Validation of Screen-Printed Electronic Skin Based on Piezoelectric Polymer Sensors

This paper proposes a validation method of the fabrication technology of a screen-printed electronic skin based on polyvinylidene fluoride-trifluoroethylene P(VDF-TrFE) piezoelectric polymer sensors. This required researchers to insure, through non-direct sensor characterization, that printed sensors were working as expected. For that, we adapted an existing model to non-destructively extract sensor behavior in pure compression (i.e., the d33 piezocoefficient) by indentation tests over the skin surface. Different skin patches, designed to sensorize a glove and a prosthetic hand (11 skin patches, 104 sensors), have been tested. Reproducibility of the sensor response and its dependence upon sensor position on the fabrication substrate were examined, highlighting the drawbacks of employing large A3-sized substrates. The average value of d33 for all sensors was measured at incremental preloads (1–3 N). A systematic decrease has been checked for patches located at positions not affected by substrate shrinkage. In turn, sensor reproducibility and d33 adherence to literature values validated the e-skin fabrication technology. To extend the predictable behavior to all skin patches and thus increase the number of working sensors, the size of the fabrication substrate is to be decreased in future skin fabrication. The tests also demonstrated the efficiency of the proposed method to characterize embedded sensors which are no more accessible for direct validation.


Introduction
Electronic skin (e-skin) is a touch-sensitive, electronic system that incorporates functional and structural materials coupled to a suitable electronic interface for sensor signal acquisition. Tactile data processing algorithms might provide information about contact properties (e.g., contact force [1] or contact shape [2]), given properties of the contact object (such as surface texture [3], object shape [4]), or contact events (e.g., discrimination between touch modalities [5]), to cite some examples. Artificial skin systems are implemented in a wide range of applications, such as robotics, prosthetics and teleoperation systems [6][7][8].
As the functional properties of the electronic skin mostly depend on the sensor type, it is worth focusing on the sensor itself. Various tactile sensors have been developed, like piezoelectric, piezoresistive, capacitive, optical, electromagnetic, ultrasonic, etc. [6]. The development of tactile sensors based on piezoelectric polymers has been extensively investigated in recent years due to their interesting features.
They exhibit high sensitivity, fast dynamic response and a large operating frequency range (from <1 Hz to 1 KHz), covering the whole frequency bandwidth of human skin mechanoreceptors [7].

Screen-Printed Sensing Patches Based on Piezoelectric Polymers
Fully screen-printed, flexible sensing patches based on P(VDF-TrFE) piezoelectric polymer sensors have been fabricated by JOANNEUM RESEARCH [19] (in the following, JNR). They patented a low-temperature, sol-gel based synthesis for P(VDF-TrFE) inks [20]. The main steps of the overall manufacturing process used by JNR to print ferroelectric sensor arrays based on P(VDF-TrFE) repeated units is illustrated in Figure 1. The fabrication of these sensing patches is done by screen-printing at a Thieme LAB 1000. A transparent and flexible (175 µm thick) DIN A4 plastic foil (Melinex ® ST 725 from DuPont Teijin films, USA) is used as the substrate; it ensures high flexibility and good adhesion of the functional materials applied during the screen-printing process ( Figure 1a). First, the circular bottom electrodes of the P(VDF-TrFE) are screen-printed (Figure 1b). In the second step, the ferroelectric polymer P(VDF-TrFE) is screen-printed onto the bottom electrodes, followed by a short curing step at 110 • C. The curing step supports the formation of the crystalline piezo-and pyroelectric β -phase and accelerates evaporation of the solvent. Figure 1c also includes the third step of screen-printing the top electrodes. Either PEDOT: PSS or silver or carbon have been used as these top electrodes [21]: it is worth noting that the carbon layer ( Figure 1d) is alternative to the usage of PEDOT:PSS or silver ( Figure 1c). Conductive silver ink has been used for electrical interconnections (Figure 1e). of interest for tactile applications (<1 Hz-1 kHz). The model cited in the previous paragraph [18] has thus been used to estimate the d33 piezoelectric coefficient of each sensor from the measure of both a basic mechanical action at the skin surface and sensor charge, meaning P(VDF-TrFE) sensor electromechanical characterization. Finding d33 values aligned with expected values from the literature in turn validates each sensor and the skin fabrication technology. Finally, a short way to characterize future e-skin systems is provided.
The paper is organized as follows: Section 2. presents the materials and methods, briefly illustrating the electronic skin design and technology, the reference skin model and the experimental setup. The results related to the validation of screen-printed sensing patches are reported in Section 3. Finally, our discussion and conclusive remarks are given in Sections 4. and 5.

Screen-printed Sensing Patches Based on Piezoelectric Polymers
Fully screen-printed, flexible sensing patches based on P(VDF-TrFE) piezoelectric polymer sensors have been fabricated by JOANNEUM RESEARCH [19] (in the following, JNR). They patented a low-temperature, sol-gel based synthesis for P(VDF-TrFE) inks [20]. The main steps of the overall manufacturing process used by JNR to print ferroelectric sensor arrays based on P(VDF-TrFE) repeated units is illustrated in Figure 1. The fabrication of these sensing patches is done by screenprinting at a Thieme LAB 1000. A transparent and flexible (175 μm thick) DIN A4 plastic foil (Melinex ® ST 725 from DuPont Teijin films, USA) is used as the substrate; it ensures high flexibility and good adhesion of the functional materials applied during the screen-printing process ( Figure 1a). First, the circular bottom electrodes of the P(VDF-TrFE) are screen-printed (Figure 1b). In the second step, the ferroelectric polymer P(VDF-TrFE) is screen-printed onto the bottom electrodes, followed by a short curing step at 110 °C. The curing step supports the formation of the crystalline piezo-and pyroelectric β -phase and accelerates evaporation of the solvent. Figure 1c also includes the third step of screen-printing the top electrodes. Either PEDOT: PSS or silver or carbon have been used as these top electrodes [21]: it is worth noting that the carbon layer ( Figure 1d) is alternative to the usage of PEDOT:PSS or silver (Figure 1c). Conductive silver ink has been used for electrical interconnections (Figure 1e). A final UV-curable lacquer layer is deposited on top for overall sensor protection. The poling procedure then aligns in the thickness direction randomly oriented dipoles contained in P(VDF-TrFE) crystallites. This has been achieved by hysteresis poling of each sensor with an alternating electric field at a frequency between 2 and 10 Hz and a magnitude of 100 MV/m, corresponding to twice the coercive field strength. Final geometries of sensor array patches have been obtained through cutting the manufactured foil with a Trotec Speedy 300 laser. The full deposition process has been thoroughly presented in [8,21], to which the reader is referred for further details.  A final UV-curable lacquer layer is deposited on top for overall sensor protection. The poling procedure then aligns in the thickness direction randomly oriented dipoles contained in P(VDF-TrFE) crystallites. This has been achieved by hysteresis poling of each sensor with an alternating electric field at a frequency between 2 and 10 Hz and a magnitude of 100 MV/m, corresponding to twice the coercive field strength. Final geometries of sensor array patches have been obtained through cutting the manufactured foil with a Trotec Speedy 300 laser. The full deposition process has been thoroughly presented in [8,21], to which the reader is referred for further details.

Design of the Sensing Patches
Two sets of sensing patches have been designed and manufactured. The former is intended for a textile glove with sensorized fingertips and palm, while the latter includes skin patches for the fingers and palm of the prosthetic Michelangelo Hand designed by Ottobock [17].
Sensor densities of the fingertips and of the palm have been oriented by psychophysical measurements of the spatial acuity of the human skin [22]. Usually to define the point-localization threshold, a stimulus is presented to the skin, followed in time by a second stimulus that may or may not be applied to the same site. Observers are required to say whether the two stimuli occur at the same or different locations. The point localization threshold is ~1-2 mm on the fingertip and around 1 cm on the palm. These values are only for reference, as the spatial acuity of the artificial skin is strongly dependent upon the thickness and on the material of the protective layer, as demonstrated in Seminara 2018 manuscript [18]. In particular, we refer to the proportionality coefficient γ plotted in [18], which gives a measure of the skin spatial acuity through the sensor receptive field, i.e., the spatial concentration of the mechanical stress information around a single sensor. The γ coefficient depends on the thickness of the elastic cover layer, and vanishes at a distance between the point force and the sensor axis, that marks the transition to the region where the force does no longer affect the given sensor.
Five different patch geometries have been experimentally characterized, and the correspondent results are presented in the current article. The patch layouts are shown in Figure 3.

Design of the Sensing Patches
Two sets of sensing patches have been designed and manufactured. The former is intended for a textile glove with sensorized fingertips and palm, while the latter includes skin patches for the fingers and palm of the prosthetic Michelangelo Hand designed by Ottobock [17].
Sensor densities of the fingertips and of the palm have been oriented by psychophysical measurements of the spatial acuity of the human skin [22]. Usually to define the point-localization threshold, a stimulus is presented to the skin, followed in time by a second stimulus that may or may not be applied to the same site. Observers are required to say whether the two stimuli occur at the same or different locations. The point localization threshold is~1-2 mm on the fingertip and around 1 cm on the palm. These values are only for reference, as the spatial acuity of the artificial skin is strongly dependent upon the thickness and on the material of the protective layer, as demonstrated in Seminara 2018 manuscript [18]. In particular, we refer to the proportionality coefficient γ plotted in [18], which gives a measure of the skin spatial acuity through the sensor receptive field, i.e., the spatial concentration of the mechanical stress information around a single sensor. The γ coefficient depends on the thickness of the elastic cover layer, and vanishes at a distance between the point force and the sensor axis, that marks the transition to the region where the force does no longer affect the given sensor.
Five different patch geometries have been experimentally characterized, and the correspondent results are presented in the current article. The patch layouts are shown in Figure 3.

Design of the Sensing Patches
Two sets of sensing patches have been designed and manufactured. The former is intended for a textile glove with sensorized fingertips and palm, while the latter includes skin patches for the fingers and palm of the prosthetic Michelangelo Hand designed by Ottobock [17].
Sensor densities of the fingertips and of the palm have been oriented by psychophysical measurements of the spatial acuity of the human skin [22]. Usually to define the point-localization threshold, a stimulus is presented to the skin, followed in time by a second stimulus that may or may not be applied to the same site. Observers are required to say whether the two stimuli occur at the same or different locations. The point localization threshold is ~1-2 mm on the fingertip and around 1 cm on the palm. These values are only for reference, as the spatial acuity of the artificial skin is strongly dependent upon the thickness and on the material of the protective layer, as demonstrated in Seminara 2018 manuscript [18]. In particular, we refer to the proportionality coefficient γ plotted in [18], which gives a measure of the skin spatial acuity through the sensor receptive field, i.e., the spatial concentration of the mechanical stress information around a single sensor. The γ coefficient depends on the thickness of the elastic cover layer, and vanishes at a distance between the point force and the sensor axis, that marks the transition to the region where the force does no longer affect the given sensor.
Five different patch geometries have been experimentally characterized, and the correspondent results are presented in the current article. The patch layouts are shown in Figure 3.

Experimental Setup
Twelve skin patches of five categories (the A, B, C, D and E samples, as shown in Figure 3) were tested using the mechanical chain shown in Figure 4 and described in Seminara's manuscript [18]. Each sensing patch was integrated on a rigid substrate and covered by an elastic protective layer, thus building a skin patch (see the bottom part of Figure 4). In particular, the same elastomer material has been used for stress transmission as in [18].
Building a skin structure that mimics, as close as possible, the conditions imposed by the model presented in [18] has two implications. On the one hand, we would like to enable sensors to work in a pure compressive mode. This would require that the coupling does not lead to the development of normal stresses T1 and T2 in the sensors which are comparable to T3. Operationally, in order to be able to keep the sensing patch intact for use after the validation stage, we have simply laid it over a rigid substrate with no further mechanical constraints (for better clarity, see Figure 5). This implies that the boundary conditions at the contact sensing patch, the rigid substrate, would be a simple roller. On the other hand, the upper protective layer is kept in contact with the substrate, constraining the lateral boundary of its bottom surface with double-sided adhesive tape (Model 3M300L, 3M). This scheme allows one to assume a roller type boundary condition at the elastomer at the bottom with constrained boundaries. The applied coupling scenario is illustrated in Figure 5.
A rigid plate was fixed on the moving head of an electromechanical shaker (Brüel and Kjaer, Minishaker Type 4810 from HBK company, Germany). A rigid spherical indenter (R = 4 mm) and a piezoelectric force transducer (Model 208C01, PCB Piezotronics, MTS system, were coupled on the upper head of the rigid frame. The skin patch assembled on the rigid circular plate was then mounted on a fixed support and faced down side. During the tests, we applied a mechanical input (force) and measured the electrical output (charge). A preload was first applied to guarantee indenter-PDMS contact during the whole mechanical stimulation. The value of the preload has been controlled by a laser (Waycon LAS TM10), allowing us to fix the displacement of the rigid plate at a certain value for a certain preload, through displacement-force calibration curves. A swept sine signal was provided to an electromechanical shaker by a graphical user interface (GUI) developed with NI LabVIEW on a host PC and NI DAQ

Experimental Setup
Twelve skin patches of five categories (the A, B, C, D and E samples, as shown in Figure 3) were tested using the mechanical chain shown in Figure 4 and described in Seminara's manuscript [18]. Each sensing patch was integrated on a rigid substrate and covered by an elastic protective layer, thus building a skin patch (see the bottom part of Figure 4). In particular, the same elastomer material has been used for stress transmission as in [18].
Building a skin structure that mimics, as close as possible, the conditions imposed by the model presented in [18] has two implications. On the one hand, we would like to enable sensors to work in a pure compressive mode. This would require that the coupling does not lead to the development of normal stresses T 1 and T 2 in the sensors which are comparable to T 3 . Operationally, in order to be able to keep the sensing patch intact for use after the validation stage, we have simply laid it over a rigid substrate with no further mechanical constraints (for better clarity, see Figure 5). This implies that the boundary conditions at the contact sensing patch, the rigid substrate, would be a simple roller. On the other hand, the upper protective layer is kept in contact with the substrate, constraining the lateral boundary of its bottom surface with double-sided adhesive tape (Model 3M300L, 3M). This scheme allows one to assume a roller type boundary condition at the elastomer at the bottom with constrained boundaries. The applied coupling scenario is illustrated in Figure 5.
A rigid plate was fixed on the moving head of an electromechanical shaker (Brüel and Kjaer, Minishaker Type 4810 from HBK company, Germany). A rigid spherical indenter (R = 4 mm) and a piezoelectric force transducer (Model 208C01, PCB Piezotronics, MTS system, were coupled on the upper head of the rigid frame. The skin patch assembled on the rigid circular plate was then mounted on a fixed support and faced down side. Sensors 2020, 20, 1160 6 of 25 elements have been accurately aligned before any test. Forces in the frequency range of (0.5-1 kHz) have been applied through the spherical indenter shown in Figure 4 and coupled to the electromechanical shaker. The force transducer (stimulus) and the charge developed by the sensor (response) were conditioned by PCB Sensor Signal Conditioner (482C54) and processed in frequency to give the System Response Function (FRF) at each frequency step. We recall that FRF corresponds to the ratio between the Fourier transform of the output charge and that of the input force.

Reference Skin Structure and Model
As mentioned in the introduction, in order to validate sensor behavior without damaging the sensors themselves, the sensing patches need to be integrated into a rigid substrate and covered by an elastomer. Hence, the indenter force is applied to the surface of the protective layer and transmitted to the sensors, working in thickness mode. In order to derive the stress acting on the sensor, our previous model [21] has been used, and is briefly summarized below ( Figure 6). The ultimate use of the model is to estimate the electrical sensor output (i.e., charge) from a measure of a During the tests, we applied a mechanical input (force) and measured the electrical output (charge). A preload was first applied to guarantee indenter-PDMS contact during the whole mechanical Sensors 2020, 20, 1160 7 of 25 stimulation. The value of the preload has been controlled by a laser (Waycon LAS TM10), allowing us to fix the displacement of the rigid plate at a certain value for a certain preload, through displacement-force calibration curves. A swept sine signal was provided to an electromechanical shaker by a graphical user interface (GUI) developed with NI LabVIEW on a host PC and NI DAQ data acquisition board. The signal was amplified using a Power Amplifier (Type 2706). All of these elements have been accurately aligned before any test. Forces in the frequency range of (0.5-1 kHz) have been applied through the spherical indenter shown in Figure 4 and coupled to the electromechanical shaker. The force transducer (stimulus) and the charge developed by the sensor (response) were conditioned by PCB Sensor Signal Conditioner (482C54) and processed in frequency to give the System Response Function (FRF) at each frequency step. We recall that FRF corresponds to the ratio between the Fourier transform of the output charge and that of the input force.

Reference Skin Structure and Model
As mentioned in the introduction, in order to validate sensor behavior without damaging the sensors themselves, the sensing patches need to be integrated into a rigid substrate and covered by an elastomer. Hence, the indenter force is applied to the surface of the protective layer and transmitted to the sensors, working in thickness mode. In order to derive the stress acting on the sensor, our previous model [21] has been used, and is briefly summarized below ( Figure 6). The ultimate use of the model is to estimate the electrical sensor output (i.e., charge) from a measure of a basic mechanical action at the skin surface. In other words, using the constitutive relationship of the sensors working in thickness-mode (purely compressive), one might write: where Q 3 is the total sensor charge measured by the charge amplifier [23], r T is the sensor radius, d 33 is the P(VDF-TrFE) piezoelectric coefficient and T 3 is the normal stress component T 3 averaged over a single sensor.
The application of the model leads to the following relationship between the charge and the applied force F 3 : where h is the elastomer thickness, a is the contact radius and σ is an output function of the theory, expressed as a double integral to be solved numerically, for each chosen value of r T h and a h . The radius a of the imprint is related to the applied load F 3 by the equation [24]: where R is the indenter radius, and E and ν are Young's modulus and the Poisson ratio of the elastic protective layer, respectively. Note that the given preload affects the contact radius a (3), while the amplitude of the dynamic swept sine force determines the PVDF charge. On the contrary, the dynamic component does not affect the computation of the contact radius, as the dynamic signal amplitude is negligible with respect to the preload. For a given skin geometry, associated with a specific r T h , (2) allows one to estimate the effective piezoelectric coefficient d 33 of each P(VDF-TrFE) sensor, once the charge Q 3 and the (normal) applied force F 3 centered on that specific sensor have been measured. Comparison with the expected value of d 33 [8,21] helps validating sensor functioning.
Sensors 2020, 20, 1160 8 of 25 Figure 6. Sketch of the general working mechanism of the P(VDF-TrFE) sensor: The Hertzian input force (with contact radius a) is transmitted to the sensor (with radius rT) through the elastomer layer of thickness h. With the presupposition that the sensor works solely in compressive mode, it directly converts the received normal stress T3 into electrical displacement D3, through a characterizing piezoelectric coefficient, namely the d33 (1). A charge amplifier is used to convert the total sensor charge into voltage.
For a given skin geometry, associated with a specific , (2) allows one to estimate the effective piezoelectric coefficient d33 of each P(VDF-TrFE) sensor, once the charge Q3 and the (normal) applied force F3 centered on that specific sensor have been measured. Comparison with the expected value of d33 [8,21] helps validating sensor functioning.
The effect of the finite thickness of the elastomer layer has been expressed by the value of sigma for the given skin geometry presented in this paper and calculated numerically through FEM simulations, as discussed in Seminara's manuscript [18]. In particular, we considered an elastic, virtually incompressible, medium (Poisson ratio sufficiently close to 0.5) consisting of a layer of finite thickness h = 2.5 mm, length l = 40 mm and width b = 20 mm. Length and width of the layer have been chosen arbitrarily, with the sole requirement of the distance between the elastomer side and the sensor center being much larger than the sensor radius, such as to justify the assumption that the lateral boundaries do not significantly affect the stress field acting on the sensor.
The elastomer surface is presumed to be subjected to an external Hertzian pressure distribution, the contact radius a being dependent from R, F3, E and ν, as for (3). The indenter radius R is 4 mm in all the present study, the employed value for the elastomer modulus E is the result of the experimental characterization of the elastic layer reported in [18] and corresponds to 16 [MPa] (slope of the linear portion of the stress-strain curve), while ν is assumed to equal 0.5.
As said above, the contact radius is mainly a function of the given preload, as the dynamic signal amplitude is negligible with respect to the preload itself. As discussed in the previous section, a roller type boundary condition was assumed at the lower boundary, while the perimeter is constrained.
The proportionality coefficient sigma, which allows to estimate the d33 value of each sensor (2), based on the measured ratio between Q3 and F3, is reported in Figure 7. The value of the contact radius a changes with the following preload values: PL = 0.6, 1, 2 and 3 N. It is worth pointing out that the present results are consistent with those found in Seminara's work [18]. As well, note that values of σ obtained for palm sensors differ slightly from the fingertip ones, as σ depends on the ratio (recall (2)).
In addition, we have verified the consistency of the experimental setup for the sensing patch with the pure compressive mode assumption. Then, we have performed a series of simulations aiming to evaluate the stress tensor in the sensing patch as a function of the preload, subject to a roller type boundary condition at the bottom and free lateral boundaries. These simulations show that the normal stresses T1 and T2 keep at least an order of magnitude smaller than T3 within the sensing patch. Recalling the complete constitutive relationship [7]: Figure 6. Sketch of the general working mechanism of the P(VDF-TrFE) sensor: The Hertzian input force (with contact radius a) is transmitted to the sensor (with radius r T ) through the elastomer layer of thickness h. With the presupposition that the sensor works solely in compressive mode, it directly converts the received normal stress T 3 into electrical displacement D 3 , through a characterizing piezoelectric coefficient, namely the d 33 (1). A charge amplifier is used to convert the total sensor charge into voltage.
The effect of the finite thickness of the elastomer layer has been expressed by the value of sigma for the given skin geometry presented in this paper and calculated numerically through FEM simulations, as discussed in Seminara's manuscript [18]. In particular, we considered an elastic, virtually incompressible, medium (Poisson ratio sufficiently close to 0.5) consisting of a layer of finite thickness h = 2.5 mm, length l = 40 mm and width b = 20 mm. Length and width of the layer have been chosen arbitrarily, with the sole requirement of the distance between the elastomer side and the sensor center being much larger than the sensor radius, such as to justify the assumption that the lateral boundaries do not significantly affect the stress field acting on the sensor.
The elastomer surface is presumed to be subjected to an external Hertzian pressure distribution, the contact radius a being dependent from R, F 3 , E and ν, as for (3). The indenter radius R is 4 mm in all the present study, the employed value for the elastomer modulus E is the result of the experimental characterization of the elastic layer reported in [18] and corresponds to 16 [MPa] (slope of the linear portion of the stress-strain curve), while ν is assumed to equal 0.5.
As said above, the contact radius is mainly a function of the given preload, as the dynamic signal amplitude is negligible with respect to the preload itself. As discussed in the previous section, a roller type boundary condition was assumed at the lower boundary, while the perimeter is constrained.
The proportionality coefficient sigma, which allows to estimate the d 33 value of each sensor (2), based on the measured ratio between Q 3 and F 3 , is reported in Figure 7. The value of the contact radius a changes with the following preload values: PL = 0.6, 1, 2 and 3 N. It is worth pointing out that the present results are consistent with those found in Seminara's work [18]. As well, note that values of σ obtained for palm sensors differ slightly from the fingertip ones, as σ depends on the ratio r T h (recall (2)). In addition, we have verified the consistency of the experimental setup for the sensing patch with the pure compressive mode assumption. Then, we have performed a series of simulations aiming to evaluate the stress tensor in the sensing patch as a function of the preload, subject to a roller type boundary condition at the bottom and free lateral boundaries. These simulations show that the normal stresses T 1 and T 2 keep at least an order of magnitude smaller than T 3 within the sensing patch.
Recalling the complete constitutive relationship [7]: Sensors 2020, 20, 1160 9 of 25 and noting that d 31 and d 32 are smaller than d 33 [7], we end up concluding that the assumption of pure compressive mode was sufficiently adequate for the experimental setting.
and noting that d31 and d32 are smaller than d33 [7], we end up concluding that the assumption of pure compressive mode was sufficiently adequate for the experimental setting. Figure 7. Results for the numerical COMSOL simulations for the finite case. The proportionality coefficient σ between average normal stress T3 on the sensor and overall (Hertzian) contact force F3 (2) is plotted versus the imprint radius a (contact size) scaled by the elastomer thickness h. Note that the applied force is centered on the sensor. The two curves are associated to two different sensor sizes: rT = 1 mm (sensors on the palm), rT = 0.5 mm (sensors on the fingertip).

Morphology of the Sensing Patches: Issues
All sensing patches have been visually inspected using first a photo scanner (EPSON perfection V800 photo) and then an optical microscope (Nikon eclipse LV100 and Wild M32).
Some fabrication defects have been detected (see Figure 8). They are listed below: 1. Faults in the top sensor electrode. The choice of silver ink for the top electrode has been the result of a compromise between resolution, conductivity and top-electrode performance. Using silver, the printing resolution was very good and the conductivity was very high at the 100 °C temperature treatment. At a careful examination, small defects were detected, due to solvents in the ink (Figure 8b). However, this does not heavily compromise sensor behavior. 2. Interrupted tracks (Figure 8c). During high-voltage hysteresis poling, sensor lines burned for current exceeding a given threshold due to short circuits between top and bottom electrodes (caused by their too small distance). 3. Short circuits. They occurred between sensor lines or due to the misalignment between top and bottom electrodes (Figure 8d). The high spatial resolution led to too small distances between lines and top/bottom electrodes, causing short-circuits due to the shrinkage of the whole DIN A3 fabrication substrate during high temperature treatment. Figure 9 shows the heat map of the substrate prone to shrinkage. We observed that certain sensing patches (such as M-Palm) lie on the blue sweet spot, corresponding to less shrinkage. This guarantees a larger number of working sensors. Other samples (such as palm right 2) are on the red zones, associated with high shrinkage. This causes higher number of short circuits, which in turn leads to less working sensors than expected.  2) is plotted versus the imprint radius a (contact size) scaled by the elastomer thickness h. Note that the applied force is centered on the sensor. The two curves are associated to two different sensor sizes: r T = 1 mm (sensors on the palm), r T = 0.5 mm (sensors on the fingertip).

Morphology of the Sensing Patches: Issues
All sensing patches have been visually inspected using first a photo scanner (EPSON perfection V800 photo) and then an optical microscope (Nikon eclipse LV100 and Wild M32).
Some fabrication defects have been detected (see Figure 8). They are listed below:

1.
Faults in the top sensor electrode. The choice of silver ink for the top electrode has been the result of a compromise between resolution, conductivity and top-electrode performance. Using silver, the printing resolution was very good and the conductivity was very high at the 100 • C temperature treatment. At a careful examination, small defects were detected, due to solvents in the ink ( Figure 8b). However, this does not heavily compromise sensor behavior.

2.
Interrupted tracks (Figure 8c). During high-voltage hysteresis poling, sensor lines burned for current exceeding a given threshold due to short circuits between top and bottom electrodes (caused by their too small distance).

3.
Short circuits. They occurred between sensor lines or due to the misalignment between top and bottom electrodes (Figure 8d). The high spatial resolution led to too small distances between lines and top/bottom electrodes, causing short-circuits due to the shrinkage of the whole DIN A3 fabrication substrate during high temperature treatment. Figure 9 shows the heat map of the substrate prone to shrinkage. We observed that certain sensing patches (such as M-Palm) lie on the blue sweet spot, corresponding to less shrinkage. This guarantees a larger number of working sensors. Other samples (such as palm right 2) are on the red zones, associated with high shrinkage. This causes higher number of short circuits, which in turn leads to less working sensors than expected. In summary, the required high resolution (i.e., small sensor size, short distance between the top and bottom electrodes, short distance between the sensor tracks) is challenging. In particular, such fine structures cannot be distributed over such a large area (DIN A3) if the substrate is not dimensionally stable during all process steps (including sensor polarization). How these fabrication defects affected sensor behavior is illustrated in Section 3.1.

Experimental Tests
A series of experiments were conducted to extract the sensor behavior, i.e., ultimately their d33 values, from indentation tests on the skin surface, by using the model illustrated in Section 2.3. Before running each test, a preload has been applied to guarantee indenter-skin contact during the entire mechanical stimulation. As specified in Section 2.3, the preload is responsible for determining the contact radius a (3), as for all tests the amplitude of the dynamic oscillation is maintained low enough (F_dyn = 0.09 N) not to significantly affect the contact area.
Different P(VDF-TrFE) sensing patches have been tested as described in Section 2.2. We applied a swept sine signal from 0.5 Hz up to 1000 Hz by the electromechanical shaker at each sensor epicenter on the e-skin outer surface, causing e-skin indentation aligned with each sensor center. We recorded the sensor frequency-response function one-shot over the whole frequency range. The numerical model described in Section 2.3 has been integrated into the LabVIEW software, directly giving the frequency behavior of the d33 piezoelectric modulus (both real and imaginary parts) of In summary, the required high resolution (i.e., small sensor size, short distance between the top and bottom electrodes, short distance between the sensor tracks) is challenging. In particular, such fine structures cannot be distributed over such a large area (DIN A3) if the substrate is not dimensionally stable during all process steps (including sensor polarization). How these fabrication defects affected sensor behavior is illustrated in Section 3.1.

Experimental Tests
A series of experiments were conducted to extract the sensor behavior, i.e., ultimately their d33 values, from indentation tests on the skin surface, by using the model illustrated in Section 2.3. Before running each test, a preload has been applied to guarantee indenter-skin contact during the entire mechanical stimulation. As specified in Section 2.3, the preload is responsible for determining the contact radius a (3), as for all tests the amplitude of the dynamic oscillation is maintained low enough (F_dyn = 0.09 N) not to significantly affect the contact area.
Different P(VDF-TrFE) sensing patches have been tested as described in Section 2.2. We applied a swept sine signal from 0.5 Hz up to 1000 Hz by the electromechanical shaker at each sensor epicenter on the e-skin outer surface, causing e-skin indentation aligned with each sensor center. We recorded the sensor frequency-response function one-shot over the whole frequency range. The numerical model described in Section 2.3 has been integrated into the LabVIEW software, directly giving the frequency behavior of the d33 piezoelectric modulus (both real and imaginary parts) of In summary, the required high resolution (i.e., small sensor size, short distance between the top and bottom electrodes, short distance between the sensor tracks) is challenging. In particular, such fine structures cannot be distributed over such a large area (DIN A3) if the substrate is not dimensionally stable during all process steps (including sensor polarization). How these fabrication defects affected sensor behavior is illustrated in Section 3.1.

Experimental Tests
A series of experiments were conducted to extract the sensor behavior, i.e., ultimately their d 33 values, from indentation tests on the skin surface, by using the model illustrated in Section 2.3. Before running each test, a preload has been applied to guarantee indenter-skin contact during the entire mechanical stimulation. As specified in Section 2.3, the preload is responsible for determining the contact radius a (3), as for all tests the amplitude of the dynamic oscillation is maintained low enough (F_dyn = 0.09 N) not to significantly affect the contact area.
Different P(VDF-TrFE) sensing patches have been tested as described in Section 2.2. We applied a swept sine signal from 0.5 Hz up to 1000 Hz by the electromechanical shaker at each sensor epicenter on the e-skin outer surface, causing e-skin indentation aligned with each sensor center. We recorded the sensor frequency-response function one-shot over the whole frequency range. The numerical model described in Section 2.3 has been integrated into the LabVIEW software, directly giving the frequency behavior of the d 33 piezoelectric modulus (both real and imaginary parts) of each solicited sensor, calculated from the sensor frequency response function as for (2). Sigma values have been extracted from Figure 7, each time in accordance with the specific preload and sensor radius.

Frequency Range Selection
In a preliminary stage, we investigated the minimal value of the applied preload that ensured a stable behavior of d 33 . Multiple tests at preloads less than 1 N have been run over the whole frequency range (0.5 Hz-1000 Hz), especially at preload 0.6 N. Main observation is that this low value for the preload does not ensure a stable contact during oscillations of the indenter over the skin patch, due to the dynamic amplitude of the indenter oscillation being not enough smaller than the preload itself. This causes noisy behavior for the d 33 . For that reason, in the rest of the study, the results at this preload are not reported.
Then, tests have been done at preloads 1, 2 and 3 N. It turned out that resonances do exist, and their characteristic frequencies depend upon the preload. In the 300-750 Hz range, a systematic preload-dependent resonance peak is responsible for sign flipping of the real part of the d 33 coefficient. At low preloads (i.e., PL = 1 N) the resonance falls in the 300-500 Hz range, while at higher preloads (i.e., PL = 2, 3 N) the resonance shifts to the 500-750 Hz frequency range. Around 950 Hz, a mechanical resonance appears due to high vibrations from the shaker system while stopping. As reported in Seminara's work [18], resonances may derive from a variety of causes (e.g., movable contacts, contact surface asperities, motor-induced vibrations), which cannot be reliably controlled. The model can only be applied with dynamic contacts with forcing frequencies that fall outside the range of any notable resonance [18]. Therefore, a non-resonant 50-250 Hz frequency range has been identified, where the frequency response function is systematically quite flat. In particular, the imaginary part of the d 33 piezoelectric coefficient, which accounts for any viscoelastic component of the response, is systematically roughly an order of magnitude smaller than the real (elastic) part. The aforementioned statements are clarified in the representative example reported in Figure 10, where both the real and imaginary parts of d 33 are expressed as a function of frequency, and the non-resonant range is highlighted. each solicited sensor, calculated from the sensor frequency response function as for (2). Sigma values have been extracted from Figure 7, each time in accordance with the specific preload and sensor radius.

Frequency Range Selection
In a preliminary stage, we investigated the minimal value of the applied preload that ensured a stable behavior of d33. Multiple tests at preloads less than 1 N have been run over the whole frequency range (0.5 Hz-1000 Hz), especially at preload 0.6 N. Main observation is that this low value for the preload does not ensure a stable contact during oscillations of the indenter over the skin patch, due to the dynamic amplitude of the indenter oscillation being not enough smaller than the preload itself. This causes noisy behavior for the d33. For that reason, in the rest of the study, the results at this preload are not reported.
Then, tests have been done at preloads 1, 2 and 3 N. It turned out that resonances do exist, and their characteristic frequencies depend upon the preload. In the 300-750 Hz range, a systematic preload-dependent resonance peak is responsible for sign flipping of the real part of the d33 coefficient. At low preloads (i.e., PL = 1 N) the resonance falls in the 300-500 Hz range, while at higher preloads (i.e., PL = 2, 3 N) the resonance shifts to the 500-750 Hz frequency range. Around 950 Hz, a mechanical resonance appears due to high vibrations from the shaker system while stopping. As reported in Seminara's work [18], resonances may derive from a variety of causes (e.g., movable contacts, contact surface asperities, motor-induced vibrations), which cannot be reliably controlled. The model can only be applied with dynamic contacts with forcing frequencies that fall outside the range of any notable resonance [18]. Therefore, a non-resonant 50-250 Hz frequency range has been identified, where the frequency response function is systematically quite flat. In particular, the imaginary part of the d33 piezoelectric coefficient, which accounts for any viscoelastic component of the response, is systematically roughly an order of magnitude smaller than the real (elastic) part. The aforementioned statements are clarified in the representative example reported in Figure 10, where both the real and imaginary parts of d33 are expressed as a function of frequency, and the nonresonant range is highlighted. Based on these results, hereafter the imaginary part of the d33 coefficient will be ignored and "Re" will be removed from the notation. In other words, the system is treated as purely elastic. Moreover, each run has been performed, stimulating the skin over the whole frequency range, yet the corresponding d33 response is averaged over the non-resonant range only. Based on these results, hereafter the imaginary part of the d 33 coefficient will be ignored and "Re" will be removed from the notation. In other words, the system is treated as purely elastic. Moreover, each run has been performed, stimulating the skin over the whole frequency range, yet the corresponding d 33 response is averaged over the non-resonant range only.

Systematic Sensor Validation
Each sensing patch has been tested by stimulating the e-skin surface with the same indenter (R = 4 mm) aligned with the epicenter of each selected sensor. As mentioned in Section 3.2.1, each run has been performed at small force amplitude (F_dyn = 0.09 N), and the corresponding d 33 response has been averaged over the non-resonant range to get a single value of that coefficient for each sensor.
Two sets of data have been obtained. The former data set (96 sensors in total, 10 different samples, four categories of patches) focuses on Palm sensors (i.e., sensors with diameter = 2 mm, belonging to arrays designed to cover the palm), all tested at different preloads ( Figure 11). on finger sensors (i.e., sensors with diameter = 1 mm, belonging to arrays designed to cover the fingertips). One-way analysis of variance (ANOVA) and Tukey-Kramer's honestly significant difference (HSD) test, for the post-hoc pairwise comparison, were used to test the statistically significant difference in the mean performance among the tested conditions.

First Analysis: Palm Sensors
We selected four palm patch designs that vary in their positions and sensor number. These designs have been classified into four categories as reported in the Table 1 below.  Figure 11 illustrates how these categories are distributed over the A3 substrate used for patch fabrication. A comparative study has been performed to examine whether the shape and position over the A3 fabrication substrate affected the sensor behavior at different preloads. 67 sensors out of the whole set (96 sensors) have been selected, eliminating sensors that did not work due to fabrication failures (see Section 3.1) and few sensors that gave physically unacceptable values for d33. Note that the number of malfunctioning sensors was quite high for this first fabrication batch, due to those issues discussed in Section 3.1. Figure 12 shows the cloud distribution of the averaged d33 values for the palm sensors. On the other hand, the second data set (eight sensors, two samples, Michelangelo little) focuses on finger sensors (i.e., sensors with diameter = 1 mm, belonging to arrays designed to cover the fingertips). One-way analysis of variance (ANOVA) and Tukey-Kramer's honestly significant difference (HSD) test, for the post-hoc pairwise comparison, were used to test the statistically significant difference in the mean performance among the tested conditions.

First Analysis: Palm Sensors
We selected four palm patch designs that vary in their positions and sensor number. These designs have been classified into four categories as reported in the Table 1 below.  Figure 11 illustrates how these categories are distributed over the A3 substrate used for patch fabrication. A comparative study has been performed to examine whether the shape and position over the A3 fabrication substrate affected the sensor behavior at different preloads.
67 sensors out of the whole set (96 sensors) have been selected, eliminating sensors that did not work due to fabrication failures (see Section 3.1) and few sensors that gave physically unacceptable values for d 33 . Note that the number of malfunctioning sensors was quite high for this first fabrication batch, due to those issues discussed in Section 3.1. Figure 12 shows the cloud distribution of the averaged d 33 values for the palm sensors. 67 sensors out of the whole set (96 sensors) have been selected, eliminating sensors that did not work due to fabrication failures (see Section 3.1) and few sensors that gave physically unacceptable values for d33. Note that the number of malfunctioning sensors was quite high for this first fabrication batch, due to those issues discussed in Section 3.1. Figure 12 shows the cloud distribution of the averaged d33 values for the palm sensors. All categories have been analyzed in order to check whether any dependence of the patch behavior on the specific category existed. This was needed to understand if a specific patch position affected sensor behavior, e.g., due to not uniform polarization or other unwanted effects related to the shrinkage of the substrate during the fabrication process.
The results presented in Figure 13 show that indeed sensor response to preload does significantly depend on the category, which is associated to a specific position on the substrate. All categories have been analyzed in order to check whether any dependence of the patch behavior on the specific category existed. This was needed to understand if a specific patch position affected sensor behavior, e.g., due to not uniform polarization or other unwanted effects related to the shrinkage of the substrate during the fabrication process.
The results presented in Figure 13 show that indeed sensor response to preload does significantly depend on the category, which is associated to a specific position on the substrate.
In particular, note that results for categories 2 ( Figure 13b) and 3 ( Figure 13c) show a dependence of d 33 on the preload, which turns out not to be statistically significant. It is worth pointing out that categories 2 and 3 are those located in the red zone of the heat map, where strong substrate shrinkage occurred. In order to check the effectiveness of the sensor fabrication technology, we have then decided to discard results referring to categories 2 and 3.
On the other hand, it is reassuring to note that, as shown in Figure 14, patches belonging to the same category (including those in the red zone) are statistically equivalent among themselves, a result which does suggest the reproducibility of the fabrication process for each patch. In particular, note that results for categories 2 ( Figure 13b) and 3 ( Figure 13c) show a dependence of d33 on the preload, which turns out not to be statistically significant. It is worth pointing out that categories 2 and 3 are those located in the red zone of the heat map, where strong substrate shrinkage occurred. In order to check the effectiveness of the sensor fabrication technology, we have then decided to discard results referring to categories 2 and 3.
On the other hand, it is reassuring to note that, as shown in Figure 14, patches belonging to the same category (including those in the red zone) are statistically equivalent among themselves, a result which does suggest the reproducibility of the fabrication process for each patch.   Results for all sensors belonging to the two categories located in the sweet spot associated with low shrinkage (i.e., categories 1 and 4) are plotted in the Figures 15 and 16. They show d33 values mostly compatible with the state of the art [8]. It turns out that as the preload increases, the average d33 decreases, and values for different sensors exhibit a lower dispersion. In Figure 16, a best-fit line is used to compute the average of the d33 values associated with all sensors. Data related to the highest preload (=3 N) are well fitted using a d33 value equal to approximately −22 pC/N, while data corresponding to the lower preload (=1 N) yield a d33 value of approximately -46 pC/N. It turns out that as the preload increases, the average d 33 decreases, and values for different sensors exhibit a lower dispersion. In Figure 16  Results for all sensors belonging to the two categories located in the sweet spot associated with low shrinkage (i.e., categories 1 and 4) are plotted in the Figures 15 and 16. They show d33 values mostly compatible with the state of the art [8]. It turns out that as the preload increases, the average d33 decreases, and values for different sensors exhibit a lower dispersion. In Figure 16, a best-fit line is used to compute the average of the d33 values associated with all sensors. Data related to the highest preload (=3 N) are well fitted using a d33 value equal to approximately −22 pC/N, while data corresponding to the lower preload (=1 N) yield a d33 value of approximately -46 pC/N.  To conclude results on the first batch, we have performed a more detailed analysis of results obtained for category 1, analyzing the behavior of each patch belonging to that category. Results are plotted in Figure 17, which shows a statistically significant systematic decrease of the d33 coefficient with a preload for all three patches. To conclude results on the first batch, we have performed a more detailed analysis of results obtained for category 1, analyzing the behavior of each patch belonging to that category. Results are plotted in Figure 17, which shows a statistically significant systematic decrease of the d 33 coefficient with a preload for all three patches. To conclude results on the first batch, we have performed a more detailed analysis of results obtained for category 1, analyzing the behavior of each patch belonging to that category. Results are plotted in Figure 17, which shows a statistically significant systematic decrease of the d33 coefficient with a preload for all three patches.

Second Analysis (Preliminary): Finger Sensors
A complementary case study has been performed in order to check whether the proposed method could be extended to sensors with lower diameter (i.e., finger sensors) or not. To this aim, a second data set only including finger sensors was analyzed. It is worth remarking that the alignment procedure was particularly critical in this case: the small sensor size would require an alignment system to more precisely align the indenter with the sensor center for reliable sensor characterization using the current model. This is the reason why this analysis has been only performed on a low number of sensing patches. Two samples of Michelangelo little finger located on the sweet spot (see Figure 18-Top) were tested using the experimental setup and method reported above. Each sample has four taxels with 1 mm diameter each. Figure 18 shows the analyzed results after applying one-Way ANOVA using Tukey-Kramer's HSD test. As for the palm, the results indicate a significant statistical difference of d33 at different applied preloads and a systematic decrease of d33 at increasing preload.

Second Analysis (Preliminary): Finger Sensors
A complementary case study has been performed in order to check whether the proposed method could be extended to sensors with lower diameter (i.e., finger sensors) or not. To this aim, a second data set only including finger sensors was analyzed. It is worth remarking that the alignment procedure was particularly critical in this case: the small sensor size would require an alignment system to more precisely align the indenter with the sensor center for reliable sensor characterization using the current model. This is the reason why this analysis has been only performed on a low number of sensing patches. Two samples of Michelangelo little finger located on the sweet spot (see Figure 18-Top) were tested using the experimental setup and method reported above. Each sample has four taxels with 1 mm diameter each. Figure 18 shows the analyzed results after applying one-Way ANOVA using Tukey-Kramer's HSD test. As for the palm, the results indicate a significant statistical difference of d 33 at different applied preloads and a systematic decrease of d 33 at increasing preload.  Table 2 shows a conclusive summary of the findings which emerged from the different experimental studies performed. A broad outcome of the performed tests is that both palm and finger sensors share the same statistically significant systematic decrease of d33 with preload. In the first analysis, for all categories, the patches are statistically equivalent among themselves when belonging to the same category, which proves the reproducibility of the whole deposition process. Excluding categories located in the red zone (i.e., CAT 2 and CAT 3) of the heat map, which is associated with high shrinkage, the single sensors belonging to the other two categories (CAT 1 and CAT 4) show a piezoelectric behavior (i.e., d33 values), which is quite compatible with the current state of the art [11]. On the other hand, the behavior of the d33 versus preload for CAT 2 and CAT 3 in the red zone shows no alignment with the decreasing behavior observed for patches located in the sweet spot. This result  Table 2 shows a conclusive summary of the findings which emerged from the different experimental studies performed. A broad outcome of the performed tests is that both palm and finger sensors share the same statistically significant systematic decrease of d 33 with preload. In the first analysis, for all categories, the patches are statistically equivalent among themselves when belonging to the same category, which proves the reproducibility of the whole deposition process. Excluding categories located in the red zone (i.e., CAT 2 and CAT 3) of the heat map, which is associated with high shrinkage, the single sensors belonging to the other two categories (CAT 1 and CAT 4) show a piezoelectric behavior (i.e., d 33 values), which is quite compatible with the current state of the art [11]. On the other hand, the behavior of the d 33 versus preload for CAT 2 and CAT 3 in the red zone shows no alignment with the decreasing behavior observed for patches located in the sweet spot. This result is a hint at the need of employing smaller fabrication substrates in future e-skin manufacturing, in order to considerably reduce red zones, which are not compliant to the expected sensing behavior. Focusing on categories located in the sweet spot, all analyzed patches belonging to categories 1 and 4 have quite systematic decreasing behavior for d 33 vs. PL. This has been checked using one-way ANOVA for statistical analysis and Tukey-Kramer's HSD test for the post-hoc pairwise comparison. Systematically, average d 33 behavior at PL = 1 N is statistically different from that at PL = 3 N, both for the two categories (Figure 13a,d) and for single patches from category 1 (Figure 16). This would be compatible with a non-linearity of d 33 with respect to the preload, and with some nonlinearity in the stress-strain curve observed for this elastomer layer around 2 MPa [21]. In the second analysis, similar results were obtained for the finger sensors, despite the high distribution error, which emerges from the low number of sensors tested.

Discussion
The dispersed behavior of d 33 (i.e., sensor response) does depend on both the fabrication process (including deposition and assembly) and on the alignment of the indenter with the sensor center. A laser-like positioning system could be used in the future to align the indenter precisely, thus avoiding errors due to wrong positioning. As for the fabrication process, these errors are the results of different factors including different point-to-point values for the sensor radius and/or for the local layer thickness and inhomogeneity in PVDF film polarization. These combined factors are considered intrinsic in the whole fabrication process, and could not be decoupled in the proposed tests.
In Section 2.2, we described how we coupled the sensing patch to the substrate and to the protective layer, to be able to test sensor behavior without damaging the sensors themselves. Applying double-sided adhesive tape all over the sensors in the validation stage is not feasible unless the cover layer is the final layer, because sensors would be damaged during tape removal ( Figure 19).
ANOVA for statistical analysis and Tukey-Kramer's HSD test for the post-hoc pairwise comparison. Systematically, average d33 behavior at PL = 1 N is statistically different from that at PL = 3 N, both for the two categories (Figure 13a,d) and for single patches from category 1 (Figure 16). This would be compatible with a non-linearity of d33 with respect to the preload, and with some nonlinearity in the stress-strain curve observed for this elastomer layer around 2 MPa [21]. In the second analysis, similar results were obtained for the finger sensors, despite the high distribution error, which emerges from the low number of sensors tested.
The dispersed behavior of d33 (i.e., sensor response) does depend on both the fabrication process (including deposition and assembly) and on the alignment of the indenter with the sensor center. A laser-like positioning system could be used in the future to align the indenter precisely, thus avoiding errors due to wrong positioning. As for the fabrication process, these errors are the results of different factors including different point-to-point values for the sensor radius and/or for the local layer thickness and inhomogeneity in PVDF film polarization. These combined factors are considered intrinsic in the whole fabrication process, and could not be decoupled in the proposed tests.
In Section 2.2, we described how we coupled the sensing patch to the substrate and to the protective layer, to be able to test sensor behavior without damaging the sensors themselves. Applying double-sided adhesive tape all over the sensors in the validation stage is not feasible unless the cover layer is the final layer, because sensors would be damaged during tape removal ( Figure 19).
It would be also better to avoid the adhesive tape between the substrate and the sensors themselves, as damages may occur during tape removal. Therefore, the choice of the coupling procedure is somehow obliged in the validation stage. Operationally, as described in Section 2.2, we placed double-sided adhesive tape around the sensing patch (Table 3 solution1), to rigidly couple to the substrate the protective layer on its boundaries, thus keeping in place the sensing patch itself. We also proved through simulations that this configuration leads to negligible normal stresses other than T33, thus confirming that sensors work in thickness mode, as required by the model. However, this coupling procedure can only be used in the validation stage, as discussed in the following. In real applications shear contact forces on the skin surface will be possible, which requires using a real rigid coupling between the sensing patch and both the cover layer and the substrate (Table 3 solution 2), to avoid any sliding due to shear forces. This is achieved in practice by using an adhesive layer below and all-over the sensing patch itself. Care would only be needed during tape integration as non-uniform stress transmission and sensor bending can be naturally induced by the It would be also better to avoid the adhesive tape between the substrate and the sensors themselves, as damages may occur during tape removal.
Therefore, the choice of the coupling procedure is somehow obliged in the validation stage. Operationally, as described in Section 2.2, we placed double-sided adhesive tape around the sensing patch (Table 3 solution1), to rigidly couple to the substrate the protective layer on its boundaries, thus keeping in place the sensing patch itself. We also proved through simulations that this configuration leads to negligible normal stresses other than T 33 , thus confirming that sensors work in thickness mode, as required by the model. patch. The result of the whole procedure is a single value of the d33 piezoelectric coefficient for each sensor, averaged over the non-resonant frequency range. An error signal can be set up to notify if any of the sensors has a value of d33 which differs from the expected value by more than a previously defined tolerance. It is important to note that, except for the initial coupling procedure and first indenter centering, the rest of the procedure can be automatized, reducing to a few minutes the validation of a sensing patch built of 15-20 sensor units.

Solution 2: Real applications
Skin patch built applying doublesided adhesive tape all over below and above the sensing patch.

Conclusions and Future Work
This article tackled some of the challenges related to employing electronic skin systems in real applications. In particular, this mainly requires validating the building blocks of the e-skin system, i.e., the sensing patches, and finding adequate ways to integrate these sensing patches into an electronic skin structure which also includes structural elements. Both these steps are preliminary to include the e-skin system into the target system, e.g., a glove or a prosthetic hand.
First, a set of tools is thus needed for the validation of the fabrication technology of the sensing patches. Throughout this study, a non-invasive method to validate the deposition technique of

Solution 2: Real applications
Skin patch built applying double-sided adhesive tape all over below and above the sensing patch.
sensor, averaged over the non-resonant frequency range. An error signal can be set up to notify if any of the sensors has a value of d33 which differs from the expected value by more than a previously defined tolerance. It is important to note that, except for the initial coupling procedure and first indenter centering, the rest of the procedure can be automatized, reducing to a few minutes the validation of a sensing patch built of 15-20 sensor units.

Conclusions and Future Work
This article tackled some of the challenges related to employing electronic skin systems in real applications. In particular, this mainly requires validating the building blocks of the e-skin system, i.e., the sensing patches, and finding adequate ways to integrate these sensing patches into an electronic skin structure which also includes structural elements. Both these steps are preliminary to include the e-skin system into the target system, e.g., a glove or a prosthetic hand.
First, a set of tools is thus needed for the validation of the fabrication technology of the sensing patches. Throughout this study, a non-invasive method to validate the deposition technique of However, this coupling procedure can only be used in the validation stage, as discussed in the following. In real applications shear contact forces on the skin surface will be possible, which requires using a real rigid coupling between the sensing patch and both the cover layer and the substrate (Table 3 solution 2), to avoid any sliding due to shear forces. This is achieved in practice by using an adhesive layer below and all-over the sensing patch itself. Care would only be needed during tape integration as non-uniform stress transmission and sensor bending can be naturally induced by the inclusion of air bubbles into the coupling adhesive layer. An underestimation of the d 33 value is expected due to the addition of deformable adhesive layers between the sensor and both the substrate and the cover, which are not accounted for in the model. This leads not to be perfectly compliant with the model, as normal stresses other than T 3 may contribute to the measured charge: preliminary simulations confirmed this prediction and hint at a contribution of normal T 1 and T 2 stresses, which is not negligible with respect to the normal T 3 component. New models and more extensive simulations will be thus needed to describe the real application system.
A time-saving protocol for future sensing patch validation can be extracted as an outcome of the analysis presented in this manuscript. It could be summarized as follows. As a first step, the sensing patch is to be coupled to the rigid substrate by only applying double-sided adhesive tape around the patch perimeter (Table 3 solution 1). As shown in Table 3 solution 1, the protective layer can then be applied on top of the sensing patch, being rigidly coupled to the substrate through the double-sided adhesive layer. After mounting the skin patch built as such along the mechanical chain illustrated in Figure 4, the indenter is to be aligned with a reference sensor. A laser positioning system would facilitate such a procedure, thus reducing the dispersion of sensor behavior. Avoiding complete systematic measures at different preloads, which are not needed if the scope is a check of the sensor manufacturing process, an indentation test over the non-resonant frequency range (50-250 Hz) can be quickly run at an average preload (i.e., =2 N). This procedure lasts no more than a few seconds. The indenter is then released and moved over a distant sensor, to avoid artifacts due to the relaxation of the protective layer after indenter release. The same procedure as before is performed, consisting of applying the given preload, running the indentation test, releasing the indenter and moving the indenter over a distant sensor. The same scheme is applied on all sensors belonging to the sensing patch. The result of the whole procedure is a single value of the d 33 piezoelectric coefficient for each sensor, averaged over the non-resonant frequency range. An error signal can be set up to notify if any of the sensors has a value of d 33 which differs from the expected value by more than a previously defined tolerance. It is important to note that, except for the initial coupling procedure and first indenter centering, the rest of the procedure can be automatized, reducing to a few minutes the validation of a sensing patch built of 15-20 sensor units.

Conclusions and Future Work
This article tackled some of the challenges related to employing electronic skin systems in real applications. In particular, this mainly requires validating the building blocks of the e-skin system, i.e., the sensing patches, and finding adequate ways to integrate these sensing patches into an electronic skin structure which also includes structural elements. Both these steps are preliminary to include the e-skin system into the target system, e.g., a glove or a prosthetic hand.
First, a set of tools is thus needed for the validation of the fabrication technology of the sensing patches. Throughout this study, a non-invasive method to validate the deposition technique of piezoelectric polymer sensors working in thickness mode has been defined and demonstrated. In particular, this paper reports the validation of the fabrication technology of flexible screen-printed sensing patches based on P(VDF-TrFE) piezoelectric polymers. This method is independent of the specific deposition technique and can cover a large number of applications requiring the employment of artificial tactile sensing through e-skin based on piezoelectric polymer sensor such as P(VDF-TrFE).
Extensive preliminary tests with an electromechanical setup have been performed on four different patch geometries/categories for the palm and one patch geometry for the fingertips. In particular, twelve sensing patches have been characterized (10 palm patches and two fingertip patches), 104 sensors in total (96 palm sensors and 8 fingertip sensors). P(VDF-TrFE) sensors worked in thickness-mode and a protective layer has been integrated on top of the sensing patch for stress transmission and sensor protection. Dynamic skin indentation with normal force centered on each sensor has been performed, with three different preloads (1, 2 and 3 N). An average value of the d 33 coefficient over a non-resonant frequency range has been extracted for each sensor, without damaging the sensor itself. Obtaining expected (modeled) behavior of the electrical response of each sensor to measured mechanical (normal) force at the skin surface proves that the combination of both fabrication and assembly processes was successful.
Throughout the study course, several issues were observed such as substrate shrinkage that occurred during the fabrication process, leading to shortcuts. The proposed validation and characterization provided us with cues to optimize the fabrication of the next-line batches such as choosing smaller fabrication substrates (and smaller masks, accordingly).
The study demonstrated that for every sensing category (i.e., CAT1, CAT 2, CAT 3 and CAT 4), the sensing patches are statistically equivalent among themselves, which proves fabrication reproducibility, one of the main requirements when fabricating large volumes.
More specifically, after excluding the sensing categories that fall in the red zone of the heat map, i.e., that have been prone to high substrate shrinkage, the remnant sensors show d 33 values which are quite compatible with the state of art. All the sensing patches that lie in categories 1 and 4 have a systematic declining behavior for d 33 versus preload. This in turn is compatible with the nonlinearity of d 33 with respect to the preload and with the few nonlinearities in the stress-strain curve observed for the PDMS protective layer [18]. The same behavior was observed from tested fingertips sensors, belonging to patches that were specifically chosen as lying in the sweet spot on the heat map.
The current paper presents an effective, repeatable and simple characterization protocol to validate the skin patches. A laser positioning system would be useful to align the indenter with the sensor center, therefore reducing errors arising from indenter misalignment, especially when testing fingertip sensors characterized by small radius. Future studies should take this into account. A critical limitation of the developed model is the inability to predict the behavior of artificial sensors in real applications, since this would require another sensor integration procedure, including double-sided adhesive layers on both sensing patch surfaces to avoid sliding. This could be done in a future work.
The usage of e-skin patches in real scenarios (e.g., biomedical applications requiring sensorized gloves or prostheses) would likely lead to film degradation and consequent P(VDF-TrFE) aging and fatigue. Estimating the piezoelectric d 33 coefficient from the overall system response function is a practical tool to measure the reliability of e-skin degradation, whenever embedded sensors are not accessible anymore for a direct characterization. The model presented in this paper could be adapted to take into account the coupling procedure required to avoid sliding, including the deformable adhesive layers. However, measuring how the film degrades over time implies differentially comparing the current value of d 33 to an initial value, with no influence of the wrong estimation of that absolute initial value.