In this paper, a rapid prototyping method for fabrication of highly conductive micropatterns on insulating substrates was developed and evaluated. Sub-20 μm microstructures were printed on flexible insulating substrates using alternating current (AC) modulated electrohydrodynamic jet (e-jet) printing. The presented technique resolved the challenge of current rapid prototyping methods in terms of limited resolution and conductivity for microelectronic components for flexible electronics. Significant variables of fabrication process, including voltage, plotting speeds, curing temperature, and multilayer effect, were investigated to achieve reliable printing of silver tracks. Sub-20 μm silver tracks were successfully fabricated with resistivity about three times than bulk silver on flexible substrates, which indicates the potential applications of electrohydrodynamic printing in flexible electronics and medical applications, such as lab-on-chip systems.

## Introduction

Printing technology and printed electronics have been one of the key technologies for flexible production of electronic devices for over the past five decades [1]. Great efforts have been made to apply printing technology into electronic manufacturing, including commonly used printed circuit boards [2], displays [3,4], and other applications for different functional materials [57]. In recent years, printed electronics has grown into new stages with advances along emerging flexible electronics [8], which significantly affect printing industry by requiring new printing techniques with various novel materials for novel device design.

Inkjet-based additive printing has been widely used for printed electronics for the deposition of functional materials onto substrates [9]. There are many successful applications based on inkjet printing, such as lighting (organic light-emitting diode), solar cells [10], displays [11], antennas of radio-frequency identification (RFID) tags [12], and electronic components like memories, batteries, interconnectors, etc. [13]. Inkjet printing provides several advantages in many applications, include: (1) it reduces setup cost and production cost comparing with silicon-based microfabrication methods; (2) it is capable of fabricating lightweight and high-quality patterns for large-area electronic devices, making it fully compatible to flexible electronics and wearable devices; (3) it is a perfect solution for rapid prototyping considering its low setup cost and flexibility, regardless of mechanical property of substrates; and (4) it is material efficient, requiring low energy both in manufacturing process and operation.

Despite its wide applications, the minimum dimension of droplets of traditional acoustic or thermal inkjet printing is limited (10–60 μm in diameter as sphere) [1416]. The final ink spot will be two to four times the droplet dimension in most cases for aqueous ink droplet falling onto substrates [17]. For micro/nano-applications where higher resolution is required, more precise fabrication techniques will be desirable. Chen and Wise described the fabrication of high-resolution nozzle array for inkjet printing [18]. However, it is costly and physically challenging to improve resolution by reducing nozzle dimension. Meanwhile, electrohydrodynamic printing was introduced as an alternative printing method to achieve better resolution [19]. Electrohydrodynamic theory was first discovered by Zeleny back in 1910s [20]. Electrospraying and electrospinning using the electrohydrodynamic behavior have already been commercialized in industry. Different functioning modes of electrohydrodynamic theory have been studied and reported, for example, cone-jet mode, multijet mode, microdripping, etc. [21]. E-jet printing is a high-resolution printing method, which prints fine droplets by applying a high voltage between the nozzle and the substrate. When the voltage is applied, electrical fields will be generated around the nozzle. With sufficient electrical potential, the liquid ink will form a meniscus at the tip of the nozzle [22]. Once electrical force is strong enough to break surface tension, there will be droplets emitting out from the meniscus [23].

E-jet printing is a promising fabrication method to achieve high-resolution printing, since the dimension of emitted droplets is significantly reduced and much smaller than nozzle dimension. E-jet printing has been reported for the fabrication of metallic patterns [24,25] and microelectrodes [26]. Compared with commercialized inkjet printing, there are many issues that remain to be experimentally and theoretically addressed for e-jet printing. First, new researches have invented many novel advanced nano-inks, including silver nano-ink [27,28], copper nano-ink [29,30], gold nano-ink [31], and high viscous pastelike silver ink [32]. Researchers have to characterize these inks before it can be adapted in the fabrication process since each of them owns different fluidic properties. Second, many parameters, such as voltages, distance between nozzle and substrate, and printing speed, are involved in the printing process, making it extremely difficult to model and simulate e-jet printing. There are previous studies on the droplet formation, flight behavior of the droplets, and the ejection modes [3336], but empirical models of the printing process need to be further studied for process planning. More researches about printing conditions and parameters for e-jet printing need to be conducted in terms of ink characterization and process control [37].

DC-voltage is commonly applied in e-jet printing but process controllability of using DC voltage is limited because the voltage affects both printing frequency and droplet size [38]. Another challenge of DC voltage based e-jet printing is residual charge problems. When printing on highly insulating substrates, such as commonly used polyethylene terephthalate (PET) film and Ajinomoto build-up films (ABF), the residue charges of the printed patterns will not dissipate quickly, which will change the electrostatic field distribution of printing setup. For microelectronic applications, electrical performance and resolution of printed devices need to be investigated at the same time. Youn reported using a tilted-outlet nozzle for better resolution of printed patterns [39]. Lee et al. reported depositing silver tracks onto polyimide film by e-jet printing, obtaining conductor lines with resistivity about three times than bulk silver (1.6 μΩ·cm) but relative low resolution (200 μm in width and 0.3–5 μm in thickness) [40]. More researches need to be conducted to address these challenges, proposing feasible techniques that can fabricate microelectronic devices with both high-resolution and great electrical performance.

In this paper, a new AC-modulated e-jet technique was applied for direct printing of high-resolution conductive patterns on highly insulating substrates. The feasibility of patterning conductive silver tracks with both high resolution and high conductivity was demonstrated in the paper. By applying modulated AC voltage to electrohydrodynamically induce fluid flows through microcapillary nozzles, a stable jet of nanometallic silver ink can be printed onto highly insulating substrates. Sub-20 μm metallic silver tracks were obtained with resistivity about three times of bulk silver. The fabrication process is capable of drop-on-demand printing on highly insulating substrate, where residue charge is difficult to be transmitted or neutralized. The presented technique is suitable to fabricate electronic components, such as resistors, inductors, and micro-interconnects, which offer a simple and versatile method to drop-on-demand direct fabricate conductive patterns for flexible electronics and printed electronics [41]. Details of the proposed AC-modulated e-jet printing were presented in Sec. 2.

## AC-Pulse Modulated E-Jet Printing

In this paper, an AC-pulse modulated e-jet printing was applied for the fabrication of conductive silver tracks. The controllable parameters during fabrication include pressure applied to syringe, height between nozzle and substrate, applied electrical potential between nozzle tip and substrate, surface thickness, and plotting speeds of the three-axis stage. Detailed characterization of these parameters for droplet formation was presented in our earlier works in Refs. [4244].

In e-jet printing, a voltage applied to the nozzle tip causes mobile charged particles to be accumulated at the tip of the nozzle, forming a meniscus. When the electrical force overcomes the surface tension of the meniscus, a droplet or a jet is formed in the cone-jet mode. As shown in Fig. 1, the three-axis positioning system was programed to provide relatively planar displacement of substrates and up-and-down displacement of nozzle, simultaneously controlling the plotting speed from the nozzle and the trajectory of tracks in order to print patterns on substrates. The voltage was applied between the nozzle and the bottom electrode by a signal generator and a voltage amplifier.

In this study, AC-pulse modulated voltage was applied to print conductive silver tracks on the substrate. It was a challenge for traditional e-jet printing that used DC voltage between nozzle and substrates to print conductive ink onto highly insulating substrates. The insulating substrate cannot dissipate residual charges remained inside printed droplets. These residual charges will affect electric field distribution between nozzle and substrate. Two scenarios can possibly happen: (1) droplets will be deflected because its net charge owns the same polarity as accumulated charges on the substrate and (2) missing printing spot and discontinuous tracks when the electrical stress is not enough for droplet formation because of residual charges on the substrate. By using AC-pulse voltage in e-jet printing, the undesired residual charge problems were minimized, which enable the printing of high-resolution features on highly insulating substrates.

Figure 2 showed the mechanism of e-jet fabrication process with the AC-pulse modulated voltage. AC-pulse signal with the waveform shown in Fig. 2 was applied between the substrate and the nozzle. Two essential parameters to control e-jet printing process were amplitude and frequency of AC-pulse voltage. Amplitude of voltage will affect electrical field and electrical stress for jet formation when electrical static force of charged particles was greater than surface tension. Frequency of pulse voltage will affect charge accumulation time at the nozzle tip and formation of droplet. With proper amplitude and frequency, each positive and negative pulse will induce a droplet sequentially, which means printing frequency is twice as pulse frequency. At the same time, the printed sequential positive and negative charged droplets will neutralize each other on the substrate. In this case, the residual charge issues for printing on insulating materials were well resolved and the printed patterns returned to electrically neutral state.

It was critical to obtain both high resolution and low resistivity of printed tracks in micromanufacturing. To achieve these objectives, several concerns need to be addressed. First, silver nano-ink was different from bulk silver. The inevitable voids generated between particles and additives in the nano-ink will reduce the conductivity of printed silver tracks. Second, as a high-resolution printing approach, very small droplets were printed by e-jet printing approach. As a result, a smaller volume of droplets included less amounts of silver nanoparticles. When printed on substrate, its interconnectivity will be poor and cannot carry satisfactory current flow. There are connectivity problems of single-layer patterns because of voids between particles and additives from nano-ink. To acquire highly conductive microtracks with good connectivity of printed metal particles, multilayered printing was attempted by direct printing on top of each other in the study with sacrificed resolution. In Sec. 3, possible technical approaches were discussed to address these issues.

## Materials and Experimental Details

In this section, experiments on process control of e-jet printing of conductive silver tracks were discussed. Electrical performance of printed patterns was also investigated. Detailed results of characterization were presented in this section.

The experimental setup for e-jet printing was shown in Fig. 3(a). The additive printing system was capable of on-demand printing of microstructures using not only conductive inks but also polymers [42], wax materials [34], etc. The positioning system was configured to move in xyz directions with 0.1 μm repeatability and accuracy. As shown in Fig. 3(a), the positioning system can be programed to provide planar movement for substrate in the X–Y direction with a displacement range of 100 × 100 mm, and up-and-down motion for nozzle in Z direction with a displacement range of 50 mm. A pneumatic syringe was used to provide pressure for e-jet printing to keep required flow rate with maximum pressure of 5 psi and 0.05 psi resolution.

AC-pulse modulated voltage was applied between top electrode (nozzle) and bottom electrode. The nozzle, which was made of glass with a conical nozzle tip, was coated with gold and platinum first in order to function as the top electrode. The bottom ground electrode was a silicon wafer with aluminum coating. The input voltage was programed by a signal generator (Agilent Technologies, Model 33220A) and amplified by a high-voltage source meter (Cole Parmer, Model 9741-50) before supplying to the electrodes.

The optical camera was adapted to monitor fabrication process with a 0.5 μm resolution, as shown in Fig. 3(b) with illumination on the other side posting shade of nozzle and jet. From the image of the camera, we were able to identify the cone-jet working mode of e-jet printing, in accordance with the functioning mode of electrohydrodynamic theory [12], indicating that silver nano-ink works well in our e-jet printing system.

We used silver nano-ink in our e-jet printing system and characterized its property in our experiment. Silver nano-ink was purchased from Advanced Nano Product with 30–35% solid content. The solvent was triethylene glycol monoethyl ether with small amounts of lubricants and surfactants to prevent agglomeration between silver nanoparticles. The curing temperature was about 120–150 °C from the company’s data sheet, and viscosity was in the range of 10−1 cP. Three types of substrates used in the study were microscopic glass slides (100 mm × 25 mm × 1 mm) and two highly insulating substrates, 1 mm thick ABF film coated on glass slides, and 1 mm thick PET film, which was one of the most widely used materials used for flexible electronics.

In this work, the experiments were conducted as follows: First, pulse frequency and voltage amplitude were investigated to achieve continuous traces on highly insulating substrate. The AC-pulse frequency was used to control printing frequency because each positive or negative pulse produced a droplet. As a result, printing frequency was expected to double pulse frequency. The amplitude of voltage determined electrical field to form droplets. An optimal frequency and voltage will be identified for obtaining stable nano-ink jet. Second, plotting speed was characterized for continuous features of printed single-layer pattern. There is a corresponding maximum plotting speed for each fixed input voltage signal. By regulating amplitude, frequency of input voltage, and plotting speed, we were able to print continuous silver tracks with best resolution. Third, electrical characterization was conducted, including effect of multilayer and curing temperature on conductivity of printed patterns. The resistance of printed silver tracks was measured using two point probe methods, and details will be discussed in Sec. 4.

The process characterization was performed on glass slides. After the process conditions were identified, continuous silver tracks and silver interconnectors were directly printed on to glass substrates as well as insulating PET and ABF film. The shape and dimension of printed patterns was observed using high-resolution microscope (KH 770 from Hirox, and infinite 1 from Lumenera Corporation) and atomic force microscope (AFM) (Park Systems).

## Modeling of Printing and Track-Formation Mechanism

A three-dimensional AFM image of printed dots was shown in Fig. 4. Based on the measurements of printed silver droplets, we were able to calculate and analyze the track-formation mechanism of the AC-modulated e-jet printing process. Our assumptions included: (1) the printed droplets were cylindrical, and their volume can be estimated by the average height h and diameter d of printed dots on substrate, which can be measured from AFM image, as shown in Fig. 4; (2) the volume loss of evaporated solvents during the printing process was negligible. An equivalent sphere was used to estimate the volume of the falling droplet; and (3) current in the meniscus was stable and proportion to voltage. During the printing process, the accumulated charges in the meniscus result in the formation of droplets. The total amount of charges in a droplet can be estimated by the integration of electrical voltage and time. As will be shown later, the track line width will be larger with increased amplitude of voltage and decreased frequency (increased cycle time), which meant more charges accumulate during the time interval.

Figure 5 showed the mechanism of track formation from the falling droplets and the microscopic measurement of cross section of printed silver tracks. As shown in Fig. 5(a), once a droplet was formed, it would fall off and flatten on the substrate to form a dot. The volume of droplets and dots was equal. For a printed track width of d, we were interested in knowing what the initial drop size d0 should be. The volume of a printed droplet was found to be

$Vprint=π×(d2)2×h$
(1)
where Vprint is the volume of printed droplets, h is the average height of printed droplets, and d is the diameter of printed droplets. The actual volume of a falling drop can be found to be
$Vdroplet=43×π×(d02)3$
(2)
where Vdroplet is the actual volume of falling droplets, and d0 is the actual diameter of falling droplets. Since the volume of the falling droplet is the same as the volume of the printed drop, one has the following equation:
$Vprint=Vdroplet, →π×(d2)2×h=43×π×(d02)3$
(3)
By rearranging Eq. (3), one can find the droplet size d0 to be
(4)

Equation (4) can be used to estimate the e-jet printing droplet size. Once we measured the average height and diameter of printed dot on the substrate, the actual size of the inflight droplet can be calculated using Eq. (4).

As shown in Fig. 5(b), in order to print connective silver tracks instead of separate dots on substrates, two adjacent droplets had to be at least tangential to each other. The time between two adjacent droplets was half of the cycle time of AC voltage. The maximum plotting speed can be calculated using the following equation. Assuming T was the cycle time of AC voltage, and f was the frequency of AC voltage, the maximum plotting speed vmax can be found as follows:
(5)

where T = 1/f, f is the frequency of AC voltage, Td = T/2, Td is the time between two adjacent droplets, d is the diameter of printed droplets, and vmax is the maximum plotting speed.

Equation (5) can be used to select a proper plotting speed in the AC-modulated e-jet printing process. As shown in Eq. (5), the plotting speed for e-jet printing was determined by the frequency of the AC voltage used in e-jet printing process. Figure 5(c) showed the cross section profile of the printed silver dots with an average height of 30.73 nm and an average line width of 6.06 μm.

## Results and Discussion

It was essential to adapt proper process parameters to obtain stable e-jet printing to achieve better printing performance. A distance of 10 μm between nozzle and substrate was chosen in our experiments. When investigating different conditions in e-jet printing, one process parameter was changed at a time while keeping all the others constant for characterization. In Sec. 5.1, effects of amplitude and frequency of the input voltage, plotting speed, curing temperature, and morphology of printed patterns were demonstrated and discussed for achieving higher resolution and conductivity of silver tracks.

### Amplitude and Frequency of AC-Pulse Voltage.

As shown in Figs. 3(b) and 3(c), in AC-pulse modulated e-jet printing, the microscale fine jet is generated at the tip of ink meniscus when enough charge accumulates at the tip of the meniscus. The system worked at cone-jet mode when electric stress resulting from applied voltage deforms the ink at the nozzle tip. A droplet was formed when the electrical force was greater than the surface tension.

As shown in Fig. 6(a), we printed silver tracks with changing amplitudes of input pulse voltage while keeping other parameters constant to find its effect on e-jet printing. The diameter of nozzle was 7 μm, feed rate was 9 mm/s, pulse frequency was fixed at 1000 Hz, and duty rate was 10%. The line width of printed silver with respect to pulse amplitude was shown in Fig. 6(b). It can be clearly observed that with increasing amplitude, line width of printed silver tracks was increased. The results were in accordance with results based on DC voltage. With larger amplitudes, there will be more charge accumulation at the meniscus, thus bigger droplet sizes.

The printing frequency was double of the pulse frequency because each positive or negative pulse would produce a droplet. This is how we solved the residual charge problems of e-jet printing by neutralizing printed charges with alternative positive and negative droplets for continuous patterning. We used a fixed voltage of 400 V, a fixed duty rate of 10%, and plotting speed of 9 mm/s with different pulse frequencies to study its effect, as shown in Fig. 6(c). Based on the measurement from Fig. 6(d), a reduced line width of printed silver tracks was observed with increased frequency. Larger pulse frequency meant shorter duration for charge accumulation with same duty cycle and amplitude of input voltage, thus generating a smaller droplet. It was noticed that when frequency was larger than 1000 Hz, discontinuous pattern was formed because duration time was too short to produce droplets to maintain a continuous track. It was the balance between amplitude and frequency that generates best resolution with continuous features. With fixed pulse amplitude of 400 V, frequency of 1000 Hz, and duty rate of 10%, we were able to print stable continuous silver tracks with smallest line width. These parameters will be adapted in the following experiments.

### Plotting Speed and Droplet Size.

Based on our previous analytical model, we were able to characterize plotting speed and estimate droplet size on single-layer printing process. Using Eqs. (1)(5), one can find the maximum e-jet printing plotting speed vmax and the actual droplet size d0 for the process, shown as follows:
Using the process parameters and Eq. (5), the maximum e-jet printing plotting speed vmax can be found as follows:
By using Eq. (4), the droplet size d0 can be found as follows:

As shown in Fig. 5(c), the cross section of printed silver dots had an average height of 30.73 nm and an average line width of 6.06 μm. By using Eqs. (4) and (5), the maximum speed vmax for connective silver tracks was 12.12 mm/s, and the actual diameter of falling droplets was 0.92 μm. The ratio of diameter of nozzle and diameter of falling droplets was about 7.6.

Plotting speed determined droplet spacing and overlap when all the other parameters were kept constant. Figure 7 showed printed patterns from discontinuous silver dots to continuous silver with decreasing plotting speed from 16.5 mm/s to 7.5 mm/s. When plotting at a smaller plotting speed slower than the calculated vmax by Eq. (5), we were able to acquire stable and continuous silver tracks during our experiments. As the plotting speed increased, the width of silver tracks reduced gradually because of less ink accumulation along printed silver tracks, as shown in Fig. 7 with plotting speed increased from 7.5 mm/s to 10 mm/s. Two adjacent droplets had to have a minimum overlap in order for continuous patterns. As observed from experiments, with high plotting speed (13.5–16 mm/s), there was no or not enough overlap between two adjacent droplets, thus resulting in discontinuous patterns. Though some of the droplets were connected, the overall continuity was interrupted. The results helped to prove that the maximum speed for connective silver tracks was about 12.12 mm/s predicted by Eq. (5).

### Multilayer Printing.

During the printing process, the substrate was moved with programed trajectory for single-layer and multilayer printing in order to study the effect of connectivity on electrical performance. To achieve good conductivity of the printed trackers, the connectivity of the conductive components (silver nanoparticles in this study) in the ink was an important factor that needs to be controlled. The dimension of silver nanoparticles in the ink was about 30–50 nm, encapsulated by polymer shell to avoid coagulation. There were also certain amount of lubricants, surfactants, and solvent in the nano-ink to keep it at the stable suspension state. Silver nano-ink will transfer from liquid suspension state into solid state when most of the solvents are evaporated. In this paper, the effects of nanoparticle connectivity and its impact on the conductivity of the printed tracks were studied. Figure 8 showed the connectivity of silver nanoparticles on the printed single-layer and multilayers silver tracks.

Due to the low viscosity of silver nano-ink, as droplets fall onto the substrate, the droplets will spread on the substrate. As shown in Fig. 8(a), single particle hillocks can be observed in single-layer e-jet printed silver track. The separate particle hillocks resulted in a poor connectivity condition for silver tracks. As a result, these cracks and gaps inside silver tracks significantly reduce the conductivity of printed patterns. From Fig. 8(c), the maximum height for printed single-layer silver track was measured to be 46 nm. Only one or two nanoparticles were overlaid in the silver track considering that the diameter of silver nanoparticles was about 30–50 nm.

By printing multiple times at the same position, we can print multiple silver layers (20 layers in this example) for the track with fine semi-ellipse cross section, as shown in Fig. 8(b). It was clearly shown in the figure that interconnectivity of printed pattern was improved with multilayer printing. A maximum height of 277 nm was measured as shown in Fig. 8(d). However, the average line width was increased from 5.9 μm for single-layer printing to 13.1 μm for multilayer printing due to ink spreading when droplets stacked layer by layer. For a pattern with fixed length, the corresponding resistance was inversely proportional to cross section area of the pattern. An increased cross section area had the ability to drive higher current and consume less power.

### Postcuring Process and Electrical Characterization.

The printed multilayer silver tracks in Sec. 5.3 showed a well interconnected profiles, however, they did not show good electrical conductivity. The reason for its extremely large resistance was that there were still polymers shell and residual solvents impeding nanoparticles connecting with each other. A postcuring process was necessary in order to remove all the impurities inside silver tracks and reform its structure for better electrical performance. As shown in Fig. 9, curing process will first remove lubricants, surfactants, solvents, and polymers out of silver patterns. The next step was a diffusion mechanism, where the heat will reform the silver nanoparticles, creating necks between adjacent silver particles and later transforming the necks into grain boundaries. During curing, pores and interstices will be removed once grain boundaries form, resulting in a denser structure of printed patterns and better conductivity as well.

We first compared influences of different curing procedures on resistivity and morphography of printed patterns, as shown in Fig. 10. A 20-layer silver track was printed under the same condition, where the diameter of nozzle is 7 μm, frequency of voltage is 150 Hz, and amplitude is 800 volts. The first sets of samples were instantly cured at 220 °C for 30 min, and the result was shown in Fig. 10(a). The morphography indicated that silver nanoparticles went through violent crystallization, forming particle clusters when solvent inside was removed drastically. The independent undulating topography resulted in poor connectivity of printed patterns and thus poor conductivity.

A ramped curing temperature modality was adapted in which the silver tracks were cured from 40 °C to 220 °C at 30 min time interval in a linear growth pattern. The temperature was increased 18 °C per 3 min in the 30 min time frame and then kept at 220 °C for 15 min. As we can see from the topography shown in Fig. 10(b), the ramped curing procedure leads to a smooth diffusion and curing process for silver tracks. The ramped temperature modality was adapted in the fabrication process for the experiments presented in the Secs. 5.4 and 5.5.

A contacting two-probe method was adapted for measurement of resistance of printed silver patterns. An ohmmeter (Fluke) was used to detect the resistance when two contact probes were placed at two ends of silver tracks in a fixed length. The resistance of printed patterns can be calculated using Eq. (6)
(6)

where R is the resistance of printed silver tracks, $ρ$ is the resistivity of printed silver tracks, A is the area of cross section of printed silver tracks, and L is the length between the two contact probes.

To find the effect of curing temperature on the resistivity of printed patterns, 10-layer silver tracks and 20-layer silver tracks were printed when the pulse frequency, amplitude, plotting speed, and nozzle diameter were fixed at 150 Hz, 800 V, 7 mm/s, and 7 μm, respectively. Five different curing temperatures (140 °C, 160 °C, 180 °C, 200 °C, and 220 °C) were applied on 10-layer and 20-layer samples using ramped modality as shown in the Secs. 5.3 and 5.4. After postcuring, we measured each sample at five different positions and averaged for its resistance. The average cross section area of samples was measured by an AFM.

Table 1 and Fig. 11 demonstrated resistivity changes and constriction of printed silver tracks with respect to curing process. From Eq. (6), resistance was a product of resistivity and cross section area with fixed line length. The geometric dimension of printed silver track played a significant role in electrical performance. At room temperature of 25 °C, the line widths of printed 10-layer silver tracks and 20-layer silver tracks provided almost same line width, but the thickness was increased from 167 nm to 247 nm with ten more layers printing. Printed patterns shrink during curing process to get rid of impurities inside, defusing and reforming nanoparticles, resulting in reduction of cross section area. With higher temperature, the deduction ratio becomes higher. A maximal 29.6% reduction of cross section area was observed in the 10-layer sample at curing temperature of 200 °C. But the resistance was tremendously reduced because of improved resistivity.

Curing process improved conductivity of printed patterns, as shown in Fig. 11(a). The optimal temperature for curing was 200 °C where conductivity of silver tracks reached a peak value. The minimum resistivity measured was 5.1 μΩ cm, about three times than that of bulk silver at room temperature. The electrical performance of printed silver patterns was no better than bulk silver because of unavoidable voids and inter coarse network between silver particles inside the track.

### Printing of Electronic Components on Insulating Substrates.

To demonstrate the capability of the process control using AC-pulse modulated e-jet printing, we printed high-resolution interconnector patterns on PET and ABF films, as shown in Fig. 12. The printed contact pads and interconnector on PET film indicated that residual charge issues were well resolved. Thus, AC-pulse modulated e-jet printing can be possibly applied for the fabrication of flexible electronics and printed electronics.

## Conclusions

In this paper, a novel AC-pulse modulated e-jet printing and postprocessing process were developed with improved controllability, resolution, and electrical performance for printed patterns. The fabrication process and analytical modeling of the track-formation mechanism were investigated and validated experimentally. AC-pulse modulated e-jet printing alternates charge polarity of adjacent droplets to neutralize charges remained on the substrate, which enables high-resolution printing on highly insulating materials. Pulse frequency, pulse amplitude, and plotting speed can be controlled independently for the fabrication of continuous features with sub-10 μm resolution. Multilayer printing technique and postprocessing (i.e., curing) were applied for achieving desired resistivity of silver tracks. It was demonstrated that the e-jet printing based fabrication technique can achieve high-resolution and high-conductive patterns on the insulating surfaces, showing great potential in flexible electronic and printed electronic applications. The presented technique is capable to fabricate resistors, inductors, and micro-interconnects, which offer a simple and versatile method to direct fabricate conductive patterns in flexible electronic manufacturing.

## Acknowledgment

This work was supported in part by the National Science Foundation (NSF) under grant awards (Nos. CMMI-1333775, CBET-1344618, and CMMI-1404916) to the North Carolina State University. The authors gratefully appreciate their support.

## Nomenclature

• A =

cross section area of printed patterns

•
• d =

line width of printed tracks, diameter of printed droplets

•
• d0 =

actual diameter of falling droplets

•
• f =

frequency of AC voltage

•
• h =

average height of printed droplets

•
• L =

length between two measuring points

•
• R =

resistance of pattern measured

•
• T =

circle time of AC voltage

•
• Td =

•
• Vdroplet =

actual volume of falling droplets

•
• Vprint=

volume of printed droplets

•
• vmax =

maximum plotting speed for continuous silver tracks

•
• ρ =

electrical resistivity of printed silver patterns

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