figure 1b shows the situation with flexible material. As shown in Figure 1a, as the applied pressure is increased, if the change in resistivity ρ (piezoresistive effect) is not considered, the electrical path length L should be changed accordingly. On the other hand, as shown in Figure 1b, with the flexible material, in addition to the resulting change in L, the contact area with the negative electrode is also increased due to squeezing the material. The combined changes caused by the pressure on the flexible material could result in an obvious improved change in the resistance. In this way, the sensitivity of the sensor based on the flexible material is improved. Based on this idea, various microstructures are proposed to enhance the sensitivity by augmenting the contact area or conduction paths upon pressure application.

The related change of the resistance can be expressed with the following equation:

$${\displaystyle \frac{\mathsf{\Delta }R}{R}}=(1+2v)+{\displaystyle \frac{\mathsf{\Delta }\rho }{\rho }}$$

(2)

The term (1 + 2ν) denotes the impact of geometric alterations, while the latter signifies the piezoresistive effect intrinsic to the material itself. With the applied metals and metal alloys, the resistance is typically increased by several times. However, the semiconductor materials, such as germanium (Ge) and silicon (Si), exhibit a significant increase in resistance due to changes in their band gap or atomic spacing, often achieving enhanced performance through a substantial coefficient [18].

Figure 2 shows the cross-sectional schematic of the piezoresistive pressure sensor. When pressure is applied, both the piezoresistive film and the piezoresistors are deformed, leading to varying stresses across different locations of the piezoresistors, thereby causing changes in resistance. These resistance changes can be converted into voltage outputs through the Wheatstone bridge structure [19].

The piezoresistive effect indicates the alteration in energy bands within a semiconductor material with the subjected stress, resulting in shifts in energy valleys and subsequent changes in resistivity. The magnitude of this effect is quantified by the piezoresistive coefficient π, defined as the relative change in resistivity per unit stress.

$${\displaystyle \frac{\mathsf{\Delta }R}{R}}=\pi P$$

(3)

The sensitivity denotes the extent of resistance change in response to variations in the pressure. Higher sensitivity signifies greater measurement accuracy, indicating that the sensor can detect smaller changes in pressure with higher precision.

$$S={\displaystyle \frac{\mathsf{\Delta }R}{R}}/\mathsf{\Delta }P$$

(4)

Figure 3 shows the schematic diagram of the Wheatstone bridge structure based on the flexible pressure sensors. In the figure, V_dd represents the power supply voltage applied to the bridge, while R₁, R₂, R₃, and R₄ denote the resistors positioned on the four arms of the bridge. The output voltage Vout is the measured voltage, which is used to calculate the strain value. If Vout is equal to zero, it means there is no pressure applied to any part of the bridge. With the applied pressure on the resistance, Vout can be expressed as the following equation:

$$V_{OUT}=({\displaystyle \frac{R_2}{R_1+R_2}}-{\displaystyle \frac{R_4}{R_3+R_4}})•V_{dd}$$

(5)

The Wheatstone bridge structure is employed for the symmetric connection, serving to not only mitigate the zero temperature drift of the sensor, but also to convert the challenging-to-measure variations of the varistor into easily detectable current or voltage outputs. This configuration facilitates convenient integration with subsequent detection circuits.

2.2. Structural Design

In the paper, 2D-MoS₂ is adopted as the piezoresistive material, while PDMS is the substrate. A symmetrical Wheatstone bridge structure is adopted to construct a flexible piezoresistive pressure sensor.

Polydimethylsiloxane (PDMS) is widely utilized in the fabrication of electronic skin and other stretchable electronic devices due to its commercial availability and well-established properties. Its advantages include chemical inertness, stability across a broad temperature range, transparency, tunable mechanical properties, and the capability to define adhesive and non-adhesive regions through UV irradiation, which is crucial for bonding electronic materials to its surface [20].

To fabricate the sensor, firstly, PDMS is cast onto a mold to create a cavity structure. ITO/Al electrodes are deposited onto the PDMS surface. A monolayer of MoS₂ is grown on another Si/SiO₂ surface and subsequently transferred to the PDMS surface using a PLLA rapid transfer method. The MoS₂ layer is then photo-lithographically etched using Cl radicals and Ar⁺ ion beams before being covered with another layer of PDMS.

The schematic of the fabricated flexible pressure sensor is shown in Figure 4a, including the upper PDMS, lower PDMS, MoS₂, and electrodes. The facilities for the measurement of the flexible pressure sensor are shown in Figure 4b. The measured flexible pressure sensor is placed in a test chamber (KOMEG KMT-64-S). A Druck PACE5000 gas pressure controller is used to control the pressure on the sensor. A digital multimeter (DMM) UT60B is used to measure the output of the Wheatstone structure.

2.3. Manufacturing Process

Figure 5 shows the soft lithography process for the PDMS cavity. The silanization treatment is shown in Figure 5a. The mold is placed in a culture dish, and a few drops of TMCS (trimethylchlorosilane) are applied around the mold. The dish is sealed for 15 min. Afterward, the dish is opened, allowing an additional 10 min for all the TMCS to evaporate. The contact angle of the treated mold is measured. The PDMS is mixed with a curing agent with a ratio of 10:1. The bubbles in the PDMS mixture are removed by initiating a vacuum and maintaining it for 30 min. Then, the mixture is continuously baked. The degassed PDMS is poured onto the silanized mold, as shown in Figure 5b. The PDMS is baked at 80 °C for 2 h. It can be demolded after the cooling process (as shown in Figure 5c).

The production process follows the method for preparing MoS₂/Au composite electrodes as described by D. D. Xu et al. [17].The PLLA rapid transfer method, proposed by Hai Li et al. [21], is utilized to transfer the layered MoS₂ grown on a silicon/silicon dioxide (Si/SiO₂) substrate.

Figure 6 shows the fabrication process of the flexible pressure sensor, with 2D MoS₂ materials on a PDMS substrate. Initially, a single layer MoS₂ is grown on a silicon/silicon dioxide (SiO₂) wafer using chemical vapor deposition (CVD) (as shown in Figure 6a). First, the silicon wafer is pretreated, and plasma cleaning is used to remove organic pollutants and oxide layers on the surface of the silicon wafer, increasing the surface energy to improve the adhesion of MoS₂. Then, the silicon wafer is placed in a CVD furnace (SENTECH Instruments (Berlin-Adlershof): SENTECH SI 500), heated (650–850 °C), and a precursor nitrogen gas containing sulfur and molybdenum is introduced. The precursor is de-composed. The sulfur and the molybdenum atoms react on the surface of the silicon wafer to form a single layer of MoS₂. Post annealing is conducted in a nitrogen atmosphere on the grown 2-D material.

PLLA in dichloromethane solution (3.0 wt %) is applied as a carrier on top of the MoS₂ layer by spin coating at 3000 rpms. Subsequently, a polymer strip with a width of 1 mm is scratched along the edge of the SiO₂/Si substrate to expose the hydrophilic SiO₂ surface. Then, PDMS film is pressed onto the PLLA film. Deionized water is dripped onto the exposed hydrophilic SiO₂ area, allowing it to penetrate between the substrate and the hydrophobic PLLA film. After 5–10 min, the PDMS/PLLA film is peeled off from the SiO₂/Si substrate, as shown in Figure 6b. At the same time, ITO (indium tin oxide)/Al is deposited onto the PDMS substrate, as shown in Figure 6c. It is patterned as the sensor’s electrode, as shown in Figure 6d. Subsequently, the PDMS/MoS₂ composite is transferred onto the ITO/Al electrode (Figure 6e). The PDMS/PLLA/MoS₂ film is initially transferred and pressed onto the surface of the target substrate (Figure 6f). Utilizing the differential thermal expansion coefficients of PDMS and PLLA, the PDMS film is heated to 50 °C and then peeled off from the PLLA film’s surface. Finally, the PLLA film is dissolved using dichloromethane (DCM) to facilitate the transfer of MoS₂ (Figure 6g).

Following the electrode deposition and MoS₂ transfer processes described above (Figure 6g or Figure 7c), the photolithography of MoS₂ is conducted. The Atomic Layer Etching (ALET) method, reported by T.Z. Lin et al. [22], is employed in this paper. ALET involves a cyclic process, in which chlorine (Cl) radicals are adsorbed onto the MoS₂ surface. The followed desorption process, by using argon (Ar⁺) ion beams, can remove MoS₂ layer by layer. Initially, chlorine radicals are generated using an inductively coupled plasma (ICP) system and are adsorbed onto the surface of MoS₂. Subsequently, the MoS₂ surface undergoes chlorination using a low-energy Ar⁺ ion beam, as shown in Figure 7d.

To determine the MoS₂ size, we use photolithography to determine the size of the device, and then use a microscope to measure the planar dimensions and an Ellipsometer to measure the thickness.

3. Results and Discussion

COMSOL 6.1 software is used to simulate the piezoresistive effects of MoS₂ on PDMS substrate.

Table 1. Material modeling parameters of MoS₂ and PDMS for simulation.

Material	PDMS	MoS2
Conductivity	0.1 [S/cm]	0.5 [S/cm]
Young’s modulus	750 [kPa]	280 [GPa]
Poisson’s ratio	0.49	0.29
Piezoresistive coupling matrix		22.62 [1/MPa] [15]
	MoS2 + PDMS
Size (μm)	Upper MoS2: 0.5 × 0.8 × 0.1 Lower layer PDMS: 0.5 × 0.8 × 0.1

presents various material performance parameters of PDMS and MoS₂ used in the simulation.

According to the geometrical dimensions listed in Table 1, the upper layer consists of MoS₂ measuring 0.5 × 0.8 × 0.1 microns (colored yellow in Figure 8a), while the lower layer is PDMS of identical dimensions (colored gray in Figure 8a). A pressure of 20 kPa is applied on the MoS₂ + PDMS compound materials to observe the stress properties.

The constructed device model features PDMS as the substrate encapsulating MoS₂. With the applied external pressure, PDMS undergoes deformation, exerting forces on MoS₂ due to this deformation. Consequently, the force acting on MoS₂ can be transferred to a vertical pressure p combined with a horizontal force p × 0.49 (where 0.49 represents Poisson’s ratio of PDMS), as illustrated in Figure 8b.

An ITO/Al electrode is deposited onto the PDMS surface. The test voltage ranging from 0 to 10 V is applied. Changes in the current under varying pressures can be observed. The relationship between ΔR/R and p can be established.

The relationships between the current and the voltage with different applied pressures are shown in Figure 9a, while the relationships between the resistance and the pressure are shown in Figure 9b. It is evident that the resistance increases with the increase in the applied pressure. This is mainly attributed to the piezoresistant effect of the MoS₂ material. When MoS₂ experiences a compressive strain less than 2%, its band gap would be widened, resulting in higher resistance [23]. Figure 9b illustrates the flexible pressure sensor with a sensitivity of 1.13 kPa⁻¹.

To further enhance the sensitivity of PDMS + MoS₂, a cavity structure within the PDMS substrate is introduced in the design. This exploration optimizes the stress conditions, strategically placing the piezoresistive material in areas of optimal stress to improve the sensitivity. Furthermore, the ratios of cavity height to PDMS thickness are varied, which are used to investigate their impacts on the stress conditions. The detailed parameters are listed in

Table 2. Dimensions of PDMS and cavity in flexible pressure sensor.

Size (μm)	PDMS	Cavity
Length × Width	1 × 1	0.5 × 0.5
Height	H (From 0.12 μm to 0.2 μm)	0.1
Pressure applied	20 kPa

.

Figure 10 illustrates how stress varies with the different thickness of PDMS. Firstly, regardless of PDMS thickness, the cavity structure can amplify the pressure at its edges. If MoS₂ piezoresistive material were placed at the edges, its piezoresistive performance would be significantly enhanced. Secondly, with increasing PDMS thickness, from 0.12 μm to 0.2 μm, the intensity of the pressure on the edge is gradually decreased. Therefore, to maximize sensitivity without compromising structural integrity under stress, the PDMS thickness with 0.12 μm shows the optimized performance.

In order to further explore the optimal PDMS cavity depth, we set the maximum deformation of the middle PDMS membrane to not exceed 30%.

Based on the results in Figure 11, the stability and the reliability of the sensor can be observed. It can be seen that the optimal PDMS thickness is 0.25 μm, which is 2.5 times the cavity depth.

Based on the results shown in Figure 10, the MoS₂ piezoresistive materials are positioned at the point of maximum force to get the optimal result. Constructing the Wheatstone structure, its output voltage can be expressed with the following equation:

$$V_{OUT}=({\displaystyle \frac{R_2}{R_1+R_2}}-{\displaystyle \frac{R_4}{R_3+R_4}})•V_{dd}$$

(6)

The resistors R₁~R₄ can be expressed according to the piezoresistive effect:

$$\left\{\begin{array}{c}{R}_1=R_0(1+{\mathsf{\Delta }}_1)(1-P•sensitivity)\\ R_2=R_0(1+{\mathsf{\Delta }}_2)(1+P•sensitivity)\\ R_3=R_0(1+{\mathsf{\Delta }}_3)(1+P•sensitivity)\\ R_4=R_0(1+{\mathsf{\Delta }}_4)(1-P•sensitivity)\end{array}\right\}$$

(7)

Substituting the value of resistor R into the Wheatstone bridge output expression:

$$V_{OUT}=({\displaystyle \frac{(1+{\mathsf{\Delta }}_2)(1+P•S)}{(1+{\mathsf{\Delta }}_1)(1-P•S)+(1+{\mathsf{\Delta }}_2)(1+P•S)}}-{\displaystyle \frac{(1+{\mathsf{\Delta }}_4)(1-P•S)}{(1+{\mathsf{\Delta }}_3)(1+P•S)+(1+{\mathsf{\Delta }}_4)(1-P•S)}})•V_{dd}$$

(8)

If we consider the ideal situation ${\mathsf{\Delta }}_1={\mathsf{\Delta }}_2={\mathsf{\Delta }}_3={\mathsf{\Delta }}_4$,

then Formula (8) becomes:

$$=({\displaystyle \frac{1+P•S}{2}}-{\displaystyle \frac{1-P•S}{2}})V_{dd}=P•S•V_{dd}$$

(9)

It can be seen from Formula (9) that under ideal conditions, the final output voltage Vout of the sensor is related to three quantities, namely, the applied pressure p, the sensor sensitivity S, and the sensor operating voltage V_dd. When the operating voltage V_dd and the sensitivity S are constant, the output voltage of the sensor is solely linearly related to the applied pressure P.

Practically, variations in the manufacturing process can lead to unexpected asymmetry biases in the resistance values of the four resistors in the Wheatstone bridge. This can result in a non-zero output signal from the pressure sensor, even in the absence of applied pressure. Additionally, existing asymmetry in the piezoresistive coefficients of these resistors could further influence changes in the resistance values.

In this paper, the piezoresistive coefficient and the manufacturing process deviations are treated as the variables in the model. The simulation results of the Wheatstone bridge based on the designed flexible pressure sensors are shown in Figure 12. The sensitivity can be evaluated based on the results.

Based on the simulation results, the sensitivity S of the flexible pressure sensor is 3.729 V/kPa. The symmetrical Wheatstone bridge structure converts the pressure-induced resistance changes into voltage variations, facilitating the design of a piezoresistive pressure sensor.

To assess the impact of deviations in the piezoresistive coefficients and the manufacturing processes on the output voltage, assuming a 5% deviation, the values of variables Del1 to Del4 are adjusted accordingly.

Table 3. Changed values of Del1 ~ Del4 in different cases.

Parameter	Case1	Case2	Case3
Del1	0	0.05	−0.05
Del2	0	−0.05	0.05
Del3	0	−0.05	0.05
Del4	0	0.05	−0.05

lists the changed values of Del1 ~ Del4 in different cases.

Figure 13 shows the influences of the process variations on the sensor’s voltage output. It can be confirmed that variations in manufacturing processes and piezoresistive coefficients lead to resistance asymmetry and zero-point offset in the Wheatstone bridge structure. This offset results in an output voltage even without applied pressure. Moreover, it can also be observed that the trend of the sensor output voltage remains the same. A proportional relationship can be observed, showing good linearity of the sensor’s output.

Similarly, temperature changes also have such an impact on the output curve of the sensor. Their essence is to change the resistance through other factors, making the resistance values of various parts of the Wheatstone bridge inconsistent, resulting in zero drift. In addition to zero drift, temperature changes may affect the sensitivity of the bridge, that is, the response degree of the output voltage to input changes. This may lead to degraded accuracy of the measurement results, especially in environments with large temperature changes.

Theoretical analysis on other important characteristics of the sensor is discussed in the following section.

Response time refers to the speed at which a sensor reacts to a change in pressure, that is, the period starting from the applied pressure and ending when the sensor output reaches 90% of the stable value. It is related to the electron or ion mobility of the sensor material and the geometric characteristics of the signal transmission path in the sensor structure. MoS₂ has a unique two-dimensional electron confinement property and high electron mobility [14], which makes a great contribution to expedite the response time of the sensor.

The relaxation time is the time required for the sensor resistance signal to be recovered from a stable value to its initial state after the pressure is removed. It is related to the viscoelasticity of the material and the contact conditions of the electrodes.

$$\tau ={\displaystyle \frac{\eta }{G}}$$

(10)

where τ is the relaxation time, η is the viscosity coefficient of the material, and G is the elastic modulus of the material, which can be replaced by Young’s modulus in this case.

Studies have shown that MoS₂ interfacial adhesion energy is increased with decreasing MoS₂ thickness and is gradually decreased with increasing temperature [24]. The shorter the relaxation time, the shorter the time it takes for the sensor to recover to its normal state. Based on its response time, the designed flexible sensor can be applied to environments requiring for faster pressure measurement.

From the Figure 14, by adjusting the frequency of force variation over time and observing the output signal, it can be found that the response time of the sensor is 53 ms.

The mechanical durability of a pressure sensor refers to the ability of the sensor to withstand repeated loading and unloading during its service life, as well as the degree to which it maintains stable performance under specific conditions. The fatigue life of the material is an important consideration. MoS₂ has strong in-plane covalent bonds and atomic thickness, which gives it excellent mechanical strength (fracture strain > 2.2%) and flexibility [14]. These characteristics make MoS₂-based pressure sensors have relatively strong mechanical durability. After 3000 pressure loading and unloading cycles, the PDMS cavity structure shows a 3% offset error.

4. Conclusions

In this paper, a novel flexible pressure sensor based on 2D MoS₂ material with PDMS substrate is designed. Its detailed fabrication process is presented. Utilizing soft lithography, PDMS substrates with cavities are fabricated, which employ the PLLA rapid transfer method to integrate MoS₂ onto the PDMS substrate. During the fabrication, Ar⁺ ion beam etching is utilized for MoS₂ patterning. The cavity structure shows benefit in enhancing sensitivity, while the symmetrical Wheatstone bridge configuration facilitates accurate measurement of external pressure and improved temperature stability.

As shown in

Table 4. Comparison of sensitivity of various pressure sensors.

Pressure Sensor	Sensitivity	Reference
PDMS + MoS2 (this work)	1.13 kPa−1
MoS2/HEC/PU sponge pressure sensor	0.746 kPa−1	[16]
ionic electronic pressure sensor based on MoS2 material	89.75 kPa−1	[17]
graphene-PDMS composites	15.9 kPa−1	[6]

, a comparison of the sensitivity of various pressure sensors is made. Compared with the piezoresistive pressure sensor made of the same MoS₂ material, the sensor designed in this paper has a slight advantage in terms of sensitivity. On the other hand, it can be found that the piezoresistive pressure sensor cannot be compared with the ionic electronic pressure sensor in terms of sensitivity. However, the proposed flexible sensor in this paper shows high stability and a simple structure for easy mass-fabrication. Compared with the sensor made of graphene-PDMS composites, the proposed sensor in this paper shows potential for improvement, since it can also adopt other structures, such as microstructures and arrays, to improve sensitivity.

The pressure sensor exhibits a relatively outstanding sensitivity of 1.13 kPa⁻¹. Furthermore, the sensitivity could be further enhanced by increasing the proportion of cavity to substrate. The piezoresistive characteristics of a sensor employing a MoS₂ + PDMS Wheatstone bridge structure is investigated in this paper. Overall, the results highlight the promising application potential of this new flexible pressure sensor with excellent sensitivity in fields such as medical treatment, sports monitoring, and wearable devices.