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Study on ductile mode machining of single-crystal silicon by mechanical machining
Author’s Accepted Manuscript Study on ductile mode machining of single crystal silicon by mechanical machining Dae-Hee Choi, Je-Ryung Lee, Na-Ri Kang, TaeJin Je, Ju-Young Kim, Eun-chae Jeon www.elsevier.com/locate/ijmactool
PII: DOI: Reference:
S0890-6955(16)30141-9 http://dx.doi.org/10.1016/j.ijmachtools.2016.10.006 MTM3204
To appear in: International Journal of Machine Tools and Manufacture Received date: 16 August 2016 Revised date: 31 October 2016 Accepted date: 31 October 2016 Cite this article as: Dae-Hee Choi, Je-Ryung Lee, Na-Ri Kang, Tae-Jin Je, JuYoung Kim and Eun-chae Jeon, Study on ductile mode machining of single crystal silicon by mechanical machining, International Journal of Machine Tools and Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2016.10.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study on ductile mode machining of single crystal silicon by mechanical machining Dae-Hee Choia,b, Je-Ryung Leeb, Na-Ri Kangc, Tae-Jin Jea,b, Ju-Young Kimc,*, Eun-chae Jeona,b,* a
Department of Nano Mechatronics, University of Science and Technology, Daejeon, 34113, Korea
b
Department of Nano Manufacturing Technology, Korea Institute of Machinery and Materials, Daejeon, 34103, Korea c
School of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan, 44919, Korea
[email protected] [email protected] *
Corresponding author.
Abstract Nano patterns on single crystal silicon are generally manufactured by photolithography, which can form limited cross-sectional shapes such as U-shapes or rectangular channels. Though V-shaped patterns are widely used in the optical industries because they concentrate light, they are challenging to manufacture by conventional photolithography. Mechanical machining is useful in manufacturing various kinds of cross-sectional shapes including V-shapes with various apex angles, but is hard to apply to single-crystal silicon due to its brittle fracture. Here we suggest a novel way of mechanical machining of single-crystal silicon that suppresses brittle fracture below the critical point (the ductile-brittle transition point) as determined by nano scratch testing. We find that the first drop point of the cutting force corresponds to a critical point and define the critical forces as the thrust force and the cutting force at the critical point. The critical forces are varied by the applied force per unit length, which is the possibility that the cutting tool interacts with mechanically weak atomic bonds. When the applied force per unit length is zero (a general condition of mechanical machining), the cutting speed does not affect the variation of the critical forces or the quality of the machined pattern. Based on analysis of the experimental results, we suggest that the single-crystal silicon can be mechanically machined without brittle fracture at high cutting speed if the thrust force is smaller than the critical force of zero applied force per unit length.
Keywords: Mechanical machining; Single-crystal silicon; Critical force; Ductile-brittle transition point; Brittle fracture
1. Introduction
Nano-patterned single crystal silicon is widely used in the semiconductor and nano-photonics fields [1-3]. The nano patterns on the silicon are manufactured generally by etching and lithography [4-8], which can form U-shaped patterns, holes or rectangular channels. Manufacturing V-shaped patterns, however, which are popular in the optical industry because they can concentrate light [9] by conventional methods is limited. It is difficult to change the apex angle of the V-shaped pattern because the single-crystal silicon is etched along to its crystalline direction [10]. Though E-beam lithography can change the apex angle, this method is far more expensive [11]. On the other hand, with mechanical machining, it is easier to change the apex angle of the V-shaped pattern, as doing so depends on the angle of the cutting tool; moreover, the manufacturing process is much simpler. However, single-crystal silicon cannot be mechanically machined easily because brittle fractures arise. Thus, much research has been done on machining brittle materials without brittle fractures [12-17]. Takeuchi et al. [12] machined a glass using a milling machine, and Shimada et al. [13] observed ductile-brittle transition phenomena in LiNbO3 and monocrystalline silicon by micro-indentation tests. Sumitomo et al. [14] deformed a thin-film solar panel using nanoindentation and nanoscratching, and Arif et al. [15] predicted the depth of the ductilebrittle transition point using the intrinsic properties of BK7 glass and single-crystal silicon. Chao et al. [16] analyzed the ductile behavior of single-crystal silicon with a turning machine by crystallographic direction, and Liu et al. [17] analyzed the critical undeformed chip thickness of silicon in relation to the tool cutting-edge radius. In all these studies, brittle materials are mechanically machined in the ductile mode at extremely low depth or with relatively little force. However, these previous studies only investigated the critical point of the ductile-brittle transition qualitatively and did not suggest a simple method to determine it. Therefore, in this study, a quantitative analysis method is developed for determining the critical point in the ductile-brittle transition of the single-crystal silicon where the first brittle fracture arises and for considering the variation in the critical point according to extrinsic parameters. Then, V-shaped patterns were mechanically machined on single-crystal silicon without brittle fracture.
2. Machining system for ductile-mode machining of brittle materials
According to conventional studies [15,18], in single-crystal silicon the critical point is several hundreds of nm deep and the initial crack is propagated at about 100 mN. Though an ultra-precision machining system can control the depth to hundreds of nm, it is difficult to maneuver a cutting tool precisely on a workpiece in resolutions less than 1 nm. Additionally, though the cutting force and the thrust force can be measured using a dynamometer, this instrument's force resolution cannot reach one mN scale. Therefore, a nano-scratch tester (Anton Paar Inc.), generally used to measure the adhesion of a thin film as an indenter passes the film and the substrate, was used to overcome these force-resolution limitations. A schematic of the nano-scratch tester is shown in Fig. 1. The nano-scratch tester used here has a resolution of 1.5 μN under normal force (thrust force), of 6 μN under lateral force (cutting force), and of 0.6 nm under normal displacement (depth). A nano scratchtester is feasible as a mechanical machining system because the removal of materials by the passing of an indenter involves a process identical to the cutting process in mechanical machining. Technical terminologies in nano-scratch testing correspond to those in mechanical machining, as presented in Table 1. The indenter, the normal force and the lateral force are respectively the cutting tool, the thrust force and the cutting force. Moreover, a nano-scratch tester can control extrinsic parameters such as the thrust force, cutting speed and cutting length, and provides two cutting modes. The first is the 'progressive mode', in which the cutting tool passes while the thrust force is increased linearly, and the second is the 'constant mode', in which the cutting tool passes while the thrust force is held constant. The progressive mode was used to analyze the critical point of single-crystal silicon and the constant mode was used to machine the nano-pattern on single-crystal silicon in this study.
Fig. 1. A schematic of a nano-scratch tester used for mechanical machining of single crystal silicon.
Table 1 Matching of technical terminologies between mechanical machining and nano scratch. Mechanical machining Nano scratch Cutting tool
Indenter
Thrust force
Normal force
Cutting force
Lateral force
Cutting speed
Scratch speed
Cutting depth
Scratch depth
Linear pattern
Linear track
3. Quantitative analysis of critical point of single-crystal silicon
3.1 Quantitative determination of the critical point based on cutting force Previous studies [14,16] determined the critical point of ductile-brittle transition of brittle materials with a SEM (Scanning Electron Microscope) or an AFM (Atomic Force Microscope) because they did not measure the cutting/thrust force and the depth during cutting. Using these methods makes it difficult to determine the critical point accurately by quantitative analysis. We passed a cutting tool on the surface of (100) single-crystal silicon by linearly increasing the thrust force from 0 to 50 mN (progressive mode) and measured the thrust force, the cutting force, the depth and the lateral displacement in-situ in order to determine the critical point. The cutting direction was <100>, and the cutting tool was a 90° conical single-crystal diamond tip with tip radius 1 ㎛, as shown in Fig. 2. The cutting length was 1 mm and the cutting speed was 1 mm/min. Machined patterns were observed by SEM as shown in Fig. 3 to synchronize the image with measured forces and depth. The initial stage of the machined pattern corresponding to an extremely low thrust force showed ductile-mode machining (A in Fig. 3) resulting in a smooth machined pattern. As thrust force increases, the first brittle fracture occurred at a specific point (B in Fig. 3), which was defined as the critical point in this study. The thrust force and the cutting force at the critical point were defined as the critical thrust force and critical cutting force, respectively. After the critical point, discrete brittle fractures occurred (C in Fig. 3) and finally, dominant brittle fractures were observed (D in Fig. 3).
Fig. 2. A 90° conical single crystal silicon diamond cutting tool with a tip radius of 1 ㎛.
Fig. 3. A machined pattern on single crystal silicon by increasing the thrust force from 0 to 50 mN (A : ductile mode machining, B : ductile-brittle mode machining including the first brittle fracture, C : ductile-brittle mode machining and D : brittle mode machining).
Normally in nano-scratch testing, the lateral force that matches the cutting force is analyzed to measure the adhesion strength of a thin film [19]. Similarly, we analyzed the variance of the measured cutting force in order to determine the critical point when the thrust force was increased from 0 to 50 mN because the critical point in this study was defined where the first brittle fracture arose and the adhesion strength is determined where the first brittle fracture arises between a hard coating and a substrate. Initially, the cutting force was increased
continuously with the thrust force at region E. The first drop point of the cutting force observed is indicated by dotted line in region F in Fig. 4(a). These drop points are in agreement with points of B and C in Fig. 3 where brittle fracture occurred. The cutting force repeatedly dropped in region G, indicating that brittle fracture occurred. The cause of the cutting-force drop could be catastrophic progress of scratching due to local brittle fracture. According to fracture mechanics theory [20], the fracture energy is equivalent to the surface energy newly generated by the mechanical machining in case of a perfectly brittle material. The newly created surface and corresponding number of broken atomic bonds by brittle fracture is larger than in ductile scratching mode, as shown in Figs. 3 and 5. More energy should be consumed in creating the larger new surfaces and for breaking more atomic bonds suddenly, and this makes the cutting force be dropped. Hence the drop points in the cutting force can be used as a criterion of brittle fracture. On the other hand, the thrust force increased perfectly linearly due to the closed-loop circuit of the nano-scratch tester regardless of brittle fracture. The critical thrust and the critical cutting force can be obtained quantitatively by reading the thrust force and cutting force when the first drop of the cutting force is observed. The critical thrust force is suitable as a criterion for the critical point because nano-scratch testing allows control of the thrust force as an experimental condition. Thus, analyzing the cutting force can become a new way to determine the critical point in the ductile-brittle transition without AFM or SEM observation.
Fig. 4. Variations of (a) cutting force and (b) thrust force versus lateral displacement when machining the single crystal silicon as increasing the thrust force from 0 to 50 mN.
Fig. 5. Comparison of the areas (bold dashed line) of new surfaces and the number of broken atomic bonds causing energy consumption of (a) ductile mode machining and (b) brittle mode machining.
3.2 Effects of extrinsic parameters on critical point It is known that extrinsic parameters (machining conditions) affect machining results [21-24]. The cutting speed, which is directly related to productivity and affects machining characteristics such as chip formation [21], roughness [22,23], and tool temperature [24], is an important parameter. The loading rate serves as one of the parameters when the adhesion is measured in a nano-scratch test. Thus, the effects of cutting speed and loading rate on the critical point were analyzed. The cutting speed was increased from 1 to 10 mm/min and the loading rate was increased from 20 to 60 mN/min. Details of the experimental design are shown in Table 2. The range of the cutting speed in this study is much lower than the general ultra-precision machining. Since the nano-scratch tester is designed for detecting small delamination and brittle fracture occurred at ultra-low force range, the tester is generally operated under much lower cutting speed in order to eliminate noises such as thermal effects and vibration. Arif et al. [15] set the cutting speed 10mm/min in order to ignore thermal effects when machining the single crystal silicon even though they used a commercial ultra-precision CNC machining center. Moreover, sufficient data should be measured for determining the first drop point of the measured cutting force, lower cutting speed is essential in this study. The cutting lengths were not constant so as to control the cutting speed and the loading rate separately. The thrust force was increased from 0 to 20 mN using the 'progressive mode' because the critical thrust force was less than 20mN in Fig. 4. The two kinds of critical forces varied by the extrinsic parameters were analyzed by measuring the first drop point of the cutting force, and the critical points were confirmed by SEM observation. Experiments with the same extrinsic parameters were repeated five times with the same cutting tool and the same nano-scratch tester, the average forces are shown in Figs. 6 and 7.
Table 2 An experimental design to analyze the effects of cutting speed and loading rate on variation of critical points. Cutting speed Loading rate Cutting length Applied force per Case (mm/min) (mN/min) (mm) unit length(mN/mm) 1
1
20
1
20
2
2
20
2
10
3
5
20
5
4
4
10
20
10
2
5
1
40
0.5
40
6
2
40
1
20
7
5
40
2.5
8
8
10
40
5
4
9
1
60
0.33
60.6
10
2
60
0.66
30.3
11
5
60
1.65
12.1
12
10
60
3.3
6
Fig. 6. Variation of (a) critical thrust force and (b) critical cutting force versus cutting speed from 1 to 10 mm/min.
Fig. 7. Variation of (a) critical thrust force and (b) critical cutting force versus loading rate from 20 to 60 mN/min.
The critical thrust force and critical cutting force decreased as the cutting speed was increased, as shown in Fig. 6. The curves in Fig. 6 seemed to be inversely linear functions. The cutting speed (Vc) is defined by the following equation: cutting length (dx)/cutting time (dt), and the effects of the cutting speed on the critical force (Fc) can be expressed by
FC 1 / VC (dt/dx, min/mm).
(1)
On the other hand, the critical thrust force and the critical cutting force increased as the loading rate increased, as shown in Fig. 7. The lines in Fig. 6 seemed to be linear functions. The loading rate (VL) is determined by the following equation: applied force (dL)/cutting time (dt), and the effects of the loading rate on the critical force (Fc) can be expressed as follows:
FC VL (dL/dt, mN/min).
(2)
These results are similar to those of Steinmann [25] on the effects of extrinsic parameters on the adhesion of a thin film and a substrate using a nano-scratch tester. In that work, the critical force of initial delamination increased as the scratching speed (=cutting speed) was decreased or as the loading rate was increased. The
delamination creates more new surfaces between the thin film and the substrate, which is similar to the brittle fracture of this study. Steinmann suggested a new extrinsic parameter of applied force per unit length (dL/dx). Increasing dL/dx means that the same force is applied at a shorter distance. The possibility that the indenter would pass a defect area in the interface was decreased, and the critical force can be increased because of the shorter distance. Thus, greater applied force per unit length makes greater critical force. The results in Figs. 6 and 7 can be explained similarly. The parameter of applied force per unit length can be expressed as
FC2 VL / VC (dL/dx, mN/mm)
(3)
, which combines cutting speed (Eq. (1)) and loading rate (Eq. (2)). We have calculated values of the applied force per unit length of twelve cases in Table 2, and plotted the critical forces in Fig. 8. The critical force clearly increases along the curved path in good agreement with Eq. (3) and Steinmann's research. This also can be explained as the possibility that brittle fracture has occurred. If the cutting tool passes more atomic bonds during the machining, the possibility that it will meet mechanically weak defects increases. If the probability is higher, the critical force will be lower. As shown in Table 2, the cutting length, which should be proportional to the number of atomic bonds, decreased at lower cutting speed and higher loading rate with the same maximum thrust force. At the same time, the applied force per unit length including the two extrinsic parameters in Eq. (3) is inversely proportional to the cutting length. Thus, the applied force per unit length is properly used to analyze the effects of the extrinsic parameter on the variation in the critical force. The real effects of the two parameters were verified by machining under constant applied force per unit length, as described in the next section.
Fig. 8. Variation of (a) critical thrust force and (b) critical cutting force versus applied force per unit length(dL/dx) from 2 to 60.6 mN/mm.
4. Mechanical machining of nano patterns on single-crystal silicon without brittle fracture
General mechanical machining technology in industrial fields sets the depth of cut to be constant during
machining, which is same to the 'constant mode' of nano-scratch testing. The constant depth of cut means that the thrust force is constant and the loading rate is zero, and the applied force per unit length should be also zero, as shown in Fig. 9. Subsequently, the main extrinsic factor affecting the critical force between the cutting speed and the applied force per unit length can be determined by general mechanical machining under various cutting speed conditions. We set the cutting speeds as 1, 2, 5, 10 mm/min in the constant mode and the cutting length at 1 mm. Since the critical thrust force when the applied force per unit length was zero could be assumed to be 11 mN by the extrapolation in Fig. 8(a), the constant thrust force was fixed at 10, 13.5 and 17 mN, respectively. 10 and 17 mN imply ductile mode and brittle mode, regardless of the cutting speed. However, machining at 13.5 mN should be varied with the cutting speed if the cutting speed affects the critical point. We machined singlecrystal silicon under the twelve combinations of the four cases of cutting speed and the three cases of constant thrust force using the same cutting tool and nano-scratch tester. Then, we measured the cutting force and confirmed the occurrence of brittle fracture by SEM and AFM.
Fig. 9. Diagrams of (a) progressive mode having variable applied force per unit length (dL/dx ≠ 0) and (b) constant mode having constant applied force per unit length (dL/dx = 0).
The cutting forces were stable when single-crystal silicon was machined by a constant thrust force of 10 mN in both cutting speeds of 1 mm/min and 10 mm/min, as shown in Fig. 10(a) and (b). For constant thrust force of 13.5 mN, the cutting force was somewhat unstable, and it fluctuated at constant thrust force 17 mN, meaning that brittle fracture occurred. The measured cutting forces were more unstable at higher thrust force, as expected.
The measured cutting force at higher cutting speed seems to be flatter, meaning that the higher speed is better for ductile-mode machining. However, this is not clear because the number of measured points at 10 mm/min was well below the number of points at 1 mm/min due to the fixed data-measurent frequency of the nanoscratch tester's data acquisition system, and the normalizing effect of fewer points might make the graph flat. Therefore, we compare the SEM images of the machined nano-patterns in Figs. 11, 12 and 13. For constant thrust force of 10 mN, the four machined patterns under different cutting speed in Fig. 11 showed only ductile mode with no variation. Similarly, a little brittle fracture was observed in the four machined patterns at constant thrust force 13.5 mN in Fig. 12. No variation was found in the case of the constant thrust force of 17 mN either, as shown in Fig. 13. To confirm that no brittle fracture occurred at any cutting speed at constant thrust force of 10 mN, we measured the cross-sectional profiles of the machined patterns of 1 mm/min and 10 mm/min using AFM. As shown in Fig. 14, there was no brittle fracture at the two cutting speeds and their shapes were very similar. Therefore, we conclude that cutting speed does not affect the critical point and machining mode when the thrust force (the depth of cut) is constant. This demonstrated that the applied force per unit length is the main factor affecting the critical point, thus opening the door to higher-productivity machining techniques for singlecrystal silicon.
Fig. 10. Variation of cutting forces at constant thrust force of 10 mN in (a) 1 mm/min, (b) 10 mm/min and 13.5 mN in (c) 1 mm/min, (d) 10 mm/min and 17 mN in (e) 1 mm/min, (f) 10 mm/min.
Fig. 11. Machined patterns at constant thrust force of 10 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 12. Machined patterns at constant thrust force of 13.5 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 13. Machined patterns at constant thrust force of 17 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 14. Cross-sectional profiles of machined patterns at constant thrust force of 10 mN with different cutting speed of (a) 1 mm/min and (b) 10 mm/min.
Using results above, we suggest a new method of mechanical machining of single-crystal silicon without brittle fracture. First, plot the variation in the critical thrust force at different applied forces per unit length (dL/dx) by mechanical machining in progressive mode and analyze the first drop point of measured cutting force. Then, extrapolate the plotted graph and determine the critical thrust force at zero applied force per unit
length. Last, machine the single-crystal silicon mechanically with thrust force below the determined critical thrust force using the constant mode. This method is expected to apply to other brittle materials.
5. Conclusions
We suggested a novel method for the mechanical machining of single-crystal silicon in the ductile mode suppressing brittle fracture. The details are below. 1) A nano-scratch test with outstanding resolution was suitable for measuring of the critical point (force) of the ductile machining mode and machining of the single-crystal silicon. 2) The first drop in cutting force was observed when the brittle fracture occurred because more energy is consumed to create larger areas of new surfaces (brittle fracture). Thus, critical force can be quantitatively determined by measuring the initial drop point of the cutting force without observing the pattern with a SEM or an AFM. 3) The critical force seemed to increase at lower cutting speed and higher loading rate; however, when the applied force per unit length (dL/dx) was zero (a general condition of mechanical machining), the cutting speed did not vary the critical point or the machining mode because the applied force per unit length is the parameter of the possibility that the cutting tool meets the mechanically weak defects. Therefore, the applied force per unit length is a proper parameter in analyzing the effects of the extrinsic parameter on the variation in critical force. 4) Based on the results and the analysis here, we suggested that single crystal silicon can be mechanically machined without the brittle fracture with high cutting speeds if the thrust force is below the critical force of zero applied force per unit length.
Acknowledgments
This research was supported partly by the 'Center for Advanced Meta-Materials(CAMM)' funded by the 'Ministry of Science, ICT and Future Planning' as 'Global Frontier Project(CAMM-2014M3A6B3063707)' and partly by the 'Development of Convergence Manufacturing Technology for Functional Nanostructures of Active
Devices' by the 'National Research Council of Science & Technology'.
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Highlights
Analysis of cutting force can determine the critical point of ductile machining.
Critical force is varied by the applied force per unit length.
Critical force is not varied by cutting speed.
Single crystal silicon can be mechanically machined under the critical force.
PII: DOI: Reference:
S0890-6955(16)30141-9 http://dx.doi.org/10.1016/j.ijmachtools.2016.10.006 MTM3204
To appear in: International Journal of Machine Tools and Manufacture Received date: 16 August 2016 Revised date: 31 October 2016 Accepted date: 31 October 2016 Cite this article as: Dae-Hee Choi, Je-Ryung Lee, Na-Ri Kang, Tae-Jin Je, JuYoung Kim and Eun-chae Jeon, Study on ductile mode machining of single crystal silicon by mechanical machining, International Journal of Machine Tools and Manufacture, http://dx.doi.org/10.1016/j.ijmachtools.2016.10.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Study on ductile mode machining of single crystal silicon by mechanical machining Dae-Hee Choia,b, Je-Ryung Leeb, Na-Ri Kangc, Tae-Jin Jea,b, Ju-Young Kimc,*, Eun-chae Jeona,b,* a
Department of Nano Mechatronics, University of Science and Technology, Daejeon, 34113, Korea
b
Department of Nano Manufacturing Technology, Korea Institute of Machinery and Materials, Daejeon, 34103, Korea c
School of Materials Science and Engineering, Ulsan National Institute of Science and Technology, Ulsan, 44919, Korea
[email protected] [email protected] *
Corresponding author.
Abstract Nano patterns on single crystal silicon are generally manufactured by photolithography, which can form limited cross-sectional shapes such as U-shapes or rectangular channels. Though V-shaped patterns are widely used in the optical industries because they concentrate light, they are challenging to manufacture by conventional photolithography. Mechanical machining is useful in manufacturing various kinds of cross-sectional shapes including V-shapes with various apex angles, but is hard to apply to single-crystal silicon due to its brittle fracture. Here we suggest a novel way of mechanical machining of single-crystal silicon that suppresses brittle fracture below the critical point (the ductile-brittle transition point) as determined by nano scratch testing. We find that the first drop point of the cutting force corresponds to a critical point and define the critical forces as the thrust force and the cutting force at the critical point. The critical forces are varied by the applied force per unit length, which is the possibility that the cutting tool interacts with mechanically weak atomic bonds. When the applied force per unit length is zero (a general condition of mechanical machining), the cutting speed does not affect the variation of the critical forces or the quality of the machined pattern. Based on analysis of the experimental results, we suggest that the single-crystal silicon can be mechanically machined without brittle fracture at high cutting speed if the thrust force is smaller than the critical force of zero applied force per unit length.
Keywords: Mechanical machining; Single-crystal silicon; Critical force; Ductile-brittle transition point; Brittle fracture
1. Introduction
Nano-patterned single crystal silicon is widely used in the semiconductor and nano-photonics fields [1-3]. The nano patterns on the silicon are manufactured generally by etching and lithography [4-8], which can form U-shaped patterns, holes or rectangular channels. Manufacturing V-shaped patterns, however, which are popular in the optical industry because they can concentrate light [9] by conventional methods is limited. It is difficult to change the apex angle of the V-shaped pattern because the single-crystal silicon is etched along to its crystalline direction [10]. Though E-beam lithography can change the apex angle, this method is far more expensive [11]. On the other hand, with mechanical machining, it is easier to change the apex angle of the V-shaped pattern, as doing so depends on the angle of the cutting tool; moreover, the manufacturing process is much simpler. However, single-crystal silicon cannot be mechanically machined easily because brittle fractures arise. Thus, much research has been done on machining brittle materials without brittle fractures [12-17]. Takeuchi et al. [12] machined a glass using a milling machine, and Shimada et al. [13] observed ductile-brittle transition phenomena in LiNbO3 and monocrystalline silicon by micro-indentation tests. Sumitomo et al. [14] deformed a thin-film solar panel using nanoindentation and nanoscratching, and Arif et al. [15] predicted the depth of the ductilebrittle transition point using the intrinsic properties of BK7 glass and single-crystal silicon. Chao et al. [16] analyzed the ductile behavior of single-crystal silicon with a turning machine by crystallographic direction, and Liu et al. [17] analyzed the critical undeformed chip thickness of silicon in relation to the tool cutting-edge radius. In all these studies, brittle materials are mechanically machined in the ductile mode at extremely low depth or with relatively little force. However, these previous studies only investigated the critical point of the ductile-brittle transition qualitatively and did not suggest a simple method to determine it. Therefore, in this study, a quantitative analysis method is developed for determining the critical point in the ductile-brittle transition of the single-crystal silicon where the first brittle fracture arises and for considering the variation in the critical point according to extrinsic parameters. Then, V-shaped patterns were mechanically machined on single-crystal silicon without brittle fracture.
2. Machining system for ductile-mode machining of brittle materials
According to conventional studies [15,18], in single-crystal silicon the critical point is several hundreds of nm deep and the initial crack is propagated at about 100 mN. Though an ultra-precision machining system can control the depth to hundreds of nm, it is difficult to maneuver a cutting tool precisely on a workpiece in resolutions less than 1 nm. Additionally, though the cutting force and the thrust force can be measured using a dynamometer, this instrument's force resolution cannot reach one mN scale. Therefore, a nano-scratch tester (Anton Paar Inc.), generally used to measure the adhesion of a thin film as an indenter passes the film and the substrate, was used to overcome these force-resolution limitations. A schematic of the nano-scratch tester is shown in Fig. 1. The nano-scratch tester used here has a resolution of 1.5 μN under normal force (thrust force), of 6 μN under lateral force (cutting force), and of 0.6 nm under normal displacement (depth). A nano scratchtester is feasible as a mechanical machining system because the removal of materials by the passing of an indenter involves a process identical to the cutting process in mechanical machining. Technical terminologies in nano-scratch testing correspond to those in mechanical machining, as presented in Table 1. The indenter, the normal force and the lateral force are respectively the cutting tool, the thrust force and the cutting force. Moreover, a nano-scratch tester can control extrinsic parameters such as the thrust force, cutting speed and cutting length, and provides two cutting modes. The first is the 'progressive mode', in which the cutting tool passes while the thrust force is increased linearly, and the second is the 'constant mode', in which the cutting tool passes while the thrust force is held constant. The progressive mode was used to analyze the critical point of single-crystal silicon and the constant mode was used to machine the nano-pattern on single-crystal silicon in this study.
Fig. 1. A schematic of a nano-scratch tester used for mechanical machining of single crystal silicon.
Table 1 Matching of technical terminologies between mechanical machining and nano scratch. Mechanical machining Nano scratch Cutting tool
Indenter
Thrust force
Normal force
Cutting force
Lateral force
Cutting speed
Scratch speed
Cutting depth
Scratch depth
Linear pattern
Linear track
3. Quantitative analysis of critical point of single-crystal silicon
3.1 Quantitative determination of the critical point based on cutting force Previous studies [14,16] determined the critical point of ductile-brittle transition of brittle materials with a SEM (Scanning Electron Microscope) or an AFM (Atomic Force Microscope) because they did not measure the cutting/thrust force and the depth during cutting. Using these methods makes it difficult to determine the critical point accurately by quantitative analysis. We passed a cutting tool on the surface of (100) single-crystal silicon by linearly increasing the thrust force from 0 to 50 mN (progressive mode) and measured the thrust force, the cutting force, the depth and the lateral displacement in-situ in order to determine the critical point. The cutting direction was <100>, and the cutting tool was a 90° conical single-crystal diamond tip with tip radius 1 ㎛, as shown in Fig. 2. The cutting length was 1 mm and the cutting speed was 1 mm/min. Machined patterns were observed by SEM as shown in Fig. 3 to synchronize the image with measured forces and depth. The initial stage of the machined pattern corresponding to an extremely low thrust force showed ductile-mode machining (A in Fig. 3) resulting in a smooth machined pattern. As thrust force increases, the first brittle fracture occurred at a specific point (B in Fig. 3), which was defined as the critical point in this study. The thrust force and the cutting force at the critical point were defined as the critical thrust force and critical cutting force, respectively. After the critical point, discrete brittle fractures occurred (C in Fig. 3) and finally, dominant brittle fractures were observed (D in Fig. 3).
Fig. 2. A 90° conical single crystal silicon diamond cutting tool with a tip radius of 1 ㎛.
Fig. 3. A machined pattern on single crystal silicon by increasing the thrust force from 0 to 50 mN (A : ductile mode machining, B : ductile-brittle mode machining including the first brittle fracture, C : ductile-brittle mode machining and D : brittle mode machining).
Normally in nano-scratch testing, the lateral force that matches the cutting force is analyzed to measure the adhesion strength of a thin film [19]. Similarly, we analyzed the variance of the measured cutting force in order to determine the critical point when the thrust force was increased from 0 to 50 mN because the critical point in this study was defined where the first brittle fracture arose and the adhesion strength is determined where the first brittle fracture arises between a hard coating and a substrate. Initially, the cutting force was increased
continuously with the thrust force at region E. The first drop point of the cutting force observed is indicated by dotted line in region F in Fig. 4(a). These drop points are in agreement with points of B and C in Fig. 3 where brittle fracture occurred. The cutting force repeatedly dropped in region G, indicating that brittle fracture occurred. The cause of the cutting-force drop could be catastrophic progress of scratching due to local brittle fracture. According to fracture mechanics theory [20], the fracture energy is equivalent to the surface energy newly generated by the mechanical machining in case of a perfectly brittle material. The newly created surface and corresponding number of broken atomic bonds by brittle fracture is larger than in ductile scratching mode, as shown in Figs. 3 and 5. More energy should be consumed in creating the larger new surfaces and for breaking more atomic bonds suddenly, and this makes the cutting force be dropped. Hence the drop points in the cutting force can be used as a criterion of brittle fracture. On the other hand, the thrust force increased perfectly linearly due to the closed-loop circuit of the nano-scratch tester regardless of brittle fracture. The critical thrust and the critical cutting force can be obtained quantitatively by reading the thrust force and cutting force when the first drop of the cutting force is observed. The critical thrust force is suitable as a criterion for the critical point because nano-scratch testing allows control of the thrust force as an experimental condition. Thus, analyzing the cutting force can become a new way to determine the critical point in the ductile-brittle transition without AFM or SEM observation.
Fig. 4. Variations of (a) cutting force and (b) thrust force versus lateral displacement when machining the single crystal silicon as increasing the thrust force from 0 to 50 mN.
Fig. 5. Comparison of the areas (bold dashed line) of new surfaces and the number of broken atomic bonds causing energy consumption of (a) ductile mode machining and (b) brittle mode machining.
3.2 Effects of extrinsic parameters on critical point It is known that extrinsic parameters (machining conditions) affect machining results [21-24]. The cutting speed, which is directly related to productivity and affects machining characteristics such as chip formation [21], roughness [22,23], and tool temperature [24], is an important parameter. The loading rate serves as one of the parameters when the adhesion is measured in a nano-scratch test. Thus, the effects of cutting speed and loading rate on the critical point were analyzed. The cutting speed was increased from 1 to 10 mm/min and the loading rate was increased from 20 to 60 mN/min. Details of the experimental design are shown in Table 2. The range of the cutting speed in this study is much lower than the general ultra-precision machining. Since the nano-scratch tester is designed for detecting small delamination and brittle fracture occurred at ultra-low force range, the tester is generally operated under much lower cutting speed in order to eliminate noises such as thermal effects and vibration. Arif et al. [15] set the cutting speed 10mm/min in order to ignore thermal effects when machining the single crystal silicon even though they used a commercial ultra-precision CNC machining center. Moreover, sufficient data should be measured for determining the first drop point of the measured cutting force, lower cutting speed is essential in this study. The cutting lengths were not constant so as to control the cutting speed and the loading rate separately. The thrust force was increased from 0 to 20 mN using the 'progressive mode' because the critical thrust force was less than 20mN in Fig. 4. The two kinds of critical forces varied by the extrinsic parameters were analyzed by measuring the first drop point of the cutting force, and the critical points were confirmed by SEM observation. Experiments with the same extrinsic parameters were repeated five times with the same cutting tool and the same nano-scratch tester, the average forces are shown in Figs. 6 and 7.
Table 2 An experimental design to analyze the effects of cutting speed and loading rate on variation of critical points. Cutting speed Loading rate Cutting length Applied force per Case (mm/min) (mN/min) (mm) unit length(mN/mm) 1
1
20
1
20
2
2
20
2
10
3
5
20
5
4
4
10
20
10
2
5
1
40
0.5
40
6
2
40
1
20
7
5
40
2.5
8
8
10
40
5
4
9
1
60
0.33
60.6
10
2
60
0.66
30.3
11
5
60
1.65
12.1
12
10
60
3.3
6
Fig. 6. Variation of (a) critical thrust force and (b) critical cutting force versus cutting speed from 1 to 10 mm/min.
Fig. 7. Variation of (a) critical thrust force and (b) critical cutting force versus loading rate from 20 to 60 mN/min.
The critical thrust force and critical cutting force decreased as the cutting speed was increased, as shown in Fig. 6. The curves in Fig. 6 seemed to be inversely linear functions. The cutting speed (Vc) is defined by the following equation: cutting length (dx)/cutting time (dt), and the effects of the cutting speed on the critical force (Fc) can be expressed by
FC 1 / VC (dt/dx, min/mm).
(1)
On the other hand, the critical thrust force and the critical cutting force increased as the loading rate increased, as shown in Fig. 7. The lines in Fig. 6 seemed to be linear functions. The loading rate (VL) is determined by the following equation: applied force (dL)/cutting time (dt), and the effects of the loading rate on the critical force (Fc) can be expressed as follows:
FC VL (dL/dt, mN/min).
(2)
These results are similar to those of Steinmann [25] on the effects of extrinsic parameters on the adhesion of a thin film and a substrate using a nano-scratch tester. In that work, the critical force of initial delamination increased as the scratching speed (=cutting speed) was decreased or as the loading rate was increased. The
delamination creates more new surfaces between the thin film and the substrate, which is similar to the brittle fracture of this study. Steinmann suggested a new extrinsic parameter of applied force per unit length (dL/dx). Increasing dL/dx means that the same force is applied at a shorter distance. The possibility that the indenter would pass a defect area in the interface was decreased, and the critical force can be increased because of the shorter distance. Thus, greater applied force per unit length makes greater critical force. The results in Figs. 6 and 7 can be explained similarly. The parameter of applied force per unit length can be expressed as
FC2 VL / VC (dL/dx, mN/mm)
(3)
, which combines cutting speed (Eq. (1)) and loading rate (Eq. (2)). We have calculated values of the applied force per unit length of twelve cases in Table 2, and plotted the critical forces in Fig. 8. The critical force clearly increases along the curved path in good agreement with Eq. (3) and Steinmann's research. This also can be explained as the possibility that brittle fracture has occurred. If the cutting tool passes more atomic bonds during the machining, the possibility that it will meet mechanically weak defects increases. If the probability is higher, the critical force will be lower. As shown in Table 2, the cutting length, which should be proportional to the number of atomic bonds, decreased at lower cutting speed and higher loading rate with the same maximum thrust force. At the same time, the applied force per unit length including the two extrinsic parameters in Eq. (3) is inversely proportional to the cutting length. Thus, the applied force per unit length is properly used to analyze the effects of the extrinsic parameter on the variation in the critical force. The real effects of the two parameters were verified by machining under constant applied force per unit length, as described in the next section.
Fig. 8. Variation of (a) critical thrust force and (b) critical cutting force versus applied force per unit length(dL/dx) from 2 to 60.6 mN/mm.
4. Mechanical machining of nano patterns on single-crystal silicon without brittle fracture
General mechanical machining technology in industrial fields sets the depth of cut to be constant during
machining, which is same to the 'constant mode' of nano-scratch testing. The constant depth of cut means that the thrust force is constant and the loading rate is zero, and the applied force per unit length should be also zero, as shown in Fig. 9. Subsequently, the main extrinsic factor affecting the critical force between the cutting speed and the applied force per unit length can be determined by general mechanical machining under various cutting speed conditions. We set the cutting speeds as 1, 2, 5, 10 mm/min in the constant mode and the cutting length at 1 mm. Since the critical thrust force when the applied force per unit length was zero could be assumed to be 11 mN by the extrapolation in Fig. 8(a), the constant thrust force was fixed at 10, 13.5 and 17 mN, respectively. 10 and 17 mN imply ductile mode and brittle mode, regardless of the cutting speed. However, machining at 13.5 mN should be varied with the cutting speed if the cutting speed affects the critical point. We machined singlecrystal silicon under the twelve combinations of the four cases of cutting speed and the three cases of constant thrust force using the same cutting tool and nano-scratch tester. Then, we measured the cutting force and confirmed the occurrence of brittle fracture by SEM and AFM.
Fig. 9. Diagrams of (a) progressive mode having variable applied force per unit length (dL/dx ≠ 0) and (b) constant mode having constant applied force per unit length (dL/dx = 0).
The cutting forces were stable when single-crystal silicon was machined by a constant thrust force of 10 mN in both cutting speeds of 1 mm/min and 10 mm/min, as shown in Fig. 10(a) and (b). For constant thrust force of 13.5 mN, the cutting force was somewhat unstable, and it fluctuated at constant thrust force 17 mN, meaning that brittle fracture occurred. The measured cutting forces were more unstable at higher thrust force, as expected.
The measured cutting force at higher cutting speed seems to be flatter, meaning that the higher speed is better for ductile-mode machining. However, this is not clear because the number of measured points at 10 mm/min was well below the number of points at 1 mm/min due to the fixed data-measurent frequency of the nanoscratch tester's data acquisition system, and the normalizing effect of fewer points might make the graph flat. Therefore, we compare the SEM images of the machined nano-patterns in Figs. 11, 12 and 13. For constant thrust force of 10 mN, the four machined patterns under different cutting speed in Fig. 11 showed only ductile mode with no variation. Similarly, a little brittle fracture was observed in the four machined patterns at constant thrust force 13.5 mN in Fig. 12. No variation was found in the case of the constant thrust force of 17 mN either, as shown in Fig. 13. To confirm that no brittle fracture occurred at any cutting speed at constant thrust force of 10 mN, we measured the cross-sectional profiles of the machined patterns of 1 mm/min and 10 mm/min using AFM. As shown in Fig. 14, there was no brittle fracture at the two cutting speeds and their shapes were very similar. Therefore, we conclude that cutting speed does not affect the critical point and machining mode when the thrust force (the depth of cut) is constant. This demonstrated that the applied force per unit length is the main factor affecting the critical point, thus opening the door to higher-productivity machining techniques for singlecrystal silicon.
Fig. 10. Variation of cutting forces at constant thrust force of 10 mN in (a) 1 mm/min, (b) 10 mm/min and 13.5 mN in (c) 1 mm/min, (d) 10 mm/min and 17 mN in (e) 1 mm/min, (f) 10 mm/min.
Fig. 11. Machined patterns at constant thrust force of 10 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 12. Machined patterns at constant thrust force of 13.5 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 13. Machined patterns at constant thrust force of 17 mN with different cutting speed of (a) 1 mm/min, (b) 2 mm/min, (c) 5 mm/min and (d) 10 mm/min.
Fig. 14. Cross-sectional profiles of machined patterns at constant thrust force of 10 mN with different cutting speed of (a) 1 mm/min and (b) 10 mm/min.
Using results above, we suggest a new method of mechanical machining of single-crystal silicon without brittle fracture. First, plot the variation in the critical thrust force at different applied forces per unit length (dL/dx) by mechanical machining in progressive mode and analyze the first drop point of measured cutting force. Then, extrapolate the plotted graph and determine the critical thrust force at zero applied force per unit
length. Last, machine the single-crystal silicon mechanically with thrust force below the determined critical thrust force using the constant mode. This method is expected to apply to other brittle materials.
5. Conclusions
We suggested a novel method for the mechanical machining of single-crystal silicon in the ductile mode suppressing brittle fracture. The details are below. 1) A nano-scratch test with outstanding resolution was suitable for measuring of the critical point (force) of the ductile machining mode and machining of the single-crystal silicon. 2) The first drop in cutting force was observed when the brittle fracture occurred because more energy is consumed to create larger areas of new surfaces (brittle fracture). Thus, critical force can be quantitatively determined by measuring the initial drop point of the cutting force without observing the pattern with a SEM or an AFM. 3) The critical force seemed to increase at lower cutting speed and higher loading rate; however, when the applied force per unit length (dL/dx) was zero (a general condition of mechanical machining), the cutting speed did not vary the critical point or the machining mode because the applied force per unit length is the parameter of the possibility that the cutting tool meets the mechanically weak defects. Therefore, the applied force per unit length is a proper parameter in analyzing the effects of the extrinsic parameter on the variation in critical force. 4) Based on the results and the analysis here, we suggested that single crystal silicon can be mechanically machined without the brittle fracture with high cutting speeds if the thrust force is below the critical force of zero applied force per unit length.
Acknowledgments
This research was supported partly by the 'Center for Advanced Meta-Materials(CAMM)' funded by the 'Ministry of Science, ICT and Future Planning' as 'Global Frontier Project(CAMM-2014M3A6B3063707)' and partly by the 'Development of Convergence Manufacturing Technology for Functional Nanostructures of Active
Devices' by the 'National Research Council of Science & Technology'.
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Highlights
Analysis of cutting force can determine the critical point of ductile machining.
Critical force is varied by the applied force per unit length.
Critical force is not varied by cutting speed.
Single crystal silicon can be mechanically machined under the critical force.