A flexible tactile-feedback touch screen using transparent ferroelectric polymer film vibrators

In this section, we propose a film vibrator to provide haptic sensation to a flexible, tactile-feedback touch screen, whose schematic illustration and cross-sectional design are shown in figures 1(a) and (b), respectively. Capacitive touch sensors are located underneath the cover protection layer. Therefore, when a user's fingertips come into direct contact with the cover layer, the touch sensors detect the contact of the user's fingertips. A film vibrator can be placed underneath the touch sensors as shown in figure 1(b); such a film vibrator is composed of an upper transparent electrode, ferroelectric polymer film, and a lower transparent electrode. Therefore, the cover layer, touch sensors, upper electrode, ferroelectric polymer film, and lower electrode form a multilayered structure. Since all of the components of the multilayered structure are transparent and do not hinder light transmittance, the flexible display panel can be placed under the multilayered structure. When an alternating electric field is applied to the ferroelectric polymer film through the upper and lower electrodes, the ferroelectric polymer film produces repeated contraction and expansion, which are converted to a bending vibration of the multilayered structure; in turn, human fingertips can sense the bending vibration. Therefore, the touch sensors and the film vibrator may incorporate the content displayed in the flexible display panel to provide a realistic user experience.

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It is worth noting that transparent electrodes have higher electrical resistance than metal electrodes, so when the size of the transparent electrodes increases, the voltage drop within transparent electrodes becomes significant. To reduce the resistance of the transparent electrodes, the thickness of the transparent electrodes must increase. However, such an increase would cause a decrease in the transparency and performance of the film vibrator. In addition, when voltage is applied to the transparent upper and lower electrodes, a minute amount of current leaks through the ferroelectric polymer film. This results in the ferroelectric polymer film having both capacitance and resistance, like a dielectric material. Therefore, in order to apply a uniform electric field to the ferroelectric polymer film, high-electric-conductivity metal electrodes must be placed as distribution electrodes at the edges of the display area, as shown in figure 1(b). Upper and lower metal electrodes, as the distribution electrodes, are located on opposite sides of the display device, and thus the sum of the distances from any point on the actuator to the upper and lower metal electrodes are equal. Therefore, the voltage drop produced at the transparent electrodes is the same everywhere, making the magnitude of the electric field on the ferroelectric polymer film equal everywhere, and making the actuation performance consistent.

In this section, the principle behind the deformation of the transparent ferroelectric polymer film vibrator shown in figure 1(b) is examined and its deflection size is estimated. When voltage is applied to the upper and lower transparent electrodes, the relaxor ferroelectric polymer contracts in the thickness direction and expands in the length direction. Here, a longitudinal strain, $\varepsilon (E)$, in the relaxor ferroelectric polymer layer sandwiched between two electrodes is a monotonically increasing function of the applied electric field, $E$. This longitudinal strain can be converted into bending deformation by using bimorph structures composed of an active layer and an inactive layer. The upper part of the flexible, tactile-feedback touch screen in figure 1(b) consists of a cover, capacitive touch sensors, upper transparent electrode, ferroelectric polymer film, and lower transparent electrode; it is considered to be a bimorph structure with an active layer (ferroelectric polymer film and electrodes) and an inactive layer (cover and capacitive touch sensors). Therefore, a composite beam analysis of the flexible, tactile-feedback touch screen shown in figure 2 is conducted here, in which multilayered, ferroelectric polymer actuators are considered to be the film vibrator. If there are N ferroelectric polymer layers for actuation, the multilayered film vibrator is composed of (2N + 3) layers, as shown in figure 2. To estimate the bending deformation caused by the longitudinal strain, $\varepsilon (E)$, we used the so-called 'cut and paste' technique, which is a well-known procedure for calculating the bending deformation of composite beams due to eigenstrains, e.g., thermal strain, as illustrated in Ref. [32]. The $i{\mbox{th}}$ ferroelectric polymer layer would undergo the longitudinal strain, $\varepsilon ({{E}_{i}})$, under the electric field ${{E}_{i}}=\Delta {{V}_{i}}/{{h}_{2i}}$, if the $i{\mbox{th}}$ ferroelectric layer were free of any constraint. In order to recover the original length of the $i{\mbox{th}}$ ferroelectric layer, the fictitious stress ${{\sigma }_{i}}={{Y}_{FP}}\varepsilon \left( \Delta {{V}_{i}}/{{h}_{2i}} \right)$ needs to be applied at both ends of the $i{\mbox{th}}$ ferroelectric layer. The fictitious bending moment, $M$, with respect to the neutral axis of the composite beam, can also be calculated with these fictitious stresses. Therefore, the bending moment, $M$, per unit length caused by the longitudinal strain of ferroelectric polymer layers under the applied electric field, is given as [33]

$$\begin{eqnarray}&&M={{Y}_{FP}}\mathop \sum \limits_{i=1}^{N} \varepsilon \left( \frac{\Delta {{V}_{i}}}{{{h}_{2i}}} \right){{h}_{2i}}\left( {{\eta }_{2i}}-\eta \right),\end{eqnarray} \tag{ 1 }$$

where ${{Y}_{FP}}$ is Young's modulus of ferroelectric polymer layers, ${{h}_{i}}$ is the thickness of the $i{\mbox{th}}$ layer, and $\Delta {{V}_{i}}$ represents the voltage difference between the $i{\mbox{th}}$ and $(i+1){\mbox{th}}$ electrodes. The strain response of the relaxor ferroelectric polymers, such as P(VDF-TrFE-CFE) and P(VDF-TrFE-CTFE), was measured as a function of the electric field by Zhang et al [26]. As a rough approximation, the longitudinal strain, $\varepsilon (E)$, can be assumed to be linearly proportional to the applied electric field, ${{E}_{i}}=\Delta {{V}_{i}}/{{h}_{2i}}$—that is, $\varepsilon (E)={{\varepsilon }_{0}}{{E}_{i}}={{\varepsilon }_{0}}\Delta {{V}_{i}}/{{h}_{2i}}$, where ${{\varepsilon }_{0}}=\;1.93\times {{10}^{-4}}\mu {\mbox{m}}/{\mbox{V}}$ [26]. If needed, the experimental results can be curve-fitted. In our study, the longitudinal strain is assumed to be a special function of the electric field in section 4.1, in order to take the nonlinear strain response into account in the range of low electric field. The positions of the neutral axis of the $i{\mbox{th}}$ layer and the composite beam measured along the y axis, as shown in figure 2, are respectively given as

$$\begin{eqnarray}&&{{\eta }_{i}}=\mathop \sum \limits_{k=1}^{i} {{h}_{k}}-\frac{{{h}_{i}}}{2},\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\eta =\frac{\left( \mathop \sum \limits_{i=1}^{2N+3} {{Y}_{i}}{{h}_{i}}{{\eta }_{i}} \right)}{\left( \mathop \sum \limits_{j=1}^{2N+3} {{Y}_{j}}{{h}_{j}} \right)},\end{eqnarray} \tag{ 3 }$$

where ${{Y}_{i}}$ is Young's modulus of the $i{\mbox{th}}$ layer. Then, a composite beam subject to the moment given in equation (1) may be in a state of pure bending deformation, for which the maximum deflection, $\delta$, can be expressed as [33]

$$\begin{eqnarray}&&\delta =\frac{Ml_{eff}^{2}}{8{{(YI)}_{eff}}}.\end{eqnarray} \tag{ 4 }$$

Here, ${{(YI)}_{eff}}$ is the effective flexural modulus per unit length of the film vibrator, expressed as

$$\begin{eqnarray}&&{{(YI)}_{eff}}=\mathop \sum \limits_{i=1}^{2N+3} {{Y}_{i}}{{h}_{i}}\left[ \frac{h_{i}^{2}}{12}+{{\left( {{\eta }_{i}}-\eta \right)}^{2}} \right].\end{eqnarray} \tag{ 5 }$$

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Also, ${{l}_{eff}}$ is the effective length of the composite beam, which varies according to the boundary conditions and the resonance mode. Equation (4) can be used to calculate the maximum deflection of the film vibrator using static composite beam analysis. To simplify the calculation, it is assumed that the thicknesses of all the ferroelectric polymer layers are equal, i.e. ${{h}_{2i}}={{h}_{FP}}\;(i=1,2,\cdots ,N)$, and the applied voltage differences are the same, i.e. $\Delta {{V}_{i}}=\Delta V\;(i=1,2,\cdots ,N)$. Then, the following equation can be obtained by substituting equation (1) into equation (4):

$$\begin{eqnarray}&&\delta =\varepsilon \left( \frac{\Delta V}{{{h}_{FP}}} \right)l_{eff}^{2}\left[ \frac{{{Y}_{FP}}{{h}_{FP}}\mathop \sum \limits_{i=1}^{N} \left( {{\eta }_{2i}}-\eta \right)}{8{{(YI)}_{eff}}} \right].\end{eqnarray} \tag{ 6 }$$

Equation (6) predicts the deflection magnitude generated by the film vibrator and can be used in the design of the film vibrator, since the effects of various design parameters on the deflection can be identified from equation (6).

In order to provide excellent haptic sensation to the user by means of the vibration generated by the transparent ferroelectric polymer film vibrator designed in previous sections, this section discusses the vibration design of flexible, tactile-feedback touch screens. When periodic voltage is applied to a ferroelectric polymer film, periodic lateral vibration is generated by the film vibrator, which can provide tactile sensation. Resonance design is applied to maximize the lateral vibration of the film vibrator. In other words, the upper part of the flexible, tactile-feedback touch screen is designed to have its resonant frequency equal to the frequency at which human fingertips most effectively sense vibrations (150–250 Hz). When a driving voltage is applied at the resonant frequency, the vibration amplitude dramatically increases due to the resonance of the upper part of the flexible, tactile-feedback touch screen. This dramatic increase in the vibration amplitude provides excellent haptic sensation. The natural frequency of the composite beam, ${{\omega }_{n}}$, can be calculated by the following formula [34]:

$$\begin{eqnarray}&&{{\omega }_{n}}={{\left( {{\beta }_{n}}l \right)}^{2}}\sqrt{\frac{{{\left( YI \right)}_{eff}}}{{{\left( \rho h \right)}_{eff}}{{l}^{4}}}}.\end{eqnarray} \tag{ 7 }$$

Here, the effective mass per unit area of the composite beam, ${{(\rho h)}_{eff}}$, can be expressed as

$$\begin{eqnarray}&&{{(\rho h)}_{eff}}=\mathop \sum \limits_{i=1}^{2N+3} {{\rho }_{i}}{{h}_{i}},\end{eqnarray} \tag{ 8 }$$

where ${{\rho }_{i}}$ is the density of the $i{\mbox{th}}$ layer. Also, ${{\beta }_{n}}$ of equation (7) is the eigenvalue of the $n\;{\mbox{th}}$ vibration mode determined by the boundary condition. Therefore, the natural frequency calculated from equation (7) depends on the boundary condition, such as whether the film vibrator is simply supported or fixed on the edge of the flexible display panel. Thus, equation (7) and equation (6) predict the magnitude of the vibration generated by the film vibrator and determine the effects of various design parameters, which makes the equations valuable in the vibration design of the film vibrator. For example, the effective flexural modulus ${{(YI)}_{eff}}$ of the film vibrator, including the cover, has to be designed to be greater than the specific value for the reliability of the device. However, as seen in equation (6), if ${{(YI)}_{eff}}$ becomes too large, the deflection value, which is inversely proportional to ${{(YI)}_{eff}}$, decreases, resulting in the reduction of the haptic-feedback effect. Moreover, since the natural frequency is proportional to the square root of ${{(YI)}_{eff}}$, as seen in equation (7), it can be used when designing the resonant frequency to match the frequency range at which human fingertips most effectively sense vibrations (150–250 Hz). The application of the modal analysis presented in this section is explained in more detail in section 4.

Relaxor ferroelectric polymer P(VDF-TrFE-CTFE), in which mole fractions of VDF, TrFE, and CTFE monomers are 62.7, 29.6, and 7.7 percent, respectively, was synthesized at Piezotech S.A. in France [35]. Ten grams of P(VDF-TrFE-CTFE) polymer were dissolved in 90 g of methylisobutylketone and the solution was filtered with a polytetrafluoroethylene filter with 1.0 μm-sized pores. The filtered solution was kept at room temperature for 24 h to remove trapped microbubbles. To fabricate and handle P(VDF-TrFE-CTFE) films, the adhesion-mediated film-transfer technique developed by Choi et al [29] was used. To conduct this detailed procedure, the P(VDF-TrFE-CTFE) polymer solution is dispensed and applied onto a glass plate with a film applicator. The film applicator has a fixed gap thickness, so the solution is spread uniformly onto the glass plate. The solvent is evaporated from the solution, and a dry P(VDF-TrFE-CTFE) film is formed on the glass plate. A silicone elastomer film, acting as a support film, is laminated at room temperature on top of the dry P(VDF-TrFE-CTFE) film on the glass plate. To weaken the interfacial adhesion between the P(VDF-TrFE-CTFE) film and the glass plate by diffusion of water molecules along the interface, the P(VDF-TrFE-CTFE) film sandwiched between the support film and the glass plate is immersed in deionized water for two hours. The P(VDF-TrFE-CTFE) film and the support film are debonded from the glass plate in deionized water. The P(VDF-TrFE-CTFE) film on the support film is annealed at 115 °C for two hours to remove any remaining solvent and to increase crystallinity.

This section describes a method for patterning organic electrodes on a P(VDF-TrFE-CTFE) film. PEDOT:PSS (ORGACON IJ-1005, Agfa-Gevaert Group) was used as the conducting polymer. Since the P(VDF-TrFE-CTFE) film fabricated by the adhesion-mediated film-transfer technique is placed on a support film, PEDOT:PSS can be deposited onto the P(VDF-TrFE-CTFE) film. Dark-blue-colored PEDOT:PSS needs to be applied with minimum thickness in order to obtain high transparency. In this research, a digital ultrasonic generator (Sonaer Inc.) was used to excite a wide-spray atomizer nozzle (WS130K50S, Sonaer Inc.) at a frequency of 130 kHz, and PEDOT:PSS solution was sprayed as droplets with an average diameter of 11.8 μm (see figure 3(a)). Before the spray coating, the surface of the P(VDF-TrFE-CTFE) film was treated with O₂ plasma at 50 W for five minutes in order to enhance the adhesion of the PEDOT:PSS to the P(VDF-TrFE-CTFE) film. Also, to pattern the PEDOT:PSS electrode, a shadow mask, as shown in figure 3(b), was fabricated and placed on the P(VDF-TrFE-CTFE) film. When the PEDOT:PSS solution was sprayed with the ultrasonic atomizer on the P(VDF-TrFE-CTFE) film covered with the shadow mask, a PEDOT:PSS electrode pattern was formed, as shown in figure 3(c).

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In this section, we explore how the flexible, tactile-feedback touch screen shown in figure 1(b) was integrated with the parts prepared in previous sections. A 188 μm-thick polyethylene terephthalate (PET) film covered with a thin ITO electrode was used as the cover film. Although figure 1(b) shows the capacitive touch sensors placed underneath the cover, capacitive touch sensors were not considered in this study since this research focused on the fabrication of the flexible, tactile-feedback film vibrator. The P(VDF-TrFE-CTFE) film atop a support film was first laminated at 110 °C onto the PET film cover with the ITO electrode; then, the support film was removed. Since the P(VDF-TrFE-CTFE) film undergoes partial melting depending on the micro-phases at about 110 °C (which is just below the melting temperature of P(VDF-TrFE-CTFE) film), the P(VDF-TrFE-CTFE) film and ITO coating adhere with appropriate adhesion strength. The organic electrode, PEDOT:PSS, was deposited onto the P(VDF-TrFE-CTFE) film/ITO/PET structure according to the procedure described in section 3.2. Here, the PEDOT:PSS electrode and ITO electrode were arranged so that their edges do not overlap, as shown in figure 1(b). Conducting tape was attached on exposed ITO and PEDOT:PSS surfaces to act as the upper and lower distribution electrodes, respectively. Finally, another PET film and color-printed paper were placed as a mock-up of the flexible display panel, as shown in figure 1(b). Figure 4 shows the flexible, tactile-feedback touch screen developed in this study.

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To investigate the vibration characteristics of the fabricated, flexible, tactile-feedback touch screen, the composite beam analysis explained in section 2.3 was performed. Figure 1(b) shows the schematic view of the cross section of the flexible, haptic-feedback touch screen. Here, the cover layer was a 188 μm-thick PET film; the capacitive touch sensor was not integrated, for manufacturing convenience. Also, the upper and lower electrodes used were ITO and PEDOT:PSS, respectively, and P(VDF-TrFE-CTFE) film was used as the ferroelectric polymer. The total dimensions were 85 mm × 60 mm and the dimensions of the actuation region were 65 mm × 40 mm. Table 1 shows the Young's modulus, density, and thickness of each material used in the fabrication of the flexible, haptic-feedback touch screen. Although vibration analysis may be necessary to optimize the flexible, haptic-feedback touch screen and to estimate its maximum deflection, the design parameters of the film vibrator can be qualitatively determined by the static deflection given in equation (6). First, the longitudinal strain, $\varepsilon (E)$, induced in the P(VDF-TrFE-CTFE) film under an applied electric field, $E$, is assumed to have the following mathematical form:

$$\begin{eqnarray}&&\varepsilon (E)=0.07\left[ 1-{{e}^{-E/100}} \right]-0.0008E{{e}^{-E/2.5}}.\end{eqnarray} \tag{ 9 }$$

It should be noted from equation (9) that $\varepsilon (0)=0$ and $\varepsilon (\infty )=0.07$, and the strain monotonically increases as the electric field increases. The longitudinal strain given in equation (9) can be considered an approximation of the measured strain response [26]; the unit of electric field is MV m⁻¹. It is worth noting that the second term of equation (9) was introduced to account for the reduction of the longitudinal strain response in the range of electric field, 0 ∼ 10 MV m⁻¹. Figure 5 shows the normalized deflection of the film vibrator as a function of the thickness of the P(VDF-TrFE-CTFE) film for the various applied voltages and number of P(VDF-TrFE-CTFE) films. It should be noted that as the thickness of the P(VDF-TrFE-CTFE) film, ${{h}_{FP}}$, decreases for a given voltage, the electric field applied to the P(VDF-TrFE-CTFE) film increases, but the force generated by the P(VDF-TrFE-CTFE) film decreases. As can be seen in figure 5, the compromise between the electric field and the force results in an optimal thickness of the P(VDF-TrFE-CTFE) film around ${{h}_{FP}}$ = 5 μm, for which the film vibrator produces maximum deflection. This trend can be changed if the longitudinal strain, $\varepsilon (E)$, has a function form different from equation (9). Unfortunately, the experimentally measured longitudinal strain, $\varepsilon (E)$, especially in the low electric field region of less than 10 V μm⁻¹, is not sufficient to determine a precise function form. However, it is certain from figure 5 that the optimal thickness of the P(VDF-TrFE-CTFE) film, which gives the maximum deflection, is between five and 15 micrometers.

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Meanwhile, the tactile-feedback touch screen developed in this study is transparent and flexible, making it suitable for application in future flexible-display devices, but one disadvantage may be that it requires a high driving voltage. It can be seen in figure 5 that the normalized deflection is almost linearly proportional to the applied voltage. When the driving voltage increases, the displacement and the vibration strength increase, but the high driving voltage may not be available in mobile electronic devices. To decrease the driving voltage, the thickness of the P(VDF-TrFE-CTFE) film must be decreased, but doing so makes it difficult to obtain the desired level of power. To overcome this obstacle, P(VDF-TrFE-CTFE) films need to be stacked to form multilayered film vibrators. Figure 5 also shows that when double layers of P(VDF-TrFE-CTFE) film are used as the film vibrator, the normalized deflection becomes almost double with the same voltage. Of course, it can be inferred that stacking more layers will proportionally increase the generated amplitude at the same voltage. Therefore, a multilayered structure is advantageous for producing vibrations of great amplitude at a low voltage.

The flexible, tactile-feedback film vibrator developed in this study was attached to a fixture, as shown in figure 6, and operated to measure its dynamic performance. A sinusoidal-waveform voltage was generated by an arbitrary waveform generator (Agilent, Model: 33210A). Then, the sinusoidal-waveform voltage was amplified by a high-voltage amplifier (Trek, Model: 623B). The vibration amplitude produced by the film vibrator was measured using a laser Doppler velocimetry, as shown in figure 6. Figure 7 shows the measured maximum vibration amplitude of the film vibrator as a function of frequency. Here, it was found that the resonance occurs at about 220 Hz, where the vibration amplitude dramatically increases. Calculating the resonant frequency using equation (7) gives ${{\omega }_{1}}$ = 177 Hz when the boundary condition is simply supported, and ${{\omega }_{1}}$ = 401 Hz when the boundary condition is fixed. This result shows that the boundary condition of the film vibrator supported by a fixture, as shown in figure 6, is close to the simply supported boundary condition. The resonance of the film vibrator at 220 Hz, as shown in figure 7, greatly enhances the user's haptic sensation, since human fingertips are most sensitive to vibration at frequencies between 150–250 Hz. Approximately 50 people tested the flexible, tactile-feedback touch screen and stated that the vibration it generated was strong enough for haptic sensation.

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In order to reduce the driving voltage of the flexible, tactile-feedback touch screen, a double-layered P(VDF-TrFE-CTFE) film vibrator was also fabricated. Figure 8 shows the measured maximum vibration amplitudes of the film vibrators fabricated with single P(VDF-TrFE-CTFE) films four μm and eight μm thick, and with double P(VDF-TrFE-CTFE) films four μm thick. The frequency of the applied voltage was 220 Hz for resonance, and the amplitudes were measured at the center of the film vibrator. First, the vibration amplitude of the film vibrator fabricated with the single, eight-μm-thick P(VDF-TrFE-CTFE) film was greater than that of film vibrator fabricated with the single, four-μm-thick P(VDF-TrFE-CTFE) film. This result agrees with the prediction from figure 5, in which an increase in the P(VDF-TrFE-CTFE) film's thickness leads to an increase in the deflection by a small margin, when the P(VDF-TrFE-CTFE) film's thickness is less than about 10 μm. More importantly, the vibration amplitude of the film vibrator fabricated with double P(VDF-TrFE-CTFE) films that are four μm thick is significantly greater than the vibration amplitudes in the other two cases. In other words, the single-layer film vibrator exhibited approximately 0.6 μm (${{h}_{FP}}$ = 4 μm) and 1.3 μm (${{h}_{FP}}$ = 8 μm) vibration amplitudes for 100 V, while the double-layered film vibrator showed a vibration amplitude of approximately 3.3 μm for 100 V. Therefore, stacking thin relaxor ferroelectric polymer films to construct a film vibrator provides an excellent solution for generating large vibration amplitude with reduced driving voltage.

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The flexible, tactile-feedback film vibrator fabricated in this study was shown to provide sufficient haptic sensation when the user's fingertips make physical contact with the device. Moreover, we discuss a method that makes full use of the developed film vibrator to provide various types of tactile feedback regarding the surface characteristics of objects, such as surface roughness, minute patterns, sense of heat, and friction. Tactile sensation may be realized by varying the vibration amplitude, waveform, and frequency of the tactile-feedback device [13]. The vibration amplitude and waveform of the film vibrator proposed in this study can be easily changed by controlling the applied driving voltage and waveform, respectively. However, the operation frequency cannot be arbitrarily changed, since it is restricted by the natural frequency of the film vibrator, which magnifies the vibration amplitude by resonance. To operate a flexible, tactile-feedback film vibrator in various frequency values, it is useful to design the film vibrator to have various natural frequencies, at which various tactile sensations can be realized. In other words, most touch panels have different length and width dimensions, so the natural frequencies in the length and width directions can be designed to be different, allowing two resonant frequencies. Also, when touch panels are sufficiently large in size, higher-order natural frequencies will fall into the frequency range (150–250 Hz) in which human fingertips are most sensitive, and thus, higher-order natural frequencies can be used as the operation frequencies for resonance. In particular, if the fundamental natural frequencies are only used as the resonant frequencies, the corresponding deformation shape of the film vibrator will result in reduced amplitude near the edge of the touch screen;thus, tactile sensation near the edge would be diminished. Figure 9 shows the contour plot of the measured vibration amplitude of the film vibrator fabricated with a single eight-μm-thick P(VDF-TrFE-CTFE) film. It should be noted that the largest vibration amplitude is located near the center of the film vibrator and the vibration amplitude decreases close to the edge. This implies that the edge of the tactile-feedback touch screen provides a weaker tactile sensation in comparison to the center. Even though the vibration amplitude near the edge is very weak, the vibration amplitude on almost all of the flexible screen is larger than the detection threshold of human sensitivity [16]. Furthermore, the tactile sensation near the edge can be enhanced if both the fundamental natural frequencies and the higher-order natural frequencies are used as operation frequencies to generate multiple deformation shapes, which have a considerable amount of vibration amplitude near the edge area. At the same time, the operation of the film vibrator at various higher-order resonance frequencies can be used to provide various tactile sensations to human fingertips in both the center area and the edge area.

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