Molecular Dynamics Simulations of the Roller Nanoimprint Process: Adhesion and Other Mechanical Characteristics
Molecular dynamics simulations using tight-binding many body potential are carried out to study the roller imprint process of a gold single crystal. The effect of the roller tooth’s taper angle, imprint depth, imprint temperature, and imprint direction on the imprint force, adhesion, stress distribution, and strain are investigated. A two-stage roller imprint process was obtained from an imprint force curve. The two-stage imprint process included the imprint forming with a rapid increase of imprint force and the unloading stage combined with the adhesion stage. The results show that the imprint force and adhesion rapidly increase with decreasing taper angle and increasing imprint depth. The magnitude of the maximum imprint force and the time at which this maximum occurs are proportional to the imprint depth, but independent of the taper angle. In a comparison of the imprint mechanisms with a vertical imprint case, while high stress and strain regions are concentrated below the mold for vertical imprint, they also occur around the mold in the case of roller imprint. The regions were only concentrated on the substrate atoms underneath the mold in vertical imprint. Plastic flow increased with increasing imprint temperature.
KeywordsRoller imprint Nanoimprint Molecular dynamics Nanotribology Taper
With the increasing demand for nano/micropatterns on large substrates, the establishment of large-scale nanofabrication technology has become a priority. In recent years, nanoimprint lithography (NIL) has become a popular method that offers a sub-10 nm feature size, high throughput, and low cost [1, 2]. NIL fabricates nanopatterns by pressing a hard stamp with nanopatterns into a thin film and deforming the film mechanically. A similar approach to flat imprint lithography, roller nanoimprint lithography (RNIL) with a sub-100-nm feature size, was proposed by Chou et al. in 1998 .
Roller imprint technology such as gravure offset printing and flexography printing offered an alternative approach to large-scale pattern fabrication [4, 5]. Compared with vertical NIL, RNIL has the advantages of producing better uniformity, requiring less force, and being able to repeat a mask continuously. However, most research studies for both imprint technologies have focused on experiments. Few studies have used the numerical method. The transferred pattern will be significantly damaged by a strong adhesion under smaller feature size. Molecular dynamics (MD) simulation is an effective tool for studying material behavior at the nanometer scale as it provides detailed deformation information and the size effect at the atomic level. Nanosystems that have been analyzed using MD include surface friction [6, 7], nanoscratch , lubrication , nanoimprint , contact , and nanoindentation behavior [11, 12, 13]. Several studies have recently investigated the NIL process using MD. The nanopattern formation and physical mechanism were investigated on metal film imprint by changing the imprint temperature, imprint velocity , and stamp taper angle [10, 15]. Kang et al.  studied the deformation behavior on an amorphous polymethylmethacrylate (PMMA) film by changing the stamp aspect ratio. All these studies used MD with a traditional fixed period boundary.
In this study, a movable boundary condition on a gold substrate is proposed to perform a MD simulation of the RNIL process. The objectives of this study are to understand the deformation behavior of imprinted film and the effect of adhesion and friction with changes of the roller tooth geometry, imprint temperature, and imprint depth using MD simulations. Finally, some simulation results for RNIL are compared with those for NIL under the same tooth size to better understand the deformation and physical mechanisms of the two imprint technologies.
Parameters of tight-binding many body potential 
Results and Discussion
Mechanism of Roller Nanoimprint
Initial Dislocation Nucleation and Interaction on Roller Nanoimprint
wherea is the lattice constant of Au. The Burger’s vector of the lock Open image in new window is out of the slip plane direction, which is constrained by the quasi-2D simulation. The lock is termed a nominal lock. When the roller’s rotation angle gradually increased as shown in Fig. 4b to an angle of 27°, the disorder and lattice defects zone gradually extended along the tooth shape and the orientation of dislocations became more notably visible. Each dislocation nucleation was accompanied by stress relaxation (load drop). The stress needed to build up again to trigger further activities. Further imprinting caused the slip planes of (101) and Open image in new window to occur at the left and right sides of the tooth at a rotation angle of 31°, as shown in Fig. 4c.
Effect of Taper Angle on Roller Nanoimprint
Effect of Imprint Depth on Roller Nanoimprint
The MD simulations were carried out for four imprint depths to investigate the roller imprint mechanics: 1, 3, 4.5, and 6 nm. Figure 6a, b shows
Comparison of Mechanisms Between Vertical Imprint and Roller Imprint
Effect of Imprint Temperature on Roller Nanoimprint
In order to observe the effect of temperature on the roller imprint process, three temperature conditions were studied. Figure 9c, d show the slip vector distribution at the imprint temperatures of 400 K and 500 K, respectively. Compared with the room temperature imprint of Fig. 9b, a higher magnitude of the slip vector behavior was found when the temperature increased. The plastic flow increased when the kinetic energies of material atoms increased with increasing temperature. In Fig. 9c, d, the magnitude of the slip vector is proportional to the temperature and its relative distribution scale under the specific temperature is similar. The results indicate that the processes have similar imprint mechanisms and material defaults (the same slip planes). The plastic flow was good so a lower loading force was required when the imprint temperature increased.
The real material of a roller imprint is a polymer, such as PMMA. The simulations were conducted on gold using the same mold in both nanoimprint and roller imprint processes for convenience and to simplify the comparisons. According to the loading action, some characteristics, such as the distributions of stress, the slip vector, and the effect of the tooth taper, may be similar for the roller imprint on polymers and single crystal metals. As regards the behavior of the vertical imprint process, the amount of extrusion on polymer film  was greater than that in metal film  when both films underwent loading. The forming discrepancy can be explained by the different interaction forces. Intra- and inter-chain forces are present in the polymer, so the chain molecules have complicated and lenghthy interactions, leading to elongation and entangling between chain molecules. As regards the adhesion effect for polymer imprint, it seemed that the obvious adhesion phenomena were not to be found in snapshots or force curve as were found in Ref. . Those authors found that the contribution of adhesion was small when the PMMA film was imprinted using the Ni mold.
The imprint force, adhesion, stress, and strain distributions of the roller imprint process were studied using MD simulations based on tight-binding many body potential. The results showed that the imprint force and adhesion rapidly increased with decreasing taper angle and increasing imprint depth. The magnitude of the maximum imprint force and the time when it happens were directly proportional to the imprint depth, but independent of the taper angle. A comparison of the imprint mechanisms of the roller imprint and a vertical imprint case showed that the main high stress and strain regions were concentrated on the substrate atoms underneath and around the mold during the roller imprint process whereas these regions were concentrated only on the substrate atoms underneath the mold during the latter process. The plastic flow increased with increasing imprint temperature.
This study was supported in part by the National Science Council of Taiwan under Grant No. NSC95-2221-E150-066.
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