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In situ experimental study on material removal behaviour of single-crystal silicon in nanocutting
International Journal of Mechanical Sciences 152 (2019) 378–383
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International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
In situ experimental study on material removal behaviour of single-crystal silicon in nanocutting Bing Liu a, Zongwei Xu b, Cheng Chen a,∗, Rui Li a, Chaohao Wang c, Xiong Yang a a
School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China State Key Laboratory of Precision Measuring Technology & Instruments, Tianjin University, Tianjin 300072, China c Tianjin Ju Xin Hongtai Metal Material Co., Ltd., Tianjin 300112, China b
a r t i c l e
i n f o
Keywords: Nanocutting Single-crystal silicon Material removal Brittle-ductile transition Minimum cutting thickness
a b s t r a c t Ductile-mode removal of single-crystal silicon can be achieved by strictly controlling the cutting parameters, which significantly affects the machining efficiency. To improve the surface quality without reducing the machining efficiency, nanocutting experiments were performed to study the material removal behaviour using a specially designed nanocutting platform with a scanning electron microscope (SEM). Diamond tools with different edge radii were fabricated by focused ion beam (FIB) technology. The initiation and propagation of microcracks were observed online by an SEM to analyse the material removal behaviour of single-crystal silicon in the brittle mode. The effects of the crystal orientation and tool edge radius on the critical thickness of the brittle-ductile transition were investigated. Additionally, in the ductile mode, the influence of the tool edge radius on the minimum cutting thickness (MCT) was analysed. It was determined that the ratio of the MCT to the tool edge radius was 0.32–0.50, regardless of the tool edge radius. This in situ experimental study can provide a direct verification for the material removal behaviour in nanocutting.
1. Introduction Due to its unique physical and chemical properties, single-crystal silicon is widely used in the field of optoelectronics and microelectromechanical systems, including thermal imaging lenses, solar cells, etc. [1,2] As an important means of advanced manufacturing technology, nanocutting has been widely applied in industries over the last two decades to generate components with a high surface quality and low subsurface damage [3–5]. A machined surface with an optical quality of brittle or hard materials can be obtained directly by cutting. However, there are a series of problems during the cutting process, such as cleavage fracture [6] and anisotropy of processability [7] due to the brittle natural characteristics. Ductile mode removal of single-crystal silicon can be achieved by strictly controlling the cutting parameters, but the machining efficiency will be affected. Therefore, it is urgent to clearly understand the critical thickness of the brittle-ductile transition [8,9] of single-crystal silicon and clarify the reasons and influencing factors. Then the surface quality and processing efficiency of single-crystal silicon can be simultaneously improved during nanocutting, which will play a critical role in promoting the level of ultra-precision cutting technology. In recent years, researchers have focused significant efforts on the investigation of the material removal behaviour of single-crystal sili∗
Corresponding author. E-mail address: [email protected] (C. Chen).
con, and many outstanding achievements have been obtained. The minimum cutting thickness (MCT) and the brittle-ductile transition of singlecrystal silicon are two significant research focuses. By utilizing a specially designed AFM/nanostage setup, Lee [10] performed a series of scratching tests via a measuring tip as the diamond tool and analysed the effect of the scratching depth on the chip morphology of single-crystal silicon. It was determined that with an increase in the depth of cut, the material removal process successively underwent an elastic recovery, pile-up, chip formation, and crack propagation, and the MCT was estimated to be 15 nm. Wu et al. [11] further studied the influence of crystal orientations on the material removal behaviour of single-crystal silicon and found that, on a given crystallographic plane, brittle fracture always dominated in the [100] orientation compared to the [111] orientation. Han et al. [12] thought that brittle material was the most easily removed in the ductile mode using a diamond tool with a smaller edge radius. However, Liu et al. [13] believed that a diamond tool with a larger edge radius was more conducive towards restraining the fracture of the brittle material during nanocutting. Predictably, there exists a divergence in the influence of the tool edge radius on the material removal mode of brittle materials. The main reason is that the tool edge radii studied by different researchers are inconsistent. In addition, as the experiment proceeds, the tool edge usually deviates from the original value due to tool wear. When the depth of cut decreases from the microscale to nanoscale, the material removal behaviour will be dominated by an extrusion action rather than shearing action [14–16]. In nanocutting, the MCT is usually smaller than the tool edge radius, where
https://doi.org/10.1016/j.ijmecsci.2019.01.015 Received 27 November 2018; Received in revised form 5 January 2019; Accepted 8 January 2019 Available online 9 January 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.
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International Journal of Mechanical Sciences 152 (2019) 378–383
Fig. 1. Experimental platform for nanocutting tests. (a) Physical unit (b) Schematic diagram.
the effective rake angle is negative regardless of what the nominal rake angle is. Along with the rapid development of computers, investigations on the MCT of single-crystal silicon have been extensively performed by molecular dynamics (MD) simulations [17–19]. Nevertheless, the depth of cut and the tool edge radius set in MD simulations are far less than the actual cutting parameters. To verify the MD simulation results and experimentally clarify the material removal behaviour, nanocutting tests [20–22] are usually implemented using an ultra-precision turning lathe. However, it is difficult to detect when the nanometric cutting chips are generated and the tool edge radius is usually large. The main purpose of this work is to investigate the material removal behaviour of a single-crystal silicon via a novel experimental method, which can provide the most powerful explanation. In considering the size effect [23] of the tool edge radius, nanocutting tests were performed using a scanning electron microscope (SEM), which can achieve a highresolution online observation of the material removal behaviour. The critical thickness of the brittle-ductile transition and the MCT were studied in the brittle region and ductile region, respectively.
Fig. 2. Tool setting process.
because parts of the secondary electrons excited from the specimen were warded off. Finally, as the cutting edge gradually approached the specimen, the shadow and the cutting edge tended to coincide, which can be observed clearly via SEM imaging. Therefore, it is a valuable method to estimate whether the diamond tool is in contact with the specimen surface. To verify the accuracy and reliability of the above tool setting method, pre-cutting tests were conducted on the surface of a singlecrystal silicon, where the depth of cut was set to 3 nm. The machined surface was measured by an atomic force microscope (AFM) and the measurement result is shown in Fig. 3. It can be seen that the altitude difference between the machined surface and the undeformed surface was approximately 3.142 nm, indicating that the specially designed platform has the ability of performing nanocutting tests and enables nanoscale material removal behaviour to be achieved.
2. Experimental procedure 2.1. Nanocutting platform There are extremely high demands for the nanocutting platform when the depth of cut is reduced to the nanoscale. To meet the technical requirements of nanocutting tests, nanometric positioning accuracy and motion resolution must be considered on the basis of satisfying the stiffness of the platform. Additionally, to clearly observe the material removal behaviour and determine the critical thickness of the brittleductile transition and the MCT of single-crystal silicon, a vacuum cutting environment without dust or vibration is also presented. In this paper, all nanocutting tests were performed in a scanning electron microscope (SEM) using a specially designed nanocutting platform developed by Micro-Nano Manufacturing Technology (MNMT) laboratory, which has a great influence in the field of ultra-precision machining technology. Fig. 1 shows the physical unit and the schematic diagram of the specially designed nanocutting platform. A nanoscale motion stage driven by a piezoelectric ceramic (PZT) was used to control the diamond tool with a nanometric positioning accuracy. The stiffness and stability of the nanocutting platform were verified in reference [24]. Because the depth of cut in nanocutting is much smaller than that in conventional cutting (usually less than 2 μm), an accurate tool setting between the diamond tool and the specimen is a key problem that needs to be solved. First, the diamond tool was remained stationary and the micropositioner was manually rotated to move the specimen in the X, Y or Z direction for the coarse positioning. Next, the specimen was kept static and the tool was driven by the PZT nanoscale motion stage to slowly approach the specimen with online observation by an SEM. When the cutting edge was close enough to the specimen surface, a tool shadow would appear on the specimen surface, as shown in Fig. 2. The shadow could be generated
2.2. Diamond tool The interaction between the diamond tool and the workpiece has a significant effect on the material removal behaviour, especially when the depth of cut is reduced to the nanoscale, in which case the size effect of the tool edge radius will be reflected. The edge radius of the commercial diamond tool is usually more than 50 nm, so that it cannot satisfy the requirements of nanocutting tests. Additionally, to better observe the material removal behaviour and study the minimum cutting thickness of single-crystal silicon, a diamond tool with a straight edge rather than a curved edge is more advantageous. Thus, diamond tools with straight edge and different nanometric edge radii are strongly demanded in investigations on material removal behaviour. Focused ion beam (FIB) technology has been used for the fabrication of diamond tools due to its advantages in nanomanufacturing. However, the fabrication of a diamond tool with a nanometric edge radius is extremely challenging. Because the section of the Gaussian beam intensity of the FIB would extend outside the define pattern boundary, a sharp edge would be produced on the side of the facets further from the ion source, while a rounded edge would be formed closer to the ion source [25]. Recently, appropriate FIB processing parameters for the fabrication of 379
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International Journal of Mechanical Sciences 152 (2019) 378–383
Fig. 3. AFM measurement results of a machined surface on a single-crystal silicon: (a) Three-dimensional morphology, (b) Cross-section diagram.
Fig. 4. Diamond tool with an edge radius of 20 nm fabricated by FIB. Table 1 Conditions of the nanocutting tests. Experimental apparatus Specimen material Tool rake angle Tool clearance angle Tool edge radius Straight edge length Cutting speed Depth of cut Cutting environment
A specially designed platform in a FIB/SEM dual system Single-crystal silicon Rake angle of 0° 8° 15–60 nm 10 μm 23.5 nm/s 0–100 nm Dry cutting in vacuum without coolant
Fig. 6. Material removal process of single-crystal silicon in brittle mode.
went three distinct deformation modes in the following order—elastic recovery, ductile removal and brittle removal—under the interaction between the tool and the specimen. In the ductile-cut region, the material was stacked up in an extrusion form first, and then it flowed out in a curled form along the tool rake face to form continuous chips. It was determined that the chips were similar to that in the cuttings of ductile materials, where chips formation is dominated by dislocation. When the depth of cut increased to the critical thickness of the brittle-ductile transition of a single-crystal silicon, microcracks came into being. The initiation and propagation of the microcracks, which are difficult to detect in the conventional experimental study and simulation analysis, were observed clearly online via SEM high-resolution imaging, as shown in Fig. 6(a)–(d). Initially, microcracks were generated on the silicon surface, and the crack propagation direction was related to the crystal plane, crystal orientation and cutting direction. As the cutting proceeded, the cracks grew gradually until brittle peeling occurred (Fig. 6(a)), and brittle pits appeared on the machined surface (Fig. 6(b)). When the tool moved to the edge of the pits, ductile machined surfaces were locally formed again. Because within a short cutting distance on the pits, the current depth of cut was less than the critical thickness of the brittleductile transition. Next, when the cutting edge was in contact with the undeformed silicon surface, the current depth of cut was again beyond the critical thickness of the brittle-ductile transition. Therefore, the material would be removed repeatedly in brittle mode to form microcracks (Fig. 6(c)). Fig. 6(d) shows the machined silicon with both ductile surface and brittle pits by rotating the nanocutting platform for a better view direction. According to the above experiments and analyses, it is proved that the research approach in this paper is able to deeply study the brittle/ductile removal behaviour of single-crystal silicon with an online observation.
Fig. 5. Machined surface morphology of single-crystal silicon after tapercutting.
diamond tools with a desired edge radius have been determined in the previous work of Liu et al. [26]. Fig. 4 shows the SEM image of one of the diamond tools with a straight edge fabricated by FIB technology, where the tool edge radius is approximately 20 nm, and the clearance angle is approximately 8°. 2.3. Nanocutting tests The conditions of the following nanocutting tests are listed in Table 1. To understand the material removal behaviour of single-crystal silicon with an online observation, taper-cutting tests were first performed at an ultra-low speed of 23.5 nm/s using a diamond tool with an edge radius of 40 nm. The SEM image of the machined surface is shown in Fig. 5. It can be seen from left to right in Fig. 5 that, as the depth of cut increased, the machined surface of the single-crystal silicon under380
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International Journal of Mechanical Sciences 152 (2019) 378–383
Fig. 7. Cross-section analysis of the machined surface. (a) Schematic of FIB polishing (b) Ductile-cut surface (c) Brittle-cut surface.
Fig. 9. Critical thickness of the brittle-ductile transition of single-crystal silicon at different orientations.
Fig. 8. Machined surface morphology of single-crystal silicon with different depths of cut: (a) Ductile surface formed at a depth of cut of 40 nm, (b) Brittle cracks occurred at a depth of cut of 70 nm, (c) Brittle cracks enlarged at a depth of cut of 100 nm.
The experimental results of the critical thickness of the brittle-ductile transition in different crystal orientations on single-crystal silicon are listed in Table 2. Three repeated experiments were conducted, and the average value of the critical thickness is shown in Fig. 9. It can be determined that the critical thickness of the brittle-ductile transition on the (111) crystal plane is larger than that on the (110) crystal plane, indicating that ductile material removal is more easily occurs on the (111) crystal plane. Moreover, on the same crystal plane, the critical thickness of the brittle-ductile transition in the [001] crystal orientation is obviously smaller than that in the [111] crystal orientation, indicating that the cutting direction has a significant effect on the ductile cutting of single-crystal silicon. The maximum critical thickness is approximately 80 nm in the range of the present studies.
Fig. 7 shows the cross-section analysis of the machined surface with an increasing depth of cut from 0 to 100 nm on a single-crystal silicon. The cross-sectional profile along the X-axis corresponds to the machined surface morphology. As seen in Fig. 7(b and c), both the ductile-cut surface and brittle-cut surface were obtained during this nanocutting test. Using this cross-section analysis method, a further study on the 3D subsurface damage will be addressed in a future paper. 3. Results and discussions 3.1. Brittle-ductile transition
3.1.2. The effect of tool edge radius Due to the size effect of the tool edge radius in nanocutting, its influence on the critical thickness of the brittle-ductile transition must be considered. Using a novel fabricating method elaborated in reference [26], the commercial diamond tools were efficiently processed with different controllable edge radii first by FIB. Subsequently, to avoid the effect of anisotropy on the experimental results, all cutting tests were performed on single-crystal silicon at a low speed in the [111] crystal orientation on the (110) crystal plane. Identical to the cutting process mentioned above, the depth of cut also began from 20 nm and increased by 5 nm in each test, until the brittle removal mode occurred. In addition, the roughness of the ductile-cut surfaces were measured via AFM. Fig. 10 shows the effect of the tool edge radius on the surface quality and the critical thickness of the brittle-ductile transition. It can be seen that the surface finish quality decreases with an increase in the tool edge radius. In contrast, under the conditions of the same crystal orientation, tool geometry and cutting speed, the larger the tool edge radius is, the larger the critical thickness of the brittle-ductile transition is. That is, a diamond tool with a larger edge radius is beneficial towards restraining the fracture of single-crystal silicon. It is worth noting that in the range
3.1.1. The effect of crystal orientation It is widely known that the atomic permutation density of singlecrystal materials are diverse in different crystal orientations, leading to inconsistent performances, such as the energy, bonding force, physical and mechanical properties. That means anisotropy exists in singlecrystal materials. In view of this, the effect of crystal orientation on the critical thickness of brittle-ductile transition cannot be neglected in nanocutting. In previous taper cutting tests, the critical thickness had to be measured off-line, making the experiments more complex. Accordingly, to exactly obtain the critical thickness of the brittle-ductile transition without an off-line measurement, linear cuttings were performed repeatedly in different orientations on a single-crystal silicon, using a diamond tool with an edge radius of 60 nm. The depth of cut started from 20 nm and increased by 5 nm in each test until the brittle removal mode occurred. Fig. 8(a)–(c) show the machined surface morphology along the [111] orientation on the (110) crystal plane, which revealed the cutting process mentioned above. It was determined that as the depth of cut increased, the machined surface changed from pure ductility to the coexistence of ductility and cracks, and finally to full of cracks. 381
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Table 2 Critical thicknesses of the brittle-ductile transition of single-crystal silicon at different orientations. Crystal plane
(110) (111)
Crystal orientation
[001] [111] [001] [111]
Critical thickness of brittle-ductile transition (nm) 1st
2nd
3rd
Average value
40 70 55 80
45 70 50 75
45 65 55 85
43.3 68.3 53.3 80.0
Fig. 10. Effect of the tool edge radius on the surface quality and critical thickness of the brittle-ductile transition.
Fig. 12. Continuous chips morphology with a depth of cut of 8 nm.
Fig. 11. Nanocutting model.
of the present investigations, the value of the critical thickness is close to the value of the tool edge radius. The reason for this is that when the depth of cut is less than the tool edge radius, the effective rake angle is always negative regardless of the nominal value, enabling a large compressive stress to be generated, which acts to stop the growth of preexisting flaws in the material by suppressing the stress intensity factor [13].
Fig. 13. The relationship between the tool edge radius and minimum cutting thickness.
where dmin is the MCT, R is the tool edge radius, A is the stagnation point, 𝜇 is the friction coefficient between the tool and material, and Ff and Fp are the tangential force and normal force at point A, respectively. As a matter of experience in diamond cutting, Fp is 0.9 times that of Ff , and 𝜇 is usually between 0.1 and 0.15 without lubrication. Consequently, it can be deduced that dmin = 0.26–0.47 R.
3.2. Minimum cutting thickness 3.2.1. Theoretical analysis The MCT affects the machining efficiency and accuracy, especially when the tool edge radius cannot be ignored in nanocutting, which dominates the material modelling and processing parameter selection. Researchers have found that there is a threshold of the cutting thickness, below which only elastic-plastic deformation occurs without chip formation [21]. From the nanocutting model, as illustrated in Fig. 11, equations can be derived as follows [20]: tan𝜃 =
𝑑min
𝐹𝑓 − 𝜇𝐹𝑝 𝜇𝐹𝑓 + 𝐹𝑝
⎡ ⎤ 𝐹𝑝 + 𝜇𝐹𝑓 ⎢ ⎥ = 𝑅(1 − cos 𝜃) = 𝑅 ⎢1 − √ ( 2 )( )⎥ 2 ⎢ 𝐹𝑓 + 𝐹𝑝 1 + 𝜇 2 ⎥⎦ ⎣
3.2.2. Experimental verification Using the specially designed nanocutting platform, the MCT can be accurately obtained by means of high-resolution SEM imaging. Diamond tools with different edge radii were employed for a series of cutting tests. Previous studies in references [27,28] have shown that the ratio of the MCT to the tool edge radius is between 0.2 and 0.4. Therefore, to improve the experimental efficiency, the initial depth of cut was set to 0.6 times the tool edge radius and reduced by 1 or 2 nm in each test. Once each cutting was performed, whether or not the continuous chips were formed was detected via SEM. The cutting process was repeated until no continuous chip was found, that is, the present depth of cut was considered to be the MCT of single-crystal silicon. Fig. 12 shows an image of the continuous chips observed with a depth of cut of 10 nm. The experimental results of the relationship between the tool edge radius and MCT is shown in Fig. 13.
(1)
(2)
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References
As seen in Fig. 13, the MCT increases nearly linearly with the tool edge radius. Furthermore, the ratio of the MCT to the tool edge radius is always between 0.32 and 0.50 in the range of the present studies, indicating that the MCT of single-crystal silicon strongly depends on the tool edge radius. It is worth noting that this ratio is slightly larger than that in the theoretical values and MD simulation results, because tool wear is inevitable during the nanocutting tests, resulting in an increase in the tool edge radius. From the nanocutting model in Fig. 11, the effective rake angle 𝛼 e is negative and related to the MCT and the tool edge radius, which can be derived from the following equation: sin 𝛼𝑒 =
𝑅 − 𝑑min 𝑑 = 1 − min 𝑅 𝑅
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(3)
where 𝛼 e is effective rake angle. Substituting dmin /R into formula (3), it can be determined that 𝛼 e = 30.0°–42.8°. That is, the critical value of the effective negative rake angle for chips formation is between 30.0° and 42.8°. In conventional cutting, the cutting speed would obviously affect the MCT, mainly because the cutting temperature varies with the cutting speed, thereby resulting in a change in the friction coefficient between the tool and the workpiece. In this paper, it was only necessary to detect whether continuous chips could be formed at a shorter cutting distance. Therefore, the effect of the cutting speed on the MCT is negligible here. 4. Conclusions Using a specially designed nanocutting platform with SEM online observation, in situ nanocutting tests were performed at a low speed to study the material removal behaviour of single-crystal silicon. Diamond tools with different edge radii were fabricated by FIB technology. The effects of the crystal orientation and tool edge radius on the critical thickness of the brittle-ductile transition were studied, and the effect of the tool edge radius on the MCT was investigated through the experimental method. The main conclusions can be drawn as follows: (1) In the range of the present studies, the ductile removal behaviour of single-crystal silicon more easily occurs on the (111) crystal plane in the [111] crystal orientation. The maximum critical thickness of the brittle-ductile transition is approximately 80 nm. (2) The surface finish quality decreases with an increase in the tool edge radius, but a diamond tool with a larger edge radius is beneficial for restraining the fracture of the single-crystal silicon. The value of the critical thickness of the brittle-ductile transition is close to the value of the tool edge radius. (3) The MCT increases nearly linearly with the tool edge radius, and the ratio of the MCT to the tool edge radius is always between 0.32 and 0.50. The critical value of the effective negative rake angle for chips formation is between 30.0° and 42.8°.
Acknowledgements The authors would like to express their appreciation for the support of the National Natural Science Foundation of China (Grant No. 51805371), the Natural Science Foundation of Tianjin (Grant No. 18JCQNJC75400 and 17JCZDJC38200) and the Tianjin Science and Technology Development Fund Project (Grant No. 2018KJ226). The authors thank the MNMT Lab for their support with the experimental instruments. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijmecsci.2019.01.015.
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Contents lists available at ScienceDirect
International Journal of Mechanical Sciences journal homepage: www.elsevier.com/locate/ijmecsci
In situ experimental study on material removal behaviour of single-crystal silicon in nanocutting Bing Liu a, Zongwei Xu b, Cheng Chen a,∗, Rui Li a, Chaohao Wang c, Xiong Yang a a
School of Mechanical Engineering, Tianjin University of Commerce, Tianjin 300134, China State Key Laboratory of Precision Measuring Technology & Instruments, Tianjin University, Tianjin 300072, China c Tianjin Ju Xin Hongtai Metal Material Co., Ltd., Tianjin 300112, China b
a r t i c l e
i n f o
Keywords: Nanocutting Single-crystal silicon Material removal Brittle-ductile transition Minimum cutting thickness
a b s t r a c t Ductile-mode removal of single-crystal silicon can be achieved by strictly controlling the cutting parameters, which significantly affects the machining efficiency. To improve the surface quality without reducing the machining efficiency, nanocutting experiments were performed to study the material removal behaviour using a specially designed nanocutting platform with a scanning electron microscope (SEM). Diamond tools with different edge radii were fabricated by focused ion beam (FIB) technology. The initiation and propagation of microcracks were observed online by an SEM to analyse the material removal behaviour of single-crystal silicon in the brittle mode. The effects of the crystal orientation and tool edge radius on the critical thickness of the brittle-ductile transition were investigated. Additionally, in the ductile mode, the influence of the tool edge radius on the minimum cutting thickness (MCT) was analysed. It was determined that the ratio of the MCT to the tool edge radius was 0.32–0.50, regardless of the tool edge radius. This in situ experimental study can provide a direct verification for the material removal behaviour in nanocutting.
1. Introduction Due to its unique physical and chemical properties, single-crystal silicon is widely used in the field of optoelectronics and microelectromechanical systems, including thermal imaging lenses, solar cells, etc. [1,2] As an important means of advanced manufacturing technology, nanocutting has been widely applied in industries over the last two decades to generate components with a high surface quality and low subsurface damage [3–5]. A machined surface with an optical quality of brittle or hard materials can be obtained directly by cutting. However, there are a series of problems during the cutting process, such as cleavage fracture [6] and anisotropy of processability [7] due to the brittle natural characteristics. Ductile mode removal of single-crystal silicon can be achieved by strictly controlling the cutting parameters, but the machining efficiency will be affected. Therefore, it is urgent to clearly understand the critical thickness of the brittle-ductile transition [8,9] of single-crystal silicon and clarify the reasons and influencing factors. Then the surface quality and processing efficiency of single-crystal silicon can be simultaneously improved during nanocutting, which will play a critical role in promoting the level of ultra-precision cutting technology. In recent years, researchers have focused significant efforts on the investigation of the material removal behaviour of single-crystal sili∗
Corresponding author. E-mail address: [email protected] (C. Chen).
con, and many outstanding achievements have been obtained. The minimum cutting thickness (MCT) and the brittle-ductile transition of singlecrystal silicon are two significant research focuses. By utilizing a specially designed AFM/nanostage setup, Lee [10] performed a series of scratching tests via a measuring tip as the diamond tool and analysed the effect of the scratching depth on the chip morphology of single-crystal silicon. It was determined that with an increase in the depth of cut, the material removal process successively underwent an elastic recovery, pile-up, chip formation, and crack propagation, and the MCT was estimated to be 15 nm. Wu et al. [11] further studied the influence of crystal orientations on the material removal behaviour of single-crystal silicon and found that, on a given crystallographic plane, brittle fracture always dominated in the [100] orientation compared to the [111] orientation. Han et al. [12] thought that brittle material was the most easily removed in the ductile mode using a diamond tool with a smaller edge radius. However, Liu et al. [13] believed that a diamond tool with a larger edge radius was more conducive towards restraining the fracture of the brittle material during nanocutting. Predictably, there exists a divergence in the influence of the tool edge radius on the material removal mode of brittle materials. The main reason is that the tool edge radii studied by different researchers are inconsistent. In addition, as the experiment proceeds, the tool edge usually deviates from the original value due to tool wear. When the depth of cut decreases from the microscale to nanoscale, the material removal behaviour will be dominated by an extrusion action rather than shearing action [14–16]. In nanocutting, the MCT is usually smaller than the tool edge radius, where
https://doi.org/10.1016/j.ijmecsci.2019.01.015 Received 27 November 2018; Received in revised form 5 January 2019; Accepted 8 January 2019 Available online 9 January 2019 0020-7403/© 2019 Elsevier Ltd. All rights reserved.
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International Journal of Mechanical Sciences 152 (2019) 378–383
Fig. 1. Experimental platform for nanocutting tests. (a) Physical unit (b) Schematic diagram.
the effective rake angle is negative regardless of what the nominal rake angle is. Along with the rapid development of computers, investigations on the MCT of single-crystal silicon have been extensively performed by molecular dynamics (MD) simulations [17–19]. Nevertheless, the depth of cut and the tool edge radius set in MD simulations are far less than the actual cutting parameters. To verify the MD simulation results and experimentally clarify the material removal behaviour, nanocutting tests [20–22] are usually implemented using an ultra-precision turning lathe. However, it is difficult to detect when the nanometric cutting chips are generated and the tool edge radius is usually large. The main purpose of this work is to investigate the material removal behaviour of a single-crystal silicon via a novel experimental method, which can provide the most powerful explanation. In considering the size effect [23] of the tool edge radius, nanocutting tests were performed using a scanning electron microscope (SEM), which can achieve a highresolution online observation of the material removal behaviour. The critical thickness of the brittle-ductile transition and the MCT were studied in the brittle region and ductile region, respectively.
Fig. 2. Tool setting process.
because parts of the secondary electrons excited from the specimen were warded off. Finally, as the cutting edge gradually approached the specimen, the shadow and the cutting edge tended to coincide, which can be observed clearly via SEM imaging. Therefore, it is a valuable method to estimate whether the diamond tool is in contact with the specimen surface. To verify the accuracy and reliability of the above tool setting method, pre-cutting tests were conducted on the surface of a singlecrystal silicon, where the depth of cut was set to 3 nm. The machined surface was measured by an atomic force microscope (AFM) and the measurement result is shown in Fig. 3. It can be seen that the altitude difference between the machined surface and the undeformed surface was approximately 3.142 nm, indicating that the specially designed platform has the ability of performing nanocutting tests and enables nanoscale material removal behaviour to be achieved.
2. Experimental procedure 2.1. Nanocutting platform There are extremely high demands for the nanocutting platform when the depth of cut is reduced to the nanoscale. To meet the technical requirements of nanocutting tests, nanometric positioning accuracy and motion resolution must be considered on the basis of satisfying the stiffness of the platform. Additionally, to clearly observe the material removal behaviour and determine the critical thickness of the brittleductile transition and the MCT of single-crystal silicon, a vacuum cutting environment without dust or vibration is also presented. In this paper, all nanocutting tests were performed in a scanning electron microscope (SEM) using a specially designed nanocutting platform developed by Micro-Nano Manufacturing Technology (MNMT) laboratory, which has a great influence in the field of ultra-precision machining technology. Fig. 1 shows the physical unit and the schematic diagram of the specially designed nanocutting platform. A nanoscale motion stage driven by a piezoelectric ceramic (PZT) was used to control the diamond tool with a nanometric positioning accuracy. The stiffness and stability of the nanocutting platform were verified in reference [24]. Because the depth of cut in nanocutting is much smaller than that in conventional cutting (usually less than 2 μm), an accurate tool setting between the diamond tool and the specimen is a key problem that needs to be solved. First, the diamond tool was remained stationary and the micropositioner was manually rotated to move the specimen in the X, Y or Z direction for the coarse positioning. Next, the specimen was kept static and the tool was driven by the PZT nanoscale motion stage to slowly approach the specimen with online observation by an SEM. When the cutting edge was close enough to the specimen surface, a tool shadow would appear on the specimen surface, as shown in Fig. 2. The shadow could be generated
2.2. Diamond tool The interaction between the diamond tool and the workpiece has a significant effect on the material removal behaviour, especially when the depth of cut is reduced to the nanoscale, in which case the size effect of the tool edge radius will be reflected. The edge radius of the commercial diamond tool is usually more than 50 nm, so that it cannot satisfy the requirements of nanocutting tests. Additionally, to better observe the material removal behaviour and study the minimum cutting thickness of single-crystal silicon, a diamond tool with a straight edge rather than a curved edge is more advantageous. Thus, diamond tools with straight edge and different nanometric edge radii are strongly demanded in investigations on material removal behaviour. Focused ion beam (FIB) technology has been used for the fabrication of diamond tools due to its advantages in nanomanufacturing. However, the fabrication of a diamond tool with a nanometric edge radius is extremely challenging. Because the section of the Gaussian beam intensity of the FIB would extend outside the define pattern boundary, a sharp edge would be produced on the side of the facets further from the ion source, while a rounded edge would be formed closer to the ion source [25]. Recently, appropriate FIB processing parameters for the fabrication of 379
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Fig. 3. AFM measurement results of a machined surface on a single-crystal silicon: (a) Three-dimensional morphology, (b) Cross-section diagram.
Fig. 4. Diamond tool with an edge radius of 20 nm fabricated by FIB. Table 1 Conditions of the nanocutting tests. Experimental apparatus Specimen material Tool rake angle Tool clearance angle Tool edge radius Straight edge length Cutting speed Depth of cut Cutting environment
A specially designed platform in a FIB/SEM dual system Single-crystal silicon Rake angle of 0° 8° 15–60 nm 10 μm 23.5 nm/s 0–100 nm Dry cutting in vacuum without coolant
Fig. 6. Material removal process of single-crystal silicon in brittle mode.
went three distinct deformation modes in the following order—elastic recovery, ductile removal and brittle removal—under the interaction between the tool and the specimen. In the ductile-cut region, the material was stacked up in an extrusion form first, and then it flowed out in a curled form along the tool rake face to form continuous chips. It was determined that the chips were similar to that in the cuttings of ductile materials, where chips formation is dominated by dislocation. When the depth of cut increased to the critical thickness of the brittle-ductile transition of a single-crystal silicon, microcracks came into being. The initiation and propagation of the microcracks, which are difficult to detect in the conventional experimental study and simulation analysis, were observed clearly online via SEM high-resolution imaging, as shown in Fig. 6(a)–(d). Initially, microcracks were generated on the silicon surface, and the crack propagation direction was related to the crystal plane, crystal orientation and cutting direction. As the cutting proceeded, the cracks grew gradually until brittle peeling occurred (Fig. 6(a)), and brittle pits appeared on the machined surface (Fig. 6(b)). When the tool moved to the edge of the pits, ductile machined surfaces were locally formed again. Because within a short cutting distance on the pits, the current depth of cut was less than the critical thickness of the brittleductile transition. Next, when the cutting edge was in contact with the undeformed silicon surface, the current depth of cut was again beyond the critical thickness of the brittle-ductile transition. Therefore, the material would be removed repeatedly in brittle mode to form microcracks (Fig. 6(c)). Fig. 6(d) shows the machined silicon with both ductile surface and brittle pits by rotating the nanocutting platform for a better view direction. According to the above experiments and analyses, it is proved that the research approach in this paper is able to deeply study the brittle/ductile removal behaviour of single-crystal silicon with an online observation.
Fig. 5. Machined surface morphology of single-crystal silicon after tapercutting.
diamond tools with a desired edge radius have been determined in the previous work of Liu et al. [26]. Fig. 4 shows the SEM image of one of the diamond tools with a straight edge fabricated by FIB technology, where the tool edge radius is approximately 20 nm, and the clearance angle is approximately 8°. 2.3. Nanocutting tests The conditions of the following nanocutting tests are listed in Table 1. To understand the material removal behaviour of single-crystal silicon with an online observation, taper-cutting tests were first performed at an ultra-low speed of 23.5 nm/s using a diamond tool with an edge radius of 40 nm. The SEM image of the machined surface is shown in Fig. 5. It can be seen from left to right in Fig. 5 that, as the depth of cut increased, the machined surface of the single-crystal silicon under380
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Fig. 7. Cross-section analysis of the machined surface. (a) Schematic of FIB polishing (b) Ductile-cut surface (c) Brittle-cut surface.
Fig. 9. Critical thickness of the brittle-ductile transition of single-crystal silicon at different orientations.
Fig. 8. Machined surface morphology of single-crystal silicon with different depths of cut: (a) Ductile surface formed at a depth of cut of 40 nm, (b) Brittle cracks occurred at a depth of cut of 70 nm, (c) Brittle cracks enlarged at a depth of cut of 100 nm.
The experimental results of the critical thickness of the brittle-ductile transition in different crystal orientations on single-crystal silicon are listed in Table 2. Three repeated experiments were conducted, and the average value of the critical thickness is shown in Fig. 9. It can be determined that the critical thickness of the brittle-ductile transition on the (111) crystal plane is larger than that on the (110) crystal plane, indicating that ductile material removal is more easily occurs on the (111) crystal plane. Moreover, on the same crystal plane, the critical thickness of the brittle-ductile transition in the [001] crystal orientation is obviously smaller than that in the [111] crystal orientation, indicating that the cutting direction has a significant effect on the ductile cutting of single-crystal silicon. The maximum critical thickness is approximately 80 nm in the range of the present studies.
Fig. 7 shows the cross-section analysis of the machined surface with an increasing depth of cut from 0 to 100 nm on a single-crystal silicon. The cross-sectional profile along the X-axis corresponds to the machined surface morphology. As seen in Fig. 7(b and c), both the ductile-cut surface and brittle-cut surface were obtained during this nanocutting test. Using this cross-section analysis method, a further study on the 3D subsurface damage will be addressed in a future paper. 3. Results and discussions 3.1. Brittle-ductile transition
3.1.2. The effect of tool edge radius Due to the size effect of the tool edge radius in nanocutting, its influence on the critical thickness of the brittle-ductile transition must be considered. Using a novel fabricating method elaborated in reference [26], the commercial diamond tools were efficiently processed with different controllable edge radii first by FIB. Subsequently, to avoid the effect of anisotropy on the experimental results, all cutting tests were performed on single-crystal silicon at a low speed in the [111] crystal orientation on the (110) crystal plane. Identical to the cutting process mentioned above, the depth of cut also began from 20 nm and increased by 5 nm in each test, until the brittle removal mode occurred. In addition, the roughness of the ductile-cut surfaces were measured via AFM. Fig. 10 shows the effect of the tool edge radius on the surface quality and the critical thickness of the brittle-ductile transition. It can be seen that the surface finish quality decreases with an increase in the tool edge radius. In contrast, under the conditions of the same crystal orientation, tool geometry and cutting speed, the larger the tool edge radius is, the larger the critical thickness of the brittle-ductile transition is. That is, a diamond tool with a larger edge radius is beneficial towards restraining the fracture of single-crystal silicon. It is worth noting that in the range
3.1.1. The effect of crystal orientation It is widely known that the atomic permutation density of singlecrystal materials are diverse in different crystal orientations, leading to inconsistent performances, such as the energy, bonding force, physical and mechanical properties. That means anisotropy exists in singlecrystal materials. In view of this, the effect of crystal orientation on the critical thickness of brittle-ductile transition cannot be neglected in nanocutting. In previous taper cutting tests, the critical thickness had to be measured off-line, making the experiments more complex. Accordingly, to exactly obtain the critical thickness of the brittle-ductile transition without an off-line measurement, linear cuttings were performed repeatedly in different orientations on a single-crystal silicon, using a diamond tool with an edge radius of 60 nm. The depth of cut started from 20 nm and increased by 5 nm in each test until the brittle removal mode occurred. Fig. 8(a)–(c) show the machined surface morphology along the [111] orientation on the (110) crystal plane, which revealed the cutting process mentioned above. It was determined that as the depth of cut increased, the machined surface changed from pure ductility to the coexistence of ductility and cracks, and finally to full of cracks. 381
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Table 2 Critical thicknesses of the brittle-ductile transition of single-crystal silicon at different orientations. Crystal plane
(110) (111)
Crystal orientation
[001] [111] [001] [111]
Critical thickness of brittle-ductile transition (nm) 1st
2nd
3rd
Average value
40 70 55 80
45 70 50 75
45 65 55 85
43.3 68.3 53.3 80.0
Fig. 10. Effect of the tool edge radius on the surface quality and critical thickness of the brittle-ductile transition.
Fig. 12. Continuous chips morphology with a depth of cut of 8 nm.
Fig. 11. Nanocutting model.
of the present investigations, the value of the critical thickness is close to the value of the tool edge radius. The reason for this is that when the depth of cut is less than the tool edge radius, the effective rake angle is always negative regardless of the nominal value, enabling a large compressive stress to be generated, which acts to stop the growth of preexisting flaws in the material by suppressing the stress intensity factor [13].
Fig. 13. The relationship between the tool edge radius and minimum cutting thickness.
where dmin is the MCT, R is the tool edge radius, A is the stagnation point, 𝜇 is the friction coefficient between the tool and material, and Ff and Fp are the tangential force and normal force at point A, respectively. As a matter of experience in diamond cutting, Fp is 0.9 times that of Ff , and 𝜇 is usually between 0.1 and 0.15 without lubrication. Consequently, it can be deduced that dmin = 0.26–0.47 R.
3.2. Minimum cutting thickness 3.2.1. Theoretical analysis The MCT affects the machining efficiency and accuracy, especially when the tool edge radius cannot be ignored in nanocutting, which dominates the material modelling and processing parameter selection. Researchers have found that there is a threshold of the cutting thickness, below which only elastic-plastic deformation occurs without chip formation [21]. From the nanocutting model, as illustrated in Fig. 11, equations can be derived as follows [20]: tan𝜃 =
𝑑min
𝐹𝑓 − 𝜇𝐹𝑝 𝜇𝐹𝑓 + 𝐹𝑝
⎡ ⎤ 𝐹𝑝 + 𝜇𝐹𝑓 ⎢ ⎥ = 𝑅(1 − cos 𝜃) = 𝑅 ⎢1 − √ ( 2 )( )⎥ 2 ⎢ 𝐹𝑓 + 𝐹𝑝 1 + 𝜇 2 ⎥⎦ ⎣
3.2.2. Experimental verification Using the specially designed nanocutting platform, the MCT can be accurately obtained by means of high-resolution SEM imaging. Diamond tools with different edge radii were employed for a series of cutting tests. Previous studies in references [27,28] have shown that the ratio of the MCT to the tool edge radius is between 0.2 and 0.4. Therefore, to improve the experimental efficiency, the initial depth of cut was set to 0.6 times the tool edge radius and reduced by 1 or 2 nm in each test. Once each cutting was performed, whether or not the continuous chips were formed was detected via SEM. The cutting process was repeated until no continuous chip was found, that is, the present depth of cut was considered to be the MCT of single-crystal silicon. Fig. 12 shows an image of the continuous chips observed with a depth of cut of 10 nm. The experimental results of the relationship between the tool edge radius and MCT is shown in Fig. 13.
(1)
(2)
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References
As seen in Fig. 13, the MCT increases nearly linearly with the tool edge radius. Furthermore, the ratio of the MCT to the tool edge radius is always between 0.32 and 0.50 in the range of the present studies, indicating that the MCT of single-crystal silicon strongly depends on the tool edge radius. It is worth noting that this ratio is slightly larger than that in the theoretical values and MD simulation results, because tool wear is inevitable during the nanocutting tests, resulting in an increase in the tool edge radius. From the nanocutting model in Fig. 11, the effective rake angle 𝛼 e is negative and related to the MCT and the tool edge radius, which can be derived from the following equation: sin 𝛼𝑒 =
𝑅 − 𝑑min 𝑑 = 1 − min 𝑅 𝑅
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(3)
where 𝛼 e is effective rake angle. Substituting dmin /R into formula (3), it can be determined that 𝛼 e = 30.0°–42.8°. That is, the critical value of the effective negative rake angle for chips formation is between 30.0° and 42.8°. In conventional cutting, the cutting speed would obviously affect the MCT, mainly because the cutting temperature varies with the cutting speed, thereby resulting in a change in the friction coefficient between the tool and the workpiece. In this paper, it was only necessary to detect whether continuous chips could be formed at a shorter cutting distance. Therefore, the effect of the cutting speed on the MCT is negligible here. 4. Conclusions Using a specially designed nanocutting platform with SEM online observation, in situ nanocutting tests were performed at a low speed to study the material removal behaviour of single-crystal silicon. Diamond tools with different edge radii were fabricated by FIB technology. The effects of the crystal orientation and tool edge radius on the critical thickness of the brittle-ductile transition were studied, and the effect of the tool edge radius on the MCT was investigated through the experimental method. The main conclusions can be drawn as follows: (1) In the range of the present studies, the ductile removal behaviour of single-crystal silicon more easily occurs on the (111) crystal plane in the [111] crystal orientation. The maximum critical thickness of the brittle-ductile transition is approximately 80 nm. (2) The surface finish quality decreases with an increase in the tool edge radius, but a diamond tool with a larger edge radius is beneficial for restraining the fracture of the single-crystal silicon. The value of the critical thickness of the brittle-ductile transition is close to the value of the tool edge radius. (3) The MCT increases nearly linearly with the tool edge radius, and the ratio of the MCT to the tool edge radius is always between 0.32 and 0.50. The critical value of the effective negative rake angle for chips formation is between 30.0° and 42.8°.
Acknowledgements The authors would like to express their appreciation for the support of the National Natural Science Foundation of China (Grant No. 51805371), the Natural Science Foundation of Tianjin (Grant No. 18JCQNJC75400 and 17JCZDJC38200) and the Tianjin Science and Technology Development Fund Project (Grant No. 2018KJ226). The authors thank the MNMT Lab for their support with the experimental instruments. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijmecsci.2019.01.015.
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