A novel approach for determining the minimum feed in nanochannels processing via molecular dynamics simulation

Applied Surface Science 369 (2016) 584–594

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Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc

A novel approach for determining the minimum feed in nanochannels processing via molecular dynamics simulation Jiaqi Ren, Zeguang Dong, Jinsheng Zhao, Pinkuan Liu ∗ State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e

i n f o

Article history: Received 15 September 2015 Received in revised form 13 January 2016 Accepted 2 February 2016 Available online 4 February 2016 Keywords: Nanochannels processing Minimum feed Atomic force microscope MD simulation Novel approach

a b s t r a c t A novel approach based on molecular dynamics (MD) simulation has been proposed for the first time with the focus on quantifying the minimum feed (MF) in atomic force microscope (AFM) based nanochannel fabrication. This approach involves a coarse-to-fine criterion to determine MF so that regular nanochannel patterns can be obtained. The method is first introduced step by step and then confirmatory test is performed to demonstrate the capability of this contour-based method. MF judging studies are also performed systematically in which they vary in the aspects of scratching depth, tip angles, and tip shapes. Dislocations generation, surface quality, and scratching forces in the initial and subsequent scratches are investigated in detail. This method can overcome the drawbacks of high cost and low efficiency in experimental studies. Furthermore, our method sheds light on the manufacturing technique of nanochannels, which can help to obtain the surface morphologies with higher quality than traditional approaches. © 2016 Elsevier B.V. All rights reserved.

1. Introduction As the scaling-down revolution has brought us, nanostructures especially nanochannel arrays have stimulated great interest due to their extensive application in nanometer scale devices. Wire grid polarizer (WGP), whose performance can be significantly improved by reducing the nanochannel pitch below 140 nm, could be possibly applied in microdisplay-based projection systems [1]. Deposition of target material into a template with nanochannel arrays can be one of viable approaches for fabricating nanotubes and nanowires [2]. The semiconductor industry has also been pushing high-precision nanochannel fabrication to manufacture ever-shrinking transistors and high-density integrated circuits (ICs) [3]. Introducing biomolecules into nanochannels is an effective way for studying the biosensing process and developing the nanochannel array-based bioanalytical devices [4]. Yet, the key to these components in nanometer scale leads to a basic problem: nanochannels fabrication. The state-of-art methods for nanochannel arrays fabrication include, to name a few, electron-beam lithography (EBL), nanoimprint lithography (NIL), femtosecond laser machining, and AFM-based nanoscratching [5–8]. AFM-based nanoscratching is the most notable approach due to its advantages of high resolution, low-cost, material flexibility, and ease of operation.

∗ Corresponding author. E-mail address: [email protected] (P. Liu). http://dx.doi.org/10.1016/j.apsusc.2016.02.024 0169-4332/© 2016 Elsevier B.V. All rights reserved.

In order to fabricate desired nanochannel patterns by AFMbased nanoscratching, some critical issues have been addressed for such demanding and industrially relevant process. Some researchers focused on developing theoretical prediction models for nanoscratching with expected depths [9,10]. Effects of parameters such as normal loads, reciprocal times, and scratching speed were also elucidated [11,12]. As representatives of the leadingedge research, all these researches are inspiring. However, the issue of producing nanochannels by necessary feed still remains to be solved. The feed, also known as pitch, is defined in terms of the distance between two adjacent parallel nanochannels. Unsuitable scratching feed would lead to failure of integrate nanochannel formation and required surface quality [13]. From the view of manufacturing, feed is critical for improving the machining efficiency and special attentions are needed. As mentioned before, the performance of nanodevices and ICs can be greatly improved by high-density nanostructures and minimizing the feed provides a solution for the ever-shrinking-scale nanomanufacturing. Therefore, numerous experiments were carried out to evaluate the influence of scratching feed on nanochannels formation [11,14]. However, traditional experimental method is crippled by high cost and time consumption. A deeper understanding of nanoscratching mechanisms still remains as a challenging problem. Thus, another research methodology superior to experiment is imminently required. In nanoscale processing, traditional continuum mechanisms are not suitable for analysis since the deformation is inherently atomic. As a consequence, many attempts have been made to effectively

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emulate nanoscratching process by molecular dynamics (MD) simulation. For instance, Yan et al. investigated the influence of feed on scratching depth and surface quality, and proposed a proper feed for machining non-interfering parallel nanochannels [15]. Promyoo et al. conducted MD simulations to probe the minimum distance between two nanochannels so that interference can be avoided [16]. Fang et al. demonstrated a clear relationship between the scribing feed and the resultant force. They also revealed the effects of feed on surface roughness [17]. Nevertheless, the explicit and stringent criterion for judging the minimum feed is not established and therefore, the minimal feed in their study is subjective and inaccurate. Meanwhile, Zhu et al. performed MD simulations to investigate how the tip geometrical parameters influence the nanoscratching process [18]. However, no pioneering work is presented for the investigation of minimum feed under different working conditions such as tool geometries, scratching depth or other influence factors. Since our literature survey does not furnish any particular method, judgment of the minimum feed is particular in demand. Therefore, in this article, we develop a methodology to determine the minimum feed (MF) in nanochannel arrays processing. The proposed coarse-to-fine approach starts from a coarse identification which provides a range including MF, and the process is carried onto the fine subdivision stage based on the contour-based angle measurement method. Details of the MF judging method are systematically elaborated by one example. Then MFs for different scratching depths, tip angles, and tip shapes are investigated based on our method. The scratching forces, surface deformation and dislocations generation are also compared in each condition. This coarse identification and fine subdivision method is desirable for obtaining MF in uniform nanochannel manufacturing process and could greatly benefit the nanofabrication industry. 2. Simulation methodology MD simulations in our study are conducted using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) developed by Plimpton [19]. 2.1. Geometric model for MD simulations Fig. 1 shows the schematic model used in MD simulations. The simulation model consists of two rigid diamond tips and a defectfree monocrystalline copper workpiece. The two diamond tips with identical geometry are utilized to imitate the first and second scratches. They are constructed with perfect diamond atomic lattice and are treated as rigid bodies for the high hardness. The copper workpiece assumed to be in perfect face center cubic (FCC) configuration contains 440,000 atoms within a size of 70a × 50a × 30a,

585

where a is the lattice constant of copper, a = 0.3615 nm. The crystal orientations of the workpiece along X, Y and Z axis are [100], [010] and [001]. The scratching is implemented on (001) surface along [−100] direction in all simulations. When building the model, there are two alternatives for simulating the multi-scratch process. One is to use double tips to scratch the workpiece surface simultaneously (double-tip scratch) and another is to scratch the workpiece one after another (singletip scratch). Previous studies have revealed that double-tip scratch can obtain two parallel nanochannels of high quality regardless of scratching feed, depth and orientation. However, the second scratch significantly influences the former nanochannel in the single-tip scratch [13,20]. In consideration of the real scratching process, single-tip scratch has more practical significance. Therefore, in our simulations, one tip initially scratches the workpiece surface along [−100] direction for a given length and then the tip is elevated along Z axis to depart from the workpiece. Then, the second tip thrusts into the workpiece and also scratches along [−100] direction. Two tips are separated by a distance equivalent to feed in Y direction. It should be noted that the feed could be smaller than radii summation of the two tips. In case of interference, tips are also separated by a few nanometers in X axis, which can be seen clearly from Fig. 1. The monocrystalline workpiece in MD simulations is divided into three different zones, namely: Newtonian zone, thermostat zone, and boundary zone. The relative position of the three zones is illustrated in Fig. 1. Eight layers of boundary atoms with fixed boundary conditions are placed at the bottom and left side of the workpiece and the thermostat atoms are placed in between the boundary zone and the Newtonian zone. The thermostat zone is employed to imitate heat dissipation in real scratching. The motion of atoms in the Newtonian and thermostat zones remains strictly within the limits of Newton’s equation of motion. And the motion is determined by directly integrating the classical Hamiltonian equation of motion using Velocity-Verlet algorithm. The initial temperature of the workpiece is kept constant at 298 K by velocity scaling method [21]. Periodic boundary conditions maintained along X, Y, and Z directions are adopted to enlarge the simulation scale, investigate the behavior of an isolate system, and avoid the boundary effect. All MD simulations are conducted in the NVE ensemble, where the system is isolated from changes in number of atoms (N), volume (V) and energy (E). The time step in simulations is usually on the order of femtosecond (fs), which is determined by the intrinsic inter-atomic vibration distance. In our current simulation, time step is set to be 1 fs to allow the system to reach the equilibrium configuration. Limited by our computational resource, a high scratching speed of 100 m/s is adopted in the simulation. 2.2. Potential functions for MD simulation The selection of potential energy functions is crucial to the accuracy of MD simulations as they determine the credibility of the simulation results. On the other hand, the efficiency of MD simulations depends on the complexity of the potential energy functions. There are three types of atomic interactions: Cu–Cu interaction, Cu–C interaction, and C–C interaction. The embedded atom method (EAM) potential, which provides a more realistic description of metallic cohesion and avoids ambiguity inherited by the volume dependency, is employed to describe the interaction between copper atoms [22–24]. The total atomic energy of an EAM potential system can be expressed as:

Eeam = Fig. 1. MD simulation model.

1 2

ij,i = / j

ij (rij ) +

 i

⎡ ⎤ n  Fi ⎣ i (rij )⎦ , j= / i

(1)

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where ij is the pair-interaction energy between atoms i and its neighboring atom j, and Fi is the embedded energy of atom i.  n  (r ) is the host electron density at site i induced by all other / i i ij j= atoms in the system. The Morse potential, commonly used for bonded interaction, is adopted to depict the Cu–C interaction since it is relatively simple and computationally inexpensive compared with EAM potential. The Morse potential energy function can be expressed according to the following formula: Etot =



D0 [e−2˛(r−r0 ) − 2e−˛(r−r0 ) ],

(2)

ij

where D0 is the cohesion energy; ˛ is the elastic modulus; r and r0 are the instantaneous and equilibrium distance between two atoms. The cutoff radius in the Morse potential is chosen as 0.25 nm to ensure the calculation efficiency. D0 , ˛, and r0 are constant parameters that can be determined by the physical properties of the material. The values in this study are D0 = 0.087 eV, ˛ = 51.4 nm−1 and r0 = 0.205 nm [25]. The C–C interaction of the diamond tip is neglected for the rigid body attribute. 2.3. Simulation procedure The simulation consists of two stages: the relaxation stage and the scratching stage. To begin with, the whole system undergoes relaxation for 40 ps. After the relaxation stage, atoms in the system are relaxed to minimum energy and therefore the whole system remains in the equilibrium state. Then the tip scratches along X axis for 15 nm by preserving a constant depth. The scratching depth is defined as the distance along Z axis from the workpiece surface to the lowest point of the nanochannel. In model construction, the pinpoint of the tip is positioned at a distance of scratching depth beneath the workpiece surface. With the tip processing along X axis, a nanochannel of uniform depth can be machined accordingly. The relaxation stage is also performed after the first scratch. The open visualization tool VMD (visual molecular dynamics) is utilized to animate the nanoscratching process. It should be noted that the discussions presented here are based not only on the MD simulation snapshots, but also on the observation of animations of the scratching process. Table 1 gives the parameters used in the MD simulations. Each atom in the simulation system is colored by CSP (centro-symmetry parameter), which is verified to be effective in identifying lattice defects and dislocations at finite temperature [26]. The local lattice disorder around an atom can be accurately measured by the CSP. The CSP is computed as follows: CSP =

6 

| Ri +  Ri+6 |2 ,

(3)

i=1

where  Ri and  Ri+6 are the vectors corresponding to the six pairs of opposite nearest neighbors in the FCC lattice [27]. The CSP for atoms in a perfect lattice is 0 while it is positive for atoms Table 1 Parameters used in the MD simulations. Properties

Parameters

Materials Potential function workpiece scale Time step Simulation system Initial temperature Scratching direction Scratching speed Scratching depth Scratching distance

Workpiece: copper (FCC) Tip: diamond (rigid) EAM (Cu–Cu) and Morse (Cu–C) 70a × 50a × 30a (a = 0.361 nm) 1 fs NVE 298 K [−100] on (001) surface 100 m/s 1, 1.5, 2, 2.5, and 3 nm 15 nm

near a local defect or at a surface. Forces are the summation of the interatomic forces on each atom calculated using the potential functions. 3. Results and discussions 3.1. Criteria for MF The feed is critical to determining the surface and processing quality. Although previous researchers have studied the influences of feed in nanoscratching process [11,14,15], the results are insufficient to obtain the minimum feed. Their studies mainly focus on how to obtain nanochannel arrays (series of parallel nanochannels) rather than to fabricate a concave hole. However, the integrity of nanochannels is not within their consideration. Besides, the feeds are randomly selected and there is no evidence that these feeds are the minimum. Therefore, we propose a novel MF judging method to obtain parallel nanochannels with integrate and required shapes, which could greatly benefit the nanomanufacturing. A favorable judging method should be flexible and easy to operate, cost effective, and independent of the tip or the sample material and should also give high accuracy judging results. These motivate us to propose a coarse-to-fine judging method which is capable of obtaining the MF efficiently and reliably. Our coarse-to-fine judging method involves two stages, i.e. coarse identification and the subsequent fine subdivision. The coarse identification aims at estimating the range containing MF and the further range shrinking to obtain MF is accomplished by fine subdivision. In coarse identification stage, the range containing MF is obtained by combining visual discrimination and force measurement. To be specific, the feed range in which nanochannels separate from each other but not far apart (atoms extruded out of two adjacent nanochannels do not interfere) is initially detected by visual observation. Meanwhile, according to previous study [15], a sufficient but not necessary condition for forming detached nanochannels is that the lateral force (along Y axis in our simulations) has an average value of zero when scratching is in a steady state (i.e. scratching forces do not change drastically with the scratching depth). Therefore, the feeds making the average value of lateral force be zero are gathered to give another range. The intersection of these two ranges provides the coarse range for MF. However, the coarse identification may yield errors due to the deviation of human perception. Moreover, the range obtained by examining the lateral force could only provides the upper limit. In order to compensate these deficiencies, the fine subdivision is performed to extract MF from the range detected in the coarse identification stage. The fine subdivision operates based on the contour-based angular measurement method. It is evident that the residual cross-section profiles of detached nanochannels roughly resemble the tip shape. The apex angles of the nanochannels should be approximately equal to the tip angle. Therefore, the residual cross-section profiles of nanochannels are obtained by the postprocessing software. Envelopes of these cross-section profiles are traced and apex angles of these nanochannels are measured. When nanochannel arrays of intact shape are formed, the angle difference (defined as the difference in apex angle between the second and the first nanochannels) is approximately zero (<2% of the tip angle). Therefore, the critical feed which makes the angle difference turn to zero is defined as the MF. The workflow diagram of our proposed method is shown in Fig. 2. In the section that follows, investigation of MF with conical shape tip is conducted as illustration. 3.2. Confirmatory test The methodology of MF judgment has been depicted in previous section. In this part, confirmatory test is performed to validate the

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Fig. 2. Flow chart demonstrates the judging method.

Fig. 3. (a–m) Cross-section profiles of various scratching feeds. (n) The contour line of 6.4 nm feed for angle measurement.

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Fig. 4. Variations of normal, lateral, and tangential forces with time steps at feed of 8 nm.

Fig. 5. Angle differences between the second and the first scratches under various scratching feeds.

validity of the MF judging method. The minimum feed is obtained so that the first nanochannel is not distorted by the second scratch. The tip used in the demonstration is conical shape with apex angle of 90◦ and base radius of 3 nm. Fig. 3 shows the cross-section snapshots of nanochannels with scratching depth of 2 nm and length of 15 nm. The rough range, in which detached nanochannels are formed but do not separate far from each other, is initially fixed at 5–8 nm by visual discrimination. The cross-section profiles scratched by feeds from 5 to 8 nm are shown in Fig. 3(a)–(m). It can be seen clearly from Fig. 3 that with small scratching feeds, the first nanochannel on the left side distorts and its width narrows accordingly. The distortion is particularly evident when feeds are between 5 and 5.7 nm. Atoms extruded out of two adjacent nanochannels interfere severely. These atoms incline toward the first nanochannel due to the lack of material support. Our results are consistent with the conclusions of Zhang et al. [13]. The normal, lateral, and tangential forces under the feed of 8 nm are monitored in Fig. 4. Normal force is defined perpendicular to the workpiece surface (along Z axis), and the tangential force is parallel to the scratching direction (along X axis). Lateral force oscillates around zero under the feed of 8 nm. Therefore, 8 nm is the upper limited of the rough range. For the convenience of the fine stage, contours of nanochannels are drawn and apex angles of nanochannels are measured. Fig. 3(n) illustrates the contours drawn for the feed of 6.4 nm. The variation of angle differences with scratching feeds is also monitored in Fig. 5. It is evident that when scratching feed is smaller than 6.4 nm, the angle differences between two adjacent nanochannels have positive values. However, with the feed increasing, angle differences have a decreasing trend. Meanwhile, when feed is larger than 6.4 nm, the apex angles of the two nanochannels are almost equal. The angle differences fluctuate around zero with the increasing feed. Therefore, based on previous analysis, the feed between two adjacent nanochannels should be at least 6.4 nm to avoid interference. Detached nanochannels can be essentially produced under this MF. The slight oscillation may be attributed to the elastic recovery of the scratched workpiece, which makes the surface uneven and therefore the measurement results inaccurate. However, the amplitude of fluctuation is small and will not affect the judgment. Fig. 6(a)–(c) illustrates the surface morphology and defects generation under scratching feeds of 5.0 nm (MF). The tip atoms are removed for observation convenience. Workpiece is colored with respect to CSP. Those atoms with CSP less than 3 are supposed to be in perfect crystalline network

and are eliminated in the visualizations [28–30]. From the animation of the scratching process, atoms are compressed and extruded out of the workpiece with the advancement of the tip. These amorphous structural atoms accumulate and pile up in front of and on both sides of the nanochannel. Small bump emergs between the two adjacent nanochannels because of the overlap of atoms. Dislocation networks extend into the workpiece along the scratching direction. In the first scratch, the morphologies of the nanochannels are almost the same for different scratching feeds. After the first scratch, dislocations and defect structures decrease due to the elastic recovery behavior [18,26,30,31]. With the increasing feed, dislocations and defect structures generated in the second scratch decrease and overlap ration of dislocations from two nanochannels also diminishes. As shown in Fig. 6(a), small feed makes the second scratch within the trajectory of the first scratch. Therefore, the first nanochannel is distorted. Scratching under MF produces uniform nanochannels, whereas scratching with feed larger than MF can also produce nanochannel arrays with flawless appearance. However, large number of atoms accumulates between nanochannels under large feed, which results in undulate surface and larger bump between nanochannels. This indicates that the surface quality tends to be sacrificed by too large feed. Therefore, scratching under MF can contribute to acquire an optimal surface quality and thus promote the application of the nanochannels. 3.3. Effects of scratching depth on MF Unlike in conventional machining where the depth of cut is significant compared to edge radius, depth is comparable to the dimension of tip radius in the nanoscratching process. Thus, the scratching depth is a key factor that determines the MF. The purpose of this subsection is to elaborate the influence of scratching depth on MF. Scratching with depths from 1 nm to 3 nm at 0.5 nm increment is investigated as illustration. To facilitate the discussion, the tip used in this part is conical shape with base radius of 3 nm, apex angle of 90◦ , and height of 3 nm. By adopting the method introduced in Section 3.1, MF corresponding to each scratching depth are identified in Table 2 and the variation trend is depicted in Fig. 7. As the scratching depth increases, MF increases. The relationship between MF and scratching depth can be fitted to a linear equation: y = 3.08 + 1.64x

(1 nm ≤ x ≤ 3 nm)

(4)

The fitting coefficient of the linear equation is 0.97892, which shows a good consistency with the distribution trend of MF in the

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Fig. 6. Snapshots of local top and bottom views of scratching under various feeds. The left two columns are the surface patterns of the first and second scratch, and the right two columns are the dislocation and defect patterns. The corresponding scratching feeds are (a) 5 nm, (b) 6.4 nm, and (c) 8.0 nm, respectively. (Atoms in (a), (b) and (c) are colored according to CSP value calculated by formula (3)). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Identified results of MF corresponding to scratching depth. Scratching depth/nm MF/nm

1.0 4.6

1.5 5.6

2.0 6.4

2.5 7.4

3.0 7.8

Fig. 7. Variation of MF with scratching depth and the linear fitting curve.

identification. The fitting equation can be utilized in estimating MF of various scratching depth under identical scratching conditions (i.e. tip shape, scratching velocity, and workpiece material). Moreover, the variation trend conforms to the changing regulations, which also verifies the accuracy of the MD simulations.

Fig. 8 presents the residual top and bottom views of defect structures and dislocations under various scratching depth, i.e. 1.5 nm (MF = 5.6 nm), 2.0 nm (MF = 6.4 nm), and 3.0 nm (MF = 8.0 nm). Both the first and second nanochannels maintain intact shape due to scratch under MF. Larger scratching depth leads to more atoms extruded out of the workpiece, which form protrusions along nanochannels. With increasing scratching depth, the defect structures and dislocations increase and therefore, the surface quality decreases. Dislocations and residual defects generated during the first scratch are located beneath the tip. Dislocations extended further ahead of tip for larger scratching depth. However, workpiece in the distance is immune to the scratching behavior. After the second scratch, defects and dislocations remain in the workpiece with larger quantity and wider distribution. This is mainly caused by the mechanical property change and the consequent transform of material removal mechanism in the previous scratch. Moreover, larger scratching depth could cause severe overlap of dislocations. Basically, the requirement for desirable nanochannel array is depicted by the accuracy of nanochannel shape and the favorable surface quality. Therefore, scratching under MF can help to achieve qualified nanochannel structures. Scratching forces are vital parameters in analyzing nanoscratching process. In Fig. 9, scratching forces under MF are plotted as a function of the scratching depth. Forces are averaged after the scratching distance is larger than 5 nm, i.e. scratch is stably proceeded. It can be clearly seen from Fig. 9 that during the first scratch, tangential force and normal forces increase with the scratching depth as expected. Larger scratching forces are required for the increasing scratching depth since more materials accumulate in front of the tip. In the first scratch, when depth is small (<2 nm), normal forces are larger than tangential forces. The workpiece atoms are removed by ploughing mechanism. While for large depth (≥2 nm), tangential forces surpass the normal forces. The reverse

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Fig. 8. Snapshots of local top and bottom views of scratching under MF. The left two columns are the surface patterns of the first and second scratch, and the right two columns are the dislocation patterns. The corresponding scratching depth are (a) 1.5 nm, (b) 2.0 nm, and (c) 3.0 nm, respectively. (Atoms in (a), (b) and (c) are colored by calculated value of CSP according to formula (3)). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

is always ignored in single scratch studies since it has an average value of zero throughout the nanoscratching process. This is due to the symmetrical distribution of the crystal structure in workpiece. However, as the second scratch proceeds, the crystal structures distort and forces contributing from both sides of the nanochannel are not yet balanced. Therefore, lateral force in the second scratch deviates from zero and cannot be neglected. However, they have relatively small values. This is because the decrease of dislocations and the restore of lattice structure during relaxation stage make the workpiece approach to the equilibrium state. Moreover, the non-zero lateral force also indicates that the second scratch is still influenced by the first scratch. 3.4. Effects of tip angles on MF

Fig. 9. Variation of scratching forces with various scratching depth when scratching under MF.

relationship of force magnitude is mainly due to the transformation of the scratching mechanism from ploughing to cutting [32,33]. Workpiece structure in the vicinity of the first nanochannel is changed due to the scratching behavior. As a result, in the second scratch, tangential forces are larger than the normal forces regardless of the scratching depth and atoms are removed by cutting mechanism. Meanwhile, both tangential forces and normal forces in the second scratch are larger than in the first scratch. The residual defects and dislocations introduced from the first scratch influence the nucleation and propagation of dislocations in the second scratch, which leads to the work hardening of the workpiece and makes the scratch even harder. The analysis of lateral force

The effects of the tip angles on MF are demonstrated in this section. The tip employed is cone shape and tip angles (specified as the cone angle) of 30◦ , 45◦ , 60◦ , 90◦ are studied as illustration. The height of these cone-shape tips is 3 nm and the scratching depth is kept uniformly at 2 nm. MF are obtained by the method describe in the previous section and the relationship between MF and the tip angle is shown in Fig. 10. It indicates clearly in the diagram that tip angle has approximately linear effect on the MF. Greater tip angle leads to larger MF. Furthermore, the data curve in Fig. 10 can be applied to estimate MF for various tip angles between 30◦ and 90◦ , which are not confined to the angles illustrated above. The dislocation and residual surface profiles for different tip angles are shown in Fig. 11. Workpiece around the tip exhibits elastic and plastic deformation. Dislocations accumulate in large amount in front of the tip. Dislocations and defects are pushed forward as the scratching proceeding. No chips are found in the deformation zone. When the second scratch is performed under MF, material piling up on both sides of the first nanochannel does not distort and shape of the first nanochannel remains the same.

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Fig. 10. Variation of MF with tip angles.

Fig. 12. Variation of scratching forces with various tip angles when scratching under MF.

Dislocations generated during the second scratch are much more due to the structure change in the first scratch. Through the comparison of Fig. 11(a)–(d), we find that small tip angle results in less pile ups and dislocation accumulation in front of the tip while large

tip angle extends the dislocation region. The sharp contrast can be found between scratching with tip angles of 30◦ and 90◦ . Therefore, scratching with small tip angle is prone to obtain a smooth surface.

Fig. 11. Dislocation and surface profiles of the first and second scratches for different tip angles. The tip angles are (a) 30◦ , (b) 45◦ , (c) 60◦ , and (d) 90◦ , respectively. (Atoms in (a), (b), (c) and (d) are colored by calculated value of CSP according to formula (3)). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 13. Schematic of the tip shapes and their dimensions: (a) the conical shape, (b) the triangular pyramid shape, and (c) the blunt shape.

Fig. 14. (a–c) The surface profile and dislocations of (a) blunt-shape, (b) triangular pyramid shape, and (c) conical shape. (d, e) The residual cross-section profiles after scratching under MF. (d) The blunt-shape tip and (e) is the triangular pyramid tip. (Atoms in (a), (b) and (c) are colored by calculated value of CSP according to formula (3)) (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.).

Fig. 12 demonstrates the variation of scratching forces with various tip angles under MF scratching condition. It is clearly in the diagram that tip angle have significant effect on tangential and normal forces. Forces increase with the increasing tip angles. The action range of the hardening area broadens with increasing tip angle. The main reason is that tip with larger angle is in contact with more workpiece atoms, which intensifies the interaction between workpiece and tip atoms. Another plausible explanation is that dislocations generated in the first scratch induce the work hardening and make the workpiece difficult to scratch. Therefore, both the tangential and normal forces increase to overcome the work hardening. In addition, compared with the normal force, tangential force presents larger increment, which is essential to extrude atoms out of workpiece. The increment of force varies with tip angles. When tip angle is 30◦ , tangential and normal forces are almost equal in the first and second scratches. This indicates that the influence region

of the tip is small and the subsequent scratch is almost independent of the previous scratch. However, forces vary considerably with the tip angle of 90◦ , which means the second scratch is strongly influenced by the first scratch. Lateral forces oscillate around zero in the first scratch while they deviate from zero in the second scratch for the asymmetric workpiece distribution along nanochannels. However, lateral force is still zero in the second scratch when the tip angle is 30◦ . This is attributed to the small influence region of the first scratch when the tip angle is relatively small. 3.5. Effects of tip geometry on the MF The sensitivity of MF to tip geometryis evaluated in this section. Conical, triangular pyramid and blunt shapes are investigated in current simulations. The blunt-shape tip has the configuration combining hemisphere and cylinder. Fig. 13(a)–(c) is the schematic

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drawings and dimensions of the tips. Dimensions of the tips are chosen to make the width of nanochannels identical for the same scratching depth of 2 nm. Therefore, the comparison of the MF is valid and the only difference is the tip shape. The MF of the bluntshape tip is determined by an extended method. The radius of the nanochannel contour, instead of the apex angle, is adopted as the criterion. Fig. 14(a)–(c) represents the final surface morphologies and dislocation distribution under various tip geometries. Fig. 14(d), (e) is the cross-section profiles of blunt and triangular pyramid tips. MF of the conical, triangular pyramid and blunt shape tips are 4.7 nm, 4.2 nm, and 6.0 nm, respectively. Workpiece initially undergoes elastic deformation, and then follows plastic deformation via dislocation mechanism. Atoms accumulated in front of the tip increase sharply. MF of the bluntshape tip is relatively large. Comparison of Fig. 14(a)–(c) indicates that the blunt-shape tip causes larger deformation region and more dislocations than the other tips. Moreover, as shown in Fig. 14(d), even small chips are formed between two nanochannels. The performance of the blunt tip indicates that it has adverse impacts on surface quality and the blunt tip is not suitable for nanoscratching unless certain shape is required. The triangle pyramid and conical tips have similar effects on scratching, whereas the triangle pyramid tip generates fewer dislocations and causes smaller MF. Over all, the triangle pyramid tip is shown to be the desirable scratching tool for obtaining uniform nanochannels with favorable surface quality. 4. Conclusions In this paper, we develop a methodology to determine MF in nanochannels processing. The method starts from coarse identification which provides rough range containing MF. The rough range is carried onto the fine subdivision which is based on the contourbased angular measurement method. Specific conclusions can be drawn in the following: 1 Flow chart of the method is given and confirmatory tests are carried out to validate the approach. MF of high accuracy is obtained. The residual surface morphologies and dislocation distributions under various scratching feed (i.e. MF) are compared. The results demonstrate that scratching under MF is more beneficial for achieving high surface quality. The judging result indicates that the method in our study is valid and feasible. 2 The effects of scratching depth on MF are investigated in detail and the fitting curve is given out for the extended application in the scratching depth between 1 nm and 3 nm. When scratching under MF, the defect structures of various scratching depth are investigated. Forces during scratch are also analyzed. As the first scratch changes the property of the workpiece, forces in the second scratch are larger than in the first scratch. The amplification of tangential force is larger than normal force. Average value of lateral forces deviate from zero due to the asymmetric distribution of workpiece after the first scratch. This indicates that interference between two scratches still exists even through the scratch is performed under MF. 3 The dependence of MF on tip angles is studied and the results reveal that MF increases linearly within the range of 30–90◦ . The quantity of dislocations grows with tip angles and the surface quality is higher with small tip angle. Forces are larger in the second scratch and force differences between two scratches increase with increasing tip angle. The average value of lateral forces is positive in the second scratch. 4 Our study also evaluates the effects of tip geometry and the results indicate its significant influence on MF. Three different tip shapes which are commonly used in the AFM-based

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nanoscratching process are investigated and the results show that MF is sensitive to the tip shape. MF of blunt-shape tip is the largest and scratching with it can generate rougher surface. The triangular pyramid tip is beneficial to obtain nanochannel arrays with higher surface quality and smaller MF. 5 Our study provides an optimized solution for determining MF by which overlap can be eliminated in nanochannel processing. The method proposed here enables the scale-up manufacturing for nanochannels with satisfactory structures and high surface quality. Acknowledgments This research was supported by the National Natural Science Foundation of China under Grant No. 91023035 and No. 51135009. A computing facility award on the PI cluster at Shanghai Jiao Tong University is acknowledged. References [1] S.W. Ahn, K.D. Lee, J.S. Kim, S.H. Kim, J.D. Par, S.H. Lee, P.W. Yoon, Fabrication of a 50 nm half-pitch wire grid polarizer using nanoimprint lithography, Nanotechnology 16 (2005) 1874–1877. [2] N.W. Liu, A. Datta, C.Y. Liu, C.Y. Peng, H.H. Wang, Y.L. Wang, Fabrication of anodic-alumina films with custom-designed arrays of nanochannels, Adv. Mater. 17 (2005) 222–225. [3] L.J. Guo, Nanoimprint lithography: methods and material requirements, Adv. Mater. 19 (2007) 495–513. [4] S.J. Li, J. Li, K. Wang, C. Wang, J.J. Xu, H.Y. Chen, X.H. Xia, Q. Huo, A nanochannel array-based electrochemical device for quantitative label-free DNA analysis, ACS Nano 4 (2010) 6417–6424. [5] R.J. Bojko, J. Li, L. He, T.B. Jones, M. Hochberg, Y. Aida, Electron beam lithography writing strategies for low loss, high confinement silicon optical waveguides, J. Vac. Sci. Technol. B 29 (2011) 06F309. [6] L.J. Guo, Recent progress in nanoimprint technology and its applications, J. Phys. D: Appl. Phys. 37 (2004) R123–R141. [7] D.H. Kam, L. Shah, J. Mazumder, Femtosecond laser machining of multi-depth microchannel networks onto silicon, J. Micromech. Microeng. 21 (2011) 045027. [8] S.H. Lee, Analysis of ductile mode and brittle transition of AFM nanomachining of silicon, Int. J. Mach. Tools Manuf. 61 (2012) 71–79. [9] J.Q. Ren, P.K. Liu, X.B. Zhu, F. Zhang, G.Z. Chen, Multiscale modeling and experimental validation for nanochannel depth control in atomic force microscopy-based nanofabrication, J. Appl. Phys. 116 (2014) 074301. [10] Y.Q. Geng, Y.D. Yan, Y.M. Xing, X.S. Zhao, Z.J. Hu, Modelling and experimental study of machined depth in AFM-based milling of nanochannels, Int. J. Mach. Tools Manuf. 73 (2013) 87–96. [11] Y. Sun, Y.D. Yan, Z.J. Hu, X.S. Zhao, J.C. Yan, 3D polymer nanostructures fabrication by AFM tip-based single scanning with a harder cantilever, Tribol. Int. 47 (2012) 44–49. [12] K. Bourne, S.G. Kapoor, R.E. DeVor, Study of a high performance AFM probe-based microscribing process, J. Manuf. Sci. Eng. 132 (2010) 030906. [13] P. Zhang, H.W. Zhao, C.L. Shi, L. Zhang, H. Huang, L.Q. Ren, Influence of double-tip scratch and single-tip scratch on nano-scratching process via molecular dynamics simulation, Appl. Surf. Sci. 280 (2013) 751–756. [14] Y.D. Yan, Y. Sun, Y.T. Yang, Z.J. Hu, X.S. Zhao, Effects of the AFM tip trace on nanobundles formation on the polymer surface, Appl. Surf. Sci. 258 (2012) 9656–9663. [15] Y.D. Yan, T. Sun, S. Dong, Y.C. Liang, Study on effects of the feed on AFM-based nano-scratching process using MD simulation, Comput. Mater. Sci. 40 (2007) 1–5. [16] R. Promyoo, H.E. Mounayri, K. Varahramyan, AFM-based nanoscratching: a 3D molecular dynamics simulation with experimental verification, in: Proceeding of the ASME 2014 international manufacturing science and engineering conference (MSEC 2014), Detroit, MI, USA, 2014. [17] T.H. Fang, C.I. Weng, J.G. Chang, Molecular dynamics simulation of nano-lithography process using atomic force microscopy, Surf. Sci. 501 (2002) 138–147. [18] P.Z. Zhu, Y.Z. Hu, H. Wang, T.B. Ma, Study of effect of indenter shape in nanometric scratching process using molecular dynamics, Mater. Sci. Eng. A 528 (2011) 4522–4527. [19] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [20] J. Li, Q.H. Fang, Y.W. Liu, L.C. Zhang, Scratching of copper with rough surfaces conducted by diamond tip simulated using molecular dynamics, Int. J. Adv. Manuf. Technol. 77 (2014) 01057–1070. [21] Y.H. Hu, S.B. Sinnott, Constant temperature molecular dynamics simulations of energetic particle–solid collisions: comparison of temperature control methods, J. Comput. Phys. 200 (2004) 251–266.

594

J. Ren et al. / Applied Surface Science 369 (2016) 584–594

[22] M.S. Daw, M.I. Baskes, Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals, Phys. Rev. Lett. 50 (1983) 1285–1288. [23] M.S. Daw, M.I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B 29 (1984) 6443–6453. [24] S.M. Foiles, M.I. Baskes, M.S. Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys. Rev. B 33 (1986) 7983–7991. [25] L.C. Zhang, H. Tanaka, Towards a deeper understanding of wear and friction on the atomic scale – a molecular dynamics analysis, Wear 211 (1997) 44–53. [26] Q.X. Pei, C. Lu, H.P. Lee, Large scale molecular dynamics study of nanometric machining of copper, Comput. Mater. Sci. 41 (2007) 177–185. [27] C.L. Kelchner, S.J. Plimpton, J.C. Hamilton, Dislocation nucleation and defect structure during surface indentation, Phys. Rev. B 58 (1998) 11085–11088.

[28] Z. Tong, Y.C. Liang, X.Q. Jiang, X.C. Luo, An atomistic investigation on the mechanism of machining nanostructures when using single tip and multi-tip diamond tools, Appl. Surf. Sci. 290 (2014) 458–465. [29] Q.X. Pei, C. Lu, H.P. Lee, Y.W. Zhang, Study of material deformation in nanometric cutting by large-scale molecular dynamics simulation, Nanoscale Res. Lett. 4 (2009) 444–451. [30] P.Z. Zhu, Y.Z. Hu, T.B. Ma, H. Wang, Study of AFM-based nanometric cutting process using molecular dynamics, Appl. Surf. Sci. 256 (2010) 7160–7165. [31] S. Shimada, N. Ikawa, H. Tanaka, J. Uchikoshi, Structure of micormachined surface simulated by molecular dynamics analysis, CIRP Ann.-Manuf. Technol. 43 (1994) 51–54. [32] F.Z. Fang, H. Wub, W. Zhou, X.T. Hu, A study on mechanism of nano-cutting single crystal silicon, J. Mater. Process. Technol. 184 (2007) 407–410. [33] S. Islam, R. Ibrahim, R. Das, Study of abrasive wear mechanism through nano machining, Key Eng. Mater. 462–463 (2011) 931–936.