Scholarly article on topic 'Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon'

Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon Academic research paper on "Nano-technology"

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{"Anisotropy of surface roughness" / "Cutting speed" / "Edge radius" / "Single-crystal silicon" / "Strain rate" / "Ultra-precision turning" / Weakening}

Abstract of research paper on Nano-technology, author of scientific article — Minghai Wang, Ben Wang, Yaohui Zheng

Abstract Ultra-precision machining causes materials to undergo a greatly strained deformation process in a short period of time. The effect of shear strain rates on machining quality, in particular on surface anisotropy, is a topic deserving of research that has thus far been overlooked. This study analyzes the impact of the strain rate during the ultra-precision turning of single-crystal silicon on the anisotropy of surface roughness. Focusing on the establishment of cutting models considering the tool rake angle and the edge radius, this is the first research that takes into account the strain rate dislocation emission criteria in studying the effects of the edge radius, the cutting speed, and the cutting thickness on the plastic deformation of single-crystal silicon. The results of this study show that the uses of a smaller edge radius, faster cutting speeds, and a reduced cutting thickness can result in optimally uniform surface roughness, while the use of a very sharp cutting tool is essential when operating with smaller cutting thicknesses. A further finding is that insufficient plastic deformation is the major cause of increased surface roughness in the ultra-precision turning of brittle materials. On this basis, we propose that the capacity of single-crystal silicon to emit dislocations be improved as much as possible before brittle fracture occurs, thereby promoting plastic deformation and minimizing the anisotropy of surface roughness in the machined workpiece.

Academic research paper on topic "Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon"

Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon

Wang Minghai, Wang Ben, Zheng Yaohui

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S1000-9361(15)00112-0 http://dx.doi.Org/10.1016/j.cja.2015.05.008 CJA 488

Received Date: 7 November 2014

Revised Date: 6 May 2015

Accepted Date: 6 May 2015

Please cite this article as: W. Minghai, W. Ben, Z. Yaohui, Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon, (2015), doi: http://dx.doi.org/10.1016/j.cja.2015.05.008

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Chinese Journal of Aeronautics 28 (2015) xx-xx

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AERONAUTICS

Weakening of the anisotropy of surface roughness in ultra-precision turning of single-crystal silicon

WANG Minghaia,b'*, WANG Bena, ZHENG Yaohuia Key Laboratory of Fundamental Science for National Defense of Aeronautical Digital Manufacturing Process,

Shenyang Aerospace University, China bSchool of Mechanical Engineering & Automation, Beijing University of Aeronautics & Astronautics, China Received 7 November 2014; revised 8 January 2015; accepted 29 March 2015

Abstract

Ultra-precision machining causes materials to undergo a greatly strained deformation process in a short period of time. The effect of shear strain rates on machining quality, in particular on surface anisotropy, is a topic deserving of research that has thus far been overlooked. This study analyzes the impact of the strain rate during the ultra-precision turning of single-crystal silicon on the anisotropy of surface roughness. Focusing on the establishment of cutting models considering the tool rake angle and the edge radius, this is the first research that takes into account the strain rate dislocation emission criteria in studying the effects of the edge radius, the cutting speed, and the cutting thickness on the plastic deformation of single-crystal silicon. The results of this study show that the uses of a smaller edge radius, faster cutting speeds, and a reduced cutting thickness can result in optimally uniform surface roughness, while the use of a very sharp cutting tool is essential when operating with smaller cutting thicknesses. A further finding is that insufficient plastic deformation is the major cause of increased surface roughness in the ultra-precision turning of brittle materials. On this basis, we propose that the capacity of single-crystal silicon to emit dislocations be improved as much as possible before brittle fracture occurs, thereby promoting plastic deformation and minimizing the anisotropy of surface roughness in the machined workpiece.

Keywords: Ultra-precision Turning; Single-Crystal Silicon; Strain rate; Anisotropy of surface roughness; Weakening; cutting speed; edge radius.

1. Introduction1

Single-crystal silicon is the principal material used for solid-state electronics and infrared optical technologies. The anisotropy of single-crystal silicon surfaces plays a vital role since surface roughness has a considerable influence on both product quality and functional aspects. Explanations of surface anisotropy were given by Shibata1 and Blackley et al2 from different angles, but no solution was provided. Perez and Gumbsch3 studied the cleavage fracture processes in silicon using total-energy pseudopotential calculations. They pointed out that the different lattice trapping for different crack propagation directions could explain the experimentally observed cleavage anisotropy in silicon single crystals. In recent years, the demand for surface perfection has continued to rise. Various efforts have been made to improve defects in silicon parts.4, 5 In order to improve the machinability of silicon parts, scholars have utilized different means in an attempt to understand the deformation, fracture, and microstructural changes of silicon.6, 7

* Corresponding author. Tel.: +86 24 89723877. E-mail address: wangminghai2008@163.com

For example, a recent work has demonstrated that nanosecond-pulsed laser irradiations can be used to reconstruct machining-damaged silicon substrates to perfect single crystalline structures, offering the possibility of a new processing technique for high-quality silicon wafers.5

Eric et al revisited the rotating tool concept, firstly proposed by Shaw in 1952. This approach avoids the rapid degradation of diamond tools by constantly providing a fresh cutting edge. Eric et al8 concluded that the demand for precision in infrared optics would require that Shaw's original concept be enhanced with provisions for near-perfect cutting tool roundness and centering on a stiff, accurate axis of rotation. Cheung9 noted that although some research progresses had been made on the effect of crystallographic orientation on surface quality, our technical know-how in regard to minimizing surface anisotropy during diamond turning of brittle single crystals was still far from perfect. In his paper, the effect of cutting friction on surface anisotropy in the diamond turning of brittle single crystals was investigated. Cheung then explored the relationship between the cutting friction and the anisotropy of surface roughness in the light of his experimental findings, while also discussing the implications of the findings on the minimization of surface anisotropy in the diamond turning of brittle single crystals. It was found that the anisotropy of surface roughness decreased whereas the mean arithmetic roughness increased with increasing cutting friction. The research results of other scholars investigating the mechanism of brittle ductile transition and the machinability of single-crystal silicon have also provided inspiration for reducing the anisotropy of surface roughness. In the work of Brian et al10, the critical chip thickness for ductile regime machining of electronic-grade silicon was measured as a function of crystallographic orientation on the (001) cubic face. If a diamond turning operation was configured so that the critical chip thickness was somewhere between the [110] direction limit of 40 nm and the [100] direction limit of 120 nm, a four-lobed star damage pattern would be plainly visible in the finished workpiece. Vladislav et al11 noted that if the depth of cut was less than the depth of the transformed metallic phase, the material removal process would behave as expected for a ductile material. However, if the depth of cut was too aggressive and exceeded the dimension of the metallic phase, then the material would be removed by brittle fracture. Calculations by Zhao et al12 demonstrate that the rake angle plays an important role in suppressing and minimizing the anisotropic characteristic.

It can be found that a lot of investigations have been carried out about ultra-precision turning of single-crystal silicon. However, there are few researches about the way of weakening the anisotropy of surface roughness. This study discussed the formation mechanism of surface roughness, etc. Meanwhile, the results are helpful to improve surface quality during ultra-precision turning.

2. Experiments

uniformity

ity of surface quality, a series of ultra-precision turning experiments

In order to verify how to improve the unift was conducted on the (111) crystal plane.

These experiments were carried out using ultra-precision machine tools developed internally at Harbin Institute of Technology in China, as illustrated in Fig. 1.

Fig. 1. Photo of ultra-precision machine tools.

The main spindle of the machine tools is powered by an AC servo motor capable of rotating 0-3000 r/min. The self-designed aerostatic spindle has a radial rigidity of 567 N/|m, an axial rigidity of 450 N/|m, and a rotation precision of 0.023 |m. A T-shape layout is employed, with guide rails fitted below the spindle box moving along the z-axis while the tool rest slide moving along the x-axis, which helps to enhance precision. The machine tool body is made from a 2 m x 1.2 m x 0.5 m piece of granite, and is supported by air springs to isolate perpendicular and horizontal low-frequency vibrations, as shown in Fig. 2.

Fig. 2. Photo of experimental setup during machining. The parameters used in the first series of experiments were: spindle speed = 600 r/min, ap ■■

5 and f = 2 ^/r.

The diamond tool had an 80 nm edge radius and a -40° rake angle, and the roughness of the machined surface is depicted in Fig. 3.

Cutting directions

Fig. 3. Relation between surface roughness and cutting direction (ap = 5 |am, 80 nm edge radius).

Assume that the cutting tool on the (111) crystal plane turns 360° continuously counter-clockwise, and the initial position named as 0° position in the experiment can be set to the [112] crystallographic direction. Thus, when the cutting tool rotates 30°, 60°, and 90°, the cutting directions are the [101], [211], and [110] crystallographic directions, respectively. Because the properties of single-crystal silicon are periodic, the fluctuation in surface roughness is also periodic with changing cutting directions.

AFM images of the surface topography of the (111) plane in cutting directions oof 0°, 30°, 60°, and 90° are shown in Fig. 4.

ce topogr £

Length (nm)

(c)a=60° (d)a=90°

Fig. 4. AFM images of the machined (111) crystal plane.

The second series of experiments was performed using smaller cutting parameters and a smaller edge radius. The parameters used in this series were: spindle speed = 600 r/min, ap = 2 and f = 2 ^/r. The diamond tool had a

50-nm edge radius and a -40° rake angle, while the roughness of the machined surface is depicted in Fig. 5. AFM

images showing the surface topography of the (111) plane in cutting directions of 0°, 30°, 60°, and 90° are shown in Fig. 6.

Fig. 5.

120° 180s 240" Cutting directions

Relation between surface roughness and cutting direction (ap = 2 50 nm edge radius).

Fig. 6. AFM images of surface topography.

Experimental results show that greater cutting depths and edge radii resulted in surface roughness having a greater degree of fluctuation in all cutting directions, which gave rise to a greater degree of fluctuation in cutting force, necessarily increasing the vibration between a tool and a work-piece and further intensifying surface anisotropy. For smaller cutting depths and edge radii, the absolute values of surface roughness in all directions and the fluctuation range of surface roughness decreased significantly. However, anisotropic surface quality was still not eliminated, suggesting that this was an intrinsic property of single-crystal silicon and was difficult to be completely erased.

The above experiments show that making appropriate process adjustments could not only reduce surface roughness, but also make it possible to ameliorate the anisotropic distribution of surface roughness.

3. Shear deformation process

Simulation results show that the distribution of the total number of emitted dislocations and the number of dislocations emitted from the machined crystal plane and slip plane simultaneously formed six peaks regardless of whether

loaded with the -40° or -25° rake angle cutting tool, as shown in Fig. 7.13 Besides, it can also be found that the diamond tool nose radius is ideally as small as possible in order to improve the machinability of silicon. Because the cutting process is completed within a certain time period, it follows that in addition to shear-slip, the shear strain rate is also pivotal for the brittle-ductile transition of silicon. Based on the actual shape of the tool, a schematic diagram of the shear deformation model was established as shown in Fig. 8(a). A first deformation zone model, factoring in the effects of the nose radius, was established as shown in Fig. 8(b) (in Fig. 8, R is the nose radius, y0 is the rake angle, ¿S is the displacement of the cutting chip, vs is the velocity in the chip flow direction, vc is the velocity along with the tool face, $ is the angle between the chip flow direction and the cutting velocity, ¿y is the thickness of the plastic zone in the cutting area, v is the cutting velocity, and ac is the cutting depth.).

32 28 24 20 16 12 8 4 0

■ v V V V W

-T- Total number

■ (111)

■ -.-(11!)

-o-(lll)

■V.A

\ A A A A ■ v/ y u V , A /

120° 180° 240° Cutting directions {a ) Rake angle=-40°

300° 360°

28 24 20 16 12 8 4 0

-T- Total number -•-(HI) -■-(111) —o- (111)

\VV/vA-t/vAV

\ A A A A A /1

■V ^ V V V V

,-J \-aJ \___J \___J

o- 60-

120° 180° 240° Cutting directions (b) Rake angle=-25°

300° 360°

Fig. 7. Relationship between the numbers of dislocations and cutting directions on the (111) crystal plane

r deformation model (b) First deformation zone model

Fig. 8. Shear deformation model and the first deformation zone model.

Fig. 9 is a schematic diagram depicting the shear deformation relationship and velocity relationship of the shear unit in the first deformation zone under a negative rake angle (in Fig. 9, t is the shear deformation).

According to

Fig. 9. Shear deformation and velocity relation.

, the shear strain e is calculated as follows:

The shear unit is usually involved in constant strain-rate deformation, so that the strain rate £ can be written as:

■ = £ = A£ = vs t Ayt Ay

where t is the time required for the shear deformation length to be equal to AS. From Fig. 9, it is possible to derive an expression for the velocity relationship of the shear unit:

we have:

cos Y0

Vs =-7-V

cos(0 + Y0)

cos y0 v

cos(0 + y0) Ay

According to Fig. 8(b), the thickness of the shear unit is calculated as follows:

Ay = R

The strain rate is

(1 - sinYo )cos(0 - Yo ) cos Yo

v 1 + sinY0

R cos2(0 + Y0)

An inspection of Eq. (6) reveals that the tool edge radius and the cutting speed have considerable efi strain rate of single-crystal silicon, while the impact of the rake angle on the strain rate is comparatively minor.

4. Machinability adjusted for strain rate

ely min

fe c ts o n

(6) the

Because the edge radius is very small, the cutting process of single-crystal silicon is a high strain rate deformation process, and therefore the effects of the strain rate on the brittle-ductile transition must be considered.

Under an applied external force, the energy required for the dislocations per unit length emitted from the crack tip is given as follows:14

AG = At2

where A is a constant related to material properties and A=G/[2n(1-VI, r0 is a constant and r0b2, Kcsi is the critical

stress intensity factor for dislocation emission, G is the shear modulus, Vis Poisson's ratio, and b is the Burgers vector.

According to the dislocation theory, the strain rate is proportional to the dislocation velocity, as well as to the relationship between the shear yield stress and the dislocation velocity.15 The relationship between the activation energy and the strain rate can be established as follows:

t = c£n exp

where rys is the yield stress, KB is Boltzmann constant (=1.38x10- J/K), Uan is the activation energy, T is the temperature, c is a constant, and n is a constant equal to 2.2 under uniform deformation conditions. Consider the dislocation emission criteria affected by the strain rate:

K csi =-J—exp

( f ln

t,. C£n

1 A A K„T

where e is Euler number. We know from Eq. 9 that the larger the strain rate is, the smaller the critical stress intensity factor for dislocation emission is, making it easier for dislocations to be emitted from the crack tip. More dislocations give rise to a shielding effect for the crack. This is manifested at the macro level in an increased resistance to fracture, and can promote the capacity of silicon to undergo plastic deformation.

Larger strain rates, which are conducive to dislocation emission, can be obtained by using smaller edge radii and higher cutting speeds. Changes in the rake angle have a comparatively minor effect on the strain rate when compared to the edge radius. As the cutting temperature is low during diamond turning of single-crystal silicon, it has a limited effect on the brittle ductile transition.

However, the smaller the edge radius is, the thinner the shear zone will be, so that dislocation is readily activated by higher cutting temperatures, while plastic flow is also easily formed. Besides, under the same cutting stress, a smaller edge radius induces higher pressure. In addition, silicon is easy to achieve ductile deformation under high pressure which is mainly due to phase transformations and amorphization at micro-scale. Therefore, from this perspective, the edge radius should be as small as possible.

Moreover, the strain rate and the dislocation density are both higher near the cutting edge in the first deformation zone, and thus the strain-hardening property of the material is enhanced. Consequently, in the case of a larger cutting thickness and when the diamond tool has a very small edge radius, local stress concentration readily occurs, and thus the smaller the edge radius is, the more likely the occurrence of fracture is. The strain rate is lower further away from

the cutting edge in the first deformation zone, and the cutting temperature is lower. This renders emission of dislocations more difficult and gives rise to segmental chips, impacting on cutting stability.

The above analysis shows that in the case of a very small edge radius being used in the ultra-precision turning of silicon, decreasing the cutting thickness will result in plastic deformation in the first deformation zone becoming uniform, thus improving the stress state and enhancing surface quality. It follows that in addition to employing a suitable rake angle, uniform surface quality can also be ensured by adoption of a smaller edge radius and a smaller cutting thickness. If using a very sharp cutting tool, a small chip thickness is essential as well.

5. Formation Mechanism of Surface Roughness

d a small

Is the formation of surface roughness during the ultra-precision machining of brittle single-crystal silicon related to the deformation mode of the material? Answering this question would assist in devising methods that can more reliably increase surface quality and minimize anisotropy.

As shown in Fig. 10, although the mean surface roughness is only 12.899 nm, AFM images of the surface cross-section show that there are deep cracks in the surface, with one crack as deep as 78.093 nm.

According to research results on the effect of the tool edge radius on the brittle-ductile transition of single-crystal silicon14, there is always a thin layer of silicon which cannot be removed. When the contact between the tools and the thin layer is unstable, even a blunt cutting tool will cause crack growth, resulting in the increase of surface roughness.

Furthermore, due to the presence of multiple slip systems, there are always some dislocations moving above and below the machined crystal plane when cutting along any crystallographic orientation.16 These dislocations can prevent crack extension within the silicon, but some dislocations inevitably form an atomic step on the machined surface. The heights of these atomic steps left behind in the surface of the workpiece can be considered as the scale of surface roughness that can be achieved by ultra-precision cutting.17

Under the same cutting conditions, cracks form more easily in the cutting directions with poor plastic deformation ability. Therefore, in order to ensure that plastic deformation in all cutting directions is improved, thus rendering the quality of the machined surface as uniform as possible, a feasible approach is to apply cutting parameters and tool parameters that result in favorable plastic deformation occurring in all cutting directions.

(a) AFM image of the machined surface (b) AFM image of the surface cross-scction

Fig. 10. Effect of cracks on surface roughness.

6. Experimental validation of the effects of cutting speed and edge radius on surface quality

It has already been shown in the experimental section of this paper that the appropriate adjustment of process parameters can reduce surface roughness and achieve a more uniform surface quality. In addition, it can be appreciated from Eqs. (6) and (9) that if the strain rate is taken into consideration, when within the critical cutting thickness, both the cutting speed and the edge radius have substantial effects on surface quality. The first confirmatory experiments

were directed at the effect of the cutting speed on surface quality. A -40° rake angle was adopted, the edge radius was

80 nm, and the maximum cutting thickness was 90 nm. Figures 11(a) and (b) are AFM images of the machined surface when single-crystal silicon was cut at cutting speeds of 1000 r/min and 600 r/min, respectively.

[.englh (|jm)

(a) Cutting speed of 1000 r/min (b) Cutting speed of 600 r/min

Fig. 11. Surface quality after using different cutting speeds.

The second confirmatory experiments were performed to validate the effect of the edge radius on surface quality. A -40° rake angle was adopted, and the edge radii were 50 nm and 80 nm, while other parameters of the diamond

tool were the same. The cutting speed was 600 r/min and the maximum cutting thickness was 54.5 nm.

Figure 12 shows AFM images of a surface machined along the same cutting direction by a diamond tool with different cutting edges. It can be seen from Fig. 12 that the surface quality when using a 50-nm edge radius is better than that using an 80-nm edge radius.

(a) 50 nm edge radius (b) 80 nm edge radius

Fig. 12. Images of the machined surface using a 50 nm and 80nm edge radius.

Analysis has already demonstrated that a faster cutting speed and a smaller edge radius are conducive to reducing dislocation emission critical stress intensity factors, improving the plastic deformation ability of single-crystal silicon, and thus enhancing surface quality. The experimental results provided in Figs. 11 and 12 verify the accuracy of this theoretical conclusion. At the same time, they also reveal the basic process steps that should be taken in order to obtain optimally uniform surfaces for single-crystal optical materials.

Based on a lot of experiments (as shown in Ref. 16), it is found that in order to obtain a high-quality surface with less anisotropy of surface roughness, the spindle speed should be higher than 1000 r/min, the cutting depth should be less than 2 the feed rate should be smaller than 2 цm/r, and the edge radius of the diamond tool should be less

than 50 nm with a -40° rake angle.

7. Conclusions

In this paper, approaches to improving the anisotropy of machined surfaces were studied from the point of view of increasing the machinability of single-crystal silicon. In other words, to ensure that the plastic deformation in all cutting directions is improved, thus rendering the quality of a machined surface as uniform as possible, a feasible approach is to apply cutting parameters and tool parameters that can result in favorable plastic deformation occurring in all cutting directions. The conclusions drawn from this study can be summarized as follows:

(1) By using a tool with a -40° rake angle to restrain crack propagation and promote dislocation emission, the best

possible load conditions can be provided for the plastic deformation of single-crystal silicon and surface quality can be improved. However, the rake angle of the cutting tool has little effect on the strain rate of the machined material.

(2) The tool edge radius and the cutting speed have considerable effects on the strain rate. Smaller edge radii and faster cutting speeds can induce a larger strain rate, which is conducive to dislocation emission and improving the machinability of single-crystal silicon.

(3) Smaller cutting thicknesses should be adopted when using a smaller edge radius. In this case, the plastic deformation of the first deformation zone will be more uniform. Consequently, the stress state near the primary shear zone can be improved and the machined surface quality enhanced.

In summary, in addition to using the right rake angle, a smaller edge radius, a faster cutting speed, and a smaller cutting thickness can ensure uniform surface quality. In addition, when using smaller cutting thicknesses, a very sharp cutting tool is preferable. The experimental and simulation results also show that peculiarities in the crystal structure of silicon mean that anisotropy of machined surfaces cannot be completely eliminated. Thus the only option available is to select appropriate cutting parameters which improve surface quality and minimize anisotropy.

Acknowledgements

The authors are grateful to the anonymous reviewers for their critical and constructive review of the manuscript. This study was supported by the National Defence Scientific Research of China ( A3520133004 ) .

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Wang Minghai is currently a professor in the Key Laboratory of Fundamental Science for National Defense of Aeronautical Digital Manufacturing Process at Shenyang Aerospace University in China. His research interests include

precision and ultra-precision machining technology.