A new strategy for fabricating a stacked flexible capacitive sensor

Abstract

Currently, flexible capacitive sensors have a wide range of application scenarios in the field of wearable electronic devices. In order to detect more subtle joint movements of the human body, a method of fabricating stacked capacitive sensors is demonstrated. An ultrathin dielectric elastomer film of about 110 μm by the “secondary calendering” method was prepared. The shape of the electrode layers was designed, printed the electrode materials on the dielectric elastomer film by screen-printing, realized the stacked-layer technology, and connected each sensor unit in parallel by the electrode columns formed inside. A 12-layer flexible capacitive sensor with an initial capacitance of 10.2nF, good resolution (1% strain), high sensitivity (1.09) and stability under 10,000 cycles is fabricated. The sensor fabricated in this paper can recognize the motion at various joints of the human body, such as elbow and knee joints. This paper provides a new method for fabrication of stacked flexible capacitive sensors, which opens up new applications in flexible sensors, wearable electronic devices and human-computer interaction.

Introduction

With the rapid progress and development of science and technology, a wide range of new materials are continuously being applied to various aspects of social lives. Electro Active Polymer (EAP) is a class of materials that exhibit significant shape and size changes when subjected to electrical stimulation. These materials can undergo large deformations in response to an electric field and demonstrate reversible motion [1, 2]. Due to its potential applications in fields such as robotics, actuators, sensors, and artificial muscles, EAP has garnered considerable attention. EAP can be broadly classified into two types based on their mode of action or the corresponding mechanism in response to electrical stimulation: ionic EAPs [3,4,5] and electronic EAPs [6,7,8]. Dielectric Elastomer (DE) is an electronically based EAP that consists of an elastic dielectric layer with electrode layers on both sides, resembling an elastic and flexible capacitor. They are soft and stretchable capacitors and can be made into different shapes. When an external force is applied to a DES, it deforms, causing the capacitance value to change [9,10,11].

In recent years, flexible capacitive sensors have received extensive attention, and have been gradually applied in the fields of medical detection, soft robots, electronic skin, and so on. Flexible capacitive sensors can be divided into three categories according to different working principles: piezoelectric [12, 13], piezoresistive [14, 15], capacitive [16, 17]. Flexible capacitive sensors are more suitable for making wearable electronic products due to their advantages of simple structure, low power consumption and low hysteresis.

Composition of flexible capacitive sensors

Flexible capacitive sensors are generally composed of (1) conductive electrodes; (2) a flexible dielectric layer; and (3) occasionally including encapsulation materials. The conductive electrode is an important part of the flexible sensor, and the electrode material should not only have good conductivity, but also need to have chemical stability and stretchability. At present, Ag, Silver nanowires (AgNWs), Au, graphene, etc. are often used as electrode materials, which are made into flexible capacitive sensors with the relevant parameters shown in Table 1:

Table 1 Sensitivity and response time of flexible capacitive pressure sensors with different electrodes

Flexible dielectric layer is equally important for flexible capacitive sensors. Currently, researchers often make films of materials such as polydimethylsiloxane (PDMS) [18, 19], polyurethane elastomer (TPU) [20], polyethylene terephthalate (PET) [21] and polyvinyl alcohol (PVA) [23, 24] to act as dielectric layers for flexible capacitive sensors. Among them, PDMS is widely used in sensors due to its excellent elasticity, thermal and chemical stability.

Flexible capacitive sensors working principle

Flexible capacitive sensors are based on the principle of parallel plate capacitors, which can convert mechanical deformation into changes in sensor capacitance, as shown in Fig. 1:

Fig. 1

Operating principle of capacitive flexible sensors

Highly conductive flexible electrodes are coated on both sides of the dielectric elastomer material to form an “electrode-dielectric-electrode” sandwich structure, and the theoretical capacitance of this structure is given in Eq. (1):

$$C=\frac{{{\varepsilon _0}{\varepsilon _r}{\text{A}}}}{{{{\text{d}}_0}}}=\frac{{{\varepsilon _0}{\varepsilon _r}{A^2}}}{{\text{V}}}$$

(1)

where ε_r represents the relative dielectric constant of the DE material, ε₀ represents the vacuum dielectric constant (its value is 8.854*10^-12 F/m), d₀ represents the thickness of the dielectric elastomer layer, A represents the effective area of the sandwich structure, and V represents the volume of the sandwich structure. From the equation, it can be seen that the capacitance value of the sensor is affected by three factors: εr, A, and d₀. When the structure receives an externally applied force, its effective area increases and its thickness decreases, resulting in an increase in capacitance; when the external force is withdrawn, the effective area decreases, the thickness increases, and the capacitance returns to its original value. This also gives a clear direction to optimize the design of the sensor.

Key parameters of flexible capacitive sensors

An excellent flexible capacitive sensor needs to have excellent sensing characteristics, such as high sensitivity, wide response range, high resolution, and good fatigue characteristics, etc., among which sensitivity is one of the most concerned parameters in flexible wearable devices. The sensitivity of a parallel plate capacitor is given in (2):

$$S=\frac{{\Delta C/{C_0}}}{{\Delta P}}$$

(2)

where S represents the sensitivity of the flexible capacitive sensors, ΔC is the relative change in its capacitance, C₀ is the initial capacitance when no pressure is applied, and ΔP is the change in pressure applied to the sensor. From the equation, it can be seen that in order to improve the sensitivity of the sensor, the relative change in capacitance needs to be boosted as much as possible while keeping the applied pressure constant. In order to enhance the sensitivity of flexible capacitive sensors, a great deal of research has been done, in general there are several options: (1) Constructing the microstructure of the dielectric layer. Bao [25], firstly used a silica mold to prepare a PDMS dielectric layer with a pyramidal microstructure, and the sensitivity of the sensors prepared with the microstructure-containing PDMS dielectric layer could be up to 0.55 kPa^-1. later on Luo [23] designed a dielectric layer with inclined microstructure, and its sensitivity was 0.42 kPa^-1 in the low pressure range of 0–1 kPa. (2) Composite dielectrics, people add a certain amount of conductive filler into the elastic dielectric material to produce composite dielectrics, the conductive filler usually includes carbon nanotubes, carbon black, graphene and other carbon materials, and metal particles, etc. Liu [26] and others added Ag particles to the PDMS material to produce a high sensitivity sensor of 101.5%. Chen [27] add Zinc Oxide Nanowire to PMMA solution and uniformly coated on the electrode surface to obtain a composite dielectric layer, and the sensitivity of their fabricated sensor was 9.95 kPa^-1, which was 23 times higher than that of the pure PMMA dielectric layer sensor (0.43 kPa^-1). Resolution is likewise one of the most important indicators for evaluating the excellence of a sensor. The resolution of a sensor is the smallest resolvable amount that the sensor can measure and represent a change in the input. It represents the smallest distinguishable measurement that the sensor can provide within the measurement range. It is strongly influenced by the noise of the sensor.

Fig. 2

(a) Demonstrates that the stacked sensors have a smaller area for the same capacitance. (b) Demonstrates that the stacked sensors have a larger value of capacitance change for the same strain

Capacitive flexible sensors are generally very small in initial capacitance due to their geometry. Not only does this result in a high output impedance, but the “parasitic capacitance” generated around the sensor has a significant effect on the sensor itself. Parasitic capacitance is the capacitance formed between electronic components in a circuit or between circuit modules due to their proximity to each other. In order to eliminate this effect, various means have to be used to increase the initial capacitance of the sensor. The usual ways to increase the initial capacitance of a sensor are to reduce the thickness of the sensor and to increase the area of the sensor based on Eq. (1). However, a sensor that is too thin will result in an unstable sensor that is easily damaged and poorly fabricated. Simply increasing the area of the sensor cannot be applied to the wearable field.

So a new stacking method to stack multiple unit sensors is proposed in this article. In this method, sensors with larger initial capacitance can be fabricated with limited area (Fig. 2. (a)). Moreover, the sensor after stacking will have a larger capacitance change value than a single-layer sensor at the same strain. That is, it can obtain a higher output for the same amount of input. This enables it to sense smaller strain values. This not only improves the sensitivity of the sensor but also improves the resolution of the sensor (Fig. 2. (b)). Finally, by stacking the layers, the initial capacitance of the sensor increased and then the interference of the external environment on the sensor reduced, which makes the sensor more stable.

Printing process for flexible electrodes

There is a wide range of technologies available for flexible electrode printing, each with its own advantages as well as disadvantages. The commonly used techniques are inkjet printing [28,29,30], aerosol spray printing [31,32,33], gravure printing [34, 35], screen printing [36,37,38], etc. Each technique has its own advantages: inkjet printing technology deposits small droplets of conductive ink onto the substrate through the use of a computer-controlled inkjet print head, which has high precision and resolution, as well as fast printing speed, and is commonly used to produce complex electrode patterns, Zhang et al. [39]used inkjet printing to prepare stretchable one-dimensional fibrous electronics on small and large curvature fiber surfaces, which allowed printing of fibers with diameters as low as 500 μm, a large curvature of 400 m^-1, and a minimum print line width of 133 μm; Aerosol jet printing is a digital printing technique that uses a concentrated airflow to deposit small droplets of material onto a substrate, which does not need to be in Direct contact with the substrate is not required, allowing printing on irregular surfaces with high resolution and accuracy. Screen printing is a printing method in which the ink is transferred to the substrate through patterned mesh holes by squeezing with a squeegee during printing to form the same pattern as on the screen. Currently, screen printing has also been widely used in the printing of sensors with flexible design and small size, overcoming the limitations of traditional electrodes and satisfying high repeatability and reproducibility.

Fabrication of stacked sensors

Currently, there are not many reports on the fabrication of flexible capacitive sensors with larger initial capacitance within a limited geometry using the stacking technique. Huang et al. [40] designed and fabricated multistage microstructures based on polyvinylidene fluoride/reduced graphene oxide (PVDF/rGO) multilayer membranes in order to obtain flexible sensors with high linearity. This structure consists of a superposition of three consecutive microstructured membranes with different roughness. The flexible sensor has a collar temperature of 0.18kPa^-1 and a wide linear range of 11Kpa. Yang et al. [41] used PI films as electrodes to prepare flexible sensors by printing porous PDMS media layers by 3D printing. They designed different stacking methods to arrange the dielectric layers in different shapes. Finally, two copper-coated PI films were adhered to its two sides to construct the capacitive sensor. The sensitivity of this stacked sensor can reach 1.23 kPa^-1. Giulia Baldini et al. [42] produced stacked sensors using inkjet printing and spin coating. The sensitivity ranges corresponding to single capacitors, two-stacked capacitors and three-stacked sensors fabricated were 4.7 per cent, 10.4 per cent and 32.4 per cent, respectively. Although researchers have studied stacked sensors to varying degrees. However, the way each sensor unit is connected and the stability during the stacking process could be improved. Most researchers usually directly laminate conductive materials on the outermost sides of the sensors. This way the electrode part is not only easy to fall off, but also the connection is not stable enough. To solve this problem, a new approach has been proposed. In the process of stacking, two flexible electrical conductors of the same material as the electrode layer are formed. The two flexible electrical conductors are embedded directly inside the sensor in the form of " columns “. Two " columns " run vertically through the sensors, thus connecting the individual sensor units. With this stacking, the flexible electrical leads are integrated inside the sensor.

In this work, a method for preparing high-performance flexible capacitive sensors by stacking layers was presented. Dielectric elastomer films with a thickness of 110 μm were fabricated using a calender. The electrode layer patterns used to connect each dielectric elastomer film were then designed. The dielectric elastomer films and electrode materials were laminated together by screen printing technique. Flexible capacitive sensors with 12 layers of dielectric elastomer films were finally fabricated.

The effective strain area of the flexible sensor prepared by the stacking process was 100*40 mm. The thickness varies depending on the number of effective DE layers. The thickness of a sensor having 12 effective dielectric layers is about 2.2 mm. the thickness of a sensor having 4 effective dielectric layers is about 0.7 mm. The initial capacitance value of the sensor with 12 effective dielectric layers is 10.2 nF. It can sense deformation at 1% strain. The 4-layer effective dielectric layer sensor needs to reach 2.2% strain to be sensed. As the number of stacked layers increases, so does the sensitivity of the flexible sensor. Flexible sensors with effective number of dielectric layers of 1, 4 and 12 have sensitivities of 0.51, 0.73 and 1.09, respectively. Flexible sensors with 12 effective dielectric layers maintain excellent stability under 10,000 tensile cycles. This work provides a new idea for the preparation of high performance flexible capacitive sensors.

Experiment

Materials

The following materials are used to prepare dielectric elastomer films. Methyl vinyl silicone rubber(PMVS), model 110-0. This is because it has a high modulus of elasticity. Silicon dioxide (SiO₂), model HB-132. The purpose is to fill the silicone rubber, so that its density increases, and improve the hardness and tensile degree of silicone rubber. Titanium dioxide(TiO₂). Dicumyl peroxide (DCP). It can be used as a vulcanising agent for polymer materials.

The following materials are used to make electrode materials. Silicone oil was obtained from Shin-Etsu Chemical Industry Co., Ltd. in Japan. Silicone oil acts as a binder, effectively bonding the carbon black particles together to form a strong mixture. Conductive carbon black was purchased from Shishio Corporation, Ltd. in Japan. Conductive carbon black has high electrical conductivity. It is suitable for the production of conductive electrodes. Ethyl orthosilicate (T110596-500) was obtained from Aladdin Bio-Chemistry Science & Technology Co., Ltd. in Shanghai. It creates a hard coating and protection. Dibutyl tin dilaurate (D100274-100) was obtained from Aladdin Bio-Chemistry Science & Technology Co.

Experimental equipment

The equipment designed for the experiment is shown in Table 2:

Table 2 Equipment used in the preparation of dielectric elastomer film

Preparation of dielectric elastomer silica gel

First of all, the roll spacing of the calender was adjusted thinner (about 0.2 mm), and a baffle plate with a width of about 20 cm was used. Put 10 g of silica and 2 g of silicone rubber into the calender to start the mixing, and then add 0.5 g of TiO₂ and DCP. Mixing for more than 20 min to obtain the silicone for the preparation of dielectric elastomer film.

Preparation of dielectric layer films

In order to obtain sensors with higher initial capacitance, it is necessary to reduce the thickness of the dielectric layer between the two electrodes, so it is required to make the dielectric layer film as thin as possible. In traditional ways, plate vulcanizing machine is used to make dielectric elastomer film, but the thickness can only reach about 200 μm, and the thickness of the resulting film is not uniform. If a dielectric layer film is made in this way, the initial capacitance of the sensor after stacking decreases. And due to the non-uniform thickness between the layers, the resolution of the sensor is severely reduced, and the sensitivity also decreases. At this point, the calender is a better choice. Calenders have been used to make electrodes for lithium-ion batteries [43], which can compact the electrodes by controlling the calendering parameters, and can increase the bulk energy density of lithium-ion batteries. Thus, we innovatively used calenders to make dielectric layer films. The physical drawing of the calender is shown in Fig. 3:

Fig. 3

Calendering machine physical picture

Dielectric layer films are prepared by first calendering the silica material into a thin film and then vulcanising it at high temperature. The temperature of calendering is set to room temperature (18° to 25°). The calender pressure is set at 7 MPa and the calender speed is set at 1 m/min. The specific process was shown in Fig. 4:

Fig. 4

Process of preparing DE film by secondary calendaring

• 1) First of all, the roller gap between the two rollers of the calender was adjusted to 330 μm, and the silica gel material prepared as mentioned in 2.3 was kneaded into strips (about 10 g), and fed into the entrance of the calender along the longitudinal direction.

• 2) Once the silicone material had passed through the calender, the desired silicone film was obtained. By cutting the film along the dotted line in the diagram, it could be observed that the middle part of the silicone film is slightly thicker than the edges (d1 > d2). This phenomenon was probably due to the fact that during the calendering process the silicone material overflows from both sides, resulting in a lack of material compactness at the edges. Therefore, the thickness at the edges of the film was slightly lower than the thickness in the centre.

• 3) In order to solve the above problems, this paper innovatively put the film made by primary calendering into the calender again along the transverse direction. After the second calendering process, the distribution of the silicone material could be improved to obtain a silicone film with uniform thickness.

• 4) The silicone film obtained from the second calendering was put into the plate vulcanizing machine for vulcanization, and the desired DE film could be obtained.

The length and width of the DE film made by the above method were 300*300 mm, the thickness was about 110 μm, and the thickness difference between the middle and both sides of the film was not more than plus or minus 10 μm.

Preparation of stacked flexible capacitive sensors

In this paper, the pattern of the electrode layer was designed and the electrodes were brushed onto a dielectric elastomer film by screen-printing technique to make a sensor unit. Then multiple sensor units were laminated together to finally make a stacked sensor. The whole process is done on a small screen printing machine. The picture of the screen printing machine is shown in Fig. 5:

Fig. 5

Screen printing machine physical picture

This small screen printer is a four-colour, four-station design. That is to say, it can print electrode material in two stations and filler material in two stations. This helps to improve the stacking efficiency. When stacking is performed, the electrode layer material and the filler material are done in separate stations. The specific stacking process is shown below.

Each sensor unit of the stack was connected in parallel under the design. At this point the capacitance value of the stacked sensors was each sensor unit capacitance in parallel, which could achieve the effect of increasing the initial capacitance. The capacitance change under the same strain would be higher, thus improving the resolution of the sensor. The resistance of the stacked sensor was the resistance of each sensor unit in parallel, the resistance was getting smaller and smaller, reducing the impact of the measurement due to resistance, thus improving the sensitivity of the stacked sensor. The specific stacking process was shown in Fig. 6:

Fig. 6

Preparation process of laminated flexible capacitive pressure sensors

Steps 1, 2, and 3 of Fig. 6 were the fabrication of the sensor unit, the stacking of the sensor unit, and the fabrication of the stacked sensor, respectively. Figure 6 Step1 showed the fabrication process of the unit sensor. Firstly, holes were punched in the DE film. This allowed the electrode material to leak down to form “Electrode Columns” when the electrode material was printed. Two types of screen-printed plates with electrode patterns and filler patterns were then placed on two DE films. Printing was carried out after placing the electrode material and filler material respectively. The red part of the pattern in the figure was the electrode layer and the yellow part was the filler layer. The part circled by the black dotted line was used to form the electrode post, which was connected to the next unit sensor. The two sides of the printed material were laminated vertically against each other, so that the printed electrode part and the filling part complemented each other. At this point, the basic unit of the sensor could be obtained. Then take out the two sensor units made in step one. Replace the screen printed plate with a pattern that was a mirror image of the one in step 1. If the sensor unit made in step 1 is positive, the one printed after replacing the screen printing plate at this time was negative. Repeat step 1 to print a new pattern on the sensor unit made in step 1. The two sides of the printed material were then vertically laminated. At this point, a “positive-negative-positive” three-layer sensor structure could be obtained. The two positive layers shared the same negative layer. The printing process of the negative electrode layer could be reduced, simplifying the preparation process and reducing material loss. Finally, step 2 was repeated. By continuing to stack the three layers of sensors made in step two, a stacked flexible capacitive sensor could be made.

The thin thickness of the DE film (only about 110 μm) causes the film to wrinkle easily during the stacking process. This can lead directly to problems such as bubbles during the stacking process, or even failure to align parts of the electrode pattern. To solve this problem, an alignment scheme when stacking was proposed.

Fig. 7

Schematic diagram of electrode column of Stacked sensor

Figure 7(a) shows the specific steps of the alignment. First place the screen printed DE film on a perforated iron plate. Use a hole punch to make positioning holes around the film. The stacking process required two people to work together: two people held each end of the film and aligned the positioning holes with the positioning posts. Then the film was slowly lowered (Fig. 7 (b)). Any air bubbles that might appear during the stacking process were then pushed out by hand. This ensured that all air was removed from between the films during the stacking process. At the same time, it ensured that the electrode portion of the screen printing was better aligned.

Fig. 8

Schematic diagram of electrode column of Stacked sensor

Figure 8 showed the electrode columns and the connection diagram of each layer after multiple stacking and screen printing. As can be seen from the figure, the red electrode column was the positive post of the sensor, which was connected to the positive electrode layer, and the blue electrode column was the negative post of the sensor, which was connected to the negative electrode layer. The sensor was finally connected to the positive and negative electrodes by the electrode columns.

Results and discussion

In order to prepare high-performance flexible capacitive sensors, this paper used both methods of reducing the thickness of the dielectric layer and stacking the layers simultaneously. Reducing the thickness of the dielectric layer could enhance the capacitance value of each sensor unit. By stacking multiple sensor units in parallel after stacking, the initial capacitance of the sensor could be increased to improve the sensitivity and resolution of the sensor. Both reduction of dielectric layer thickness and stacking were discussed below.

Dielectric elastomer film thickness discussion

From Eq. (1), it could be seen that the smaller the value of the dielectric layer thickness, the larger the initial capacitance of the sensor. This allowed for a larger value of capacitance change for the same external stimulus to increase the resolution of the sensor. Due to the use of silicone material exists a certain degree of elasticity, if the plate vulcanizing machine pressure vulcanization was used, the production of silicone film thickness could only reach an average of 200 μm or so, and its thickness uniformity could not be guaranteed, usually the thickness in the middle and the edge of the film varies more than 15 μm. So in this paper, calender was used to prepare silica gel film. A type I double roller calender was used for this experiment. Since the width of the silicone film to be prepared was greater than 300 mm, the roll width of the calender was selected to be 500 mm to ensure sufficient working width.

Fig. 9

(a) Thin Film Thickness Uniformity Measurement Method. (b) Film thickness uniformity test results after calendering in one pass. (c) Film thickness uniformity test results after secondary calendaring

When the relevant parameters of the calender were adjusted, the preparation of the silica gel film begins. After vulcanizing the silicone film made by calendering method at high temperature and high pressure, measure the thickness of the made silicone film point by point according to the measurement method shown in Fig. 9(a). The result was shown in Fig. 9(b), the thickness of the silica gel film at the center reaches the expectation, but the edge was too thin, and the thickness difference between the edge and the center was more than 10 μm. This might lead to uneven thickness of the sensor after stacking and affect the resolution and sensitivity of the sensor. The probable reason for this was that the silicone material overflows from both sides of the barrier film during calendering, resulting in insufficient densification at the edges, so that after vulcanization, a decrease in thickness at the edges occurs. In order to solve this problem, we put the silicone film made by primary calendering transversely back into the entrance of the calender for secondary calendering, as shown in Step2 in Fig. 4. In this way, the problem of insufficient density of silicone material due to overflow at the edges could be improved. As shown in Fig. 9(c), the thickness difference between the edge and the middle of the vulcanized silica gel film is within 5 μm.

Sensor screen printing conditions and stacking analysis

In this paper, screen printing technique was used to print the electrode layer of the sensor. The principle of the screen printing technique was to utilize the mesh portion with a pattern that transmits through the material and the non-mesh portion without a pattern that didn’t transmits through the material for printing. Then the size of the mesh of the screen printing plate determined the permeability of the material. Figure 10 showed the printing of an electrode layer on a screen printing plate with different mesh sizes:

Fig. 10

(a)-(c) show the surface morphology of the electrodes after printing with 40, 60 and 80 mesh screen printing plates, respectively

The mesh size of a screen printing plate indicates the number of mesh holes per square centimeter of area, and Fig. 10(a) -(c) showed the surface morphology of electrode materials after printing on 40, 60 and 80 mesh screen printing plates, respectively. In order to verify which of the three mesh screen printing plates was more suitable for printing sensor electrode material, a layer of electrodes on a dielectric elastomer film using 40, 60, and 80 mesh screen printing plates was printed, respectively. And the surface morphology of the electrode layer after screen printing was measured, as shown in Fig. 11(a) (b) (c):

Fig. 11

(a)-(c) shows the surface morphology characterization and cross-section contour lines after printing electrodes on different screen printed plates

As can be seen from Fig. 11: the mesh number of 40 and 80 printed electrode layer had obvious raised at the edges. This might be due to the fact that the material does not follow the mesh all the way through the DE film during printing. The residual material on the mesh leaves traces as the screen printing plate was lifted up, resulting in bumps at the edges of the mesh. When the mesh size was 60, this situation could be greatly improved, and its overall appearance was much more uniform than the other two. And then we characterized the contour lines of different mesh printed electrode layers. It could be clearly seen that when the mesh number of the screen-printed plate is 60, contour lines were clearly uniform and regular. To summarize the above, screen printing plate with a mesh number of 60 were used to print the electrode layer.

After selecting the appropriate mesh size, follow the method in Fig. 6 for sensor stacking. The cross section of the stacked multilayer sensor was scanned under an electron microscope and the resulting image was shown in Fig. 12(a) (b):

Fig. 12

(a) Cross-section of the sensor after stacking. (b) Cross-sectional view of the amplified post-stack sensor

Figure 12(a) showed the cross-section of a sensor with 14 dielectric layers stacked up with 12 effective dielectric layers. The white part of the figure was the dielectric layer and the black part was the electrode layer. Figure 12(b) was a local part obtained by enlarging the left part of the figure, which showed that the thickness of the dielectric layer of the stacked sensor was about 110 μm, and the thickness of the electrode layer was about 60 μm. Its thickness was uniform, which provided a reliable help for the stability of the sensor.

Sensor performance testing and optimization

A batch of sensor samples with different dielectric layers were fabricated following the steps shown in Fig. 6. After testing, the average initial capacitance of the single-layer sensor was about 0.882nF, while the average initial capacitance of the 12-layer sensor was able to reach 10.2nF (Fig. 13a). Moreover, with the increase of the number of dielectric layers, the capacitance value increased approximately linearly. It was also proved that the sensor was connected in parallel and its capacitance was the sum of each layer’s capacitance. Then, 4 and 12 layers of sensors were fabricated using the same method. The 12-layer sensors were placed on a universal tensile machine for tensile experiments. The capacitance value increased steadily as the stretching length increased (Fig. 13b). The capacitance value of the 12-layer sensor increased from 10.2 nF to 21.1 nF when the amount of deformation reached 100%. This not only indicated that the sensors had excellent tensile properties, but also a large amount of capacitance change.

Fig. 13(c) illustrated the resolution of the sensor in this research. It could be clearly seen that the capacitance of the 12-layer sensor started to change at 1% strain. The capacitance of the 4-layer sensor did not change until 2.2% strain. This could show that the resolution of our sensor could be increased by stacking the layers.

Fig. 13

(a) Variation of capacitance for sensors with different number of stacked layers. (b) Capacitance curves for 12-layer sensors with different morphology variables. (c) Capacitance resolution curve before and after lamination. (d) Sensitivity of sensors with different number of stacked layers. (e) Stability test under 10,000 tensile cycles. (f) Capacitance change values at different pressures

The sensitivity of the sensor is one of the indicators to evaluate the sensor well. The sensitivity GF of the capacitive strain transducer is shown in (3).

$$GF=\frac{{\Delta C/{C_0}}}{{\Delta \varepsilon }}$$

(3)

where GF is the strain gauge factor of the strain sensor, ∆C is the change in capacitance, C₀ is the initial capacitance at the time of invariant change, and ε is the strain of the sensor. The value of GF for 12 layer sensor at 100% strain is 1.09 but for single layer and 4 layer sensors the value of GF is only 0.51 and 0.73. So it can be shown that the value of GF of the sensors can be increased by stacking, that is, the sensitivity of the capacitive strain sensors can be increased (Fig. 13d). This was also higher than the sensitivities reported for capacitive sensors in the past (Table 3):

Table 3 Comparison of sensitivity of recently reported flexible capacitive sensors

This validates the previously mentioned idea. And then the 12-layer sensor was cyclically stretched 10,000 times at 100% strain. Although the capacitance of the sensor decreased a bit after 10,000 stretching cycles compared to the initial state (Fig. 13e), the decrease was very low, which still showed good stability. Finally, we applied a force of 0 ~ 5 N on the single and double layer sensors. Observing their capacitance changed, we could find that: under a tiny force, the capacitance of the two sensors could still change, and their capacitance increased slowly and regularly with the increase of loading pressure (Fig. 13f).

Sensor performance testing and optimization

From the above analysis, flexible stacked sensors have good performance and broad application scenarios in the wearable field. It is gradually showing great potential in the detection and control of medical devices.

Fig. 14

(a) Sensor attached to the elbow to detect elbow movement. (b) Sensors attached to the knee to detect motion at the knee

In particular, it has shown excellent performance in human joint motion detection. The sensors were integrated at the elbow and knee joints. The bending response curve could clearly depict the relationship between the angle of joint bending and the change of capacitance（Fig. 14）. The high resolution and sensitivity of this sensor allowed even subtle joint movements to be accurately captured, providing physicians with more detailed data for evaluating a patient’s motor function. Overall, the stacked sensors showed the great potential and value for medical applications. With the continuous development of technology, there is no doubt that such sensors will play an increasingly important role in the future medical field.

Conclusions

In conclusion, a method to fabricate capacitive sensors with high sensitivity and high resolution was proposed. Firstly, dielectric elastomer films were prepared using a calender. The “secondary calendering” method was used to achieve a thinner and more uniform film thickness (around 110 μm). Then the shape of the electrode layer was designed. The electrode material was prepared as a sensor unit by printing on a dielectric elastomer film using screen printing method. Multiple sensor units were connected in parallel by “electrode pillars” formed during the printing process, resulting in a stacked sensor (12 layers).It not only has high initial capacitance(10.02nF) but also good resolution(capable of sensing 1% strain) and sensitivity(1.09). This could facilitate the measurement of more subtle movements of the human body. And it showed excellent stability under 10,000 stretching cycles. There is no doubt that the method of improving sensor sensitivity by stacking layers will be widely used in the future. And such flexible sensors have a wide range of applications in wearable medicine and intelligent robotics.