Towards understanding the surface rippling process by periodic reciprocal nanoscratching

The bundle structure formed perpendicular to the scratching direction is a type of wear-induced structure for thermoplastics. In this study, the formation mechanism of bundle structures on polycarbonate (PC) surfaces is investigated by reciprocal scratching experiments. Based on the analysis of the morphologies, friction forces, and height signals, the formation of the bundle structure is reproduced. The influence of scratching parameters, including the feed value and scratching direction, on the formation of the bundle structure is also studied. It is found that the bundle structure is accumulated by the continuous stacking of the sample materials plowed by the tip in stick—slip motion, and that the stick—slip behavior is enhanced with increased scratching times. This work reproduces the formation process of bundle structure in experiments for the first time and demonstrates that the stick—slip enhancement mechanism exists in the reciprocal scratching process, providing further insight into the friction behavior of polymers.


Introduction
Three-dimensional (3D) functional patterns have potential applications in label-free detection, biomedicine, and gratings for micro-or nanometer-scale sensors [1][2][3]. To date, many approaches such as focused ion beam (FIB), electron beam lithography (EBL), reactive ion etching (RIE), precision grinding, and conventional photolithography have been used to fabricate 3D functional patterns [4][5][6][7][8]. However, these methods are limited by disadvantages such as the relatively high capital investment required for the facilities and low throughputs. Compared with these methods, the atomic force microscopy (AFM) tip-based nanofabrication methods have proven to be a feasible and powerful approach to fabricating 3D functional structures because of their low cost, precise spatial resolution, in-situ imaging, and easy operation.
The AFM tip-based friction-induced nanomechanical method is especially effective for machining 3D quasi-sinusoidal nanostructures [9,10]. Nanometer-size structures are obtained with this method, resulting in a periodic pattern that is perpendicular to the scan direction for most thermoplastic polymers such as polystyrene, polycarbonate (PC), and polyacetylene [11][12][13]. These quasi-sinusoidal patterns are called ripples or bundles, and they are formed by tip scanning [14]. Nanochannel arrays can be fabricated easily using this method, potentially serving as the main component of nanofluidic chips with higher detection sensitivity [15]. Other potential applications include the control fabrication of bundle structures for optical devices [16]. Numerous studies have been conducted to investigate bundle structure formation. Some researchers have proposed theoretical models to explain the formation of the bundle structure. Elkaakour et al. [13] proposed a "crack propagation" mechanism consisting of a peeling process with the materials pushed ahead of the contact via crack propagation. It was found that bundles are less stiff than that in the undamaged surface, and the bundle structure volume is larger after the scanning process, which could be evidence of microvoids or cracks in the damaged region [12,[17][18][19].
Gnecco et al. [16,[20][21][22] have recently employed the Prandtl model to describe bundle structure formation based on the tip's stick-slip motion. Based on the competition between viscoplastic indentation and elastic shear stress caused by the tip, bundle structure formation was reproduced by this model in the scanning process. However, the formation of the bundle structure was only used in predictive models, and it is still difficult to reproduce the complete formation process experimentally.
Yan et al. [14] found that more than two scratching passes on the same area are necessary to form the bundle structure, and the repeating times are determined by the feed value and the tip radius. Wang et al. [29] employed an effective scratching length to investigate the influence of the scanning angles on bundle structure formation and found that a better bundle structure was obtained at 90° because of the largest effective scratching length. However, how the feed value affects the material deformation mechanism during bundle structure formation is still not understood. In addition, the scanning angle is an essential parameter affecting the features of the bundle structure, and changing the scanning angle changes the contact area and the effective stiffness between the tip and sample materials. Therefore, this study employs a rectangular pyramidal diamond-coated AFM tip to scratch a PC surface with different reciprocal scanning times. The bundle structure formation process is reproduced in the experiments by recording the machined pattern morphologies, friction forces, and height signals.
Moreover, the effects of the scratching parameters, including feed values and scratching directions on the formation process and the feature dimensions of the bundle structures are also studied.

Experimental details
This study's scratching experiments were carried out using a commercial AFM with a Nanoscope-V controller (Dimension Icon, Bruker, Germany). Figure 1(a) shows the schematic of the machining process for the bundle structure. The AFM system was operated in contact mode, and ripples were formed along the X-direction by tip scratching along the Y-direction. The normal load applied by the tip is 45 μN, and the scratching velocity is 20 μm/s. The PC samples (CT303050, Goodfellow, UK) were used for all scratching tests.
A diamond-coated AFM tip (DT-NCLR, Nanosensors, Switzerland) was used in this study to fabricate the bundle structures. The spring cantilever of the tip was 78 N/m. The "zigzag" machining trajectory of the tip is shown in Fig. 1(b), where the solid black arrows represent the tip's reciprocal scratching motion, and the feed direction is perpendicular to this reciprocal scratching direction. The feed value is the spacing between adjacent scratching trajectories corresponding to the scanning lines set in the AFM operation system. Figure 2(a) shows the schematic diagram for different scratching angles. The effect of the scratching angle on the bundle structure formation is illustrated in Figs. 2(b)-2(d), showing the tip cantilever torsion at the scratching angles corresponding to Fig. 2(a) [30]. After the machining process, a silicon tip (RTESP, Bruker, Germany) was also employed to measure the  profile of the bundle structures in the tapping mode to avoid destroying the nanoripples. The friction force was calibrated using a standard calibration grating with sloped and flat facets (TGF11) based on the method of Varenberg et al. [31]. The recorded Z-detector signal represents the tip height variation [30]. During fabrication, the AFM tip friction and height signals were output from the Nanoscope-V controller and recorded by an external oscilloscope. (TDS 2022, Tektronix Company, USA)

Observation of the bundle formation process
A typical bundle structure machined by reciprocal tip scratching is shown in Fig. 3, with a scanning area of 20 μm × 20 μm, a scan velocity of 20 μm/s, a feed of 19.5 nm, and a normal load of 45 μN. The bundle structure formed on the PC surface is perpendicular to the scratching direction ( Fig. 3(a)). In Fig. 3(b), a groove generated at the last tip scratching time can be seen on the right side of the bundle structure. From the sectional view of the pattern in Fig. 3(c), the blue curve represents the longitudinal section of the bundle structure, and the red curve represents the section of the last-scratched groove, which are both 3D quasi-sine wave structures. From the section view of the bundle structure, the wave peak is larger than the wave trough. Compared with the bundle structure, the period of the groove is similar to the bundle structure, while the wave peak is much smaller.
From the cross-sectional view of the groove, the typical periodic features indicate that the tip moved with a stick-slip process. An investigation of the material deformation process combining the lastscratched groove and bundle structure helps us to understand the bundle structure formation. We propose an experimental method to fully reproduce the bundle structure formation process based on the above experimental results. In this experiment, the samples were scratched with different scanning times, as shown in Fig. 4(a), and each machined pattern was characterized by the AFM. In addition, the friction and   height signals during processing were also recorded simultaneously.
The complete machining process can be divided into three stages. During the initial stage in Fig. 4(b), the groove is generated by tip scratching, and material pile-up can be observed on both sides of the groove. This machining process is dominated by plastic plowing [32][33][34]. In addition, no periodic features were observed in the cross-sectional view of the groove. With an increase in the reciprocal scratching time, periodic features appeared at the left wall of the last-scratched groove from the 3D local view, and a wave structure could be observed inside the groove from the cross-section, as shown in Fig. 3(b).
In Fig. 4(c), the periodic structures on the left side of the last-scratched groove gradually propagate along the feed direction, forming the bundle structure, and the groove wave period and amplitude are larger than those in Fig. 4(b). When the number of scratches reaches a certain level (20 times), as shown in Fig. 4(e), the bundle structure becomes more visible and propagates to the feed direction after reciprocal multi-scratching. From the cross-section of the last-scratched groove, periodic features can also be observed, reflecting that the tip may be moving with a stick-slip motion. Moreover, it can be speculated that the bundle structure wave peak may be formed by stacking of the pile-up with reciprocal tip scratching, resulting in the height difference between the wave peak and trough.

Variation of scratching friction
As described above, periodic patterns can be clearly identified along the last-scratched groove after several scratches, indicating that the periodic change in stress-strain status is induced by stick-slip tip motion [35][36][37]. An external oscilloscope was used to record the friction and height signals to understand the tip motion better. Figure 5 shows that the measured friction force and height sensor reacted on the tip along the entire scratching path. At the first stage in Fig. 5(a), the friction force and height signal barely change during the first tip scratching along the groove. With the growth in reciprocal scratching times, the fluctuations appeared in the friction force and height signal, and their amplitude and period increased, indicating that the tip movement transitioned from stable to stick-slip motion. At this time, the tip experienced periodic changes in resistance during movement [38,39].
In the second stage ( Fig. 5(b)), the period and amplitude of the fluctuations increase. Combined with the periodic scratching pattern shown in Fig. 4, the tip overcomes more resistance generated from elastic and plastic deformation of the PC material, inducing a larger friction force period and amplitude. In Fig. 5(c), the friction force and height signal variations tend to be stable when the number of scans reaches a particular value, agreeing well with the longitudinal groove profile, as shown in Fig. 4(e). Then, a bundle structure with a constant size (period and amplitude) is obtained.
The stick-slip motion of the tip is relevant to the formation of the bundle structure [20,21,40]. However, www.Springer.com/journal/40544 | Friction it was found that the stick-slip phenomenon would gradually appear and be enhanced by increased scratching times characterized by an increase in period and amplitude. This fluctuating state tends to be stable until the scratching time increases to a particular value, resulting in the formation of the bundle structure with a constant period and amplitude.
To further understand the stick-slip motion, friction and height signals and the corresponding longitudinal sections of the groove in stage III are grouped, as shown in Fig. 6. Stick-slip is observed during this stage from the morphology (Fig. 6(a)) and related cross-sectional view ( Fig. 6(b)) of the scratch friction and height signals (Fig. 6(c)). The friction force peak corresponds to the longitudinal profile valley of the groove and height sensor, and a reversed correspondence can be found between the friction force valley and the groove and height sensor peak [36,41].
As shown in Figs. 6(d) and 6(e), the curve of the longitude groove section agrees well with the height signal. When the tip moves upward from point A to point B, the friction force ( Fig. 6(f)) increases because of the accumulation impediment in front of the tip, which is the sticking stage. When the tip completely overcomes the accumulation, the friction force decreases sharply, entering the slip stage. During this time, the tip moves from B to the highest point, C, then down to enter the next cycle. The material in front of the tip is then pushed to the sides.

Effect of feed on the bundle formation process
In Refs. [27,28], the feed value corresponding to the number of scanning lines is also a critical factor in the bundle structure formation. In Section 3.3.1, the feed and reciprocal scanning times are considered to investigate the bundle structure formation process. The morphologies and related cross-sectional profiles after multiple scratches on the PC surface are shown in Fig. 7, using feeds of 19.5, 39, 52, and 78 nm. It is shown that a noticeable bundle structure is obtained with a 19.5 nm feed ( Fig. 7(a)). With an increase in feed value, the bundle structure's amplitude and period dramatically decrease from the cross-sectional view. However, no apparent bundle structure can be observed with the 78 nm feed, as shown in Fig. 8(d), possibly because the contact radius between the tip and sample is smaller than that of the feed [27].
The local morphologies corresponding to different feeds are shown in Fig. 8. In Fig. 8(a), the bundle structures with the largest amplitude and period are formed after multiple scratches with the 19.5 nm feed. However, the bundle structure size with a 39 nm feed is much smaller, and continuous ridges can be observed on the bundle structures, as shown in Fig. 8(b). Similarly, the ridges are more obvious at a feed of 52 nm (Fig. 8(c)). By comparing the bundle structure morphologies with different scratching times, it is found that the convex parts of the bundle structures are formed by the accumulation of sample materials removed by plowing behavior during the tip's stick-slip movement. By contrast, in Fig. 8(d), the pattern forms by continuous accumulation during plowing under the higher feed, and the stick-slip motion of the tip is inhibited.
Based on the above experimental results, the formation of the bundle structure can be summarized as follows. When the tip moves in stick-slip motion, parts of the sample materials flow to either side of the groove. After the tip passes over the bump in the scratch, this part of the sample material accumulates www.Springer.com/journal/40544 | Friction to its left, forming the convex part bundle structure after multiple scratches ( Fig. 9(a)). When the feed is large enough, the sample materials cannot completely cover the accumulation formed by the last scratch, and continuous ridges form, as shown in Fig. 9(b). Additionally, the height of the convex part of bundle structure is closely related to the feed value. Smaller feed means larger overlapping of the area visited by the tip [28]. Then, more sample material volume is stripped, inducing higher accumulation volumes.
Yan et al. [10] pointed out that bundles in the PC sample are less stiff than that in the undamaged surface because the bundles are accumulated by the pile-up formed by tip plowing. The pile-up hardness is smaller than that of the undamaged surface [42]. According to the experimental results, this may not be evidence of microvoids or cracks in the damaged region in the microNewton (μN) range, as pointed out in Refs. [12,13,19,43].
When the feed increases to a certain value, the bundle structure and related stick-slip phenomenon disappear, as shown in Fig. 8(d). By comparing the two cases, the schematic diagrams of the cross-sectional view with small and large feeds are summarized in Figs. 9(c) and 9(d), respectively. From the cross-section, there is an undeformed contact area on the side of the tip facing the feed direction. When the feed is small enough (Fig. 9(c)), the corresponding undeformed area is also very small, which could be approximately in the same grooves as reciprocating scanning. However, when the feed increases to a particular value ( Fig. 9(d)), the undeformed area is large enough. As pointed out in Refs. [20,40,44], the stick-slip phenomenon can be explained by the competition between the driving spring force and the plastic response of the substrate. The tip must overcome more materials for large feed values before the stick-slip motion is inhibited.

Effect of scratching direction on bundle formation
The bundle structures machined using scratching angles from 0° to 165° and formed under a normal load of 45 μN, a velocity of 20 μm/s, and a feed of 19.5 nm are shown in Fig. 10. With an increase in the scratching angle, the topography of the pattern is changed in gradient regularity. In the case of 0°, the bundle structures mainly form on the right side of the pattern. The period and amplitude of the structures have the maximum values compared with those of other scratching angles. When the scratching angle is increased to 15°, sloping bundle structures are observed on the left side of the pattern, and a transition area between the two kinds of bundle structures occurs in the middle of the pattern. When increasing the scratching angle to 90°, the bundle structures twist in an anticlockwise direction, and the transition zone moves to the right side of the pattern. Meanwhile, the bundle structure on the right side gradually disappears. At 90°, the bundle structures are perpendicular to the scratching direction. However, when the scratching angle exceeds 90°, the bundle structure twists in the opposite direction.
According to the above experimental results, the bundle structure is greatly affected by the scratching direction, which is closely related to the tip geometry and the tip cantilever torsional stiffness [21,45]. At 0°, the cantilever torsion is shown in Figs. 2(c) and 2(d), which is smaller than that at 90° in Fig. 2(b) [46]. Thus, bundle structures with larger periods and amplitudes are obtained at 0° [40]. Moreover, the inclination of the bundle structures is caused by the asymmetric tip geometry and the different cantilever torsion stiffness during reciprocating scratching.
Variations in the scratching angles lead to the differences in the contact areas between the tip and sample materials, resulting in different material removal behaviors. Simultaneously, the cantilever's torsion stiffness also changes the bundle structure's amplitude and period in the machining process. At 90°, because of the symmetrical tip geometry and the same cantilever torsion stiffness, the degree of extrusion of the workpiece materials is the same during each scanning process. Thus, regular bundle structures are obtained with a 90° scratching angle.

Experimental study on a single groove with reciprocal scratching
Based on the above experimental results, the bundle structure is formed by the extrusion of the tip on the sample materials in stick-slip motion. The variation of the scratching forces and related cross-section of the last-scratched groove indicates that the stick-slip www.Springer.com/journal/40544 | Friction motion is enhanced with increased scratching times. However, it is challenging to study the stick-slip behavior of the tip further, considering the effect of the feed. Thus, a zero feed value and different reciprocal times are chosen to investigate the tip movement behavior, excluding the effect of the feed. In Section 3.4, the experiments were conducted using the NanoMan module of the AFM system, and the tip was operated for multiple reciprocal passes. The normal load applied by the tip is 50 μN, and the scratching velocity is set to 20 μm/s. The reciprocal scanning time is defined as N.
The morphologies and related longitudinal cross-sectional profiles of the groove with different reciprocal times are shown in Fig. 11. Similar to the above experimental results, no obvious periodic structure is observed in the groove at the initial stage ( Fig. 11(a)). With the growth of the N (Fig. 11(b)), a periodic pattern gradually forms at the bottom of the groove, and the structure's amplitude and period are larger (Fig. 11(c)). By analyzing the longitudinal cross-sectional diagram processed with different N (Fig. 11(d)), it is found that a periodic structure appears when the depth of the groove increases to a certain extent with the growth in the scratching times. Moreover, the structure's period and amplitude increase with the number of reciprocal scratches.
The trajectory of the tip can be designed to scratch to the middle of the groove and lift using the NanoMan module to observe the critical state of the stick-slip phenomenon. In Figs. 12(a) and 12(c), it can be seen that no periodic pattern forms in the groove, and the second scanned groove depth is larger than that in the first. After tip scratching back and forth, a periodic structure forms the third time ( Fig. 12(b)). Additionally, a hump in the periodic structure is inclined to the tip scratching direction, as shown in Fig. 12(d). The features of this periodic pattern are similar to those of fish-scaling damage [37,42], indicating that stick-slip motion appears after repeated reciprocal scratching.
As pointed out in Refs. [20,21,40], stick-slip is dominated by competition between viscoplastic tip indentation in the polymer surface caused by a constant normal force and a lateral shear caused by the driven tip's elasticity. According to the experimental results, multiple scratches can reconstruct the polymer surface, thus affecting the stick-slip behavior. As shown in Fig. 13, the formation of a periodic pattern can be divided into three stages: stick-slip inhibition, stick-slip formation, and stick-slip enhancement.
At the initial stage ( Fig. 13(a)), material accumulates    ahead of the tip, inducing resistance against its movement [47]. The torsion of the cantilever also exerts an elastic force on the tip. Because of the groove's shallow depth in the initial stage, inducing a small accumulation volume, the tip can easily overcome the accumulation resistance with the small cantilever torsion. In Fig. 13(b), the increased scratching times cause deeper tip penetration into the polymer substrate, causing a further increase in the friction force, and the tip sticks in the penetration area. When www.Springer.com/journal/40544 | Friction the stress exerted on the sample material is below its ultimate strength, the scratch tip drags the material along and slips over the ridge of the accumulation [42]. The scratch tip reestablishes its surface contact under a constant normal load and compresses the material. The sticking stage occurs again until the slipping action repeats itself. Thus, a fish-scale pattern is obtained. As shown in Fig. 13(c), the tip reciprocally scratches the groove with a periodic pattern and further drags a convex structure, raising the slip distance. Simultaneously, the amplitude of the periodic pattern increases with the number of scratches because of the larger indentation depth.

Conclusions
Based on multi-scratching experiments, the bundle structure formation mechanism was reproduced by recording its morphology and combining the friction force and height signal. Furthermore, the effect of machining parameters, including feed values and scratching direction, on the bundle structure formation process was also investigated. According to the results obtained, the following conclusions can be drawn: 1) The bundle structure is accumulated by continuous stacking of the workpiece materials plowed by the tip during stick-slip motion, which is different from the crack propagation theory at the nanoNewton scale.
2) Stick-slip is the dominant mechanism of bundle structure formation. The stick-slip phenomenon gradually appears and is enhanced by an increase in reciprocal scratching times, characterized by an increase in period and amplitude. This fluctuating state tends to be stable until the scratching times increase to a particular value, resulting in the formation of a bundle structure with a constant period and amplitude.
3) The feed value determines the degree of sample material accumulation. A smaller feed value means more time for sample material accumulation in the same area. Thus, a bundle structure with a larger amplitude can be obtained with a smaller feed value. By contrast, the tip must overcome more sample material, and stick-slip motion is inhibited when the feed value is high enough.
4) The bundle structure is significantly affected by scratching direction, which is closely related to the tip geometry and tip cantilever torsional stiffness.
When the tip geometry is symmetrical, and the torsion stiffness is consistent in the reciprocating scanning process, the bundle structure oriented perpendicular to the scanning direction can be machined.