The ink-jet printed flexible interdigital capacitors: manufacturing and ageing tests

Correct operation of electronic circuits (including those made with the ink-jet printing technique) requires the electrical parameters of the structures to be constant or to be changeable, but in a predictable way. Due to that, the flexible, ink-jet printed interdigital capacitors (IDSs) were made and then tested in various conditions. We used the conductive silver-based Amepox AX JP-60n ink. As a substrate, we chose the transparent, flexible Melinex OD foil with a thickness of 125 µm. The IDCs were designed and their capacitances were simulated using Comsol Multiphysics Software. Then the test structures were fabricated by the ink-jet printing process using Dimatix DMP 2831 printer. The printed structures were subjected to environmental exposures in a climate chamber to check the influence of temperature and humidity on the tested samples. The IDCs were also subjected to cyclic bending and straightening tests to analyze the outflow of tensile forces on the printed structures, which are exposed to the common factors, that could diminish the quality of the printed and flexible devices. Due to the small capacitance values of the designed and made IDSs, the measurements showed the key importance of the measuring table on which flexible substrates with IDC capacitors were placed for their capacitance value. Performed tests also demonstrated that in most cases, the capacitors are characterized by an increase in capacitance by a few to a dozen or so % after the ageing tests. Obtained results could be a good groundwork for further research, that will include ways of preventing the creation of discontinuities—or minimizing their impact on the printed device performance.


Introduction
Capacitors are the most commonly used passive components.Their applications are not limited to only electronic devices.However, the development of areas strictly associated with electronics are in constant relationship in the evolution of these components.For instance, capacitors are used in applications such as decoupling or interference filters, signal circuits, and many more.Other, slightly more sophisticated applications are sensors [1][2][3][4][5] and actuators [6][7][8].Simultaneously with constant development of microelectronics technology, the possibility of manufacturing of such components also is increased.Among them, many techniques can be mentioned for fabricating the microelectronic planar components.Such techniques can be divided into two main fields, the subtractive (e.g.photolithography) and additive (e.g.screen-or ink-jet printing) ones.Ink-jet printing has been a well-known method of depositing inks on a generally planar substrate for several dozen years [9].The issue of printed electronics has been ongoing for several decades [10][11][12].However, the printing leaves a wide margin for adaptation of the printed components, which can be identified as its main advantage.Ink-jet printing is a technique that has been evolving in microelectronics steadily for more than half a century [13,14].It allows the choice of many materials as a substrate for circuits, including flexible ones, addressing wearable electronics [15], which is a constantly growing area.Such materials that can act as a substrate for ink-jet printing electronic devices or circuits are i.e. paper [16,17], polyethylene terephthalate [18,19], polyimide foils, for example Kapton [20], polyethylene naphthalate (PEN) [21], ceramics [22] and many others.All circuits that have been manufactured using ink-jet printing are the significant part of the area of 'printed electronics' .Importantly, the use of this technique assumes the planarity of the circuit components.Due to this, it was decided to develop a method to fabricate interdigital capacitors (IDCs), which are mentioned in the literature [23].Such capacitors can be manufactured using various techniques near printing methods.In microelectronics, the most common are those that are made using the techniques characteristic of semiconductor technology [24].However, techniques that are dedicated to silicon or glass substrates with undoubted advantages (resolution, repeatability) are the most expensive ones.
The durability of the material from which the electronic components are made is one of the most essential aspects of printing structures.In the case of ink-jet printed layers, they are characterized by sensitivity to mechanical microdamage and the degradation of applied inks due to oxidation of the printed metallization, especially silver [25,26].Due to that, it was decided to characterize the developed structures by an ageing process in the climate chamber to verify that it took into account the functional propertiescapacitance and dielectric loss factor.
Therefore, the paper presents the characteristics of the ink-jet printed IDC capacitors with various geometrical parameters with the verification of their resistance to harsh work conditions.The capacitors analyzed and presented in the article were made without dielectric ink.Of course, there are references in the literature to publications that include dielectric ink for high-energy storage [27] or highly flexible electrochromic and energy storage devices [28].

Simulations-design
The geometry of ID capacitors was developed using COMSOL Multiphysics Software with AC/DC module, the stationary mode.The capacitors were modeled with the assumption that the area surrounding the simulated structure was filled by air with a relative permittivity of 1.The simulated voltage between the electrodes was 1 V and the zero charge on the outer surface was chosen.The constant dimensions were the thicknesses of the electrodes (0.005 mm) and the substrate (0.125 mm).The thickness of the substrate was determined by the real thickness of the Melinex OD.In the case of the thickness of the electrode, such dimension was dictated by simplifying the simulation process because, due to the literature, such dimension in the case of IDC capacitors has an omittable influence on the capacitance.The capacitor parameters, which vary during the simulations, were the number of IDC fingers as well as the width and length of these fingers.The conductivity of the electrodes was 5.3•10 6 S m −1 , which is an exact value of the ink-jet printed silver conductive paths [29].Due to the fact that the structures presented in this paper are made using a process comparable with that of the same ink-jet printer and using AMEPOX ink, it can be assumed that the final conductivity of the silver ink is comparable to that presented in [29].Furthermore, the conductivity is lower than the model value of the silver conductivity (6•10 7 S m −1 ) due to the incomplete sintering of silver nanograins as well as the coffee-ring effect and the uneven surface of the printed structures [30].The literature states that the coffee ring effect negatively affects the morphology of the structure and causes electrical changes and, obviously, the inability to obtain a uniform structure.Also, unwanted pores of air or inclusions solvents could increase the resistivity of the printed structure.Moreover, microdiscontinuities usually occur in ink-jet printed structures in the sintering process.
The relative permittivity of the Melinex substrate was 3.1, the dielectric strength was 125 kV mm −1 , the dissipation factor 0.01.The performed simulations confirmed that the change of conductivity of the electrodes has an omittable (0.0001%) influence on the capacitance.The dimensions of the capacitors (the finger's length; the height of the electrode, which is the sum of the widths of the fingers and gaps' widths; the width of the finger; the width of the length of the gap; the length of the feed line length; the substrate thickness; the thickness of the printed silver electrode) were schematically highlighted in figure 1.
The dimensions aforementioned were as follows: the width of the IDC finger (figure 1(c)) in each simulation was equal to the gap between the fingers (figure 1(d)) and have three values (0.5 mm, 1.0 mm, and 1.5 mm).The length of the IDC fingers (figure 1(a)) was 20 mm.The feed lines were characterized by a width equal to the IDC fingers, and their width was equal to the double width of the gap between fingers.The mesh during the simulation process was set on the physics-dependence.
The substrate and silver electrode thicknesses (figures 1(f) and (g)) are also constant.The results of the capacitance simulation are presented in figure 2.
As can be seen in figure 3, the area surrounding the IDC electrodes is characterized by a scattered electric field, and has a significant impact on the resultant capacitance.Such a phenomenon is typical for the chosen structure of the capacitor.Moreover, as expected, the number of fingers is strongly related to the capacitance obtained.It can be observed in figure 2,  for example, for capacitors with 4 and 8 fingers with a width of 1.5 mm, where the capacitance is about 1 pF and 2 pF, respectively.Similarly, this relationship is observable for each modeled geometry with the capacitance obtained.This capacitance can be described by the equation , where C t is the total capacitance of the IDC and n is the number of fingers in the structure.
After simulations, the development of the real capacitors could be performed.

Materials and ink-jet printing process
Regardless of which ink-jet printing process with any conductive material is considered as the functional phase of the ink, it consists of three basic steps: substrate preparation, printing, and sintering [31], as shown in figure 4.
The cleaning of the substrate ensures removal of any contamination that could affect the print quality due to the increasing heterogeneity of the printed mosaic and unpredictable changes in the surface tension of the ink.In the described research, Melinex OD (thickness: 0.125 mm) was chosen as the substrate and the cleaning process was carried out using Branson 8210 ultrasonic cleaner for 15 min at room temperature.Isopropyl alcohol was used as a solvent.Then, all substrates were dried for 15 min at room temperature.
Directly before printing, the ink (Amepox Microelectronics Ltd Nano Ink AX JP-60n) was agitated to remove aggregation and agglomeration of the particles contained there using an ultrasonic cleaner (Branson 8210) for 15 min.The ink was then placed in the 10 pl cartridge and the capacitors were printed using a Dimatix 2831 ink-jet printer with a drop spacing of 0.015 mm.A single layer was printed using three nozzles.For the duration of printing, the cartridge was at room temperature and the platen was 35 • C to make the solvent in the ink evaporate more sufficiently.
Sintering, the final step, was performed in a Binder GmbH convection oven at 160 • C for 60 min.
The exemplary printed IDC is shown in figure 5 and the finished measurement array consisting of 40 capacitors is shown in figure 6.

Capacitance measurements
The Hewlett Packard 4263A LCR meter was used to measure the capacitance and tan δ (dielectric losses) of IDC samples.For measurements a frequency of 10 kHz and a potential of 1 V were used.The capacitance values are the average of slow measurements of the same capacitor, which is an available tool using the aforementioned LCR meter and the measured mode was serial capacitance with an accuracy of 0.5%.Each printed series consisted of ten capacitors.Before measurements were performed, the LCR meter was calibrated according to the manufacturer's recommendations.The measuring cable was 1 meter long.Spring probes were used to minimize the possibility of scratching and scraping the structures, which could affect the surface and, consequently, change the electrical parameters.After calibration, measurements were performed on two media-a ceramic table and a container, which simulated the placement of the IDC directly in the air on the relatively thin substrate.It was motivated by the fact that the capacitance of IDCs strongly depends on the medium in which the measurement is performed and it is characteristic for each planar circuit.The use of two sets of controls was motivated by changing the influence of relative permittivity on the capacitance of the IDCs.As was mentioned above, the measurement using a container provided the conditions that were comparable to the simulated ones due to the provision of the surround of the whole IDC by the air (figure 7(b)).On the other hand, the use of a ceramic table allowed  one to check the surrounding with a higher effective permittivity (about 7-10, figure 7(a)).The scheme of the two setups (the IDC on the table and in air-with a container under the substrate) is shown in figure 7.
It was decided to calculate and present the average value and the median.The average value of the capacitance describes the possibly value of the capacitance that could be obtained using the technique described in this paper.The median, on the other hand, provides information about the repeatability of the IDC parameters and tolerance.Furthermore, the standard deviation shows the repeatability of  the fabricated structures and, hence, the dispersion between the designed and obtained values.This parameter can be identified as an expected tolerance.The results obtained are included in figures 8 and 9.
Based on figures 8 and 9, it can be concluded that increasing the number of fingers results in obtaining a higher capacitance, which was expected.Furthermore, the larger the number of fingers, the more noticeable the difference.Additionally, the capacitances of the capacitors measured on the ceramic table are approximately 25% higher than the capacitances measured on the container (with electrodes surrounded by air).The tan δ (dielectric losses) is 0.0018 for measurement on the table and 0.0017 for measurement on the container for each capacitor.For narrower electrodes, the standard deviation was higher than for 1.0 and 1.5 mm.The standard deviation determined for data shows that the dispersion increases for the capacitors with smaller width-the grey ones of the 0.5 mm width have the higher dispersion.This can be caused by discontinuities generated during the ink-jet printing process-the edges of the electrodes are not straight and, due to that, affect the surface between the electrodes in a random manner.

Accelerated ageing
A Binder MKF-115 climate chamber was used for the ageing tests.Ageing tests were performed on samples that contained the most silver, i.e. on capacitors with a finger width of 1.5 mm.The profile used during the ageing tests included a variable temperature cycle with extremes of −10 • C and 50 • C with a rise and fall gradient of ±2 • C min −1 (as shown in figure 10).Firstly, the samples were kept at 50 • C for 12 h, then the temperature was reduced to −10 • C in 30 min, and then the samples were kept at this temperature for 12 h.This was followed by an increase in temperature to 50 • C in 30 min and then again maintained at this temperature for 12 h.The full cycle continued uninterrupted for 125 h.The initial humidity was 40%.It was decided to choose such a temperature range to exclude substrate interaction (the effect of temperature changes on substrate parameters) [32].
After testing, the capacitors were again measured with a Hewlett Packard 4263A LCR meter.The results are shown in figure 11.The chart takes into account the percentage difference in capacity relative to the initial value.
A comparison between the capacitance before (figure 9) and after (figure 11) ageing tests shows that a slight increase of capacitance (about 0.2 pF) for each type of IDC capacitor.Analyzing figures 9 and 11, it can be observed that for 4 fingers, the average capacitance of the capacitors after the tests in the climate chamber for the measurements on the ceramic table changed: 0.17 pF (about 16%) for 4 fingers, and for 10 fingers it changed by 0.28 pF (7.9%).Similarly, for the measurements on the covered container, the average capacitance changed by 0.36 pF (23%) for 4 fingers and by 0.95 pF (10%) for 10.The medians were for ceramic table measurements: 0.16 pF (4 fingers) and 0.36 pF (10 fingers), while for containers covered measurements they were 0.39 pF (for 4 fingers) and 1.03 pF (for 10 squares).The standard deviation for fingers is 0.16 (for measurements on a ceramic table) and 0.39 (on container covered), while for 10 fingers it is 0.33 (for measurements on a ceramic table) and 1.03 (on container covered).More capacitance changes in capacitance occurred with measurements on the covered container.The close result was obtained for the dielectric losses.However, the standard deviation presented for each average capacitance is visibly higher than for the probes before ageing treatment.In addition, the average and median values for each capacitor geometry differ in contrast to those treated in the chamber samples.
Although the reproducibility of the capacitance significantly deteriorated, to characterize the changes of the electrode surface structures, it was decided to examine the printed capacitors by the LEICA 4000M optical microscope.The images obtained are presented in figure 12.
The view of electrode before exposure is shown in figure 12(a) whereas after the ageing in the chamber is visible in figure 12(b).It can be seen that the electrode after the thermal cycles in the climate chamber is slightly cracked and has a high degree of unevenness, especially at the edges.
As can be seen, there are many damages that have an influence on the characteristics of the printed structure.Visible discontinuities, mostly close to the edges of the printed structures, are possibly the cause of capacitance changes and increase the standard deviation.The microdiscontinuities are possibly caused by the absorbance of water (moisture) by the printed ink with changes in temperature in the ageing chamber.Based on the obtained results, it is  concluded that, in the case of further use of inkjet printed IDCs in harsh environments (more than once) it is necessary to protect the structure from the effects of temperature changes.

Bending tests
A self-made device based on stepper motors was used for the tensile bending test (figure 13).The components performed 100 bends and straightening cycles per minute.As in the ageing tests, the samples that contained the most silver (capacitors with a finger width of 1.5 mm) were used.The tests lasted more than 42 h, and capacitances were measured every 3 h (every 11 000 bends).After testing, the capacitors were observed under the microscope (figure 12(c)) and again measured with a Hewlett Packard 4263A LCR meter.The Analogously to chamber tests, measurements were taken on a ceramic table and a stretched Melinex film (on air).The results are shown in figure 14.
Bending tests revealed that the tested structures tended to have a decreasing capacity swap.Cracks at the edges of the structures were also observed again.This is because the thicker layers crack first.More printed material is found at the corners of the structures due to the coffee-ring effect.

Discussion
The literature shows that the capacitance of such capacitor results directly from the distance between the electrodes and the value of the permittivity of the dielectric that is between them.The investigations carried out show that each of these parameters significantly influences the capacitance value, as expected.When the measurement conditions (in air and on the ceramic table) it was possible to verify the impact of the permittivity on the capacitance value, which was also expected.Moreover, the capacitance of the IDCs tested directly on the table was higher, because of the difference in the effective permittivity of the medium, where the IDCs have been placed.For most ceramic materials, the relative permittivity is about 7-10, while for air it is very close to 1.With the interdigital geometry of the capacitor electrodes, which provides the more scattered distribution of the electric field around the electrodes, it was expected phenomenon.The table had a significantly higher value of permittivity than that of air, which should have increased the measured capacitance.Indeed, the Melinex OD substrate allowed the capacitance to vary with the measurement conditions, which offers prospects for further sensing applications of printed structures.Furthermore, as expected, it is seen that increasing the number of fingers (which has an impact on the area between the electrodes) has a linear effect on the capacitance values.Moreover, changing the distance between the electrodes affected the capacitance proportionally.Thus, the authors conclude that using the proposed technology, it is possible to produce a capacitor with the desired parameters, and the choice of IDC geometry provides a suitable basis for likely applications as sensors.One of the possible ways to check in the further research is the use of capacity changes in the i.e. temperature or humidity determining.
Due to the fact that sensors frequently work in harsh environments, it was decided to carry out ageing tests.The results show that, for sensors with IDC configuration and ink-jet printed electrodes, the change in parameters is slight but noticeable and probably irreversible.The possibly reason for changing the capacitance could be the appearance of water in the printed structure due to repeatable changes of the ambient air temperature.Thus, this water probably indicates the presence of microdiscontinuities.This issue requires further research to prevent the aforementioned risk.Moreover, the printed metallization layer itself is sensitive to mechanical damage.Therefore, in the case where an IDC would be exposed to mechanical damage to the conductive layer, it would be recommended to cover the layer with a material that would provide protection.It would have a minimal influence on the permittivity and then cause slight changes in the capacitance (to the higher values).

Conclusion
Interdigital structures are an important part of many electronic devices.Many of them are fabricated using techniques which are characteristic of microelectronics.In this work, the IDSs were designed, fabricated, measured, and treated by various conditions in the ageing chamber.The geometry varied (0.5-, 1.0-, and 1.5 mm width of each printed finger) due to the change in the area between the electrodes to test the repeatability of the printed structures.As can be seen, such capacitors in most cases are characterized by a higher capacitance (changed from 0.2 pF to almost 1 pF depending on the number of fingers) after the ageing process.This phenomenon is due to the oxidation and cracking of the printed layers.The capacitance of a fingering capacitor is also affected by the relative electrical permeability of the medium.The influence of this parameter can be seen in the difference in capacitance values measured on the ceramic table (tabletop measurement) and on the strained Melinex OD film (air measurement).The capacitance of the structures measured on the tabletop was higher, which is a direct result of the difference in the effective permeability of the medium.For most ceramic materials, the relative permeability is about 7-10, while for air, it is about 1.The developed structures can be used as a part of planar electronic circuits with relatively stable parameters.
The next part of the planned research will consist of verifying the possibilities of securing ink-jet printed layer possibilities, such as the coating of the printed layers by the various materials (i.e.polymer layers) and then performing the ageing tests.Such an approach could reduce the undesirable influence of environmental conditions on the parameters of the printed layer.Moreover, the conducted research could be a base for the fabricating a novel and promising area of capacitors-supercapacitors, that could also be designed and fabricated on the flexible substrates and gives another possibilities of improving many areas, such as textronics, sustainable building design and many others [28,33,34].

Figure 1 .
Figure 1.The scheme of the geometry of the capacitors.As an example, the IDC with 8 fingers was chosen.The dimensions of the capacitors are as follows: the length of the finger (a); the height of the electrode (b), which is the sum of the widths of the fingers and gaps' widths; the width of the finger (c); the width of the gap (d); the length of the feed line (e); the thickness of the substrate (f); the thickness of the printed silver electrode (g).

Figure 2 .
Figure 2. The results of the simulated capacitance (in stationary mode).

Figure 3 .
Figure 3.The exemplary electric potential of the presented interdigital capacitor model.In that case modeling in COMSOL Multiphysics was performed in stationary mode with the difference between the high (red electrode) and low potential (blue electrode) equal to 1 V.

Figure 4 .
Figure 4. Scheme of the ink-jet printing process (substrate preparation in ultrasonic cleaner, printing and then sintering in convection oven).

Figure 5 .
Figure 5.The printed and sintered IDC on the Melinex substrate.

Figure 6 .
Figure 6.A photo of IDC's array consisted of 40 capacitors.

Figure 7 .
Figure 7.The measurement setup scheme on the table (a) and in the air (b).

Figure 8 .
Figure 8. results of the capacitance (mean with the standard deviation and median) for the IDC's consisted of 4, 6, 8 and 10 fingers-the setup on the container (with the air as a surround).

Figure 9 .
Figure 9.The results of the capacitance (mean with the standard deviation and median) for the IDC's consisted of 4, 6, 8 and 10 fingers-the setup on the ceramic table (with the air and ceramic material as a dielectric surround).

Figure 10 .
Figure 10.One temperature cycle in the ageing chamber, on which the capacitors were exposed.

Figure 11 .
Figure 11.The received results of the IDC capacitance for the electrodes 1.5 mm width after the ageing tests.The tan δ (dielectric losses) is 0.017 for measurement on the table and 0.016 for measurement in air.

Figure 12 .
Figure 12.The exemplary structures of the capacitor (a) before, (b) the climate-chamber and (c) after bending test.The images has been taken with the use of white table to show the exact shape of the printed structure and the damages that appeared after climate chamber process.

Figure 13 .
Figure 13.The device for bending test.

Figure 14 .
Figure 14.The change of capacity after bending tests.