# Uniform Pressing Mechanism in Large-Area Roll-to-Roll Nanoimprint Lithography Process
## 3 Experiment for Uniform Pressure Distribution
### Improving Uniformity Using Multiple Rollers and Machine Learning
As shown from the left in Figure 9, the force at both ends of the imprint roller was set to \(I_{L}\), \(I_{R}\) and the load of the center backup roller was set to \(I_{C1}\), \(I_{C2}\)\(-\)\(I_{C5}\). The average values of the electronic pressure measurement sensors were set, from the left, to \(O_{L}\), \(O_{C}\) and \(O_{R}\). The test conditions were 400 kgf in total force, and the ratio of the force value of the center backup roller was increased from 0-44%. In Figure 10, the output value data measured in the center are expressed in a boxplot. Regression analysis was conducted using the force of the center backup roller (\(I_{C3}\)) and the average value of the center electronic pressure measurement sensor (\(O_{C}\)). Linear regression, decision tree and random forest techniques were applied as basic regression analysis methods. Since the amount of analysis was not large, there was no significant difference in efficiency. The random forest technique with the highest training/test scores and improved reliability was applied. The applied random forest algorithm is shown in Equation (1). For \(b=1\) to \(B\) (\(B=100\)), draw a bootstrap sample \(Z^{*}\) of size \(N\) from the training data. Grow a random forest tree \(T_{b}\) to the bootstraped data, by recursively repeating the following steps for each terminal node of the tree, until the minimum node size \(n_{min}\) is reached. As each individual model is built, \(m\) variables are randomly selected from all \(p\) variables, and the best variable/split point combination is chosen. Then, split the node into two daughter nodes [24]. Output the ensemble trees \(\{T_{b}\}_{1}^{B}\). To make a prediction at a new point x:  
\[\hat{f}_{rf}^{B}(x)\ =\frac{1}{B}\sum_{b=1}^{B}T_{b}(x) \tag{1}\]  
Figure 9: Schematic diagram of large-area R2R uniform pressing system for experiments; three output pressing forces (\(O_{L}\), \(O_{C}\) and \(O_{R}\)) are selected to check the uniformity by the input pushing forces (\(I_{L}\), \(I_{C1}\), \(I_{C2}\)\(-\)\(I_{C5}\) and \(I_{R}\)). Firstly, \(O_{C}\)’s change is investigated by engaging \(I_{C3}\) only. The regression analysis algorithm used the random forest algorithm provided by Scikit-learn, a Python machine learning library. Random forest regression analysis was performed as shown in Figure 11 to check whether the change in the output value has continuity according to the change in the input value. The total data volume used for training is 1520 sets, and the analysis was performed by adjusting the max depth of the hyper-parameter provided by Scikit-learn. Based on the training data, the random forest algorithm learned the correlation between the input and the output. As a result of learning, the average train score was 0.990 and the test score was 0.953. It was confirmed that there is continuity between them and the learning data followed the actual experimental data well. Therefore, the output value can be predicted for an input value for which the actual experiment was not conducted. Figure 11: Random forest regression analysis result of output (\(O_{C}\)) value according to input (\(I_{C3}\)) value. Figure 10: Experimental results for regression analysis; output pressing force from left (\(O_{L}\)), central (\(O_{C}\)) and right (\(O_{R}\)) sections of roller for the inputs: (**a**) Left force 200 kgf, right force 200 kgf; (**b**) Left force 165 kgf, right force 165 kgf and center force 70 kgf; (**c**) Left force 148 kgf, right force 148 kgf and center force 104 kgf; (**d**) Left force 112 kgf, right force 112 kgf and center force 176 kgf. Regression analysis was performed on all input values applied by the pneumatic actuators at both ends of the imprinting roller and the actuators of the five backup rollers. Random forest regression analysis was performed for all inputs (\(I_{L}\), \(I_{\mathrm{C1}}\)-\(I_{\mathrm{C5}}\) and \(I_{R}\)) and for all outputs (\(O_{L}\), \(O_{\mathrm{C}}\) and \(O_{R}\)).