Advertisement

Nanomanufacturing and Metrology

, Volume 2, Issue 4, pp 241–252 | Cite as

Cutting-Based Single Atomic Layer Removal Mechanism of Monocrystalline Copper: Atomic Sizing Effect

  • Wenkun Xie
  • Fengzhou FangEmail author
Original Articles
  • 286 Downloads

Abstract

This study aims to gain an in-depth understanding of atomic and close-to-atomic scale (ACS) cutting mechanism, through an investigation of a typical diamond–copper cutting system using molecular dynamics modeling. The fundamentals in the ACS cutting process towards single atomic layer removal are emphatically analyzed. The results indicate that cutting-based single atomic layer removal could be enabled on a Cu(111) surface, achieving minimum chip thickness to single atomic layer. The material removal during ACS cutting is greatly influenced by atomic sizing effect, mainly depending on the ratio of cutting depth to atomic radius. When the ratio is larger than one threshold value, plastic material removal could be realized with chip formation, and it is dominated by shear stress-driven dislocation motion, which is different from shearing-driven chip formation in conventional cutting and the extrusion-dominated chip formation in nanocutting. This study also shows that only elastic deformation occurs on the workpiece surface during ACS cutting.

Keywords

Atomic and close-to-atomic scale manufacturing Mechanical cutting Atomic sizing effect Single atomic layer removal 

1 Introduction

Atomic and close-to-atomic scale manufacturing (ACSM), i.e., manufacturing III, has become one significant trend in the research, development, and innovation (RD&I) of future manufacturing science and technology [1, 2]. It aims to enable the highly efficient manufacturing and mass production of next-generation devices with atomic scale form accuracy or functional feature size [3, 4, 5].

Mechanical cutting is one of the most efficient and low-cost methods to obtain a high-quality machined surface with extremely high surface quality. In past decades, minimum chip thickness has been successfully decreased from conventional scale, microscale down to nanoscale, enabling the nanometric form accuracy and functional feature size. Currently, minimum chip thickness is still in the nanometric order [6]. However, even at nanoscale, the cutting depth still includes several tens of atomic layers.

Different from conventional cutting and nanocutting, to obtain the processed surface with atomic scale form accuracy in atomic and close-to-atomic scale (ACS) cutting, the minimum chip thickness is required down to several atomic layers and even a single atomic layer. At such cutting depth, the cutting process would have a direct impact on atoms. Moreover, since the materials to be cut change from dozens of atomic layers to several ones, and even a single atomic layer, the fundamental material removal mechanism would be greatly changed, which should be deeply studied.

It is widely recognized that chip formation is due to the material shearing in conventional machining [7, 8], while there is the extrusion-dominated chip formation in nanocutting [9, 10]. However, there are still no reports to determine the feasibility of mechanical cutting to enable material removal at atomic and close-to-atomic scale. Thus, the present study intends to bridge this strategically significant gap in detail and the following issues in ACS cutting are intended to be clarified, including:
  1. (a)

    Whether ACS cutting is feasible for achieving controlled single atomic layer removal;

     
  2. (b)

    How workpiece material is deformed and removed.

     

As the materials to be machined in ACS cutting are only several atomic layers and even a single atomic layer, it is too challenging to experimentally observe the real material deformation and removal process. Therefore, in this study, molecular dynamics analysis, which has been extensively applied to study the material deformation and removal mechanism at nanoscale and even atomic scale, is employed to investigate the cutting mechanism in the cutting-based single atomic layer removal. The research findings are expected to advance the progress of development of next-generation mechanical cutting technology, i.e., ACS cutting.

2 Modeling Methodology

2.1 Simulation Model and Protocol

In this study, molecular dynamics analysis is employed to analyze the deformation and removal mechanism of single crystal copper during the cutting. Those analyses are conducted on a single crystal copper surface, as shown in Fig. 1. The variables of interest in this study are cutting depth and cutting velocity. The environmental temperature of the cutting system is 293 K.
Fig. 1

Schematic model of a diamond–copper atomic cutting system

The cutting system used in the present study consists of a copper workpiece and a diamond tool. The model parameters are summarized in Table 1. It is well recognized that tool edge radius effect has significantly changed the nano-cutting process, inducing great change of the underlying material deformation and removal mechanism [11, 12]. It can be expected that tool edge radius would also affect the ACS cutting process. However, there are few studies about the ACS cutting process, and the role of tool edge radius effect in ACS cutting remains doubtful. Thus, to eliminate the possible tool edge radius effect on the ACS cutting process, though a rounded-edge diamond tool is usually used in the real cutting-based process, one sharp diamond tool with a rake angle of 0° and a clearance angle of 12° is adopted in the present work.
Table 1

Machining parameters in MD modeling

Workpiece dimension

16.63 × 9.94 × 2.71 nm3

Tool clearance angle

12°

Tool rake angle

Cutting velocity

5 m/s, 10 m/s, 20 m/s, 25 m/s, 30 m/s, 42.5 m/s, 45 m/s, 50 m/s, 100 m/s

Cutting direction

[− 1 1 0] on (111) surface

[− 1 0 0] on (001) surface

[0 0 − 1] on (110) surface

Time step

1 fs

The workpiece consists of three kinds of copper atoms, including thermostatic layer, newtonian layer, and boundary layer. The boundary layer is kept fixed to eliminate the possible movement of the workpiece, induced by the action of the cutting tool. The atoms in the thermostatic layer are kept at a constant temperature of 293 K to imitate the heat dissipation in the diamond cutting process. As for newtonian atoms, they obey Newton’s law during the cutting process, which is also the analysis focus to investigate the underlying material deformation and removal mechanism in the cutting process. Besides, periodical boundary condition is applied in the y-direction of the cutting model to reduce the size effect on the cutting process while fixed boundary condition is adopted in the x- and z-directions. Molecular dynamics analysis is performed using LAMMPS [13]. Ovito and VMD are used to visualize simulation results.

2.2 Definition of Cutting Depth in ACS Cutting

In ACS cutting, different from nano-cutting and conventional machining, cutting depth would be easily affected by atomic radius (r) and interlayer distance (Dlayer), and both should be considered. Thus, the cutting depth should be specifically defined. In the diamond–copper cutting system, the atomic radiuses of diamond and copper must be in consideration. Here, the topmost surface of the workpiece is defined to be the zero-point of cutting depth. The cutting depth (a) is defined as the distance between the topmost point of the workpiece surface and the lowest point of the diamond tool. As seen in Fig. 2, three kinds of typical cutting depths, including the cases of a > 0, a = 0, and a < 0, could be used in ACS cutting.
Fig. 2

Various cases of cutting depths on the Cu(111) surface

In case 1, as the cutting tool does not directly contact with the workpiece surface, thus, the attraction interaction should be the dominating interfacial interaction between cutting tool and workpiece. With the advance of the cutting tool, the attraction interaction may induce material deformation and even removal on the workpiece surface.

It was found that at a negative cutting depth, nano-scratching could induce the material displacement and removal on the workpiece surface, further leading to the surface deformation studied by Zhu et al. [14]. It should be due to the attraction interactions between workpiece and cutting tool. In case 3, namely, a > 0, the cutting tool will come into direct contact with workpiece materials, and the repulsive interaction between cutting tool and workpiece surface will dominate the cutting-based material deformation and removal process.

Overall, as the cutting depth changes from one negative one to a larger positive one, there would be one evident transformation process of the dominated driving force for workpiece material deformation and removal process.

To determine the possible effect of cutting depth on the material deformation and removal mechanism during ACS cutting, three cases of cutting depths are considered, see Fig. 2.

2.3 Determination of Cutting Depth for Cutting-Based Single Atomic Layer Removal

This study is to enable single atomic layer removal, thus, it is significant to accurately determine the theoretical cutting depth range. Figure 3 gives maximum cutting depths for single atomic layer removal on Cu(001), Cu(110), and Cu(111) surfaces.
Fig. 3

Maximum cutting depths on different copper surfaces

On different crystallographic surfaces, the maximum cutting depth for the first atomic layer has greatly changed, due to the different spacing distances between two topmost neighboring atomic layers (Dlayer) and atomic radius (R). For instance, on Cu(111) surface, the thickness of the overlapped region is:
$$t = \left( {2*R_{\text{cu}} - D_{\text{layer}} } \right)/2 = R_{\text{cu}} - 0.5*D_{\text{layer}}$$
(1)
Here, Dlayer is 2.087 Å, while the atomic radius of copper (Rcu) is 1.28 Å. The maximum cutting depth (amax) for the first atomic layer could be calculated by:
$$a_{ \rm{max} } = 2*R_{\text{cu}} - t = 2*R_{\text{cu}} - \left( {R_{\text{cu}} - 0.5*D_{\text{layer}} } \right) = R_{\text{cu}} + 0.5*D_{\text{layer}} = 2.32\,{\AA}$$
(2)

When a is larger than its maximum value, in the cutting process, the lowest point of the diamond tool would come into direct contact with the atoms within the second atomic layer, possibly inducing the deformation, and even removal of the second atomic layer. Theoretically, the cutting depth should be smaller than the above-determined amax.

Similarly, the amax for Cu(001) and Cu(110) surfaces were also calculated, as shown in Table 2. The Dlayer follows the order of Cu(110) < Cu(001) < Cu(111). Therefore, single atomic layer removal should be most likely conducted on the Cu(111) surface, namely, the close-packed plane of monocrystalline copper.
Table 2

Crystal parameters

Crystal plane

Orientation

Spacing distance/Dlayer (Å)

Maximum cutting depth/amax (Å)

Cu(001)

x-[1 0 0], y-[0 1 0], z-[0 0 1]

1.807

2.18

Cu(110)

x-[0 0 1], y-[1 − 1 0], z-[1 1 0]

1.278

1.28

Cu(111)

x-[1 − 1 0], y-[1 1 2], z-[1 1 1]

2.087

2.32

2.4 Determination of Potential Function

The copper–diamond cutting system mainly involves two types of atoms, namely, copper and diamond atoms. In the MD simulations, the interatomic interactions should be accurately described to ensure the computational accuracy of simulation results. Thus, reasonable selection of potential function is critically significant. In the present study, the frequently used embed atom method (EAM) is adopted to describe the interatomic interactions of copper atoms [15], while Morse function is applied to calculate the interactions between copper atoms and carbon atoms (Cu–C) [16].

For single atomic layer removal, the interatomic repulsive interactions between copper and diamond tools dominate the material removal process during cutting. As for the interactions between carbons in diamond tool (C–C), due to significantly stronger bond strength between diamond atoms than copper atoms, these are negligible. During MD simulations, a diamond tool is regarded as a rigidity.

3 Results and Discussion

To clearly indicate the feasibility of cutting in atomic and close-to-atomic manufacturing, the analysis results are analyzed and discussed from the aspects of surface topography, cutting force, material deformation, and removal mechanism as follows.

3.1 Surface Topography

3.1.1 Effect of Cutting Depth

Cutting depth, as one of the key process parameters, is expected to have a great influence on surface generation in the ACS cutting process. This section first emphatically analyzes the effect of cutting depth on surface topography. As given above, the theoretical cutting depth is [0, 2.32 Å] for Cu(111) surface. Figure 4 shows the surface topographies of the Cu(111) surfaces obtained at various cutting depths.
Fig. 4

Cu(111) surface topographies versus cutting depths, cutting velocity = 25 m/s. Atoms are colored based on their z-direction height

When cutting depth is decreased to be comparable or lower-than-atomic size of copper (1.28 Å), evident material deformation and/or removal occurs on the processed surface. However, as cutting depth changes, different types of material removal occurs. As a result, the newly formed Cu(111) surfaces have exhibited significantly different surface topographies.

When cutting depth is lower than 1.0–1.2 Å, no evident material removal has occurred on workpiece surface, as shown in Fig. 4a. Only when the cutting depth was larger than 1.0–1.2 Å was material removal achievable on the Cu(111) surface. It also indicates that a negative or zero-cutting depth could not enable material removal. A positive cutting depth of larger than 0 Å should be used to achieve the ACS cutting on monocrystalline copper surface.

When cutting depth is larger than 1.0–1.2 Å, evident material removal occurs on the workpiece surface. However, at a cutting depth of 1.2 to 1.6 Å, there are many plate-like defects formed on the newly formed processed surface. Consequently, the surface quality has been seriously deteriorated, as given in Fig. 4b–d. At such case, the materials of less than 1 atomic layer is removed from workpiece surface. But the material removal is not continuous, due to the low cutting depth. Finally, a large amount of materials within the first atomic layer remain on the workpiece surface. Thus, it is regarded as non-continuous material removal.

When the cutting depth is larger than 1.6–1.8 Å, singe atomic layer removal is successfully achieved, and the processed surface with ideal crystalline structure is obtained, as shown in Fig. 4e–g. Though there is still a small number of surface defects formed, this should be due to the material deformation at the cutting-in and/or exit sides of workpiece. During stable cutting, there is no defect formation.

Overall, it can be concluded that on the Cu(111) surface, the cutting depth should be accurately controlled to be larger than about 1.6–1.8 Å, in order to achieve cutting-based singe atomic layer removal. The large cutting-depth range of 1.8–2.6 Å also sufficiently indicates the repeatability of single atomic layer removal on Cu(111) surface by mechanical cutting. Moreover, from the above analysis, it can be found that there are two critical cutting depths, and they divide the material removal process into three types, including no material removal, non-continuous material removal, and single atomic layer removal.

3.1.2 Effect of Cutting Velocity

Cutting velocity, as one significant process parameter, may affect the surface generation during ACS cutting process, further changing the surface topographies of the processed surface. Figure 5 gives the surface topographies of the processed Cu(111) surfaces at various cutting velocities. As shown in Fig. 4, when the cutting depth is [1.8 Å, 2.6 Å], the processed surface with ideal crystal structure is obtained. Here, the cutting depth of 2.0 Å is employed. As displayed in Fig. 5, the processed surfaces have exhibited different topographies, because of cutting velocity. When the cutting velocity is smaller than about 42.5 m/s, the processed surface has an ideal crystalline structure. Once the cutting velocity is larger than 42.5 m/s, many surface defects would be generated. Therefore, it can be inferred that a lower cutting velocity should be adopted to enable single atomic layer removal.
Fig. 5

Surface topographies of processed Cu(111) surfaces at various cutting velocities. Atoms are colored based on their z-direction height

3.1.3 Effect of Crystallographic Orientation

Similar analysis is also conducted on the Cu(001) and Cu(110) surfaces to indicate the effect of crystallographic orientation. As shown in Figs. 6 and 7, when the cutting depth is decreased to atomic scale, material removal also occurs on Cu(110) and Cu(001) surfaces. However, many surface defects are formed on the newly formed processed surfaces, particularly, Cu(110) surfaces.
Fig. 6

Cu(001) surface topographies versus cutting depths at a cutting velocity of 25 m/s. Atoms are colored based on their z-direction height

Fig. 7

Surface topographies versus cutting depths of Cu(110) at cutting velocity of 25 m/s. Atoms are colored based on their z-direction height

As per MD trajectory files, although the number of surface defects could be decreased by adjusting process parameters, they could not be fully eliminated. Consequently, the processed surface with ideal crystalline structure could not be achieved on Cu(001) and Cu(110) surfaces. It indicates that when the cutting depth is decreased to atomic scale, though material removal could be realized, controlled single atomic layer removal is not feasible on Cu(001) and Cu(110) surface. Thus, it can be determined that cutting-based single atomic layer could only be achieved on Cu(111) surface, namely, the close-packed plane of monocrystalline copper.

Additionally, it can be found from Figs. 6 and 7 that the critical cutting depths for enabling material removal on Cu(001) and Cu(110) surfaces are about 0.2 Å and 0.6 Å. However, the defect-free processed surface could not be achieved.

Overall, when the cutting depth is decreased to atomic scale, single atomic layer removal could be realized on Cu(111) surfaces by mechanical cutting and defect-free processed surface could be obtained.

3.2 Cutting Force

Figure 8 shows the plot of average cutting force components versus cutting depths. The tangential cutting force (Ft) and normal cutting force (Fn) are mainly focused. Because of the effects of crystallographic orientations, Ft and Fn on each surface have exhibited different changes. As single atomic layer removal could be only achieved on the Cu(111) surfaces (see Fig. 4), the cutting forces on the Cu(111) surface are emphatically analyzed, as given in Fig. 8a.
Fig. 8

Plots of cutting forces versus cutting depth

As cutting depth increases to about 2.32 Å, both of the cutting forces on Cu(111) surfaces have undergone evident growth, but different trends could be observed. When the cutting depth is smaller than about 1.0–1.2 Å, Ft is always about 0 nN, but Fn exhibits a linear growth, indicating that the normal cutting force dominates the material removal process at such cutting depth. This should be due to the occurrence of elastic deformation on the workpiece surface. After the cutting tool passes over the workpiece surface, the deformed part would completely spring back. Consequently, no material removal occurs on the processed surface. Moreover, at a cutting depth of about 0.2 Å, it can be observed that Fn has changed to a positive value from a negative value, indicating that the main component of cutting forces has changed from attraction interaction to repulsive interaction between cutting tool and workpiece.

When cutting depth increases to be larger than 1.0–1.2 Å, differently, both Ft and Fn significantly change. As given in Fig. 8a, at a cutting depth of 1.0–1.2 Å, Ft has rapidly increased to about 20 nN, while Fn has slightly decreased from about 29 to 23.1 nN. The significantly different changes of Ft and Fn mean that the targeted first atomic layer has conducted yield-like behavior in a normal direction, and plastic material deformation and removal starts to occur. Consequently, there is material removal on the workpiece surface. During the cutting process, there is elastic and plastic deformation at the contact region between the cutting tool and workpiece. After the lowest point of cutting tool passes over the workpiece surface, the elastically deformed part would spring back. However, as the cutting depth is still not large enough, under the action of the cutting tool, many atoms within the targeted first atomic layer could not be removed from the topmost surface and non-continuous material removal occurs. The unremoved atoms remain on the workpiece surface, forming plate-like surface defects. Moreover, as the cutting depth increases, both Ft and Fn tend to slightly increase, further inducing the transformation of cutting towards continuous material removal, which could also be determined by the decreased number of plate-like defects (see Fig. 4).

When the cutting depth is larger than 1.6–1.8 Å, stable and continuous material removal is achieved on the Cu(111) surface. Consequently, Ft approximately stabilizes to about 20 nN, while Fn fluctuates around about 30 nN. However, when the cutting depth is larger than about 2.0 Å, Ft approximately remains unchanged, but Fz has evidently decreased to about 7 nN at a cutting depth of 2.2 Å, evidently lower than Fn. This should be due to the change of the normal cutting force exerted by cutting tool on the targeted atom.

When the cutting depth is decreased to atomic scale, the cutting process could be simplified into the interactions between single workpiece atom (copper) and tool atom (diamond). As illustrated in Fig. 9, as the cutting depth changes from 0 to about 2.32 Å, there are three kinds of contact states between tool atom (carbon) and targeted workpiece atom (copper) at different cutting depths. It also induces three types of forced conditions on the targeted workpiece atom.
Fig. 9

Schematic diagram for force state of targeted copper atom on copper surface

When the cutting depth is lower than about 2.0 Å, the normal cutting force is pointed downward and leads to the downward movement of targeted atom, as shown in Fig. 9a. To successfully ensure the downward movement of the targeted atom, the normal cutting force will be applied to overcome the repulsive interaction from other atomic layers. Differently, when the cutting depth is larger than about 2.0 Å, an upward normal force would be exerted by the cutting tool on the targeted atom to drive it upward, as illustrated in Fig. 9c.

In such a case, the upward normal cutting force is used to overcome the attraction interactions on the targeted atoms from other atomic layers, thereby realizing the downward migration of the targeted atom. For interatomic interactions, generally, the attraction interaction has lower strength than repulsive interactions. Thus, the normal cutting force required to ensure the movement in the normal direction would be evidently decreased when the cutting depth is larger than about 2.0 Å. A similar finding is also obtained on Cu(001) surface at a cutting depth of about 2 Å. However, on the Cu(110) surface, as the spacing distance between neighboring atomic layers is decreased to about 1.28 Å, there is only case 1 (see Fig. 9a).

3.3 Atomic Displacement Behavior

Figures 10, 11, and 12 illustrate the displacement vectors of workpiece atoms on different crystal planes. The arrow clearly indicates the cutting tool-driven displacement direction of workpiece atoms.
Fig. 10

Simulation results of Cu(111) surface at cutting depth of 2 Å

Fig. 11

Simulation results on Cu(001) surface at cutting depth of 2.0 Å

Fig. 12

Simulation results on Cu(110) at cutting depth of 1.0 Å

As the cutting distance (L) increases, there is chip formation on Cu(111), Cu(001), and Cu(110) surface, but there is an evident difference in the chip formation mechanism on each surface.

From the displacement vectors in Fig. 10c, one evident slip plane could be noted. The workpiece material above this slip plane tends to slip along the cutting direction. Differently, the material below the slip plane is immobilized during the cutting process. The different atomic migration behavior of workpiece material above or below the slip plane indicates that there is one shear stress-driven edge dislocation formed during the ACS cutting process. The tangential component of the cutting force provides the shear stress to enable dislocation slip with a Burgers vector along the cutting direction, namely, [− 1 1 0]. Meanwhile, elastic deformation has occurred on the processed surface, during the cutting process. Moreover, it can be found that one atom has moved upward, indicating that the edge dislocation has moved perpendicular to the slip plane, namely, dislocation climb.

On the Cu(001) and Cu(110) surfaces, there is also chip formation at the rake face of the cutting tool, as given in Figs. 11 and 12. However, different from Cu(111) surface, no slip plane could be observed over the cutting process. In such a case, as the cutting tool advances, though material removal also occurs, more than one atomic layer has been removed from workpiece surface. Consequently, single atomic layer removal could not be realized on Cu(110) and Cu(001) surfaces. In the cutting process, the materials that are removed from the workpiece come from different topmost atomic layers rather than the targeted first atomic layer.

Comparing the results among Figs. 10, 11, and 12 , it can be inferred that the material removal is mainly conducted in the form of dislocation motion in order to achieve single atomic layer removal.

Figure 13 gives the slip process of edge dislocation at the cutting depth of 2 Å. The moved atoms are colored as per their x-direction atomic displacement values (x-AD). The immobilized atoms are colored to purple. In this work, the targeted first topmost atomic layer is located within the region of ABCD. As shown, at a cutting distance of about 3.6 nm, the curve EF represents dislocation line, BCEF and ADEF refers to the slipped and un-slipped zones. As the cutting tool advances, the area of BCEF evidently increases, indicating the slip process of the cutting-induced edge dislocation. When the cutting distance is about 9.5 nm, the dislocation line has contacted with the edge of the workpieces surface. At a cutting depth of about 12.5 nm, the area of slipped zone (BCEF) has increased to be approximately that of ABCD, leading to the formation of cutting-exit edge burr. Subsequently, as the cutting tool advances, the slipped material would be further formed into burr, inducing the increased volume of edge burr.
Fig. 13

Slip process of edge dislocation on Cu(111) surface at cutting depth of 2 Å. Atoms are colored as per their x-direction atomic displacement values

4 Single Atomic Layer Removal Regime

In the cutting towards single atomic layer removal, distinct material removal regimes arise, including no material removal, non-continuous material removal, and continuous material removal. Thereinto, continuous material removal could be further divided into single atomic layer removal and multi-atomic layer removal. Therefore, there are four kinds of material deformation and removal regimes in the cutting-based single atomic layer removal.

As shown in Fig. 14, the transition of material removal regimes could be characterized by the non-dimensional cutting depth δ, which is defined at a/Rw. Here, the Rw and Rt refer to the atomic radius of workpiece material and tool material. Dlayer is the space distance between neighboring atomic layers, which is mainly dependent on the crystallographic orientations and material properties.
Fig. 14

Schematic diagram for atomic sizing effect in cutting-based single atomic layer removal

The detailed material deformation and removal mechanism in each kind of regime is summarized as follows:
  1. (1)

    No-material removal (elastic deformation) The atomic lattice of copper is deformed purely elastically. After the cutting tool passes over the workpiece surface, the deformed lattice recovers completely. In this case, cutting does not lead to material removal or damage on the workpiece surface, as illustrated in Fig. 4a.

     
  2. (2)

    Non-continuous material removal When δ increases and reaches its first critical value, \(\delta_{1}^{{\left( {\text{c}} \right)}}\), as the cutting tool advances, there is material removal occurring on the workpiece surface. However, as the cutting depth is too small to enable stable and continuous material removal, only non-continuous material removal occurs and the defect-free processed surface with ideal crystalline structure could not be obtained by mechanical cutting. After the tool passes over the workpiece surface, atoms less than one atomic layer will be removed. Finally, there are many plate-like defects formed on the processed surface, see Fig. 4b–d.

     
  3. (3)

    Single atomic layer removal As δ further increases to its second critical value, \(\delta_{2}^{\left( c \right)}\), the first atomic layer on the topmost workpiece surface can be fully removed (see Fig. 4e–h). The processed surface exhibits ideal crystalline structure. In such cases, there is chip formation via shear stress-driven dislocation motion while elastic deformation occurs on the processed surface. After the tool passes over the workpiece surface, the elastically deformed portion of the processed surface would recover completely. In this case, the minimum chip thickness could be decreased to single atomic layer, enabling the fabrication of a next-generation device with atomic scale features.

     
  4. (4)

    Multi-atomic layer removal When δ reaches its third critical value, \(\delta_{3}^{\left( c \right)}\), more than the first layer of atoms can be removed from the workpiece surface. There are many pitted or vacancy defects formed on the processed surfaces, seriously deteriorating the surface quality. Moreover, in this case, during the cutting process, elastic deformation also occurs on the processed surfaces. After the tool passes over the workpiece surface, the elastically deformed portion will spring back.

     

The above material deformation and removal regimes represent the most general cases. Under specific process conditions, most of the regimes would appear except for the single atomic layer removal mechanism.

5 Conclusions

The material deformation and removal mechanism in atomic or close-to-atomic scale (ACS) cutting process, based on molecular dynamics analysis, has been investigated, and the following findings were obtained:
  1. (1)

    When the cutting depth is decreased to atomic scale, single atomic layer removal could be realized on Cu(111) surface by mechanical cutting. Minimum chip thickness could be down to single atomic layer, with the cutting depth of about 0.2 nm.

     
  2. (2)

    ACS cutting undergoes an elastic–plastic deformation process on the processed surface with an increase in cutting depth. There is one critical ratio of cutting depth to atomic radius, which divides deformation into two schemes: elastic deformation and plastic deformation.

     
  3. (3)

    The material removal in ACS cutting is dominated by shear stress-driven dislocation motion under the action of a cutting tool.

     
  4. (4)

    For single atomic layer removal, depending on the ratio of cutting depth to atomic radius (δ), there are four kinds of atomic layer removal regimes, including no material removal, non-continuous material removal, single atomic layer removal, and multi-atomic layer removal.

     

A new cutting theory needs to be gradually established to bridge the gaps among ACS cutting to micro/nanoscale cutting and conventional machining.

Notes

Acknowledgements

The authors would like to acknowledge the support received from the Science Foundation Ireland (SFI) (No. 15/RP/B3208) and ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (Grant No. B07014).

References

  1. 1.
    Fang FZ (2016) Atomic and close-to-atomic scale manufacturing—a trend in manufacturing development. Front Mech Eng 11(4):325–327MathSciNetCrossRefGoogle Scholar
  2. 2.
    Fang FZ, Zhang N, Guo D, Ehmann K, Cheung B, Liu K, Yamamura K (2019) Towards atomic and close-to-atomic scale manufacturing. Int J Extreme Manuf 1:012001–012033CrossRefGoogle Scholar
  3. 3.
    Pierre M, Wacquez R, Jehl X, Sanquer M, Vinet M, Cueto O (2010) Single-donor ionization energies in a nanoscale CMOS channel. Nat Nanotechnol 5(2):133CrossRefGoogle Scholar
  4. 4.
    Zhao M, Yu Y, Yimo H, Yang X, Zhu H, Wang S, Wang Y, Muller DA, Zhang X (2016) Large-scale chemical assembly of atomically thin transistors and circuits. Nat Nanotechnol 11(11):954CrossRefGoogle Scholar
  5. 5.
    Koch M, Keizer JG, Pakkiam P, Keith D, House MG, Peretz E, Simmons MY (2019) Spin read-out in atomic qubits in an all-epitaxial three-dimensional transistor. Nat Nanotechnol 14(2):137CrossRefGoogle Scholar
  6. 6.
    Fang FZ, Xu FF (2018) Recent advances in micro/nano-cutting: effect of tool edge and material properties. Nanomanuf Metrol 1:4–31CrossRefGoogle Scholar
  7. 7.
    Komanduri R, Von Turkovich BF (1981) New observations on the mechanism of chip formation when machining titanium alloys. Wear 69(2):179–188CrossRefGoogle Scholar
  8. 8.
    Xie JQ, Bayoumi AE, Zbib HM (1995) Analytical and experimental study of shear localization in chip formation in orthogonal machining. J Mater Eng Perform 4(1):32–39CrossRefGoogle Scholar
  9. 9.
    Fang FZ, Wu H, Zhou W, Hu XT (2007) A study on mechanism of nano-cutting single crystal silicon. J Mater Process Technol 184(1–3):407–410CrossRefGoogle Scholar
  10. 10.
    Fang FZ, Wu H, Liu YC (2005) Modelling and experimental investigation on nanometric cutting of monocrystalline silicon. Int J Mach Tools Manuf 45(15):1681–1686CrossRefGoogle Scholar
  11. 11.
    Xu F, Wang J, Fang FZ, Zhang X (2017) A study on the tool edge geometry effect on nano-cutting. Int J Adv Manuf Technol 91(5–8):2787–2797CrossRefGoogle Scholar
  12. 12.
    Yan J, Zhao H, Kuriyagawa T (2009) Effects of tool edge radius on ductile machining of silicon: an investigation by FEM. Semicond Sci Technol 24(7):075018CrossRefGoogle Scholar
  13. 13.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117:1–19CrossRefGoogle Scholar
  14. 14.
    Zhu PZ, Fang FZ (2016) Study of the minimum depth of material removal in nanoscale mechanical machining of single crystalline copper. Comput Mater Sci 118:192–202CrossRefGoogle Scholar
  15. 15.
    Foiles SM, Baskes MI, Murray SD (1986) Embedded-atom-method functions for the FCC metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B 33(12):7983CrossRefGoogle Scholar
  16. 16.
    Girifalco LA, Victor GW (1959) Application of the Morse potential function to cubic metals. Phys Rev 114(3):687CrossRefGoogle Scholar

Copyright information

© International Society for Nanomanufacturing and Tianjin University and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Centre of Micro/Nano Manufacturing Technology (MNMT-Dublin)University College DublinDublinIreland
  2. 2.State Key Laboratory of Precision Measuring Technology and Instruments, Centre of Micro/Nano Manufacturing Technology (MNMT)Tianjin UniversityTianjinChina

Personalised recommendations