A mathematical model to predict surface roughness and pattern thickness in roll-to-roll gravure printed electronics
Highlights
► This paper shows that why we have to control tension of a moving web in roll to roll printing systems. ► The geometry of engraved pattern on the printing cylinder and characteristics of ink could affect the printability of R2R printed pattern. ► But, the printability of a R2R printed pattern could be changed due to tension level even other conditions are fixed.
Introduction
Roll-to-roll gravure printed electronics are increasingly common in a variety of electronic applications, such as radio-frequency identification, sensors, photovoltaics (solar cells), displays and lighting because of their tremendous advantages compared to conventional semiconductor fabrication, namely, their high-throughput, large scale and low cost. Although gravure printing has suffered from some resolution and accuracy issues, it is still attractive for the high-volume mass production of flexible printed electronics. Like conventional graphical printing, each layer of the electronic device is printed on various substrates, ranging from paper to plastic web, to achieve a desired functionality instead of color. The properties of the paper substrate, such as smoothness, absorption capacity and wettability, significantly affect the gravure printability and therefore the resulting functionality of the printed electronics [1], [2]. These results can be predicted by the well-known Walker–Fetsko equation, which decomposes the process into three separate phases: contact, immobilization and splitting [3]. This equation showed the effect of different parameters, such as the nip pressure, printing speed, ink viscosity and substrate properties, on the ink transfer. Many studies have been conducted on this topic, especially for conventional graphical gravure printing on paper substrates [4], [5]. Of the abovementioned parameters, the substrate properties, namely, the porosity, roughness and compressibility, are the most important in the ink transfer and the ink-setting under nip pressure [5], [6], [7], [8], [9].
Unfortunately, most applications of printed electronics, such as organic photovoltaics (solar cells), displays and lighting, are more likely to involve non-absorption substrates, especially plastic [10], [11], [12], [13], [14]. Because plastic, in contrast to paper, has characteristics that do not affect the homogeneity of the conductive deposit, including high dimensional stability [15], incompressibility [16], non-absorption and high smoothness (nano-scale Ra) [17], [18], the ink transfer and ink-setting process on plastic substrate are completely different from that on paper substrate. This substrate is a new challenge for gravure printed electronics. Many studies have attempted to overcome this issue. Sung [19] presented the effect of various cell and ink parameters on the print width and thickness of gravure-printed patterns. The pattern thickness increases significantly with increasing ink viscosity. However, when the ink is too viscous, “cell clogging” occurs, which reduces the print thickness. Noh [20] presented an optimized roll-to-roll gravure printing system using silver-nanoparticle-based inks as follows: (i) a high thickness and ink viscosity results in a low aspect ratio and a high print speed and (ii) a high surface roughness and a low ink viscosity results in a high aspect ratio and print speed. Michels [12] studied the influence of cell engraving depth, print speed and polymer concentration on the mean printed layer thickness, relative root mean square roughness and feature anisotropy for gravure printed light-emitting polymers. This approach used artificial neural network modeling to predict the process dependence.
When roll-to-roll machines are used for printed electronics, the web is sent through an un-winding roll, printing unit, drying section and re-winding roll. The web or substrate is driven under tension. Tension control is important in web handling [21], [22]. A disturbance in the tension could affect the layer-to-layer registration error [23]. The thickness and surface roughness of a printed pattern are expressible in terms of the tension variation of the moving substrate [24], [25]. Furthermore, for a brittle pattern like TiO2, the printed pattern is subjected to external forces, such as bending and tension, as the web moves. Accordingly, the characteristics of the printed pattern, for example, its conductivity, may decrease under high operating tension [26], [27]. Thus, the operating tension must be considered as significant factor affecting printed quality.
Most of the studies on gravure printing processes for printing electronics have shown that ink formulation, print speed and cell geometry have a significant effect on the thickness and surface roughness of the printed pattern. In this work, a mathematical model has been developed to predict the surface roughness and thickness of roll-to-roll printed patterns using the operating tension as an independent variable. Because gravure printing is a complex process with a nonlinear relationship between input and output, a statistical model is preferred over a physical model. Furthermore, design of experiments (DOE) is an effective method that requires less experimental data than artificial neural network modeling [12]. Additionally, due to the use of an orthogonal array in the DOE method, the effect of each parameter can be independently investigated to reduce the cost of performing the necessary experiments [28]. Thus, in this study, a meta-model was developed using a full factorial method with 24 factors for the independent variables of tension, print speed, viscosity and theoretical transfer volume. Within the range of independent variables studied, the meta-model effectively predicted the dependent variables, namely, surface roughness and thickness.
Section snippets
Experimental setup
The image was designed to evaluate the printed pattern at two cell geometries. The printed lines were used to check stability (without missing dots) of the printing condition. To facilitate a measurement of thickness and surface roughness of printed patterns in one shot, a 1×1 mm2 square and a 1×2 mm2 rectangle were used. Fig. 1(a) showed the printing layout.
To print the pattern using different volumes while keeping all other parameters constant, two cell depths, 15 μm and 20 μm, were used. The
Results and discussion
Fig. 3 shows the mean value of the measured thickness and roughness for all 16 trials, including error bars based on the standard deviation (St Dev.) from Table 3. The roughness of the printed pattern was high (RMSMIN=1.24 μm, RMSMAX=1.5 μm). In general, the ink will be absorbed when printed on the porous substrate, paper [7]. In contrast, the ink was unable to penetrate into the smooth, non-absorptive PET substrate [31]. Accordingly, the ink-setting on the PET substrate depends mainly on the ink
Conclusions
In this study, a mathematical model was developed using the DOE method to predict surface roughness and pattern thickness considering the operating conditions of web handling (i.e., operating tension). Using the meta-model, the contribution of each variable and their interactions on the output were identified and shown in a Pareto chart. This model can effectively predict the effect of the independent variables and their interactions on the outputs. The confidence levels (R2) could be improved
Acknowledgments
This research was supported by the Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) (2011-00260) and the Industrial Core Technology Development Project through the Ministry of Knowledge Economy (grant number: 10035641).
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