Skip to main content
SpringerLink
Log in

Mapping ductile-to-fragile transition and the effect of tool nose radius in diamond turning of single-crystal silicon

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Although it has long been known that tools with more negative rake angles allow the ductile regime when machining monocrystalline silicon, little has been discussed about the tool-material interaction. The microgeometric contact of the tool tip at this interface plays an essential role in the material remotion (ductile or brittle). In this paper, the tool rake angle was varied in order to change the value of the undeformed chip thickness once the tool cutting radius, formed in front of the tool rake face, changes when the tool rake angle becomes more negative. Based on the statistical design of the experiment applied to cutting tests, a map is built to relate the values of transition pressure in different crystallographic directions. This map assisted in determining the machining conditions with a ductile response into a broader spectrum based on the variation of the tool rake angle. The results obtained allowed to answer questions under which machining conditions and tool geometry account for better surface finishes, lower machining forces, and lower residual stresses. The response surfaces, from statistical design, provided answers capable of establishing under which cutting radii yielded more ductile material removal and avoided a brittle response related to the anisotropic behavior of the material. Finally, the brittle-to-ductile transition mapping determined a more suitable machining condition to diamond turn Fresnel lenses in single crystal silicon.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

Availability of data and material

The data sets generated and analyzed from the current study are available upon request from the corresponding author.

Code availability

The software application developed for the analysis of cutting forces is available on request from the corresponding author.

Abbreviations

Rc:

Cutting radius (µm)

α:

Tool rake angle (°)

Rε:

Tool nose radius (µm)

dc:

Depth of cut (µm)

\({\mathrm{dc}}^{*}\)  :

Critical depth of cut (µm)

\({\mathrm{dc}}_{\mathrm{e}}\) :

Effective depth of cut (µm)

\({{\mathrm{dc}}_{\mathrm{e}}}^{*}\) :

Critical-effective depth of cut (µm)

\({\mathrm{dc}}_{110}^{*}\) :

Critical depth of cut in the direction [110] (µm)

\({\mathrm{r}}_{\mathrm{e}}\) :

Cutting edge radius (nm)

\(f\) :

Feedrate (µm/revolution)

Fc:

Cutting force (N)

Ft:

Thrust force (N)

Ff:

Feed force (N)

\({k}_{\mathrm{N}}\) :

Transition pressure (GPa)

h:

Thickness of cutting (nm)

\({\mathrm{h}}_{\mathrm{e}}\) :

Effective thickness of cutting (nm)

\({\mathrm{h}}_{\mathrm{e}}^{*}\) :

Critical-effective thickness of cutting (nm)

\({{\mathrm{h}}_{\mathrm{e}}}_{\mathrm{max}}\) :

Maximum-effective thickness of cutting (nm)

\(h_{e110}^{*}\) :

Critical-effective thickness of cutting in the direction [110] (nm)

As:

Cutting section area (µm2)

\({\mathrm{As}}_{\mathrm{e}}\) :

Effective area of cutting section (µm2)

Ra:

Arithmetic average of surface roughness (nm)

Rq:

Root-mean-square surface roughness (nm)

Rt:

Maximum height of the surface roughness (nm)

C:

Safety factor

References

  1. Abdulkadir LN, Abou-El-Hossein K, Jumare AI et al (2018) Review of molecular dynamics/experimental study of diamond-silicon behavior in nanoscale machining. Int J Adv Manuf Technol 98:317–371. https://doi.org/10.1007/s00170-018-2041-7

    Article  Google Scholar 

  2. Langfelder G, Bestetti M, Gadola M (2021) Silicon MEMS inertial sensors evolution over a quarter century. J Micromechanics Microengineering 31:084002. https://doi.org/10.1088/1361-6439/ac0fbf

    Article  Google Scholar 

  3. Olufayo OA, Abou-El-Hossein K (2013) Molecular dynamics modeling of nanoscale machining of silicon. Procedia CIRP 8:504–509. https://doi.org/10.1016/j.procir.2013.06.141

    Article  Google Scholar 

  4. Budnitzki M, Kuna M (2016) Stress induced phase transitions in silicon. J Mech Phys Solids 95:64–91. https://doi.org/10.1016/j.jmps.2016.03.017

    Article  MathSciNet  MATH  Google Scholar 

  5. Gilman JJ (1992) Insulator-metal transitions at microindentations. J Mater Res 7:535–538. https://doi.org/10.1557/JMR.1992.0535

    Article  Google Scholar 

  6. Domnich V, Gogotsi Y (2001) Pressure-induced phase transformations in semiconductors under contact loading. Front High Press Res II Appl High Press Low-Dimens Nov Electron Mater 291–302. https://doi.org/10.1007/978-94-010-0520-3_22

  7. O’Connor BP, Marsh ER, Couey JA (2005) On the effect of crystallographic orientation on ductile material removal in silicon. Precis Eng 29:124–132. https://doi.org/10.1016/j.precisioneng.2004.05.004

    Article  Google Scholar 

  8. Morris JC, Callahan DL (1994) Origins of microplasticity in low-load scratching of silicon. J Mater Res 9:2907–2913. https://doi.org/10.1557/JMR.1994.2907

    Article  Google Scholar 

  9. Morris JC, Callahan DL, Kulik J et al (1995) Origins of the ductile regime in single-point diamond turning of semiconductors. J Am Ceram Soc 78:2015–2020. https://doi.org/10.1111/j.1151-2916.1995.tb08612.x

    Article  Google Scholar 

  10. Kunz RR, Clark HR, Nitishin PM et al (1996) High resolution studies of crystalline damage induced by lapping and single-point diamond machining of Si(100). J Mater Res 11:1228–1237. https://doi.org/10.1557/JMR.1996.0157

    Article  Google Scholar 

  11. Tanikella BV, Somasekhar AH, Sowers AT et al (1996) Phase transformations during microcutting tests on silicon. Appl Phys Lett 69:2870–2872. https://doi.org/10.1063/1.117346

    Article  Google Scholar 

  12. Pizani PS, Jasinevicius R, Duduch JG, Porto AJV (1999) Ductile and brittle modes in single-point-diamond-turning of silicon probed by Raman scattering. J Mater Sci Lett 18:1185–1187. https://doi.org/10.1023/A:1006694310171

    Article  Google Scholar 

  13. Jamieson JC (1963) Crystal structures at high pressures of metallic modifications of silicon and germanium. Science

    Book  Google Scholar 

  14. Jayaraman A, Klement W, Kennedy GC (1963) Melting and polymorphism at high pressures in some group IV elements and III-V compounds with the diamond/zincblende structure. Phys Rev 130:540–547. https://doi.org/10.1103/PhysRev.130.540

    Article  Google Scholar 

  15. Bundy FP (1964) Phase diagrams of silicon and germanium to 200 kbar, 1000°C. J Chem Phys 41:3809–3814. https://doi.org/10.1063/1.1725818

    Article  Google Scholar 

  16. Minomura S, Drickamer HG (1962) Pressure induced phase transitions in silicon, germanium and some III–V compounds. J Phys Chem Solids 23:451–456. https://doi.org/10.1016/0022-3697(62)90085-9

    Article  Google Scholar 

  17. R. H. Wentorf J, Kasper JS, (1963) Two new forms of silicon. Science 139:338–339. https://doi.org/10.1126/science.139.3552.338.b

    Article  Google Scholar 

  18. Hu JZ, Merkle LD, Menoni CS, Spain IL (1986) Crystal data for high-pressure phases of silicon. Phys Rev B 34:4679–4684. https://doi.org/10.1103/PhysRevB.34.4679

    Article  Google Scholar 

  19. Gogotsi Y, Rosenberg MS, Kailer A, Nickel KG (1998) Phase transformations in semiconductors under contact loading. Tribol Issues Oppor MEMS 431–442. https://doi.org/10.1007/978-94-011-5050-7_30

  20. Pharr GM, Oliver WC, Harding DS (1991) New evidence for a pressure-induced phase transformation during the indentation of silicon. J Mater Res 6:1129–1130. https://doi.org/10.1557/JMR.1991.1129

    Article  Google Scholar 

  21. Cai MB, Li XP, Rahman M (2007) High-pressure phase transformation as the mechanism of ductile chip formation in nanoscale cutting of silicon wafer. Proc Inst Mech Eng Part B J Eng Manuf 221:1511–1519. https://doi.org/10.1243/09544054JEM901

    Article  Google Scholar 

  22. Clarke DR, Kroll MC, Kirchner PD et al (1988) Amorphization and conductivity of silicon and germanium induced by indentation. Phys Rev Lett 60:2156–2159. https://doi.org/10.1103/PhysRevLett.60.2156

    Article  Google Scholar 

  23. Gupta MC, Ruoff AL (1980) Static compression of silicon in the [100] and in the [111] directions. J Appl Phys 51:1072–1075. https://doi.org/10.1063/1.327714

    Article  Google Scholar 

  24. Blake PN, Scattergood RO (1990) Ductile-regime machining of germanium and silicon. J Am Ceram Soc 73:949–957. https://doi.org/10.1111/j.1151-2916.1990.tb05142.x

    Article  Google Scholar 

  25. Gilman JJ (1993) Shear-induced metallization Philos Mag B 67:207–214. https://doi.org/10.1080/13642819308207868

    Article  Google Scholar 

  26. Xiao GB, To S, Jelenković EV (2015) Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon. J Mater Process Technol 225:439–450. https://doi.org/10.1016/j.jmatprotec.2015.06.017

    Article  Google Scholar 

  27. Yan J, Asami T, Harada H, Kuriyagawa T (2009) Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining. Precis Eng 33:378–386. https://doi.org/10.1016/j.precisioneng.2008.10.008

    Article  Google Scholar 

  28. Blackley WS, Scattergood RO (1991) Ductile-regime machining model for diamond turning of brittle materials. Precis Eng 13:95–103. https://doi.org/10.1016/0141-6359(91)90500-I

    Article  Google Scholar 

  29. Jasinevicius RG, Pizani PS, Duduch JG (2000) Brittle to ductile transition dependence upon the transition pressure value of semiconductors in micromachining. J Mater Res 15:1688–1692. https://doi.org/10.1557/JMR.2000.0243

    Article  Google Scholar 

  30. Tanaka H, Shimada S, Anthony L (2007) Requirements for ductile-mode machining based on deformation analysis of mono-crystalline silicon by molecular dynamics simulation. CIRP Ann 56:53–56. https://doi.org/10.1016/j.cirp.2007.05.015

    Article  Google Scholar 

  31. Venkatachalam S, Li X, Liang SY (2009) Predictive modeling of transition undeformed chip thickness in ductile-regime micro-machining of single crystal brittle materials. J Mater Process Technol 209:3306–3319. https://doi.org/10.1016/j.jmatprotec.2008.07.036

    Article  Google Scholar 

  32. Hung NP, Fu YQ (2000) Effect of crystalline orientation in the ductile-regime machining of silicon. Int J Adv Manuf Technol 16:871–876. https://doi.org/10.1007/s001700070004

    Article  Google Scholar 

  33. Yu B, Qian L (2013) Effect of crystal plane orientation on the friction-induced nanofabrication on monocrystalline silicon. Nanoscale Res Lett 8:137. https://doi.org/10.1186/1556-276X-8-137

    Article  Google Scholar 

  34. Blackley WS, Scattergood RO (1990) Crystal orientation dependence of machning damage—a stress model. J Am Ceram Soc 73:3113–3115. https://doi.org/10.1111/j.1151-2916.1990.tb06730.x

    Article  Google Scholar 

  35. Mukaida M, Yan J (2017) Ductile machining of single-crystal silicon for microlens arrays by ultraprecision diamond turning using a slow tool servo. Int J Mach Tools Manuf 115:2–14. https://doi.org/10.1016/j.ijmachtools.2016.11.004

    Article  Google Scholar 

  36. Jasinevicius RG, Duduch JG, Montanari L, Pizani PS (2012) Dependence of brittle-to-ductile transition on crystallographic direction in diamond turning of single-crystal silicon. Proc Inst Mech Eng Part B J Eng Manuf 226:445–458. https://doi.org/10.1177/0954405411421108

    Article  Google Scholar 

  37. Jasinevicius RG, Pizani PS (2007) Annealing treatment of amorphous silicon generated by single point diamond turning. Int J Adv Manuf Technol 34:680–688. https://doi.org/10.1007/s00170-006-0650-z

    Article  Google Scholar 

  38. Lucca DA, Seo YW, Komanduri R (1993) Effect of tool edge geometry on energy dissipation in ultraprecision machining. CIRP Ann 42:83–86. https://doi.org/10.1016/S0007-8506(07)62397-X

    Article  Google Scholar 

  39. Box GEP, Hunter JS, Hunter WG (2005) Statistics for Experimenters: Design, Innovation, and Discovery. Wiley

    MATH  Google Scholar 

  40. Jumare AI, Abou-El-Hossein K, Goosen WE et al (2018) Prediction model for single-point diamond tool-tip wear during machining of optical grade silicon. Int J Adv Manuf Technol 98:2519–2529. https://doi.org/10.1007/s00170-018-2402-2

    Article  Google Scholar 

  41. Jasinevicius RG, Duduch JG, Pizani PS (2008) The influence of crystallographic orientation on the generation of multiple structural phases generation in Silicon by cyclic microindentation. Mater Lett 62:812–815. https://doi.org/10.1016/j.matlet.2007.06.071

    Article  Google Scholar 

  42. Gerbig YB, Stranick SJ, Morris DJ et al (2009) Effect of crystallographic orientation on phase transformations during indentation of silicon. J Mater Res 24:1172–1183. https://doi.org/10.1557/jmr.2009.0122

    Article  Google Scholar 

  43. Zong WJ, Cao ZM, He CL, Xue CX (2016) Theoretical modelling and FE simulation on the oblique diamond turning of ZnS crystal. Int J Mach Tools Manuf 100:55–71. https://doi.org/10.1016/j.ijmachtools.2015.10.002

    Article  Google Scholar 

  44. Mir A, Luo X, Cheng K, Cox A (2018) Investigation of influence of tool rake angle in single point diamond turning of silicon. Int J Adv Manuf Technol 94:2343–2355. https://doi.org/10.1007/s00170-017-1021-7

    Article  Google Scholar 

  45. Gogotsi Y, Baek C, Kirscht F (1999) Raman microspectroscopy study of processing-induced phase transformations and residual stress in silicon. Semicond Sci Technol 14:936–944. https://doi.org/10.1088/0268-1242/14/10/310

    Article  Google Scholar 

  46. Yan J, Asami T, Harada H, Kuriyagawa T (2012) Crystallographic effect on subsurface damage formation in silicon microcutting. CIRP Ann 61:131–134. https://doi.org/10.1016/j.cirp.2012.03.070

    Article  Google Scholar 

  47. Shibata T, Fujii S, Makino E, Ikeda M (1996) Ductile-regime turning mechanism of single-crystal silicon. Precis Eng 18:129–137. https://doi.org/10.1016/0141-6359(95)00054-2

    Article  Google Scholar 

  48. Jasinevicius RG, Duduch JG, Pizani PS (2007) Structure evaluation of submicrometre silicon chips removed by diamond turning. Semicond Sci Technol 22:561–573. https://doi.org/10.1088/0268-1242/22/5/019

    Article  Google Scholar 

Download references

Funding

The experiment has been performed in the Precision Engineering Laboratory (PEL) at the Department of Mechanical Engineering, School of Engineering of São Carlos, University of São Paulo, Brazil. The study was supported by Federal Institute of Education, Science and Technology of São Paulo (IFSP), and Brazilian grants from São Paulo Research Foundation (FAPESP), Education Ministry Foundation (CAPES), and National Council for Scientific and Technological Development (CNPq).

Author information

Authors and Affiliations

  1. Department of Industry, Federal Institute of Education, Science and Technology of São Paulo, Araraquara, SP, 14804-296, Brazil

    Marcel Henrique Militão Dib

  2. Department of Industry, Federal Institute of Education, Science and Technology of São Paulo, São Carlos, SP, 13.565-820, Brazil

    José Antonio Otoboni

  3. Department of Mechanical Engineering, University of São Paulo, Engineering School at São Carlos, São Carlos, SP, 13.566-590, Brazil

    Renato Goulart Jasinevicius

Authors
  1. Marcel Henrique Militão Dib
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José Antonio Otoboni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Renato Goulart Jasinevicius
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Marcel Henrique Militão Dib: conceptualization, investigation, methodology, data curation, formal analysis, software for cutting forces, writing—original draft, visualization, validation. José Antonio Otoboni: methodology, validation, writing—review and editing. Renato Goulart Jasinevicius: supervision, conceptualization, methodology, resources, validation, investigation, data curation, writing—review and editing.

Corresponding author

Correspondence to Marcel Henrique Militão Dib.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Highlights

• Cutting forces used to show anisotropy effects with changes in crystallographic direction.

• Inverse relation between residual stress and cutting forces.

• Establish optimal surface finish condition as a function of the rake angle value.

• Negative rake angle increases cutting radius enhancing the critical thickness of cutting

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Militão Dib, M.H., Otoboni, J.A. & Jasinevicius, R.G. Mapping ductile-to-fragile transition and the effect of tool nose radius in diamond turning of single-crystal silicon. Int J Adv Manuf Technol 120, 843–867 (2022). https://doi.org/10.1007/s00170-021-08528-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-021-08528-8

Keywords

Search

Navigation