Abstract

A spatial axisymmetric finite element model of single-crystal silicon irradiated by a 1064nm millisecond laser is used to investigate the thermal stress damage induced by a millisecond laser. The transient temperature field and the thermal stress field for 2ms laser irradiation with a laser fluence of 254J/cm2 are obtained. The numerical simulation results indicate that the hoop stresses along the r axis on the front surface are compressive stress within the laser spot and convert to tensile stress outside the laser spot, while the radial stresses along the r axis on the front surface and on the z axis are compressive stress. The temperature of the irradiated center is the highest temperature obtained, yet the stress is not always highest during laser irradiation. At the end of the laser irradiation, the maximal hoop stress is located at r=0.5mm and the maximal radial stress is located at r=0.76mm. The temperature measurement experiments are performed by IR pyrometer. The numerical result of the temperature field is consistent with the experimental result. The damage morphologies of silicon under the action of a 254J/cm2 laser are inspected by optical microscope. The cracks are observed initiating at r=0.5mm and extending along the radial direction.

© 2011 Optical Society of America

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    [Crossref] [PubMed]
  2. V. Zorba, N. Boukos, I. Zergioti, and C. Fotakis, “Ultraviolet femtosecond, picosecond, and nanosecond laser microstructuring of silicon: structural and optical properties,” Appl. Opt. 47, 1846–1850 (2008).
    [Crossref] [PubMed]
  3. X. R. Zhang and X. Xu, “High precision microscale bending by pulsed and CW lasers,” J. Appl. Mech. 125, 512–518 (2003).
  4. J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
    [Crossref]
  5. H. Exner and U. Loschnner, “Contactless laser bending of silicon microstructures,” Proc. SPIE 5116, 383–392 (2003).
    [Crossref]
  6. L. Zhang and I. Zarudi, “Towards a deeper understanding of plastic deformation in monocrystalline silicon,” Int. J. Mech. Sci. 43, 1985–1996 (2001).
    [Crossref]
  7. T. S. Gross, S. D. Hening, and D. W. Watt, “Crack formation during laser cutting of silicon,” J. Appl. Phys. 69, 983–989(1991).
    [Crossref]
  8. G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
    [Crossref]
  9. B. Wang, Y. Qin, X. W. Ni, Z. H. Shen, and J. Lu, “Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films,” Appl. Opt. 49, 5537–5544 (2010).
    [Crossref] [PubMed]
  10. J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Proc. Cambridge Philos. Soc. 43, 50–67 (1947).
    [Crossref]
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    [Crossref]
  12. Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
    [Crossref]
  13. O. C. Zienkiewicz and R. L. Tayor, The Finite Element Method (Butterworth-Heinemann, 2000).
  14. Semiconductors and Semimetals, R.F.Wood, C.W.White, and R.T.Young, eds., Vol. 23 of Pulsed Laser Processing of Semiconductors (Academic, 1984).
  15. R. Hull, Properties of Crystalline Silicon (INSPEC, 1999).
  16. H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
    [Crossref]
  17. A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
    [Crossref]
  18. N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
    [Crossref]
  19. J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
    [Crossref]
  20. J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
    [Crossref]
  21. X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
    [Crossref]
  22. Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
    [Crossref]

2010 (3)

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

B. Wang, Y. Qin, X. W. Ni, Z. H. Shen, and J. Lu, “Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films,” Appl. Opt. 49, 5537–5544 (2010).
[Crossref] [PubMed]

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

2008 (4)

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

V. Zorba, N. Boukos, I. Zergioti, and C. Fotakis, “Ultraviolet femtosecond, picosecond, and nanosecond laser microstructuring of silicon: structural and optical properties,” Appl. Opt. 47, 1846–1850 (2008).
[Crossref] [PubMed]

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

2004 (1)

J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
[Crossref]

2003 (3)

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

X. R. Zhang and X. Xu, “High precision microscale bending by pulsed and CW lasers,” J. Appl. Mech. 125, 512–518 (2003).

H. Exner and U. Loschnner, “Contactless laser bending of silicon microstructures,” Proc. SPIE 5116, 383–392 (2003).
[Crossref]

2001 (2)

L. Zhang and I. Zarudi, “Towards a deeper understanding of plastic deformation in monocrystalline silicon,” Int. J. Mech. Sci. 43, 1985–1996 (2001).
[Crossref]

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

2000 (1)

O. C. Zienkiewicz and R. L. Tayor, The Finite Element Method (Butterworth-Heinemann, 2000).

1999 (3)

R. Hull, Properties of Crystalline Silicon (INSPEC, 1999).

H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
[Crossref]

J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
[Crossref]

1996 (2)

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Reprinted in Adv. Comput. Math. 6, 207–226 (1996).
[Crossref]

V. K. Arora and A. L. Dawar, “Laser-induced damage studies in silicon and silicon-based photodetectors,” Appl. Opt. 35, 7061–7065 (1996).
[Crossref] [PubMed]

1991 (1)

T. S. Gross, S. D. Hening, and D. W. Watt, “Crack formation during laser cutting of silicon,” J. Appl. Phys. 69, 983–989(1991).
[Crossref]

1984 (1)

Semiconductors and Semimetals, R.F.Wood, C.W.White, and R.T.Young, eds., Vol. 23 of Pulsed Laser Processing of Semiconductors (Academic, 1984).

1947 (1)

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Proc. Cambridge Philos. Soc. 43, 50–67 (1947).
[Crossref]

Arora, V. K.

Bao, Y.

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Bi, J.

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

Boukos, N.

Brion, H. G.

H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
[Crossref]

Cai, M.

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

Chen, Y.

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

Cheng, G. J.

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

Chiussi, S.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Conde, J. C.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Crank, J.

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Reprinted in Adv. Comput. Math. 6, 207–226 (1996).
[Crossref]

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Proc. Cambridge Philos. Soc. 43, 50–67 (1947).
[Crossref]

Dawar, A. L.

Exner, H.

H. Exner and U. Loschnner, “Contactless laser bending of silicon microstructures,” Proc. SPIE 5116, 383–392 (2003).
[Crossref]

Fiory, A. T.

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

Fischer, A.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Fornarini, L.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Fotakis, C.

Frühauf, J.

J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
[Crossref]

Garther, E.

J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
[Crossref]

Gontad, F.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Gross, T. S.

T. S. Gross, S. D. Hening, and D. W. Watt, “Crack formation during laser cutting of silicon,” J. Appl. Phys. 69, 983–989(1991).
[Crossref]

Guinel, M. J.

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

Hening, S. D.

T. S. Gross, S. D. Hening, and D. W. Watt, “Crack formation during laser cutting of silicon,” J. Appl. Phys. 69, 983–989(1991).
[Crossref]

Hull, R.

R. Hull, Properties of Crystalline Silicon (INSPEC, 1999).

Jansch, E.

J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
[Crossref]

Ji, L. F.

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Jiang, Y. J.

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Krottenthaler, P.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Lambert, U.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

León, B.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Li, J. F.

J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
[Crossref]

Li, L.

J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
[Crossref]

Loschnner, U.

H. Exner and U. Loschnner, “Contactless laser bending of silicon microstructures,” Proc. SPIE 5116, 383–392 (2003).
[Crossref]

Lu, J.

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

B. Wang, Y. Qin, X. W. Ni, Z. H. Shen, and J. Lu, “Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films,” Appl. Opt. 49, 5537–5544 (2010).
[Crossref] [PubMed]

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

Mahendra, S.

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

Martín, E.

J. C. Conde, E. Martín, F. Gontad, S. Chiussi, L. Fornarini, and B. León, “Numerical analysis of temperature profile and thermal-stress during excimer laser induced heteroepitaxial growth of patterned amorphous silicon and germanium bi-layer deposited on Si (100),” Thin Solid Films 518, 2431–2436 (2010).
[Crossref]

Ni, X.

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

Ni, X. W.

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

B. Wang, Y. Qin, X. W. Ni, Z. H. Shen, and J. Lu, “Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films,” Appl. Opt. 49, 5537–5544 (2010).
[Crossref] [PubMed]

Nicolson, P.

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Reprinted in Adv. Comput. Math. 6, 207–226 (1996).
[Crossref]

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Proc. Cambridge Philos. Soc. 43, 50–67 (1947).
[Crossref]

Norton, M. G.

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

Obermeier, G.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Pirzada, D.

G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

Qin, Y.

Ravindra, K.

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

Ravindra, N. M.

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

Richter, H.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Schroter, W.

H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
[Crossref]

Shalynin, A.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Shen, Z. H.

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

B. Wang, Y. Qin, X. W. Ni, Z. H. Shen, and J. Lu, “Effect of defects on long-pulse laser-induced damage of two kinds of optical thin films,” Appl. Opt. 49, 5537–5544 (2010).
[Crossref] [PubMed]

Siethoff, H.

H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
[Crossref]

Sopori, B.

N. M. Ravindra, K. Ravindra, S. Mahendra, B. Sopori, and A. T. Fiory, “Modeling and simulation of emissivity of silicon-related materials and structures,” J. Electron. Mater. 32, 1052–1058 (2003).
[Crossref]

Stott, F. H.

J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
[Crossref]

Tayor, R. L.

O. C. Zienkiewicz and R. L. Tayor, The Finite Element Method (Butterworth-Heinemann, 2000).

Wahlich, R.

A. Fischer, H. Richter, A. Shalynin, P. Krottenthaler, G. Obermeier, U. Lambert, and R. Wahlich, “Upper yield point of large diameter silicon,” Microelectron. Eng. 56, 117–122(2001).
[Crossref]

Wang, B.

Wang, X.

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

Watt, D. W.

T. S. Gross, S. D. Hening, and D. W. Watt, “Crack formation during laser cutting of silicon,” J. Appl. Phys. 69, 983–989(1991).
[Crossref]

Xu, X.

X. R. Zhang and X. Xu, “High precision microscale bending by pulsed and CW lasers,” J. Appl. Mech. 125, 512–518 (2003).

Yan, Y. Z.

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Zarudi, I.

L. Zhang and I. Zarudi, “Towards a deeper understanding of plastic deformation in monocrystalline silicon,” Int. J. Mech. Sci. 43, 1985–1996 (2001).
[Crossref]

Zergioti, I.

Zhang, L.

L. Zhang and I. Zarudi, “Towards a deeper understanding of plastic deformation in monocrystalline silicon,” Int. J. Mech. Sci. 43, 1985–1996 (2001).
[Crossref]

Zhang, X.

Y. Chen, J. Lu, X. Ni, J. Bi, and X. Zhang, “Plastic penetration during laser heating of a metal plate,” J. Mater. Process. Technol. 205, 9–15 (2008).
[Crossref]

Zhang, X. R.

X. R. Zhang and X. Xu, “High precision microscale bending by pulsed and CW lasers,” J. Appl. Mech. 125, 512–518 (2003).

Zhu, D. H.

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

Zienkiewicz, O. C.

O. C. Zienkiewicz and R. L. Tayor, The Finite Element Method (Butterworth-Heinemann, 2000).

Zorba, V.

Acta Mater. (1)

J. F. Li, L. Li, and F. H. Stott, “Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52, 4385–4398 (2004).
[Crossref]

Adv. Comput. Math. (1)

J. Crank and P. Nicolson, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Reprinted in Adv. Comput. Math. 6, 207–226 (1996).
[Crossref]

Appl. Opt. (3)

Appl. Phys. A (1)

J. Frühauf, E. Garther, and E. Jansch, “New aspects of the plastic deformation of silicon-prerequisites for the reshaping of silicon microelements,” Appl. Phys. A 68, 673–679 (1999).
[Crossref]

Appl. Phys. Lett. (1)

H. Siethoff, H. G. Brion, and W. Schroter, “A regime of the yield point of silicon at high temperature,” Appl. Phys. Lett. 75, 1234–1236 (1999).
[Crossref]

Appl. Surf. Sci. (1)

X. Wang, D. H. Zhu, Z. H. Shen, J. Lu, and X. W. Ni, “Surface damage morphology investigations of silicon under millisecond laser irradiation,” Appl. Surf. Sci. 257, 1583–1588 (2010).
[Crossref]

Chin. J. Lasers (1)

Y. Z. Yan, L. F. Ji, Y. Bao, and Y. J. Jiang, “Theory analysis and experiment verification on crack characters during laser processing ceramics,” Chin. J. Lasers 35, 1401–1408(2008).
[Crossref]

Int. J. Mech. Sci. (1)

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[Crossref]

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[Crossref]

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G. J. Cheng, M. Cai, D. Pirzada, M. J. Guinel, and M. G. Norton, “Plastic deformation in silicon crystal induced by heat-assisted laser shock peening,” J. Manuf. Sci. Eng. 130, 011008 (2008).
[Crossref]

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[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram of the silicon sample irradiated by laser. O, center point of the front surface; r, the radial direction, z axis, symmetry axis, b and h, length and the thickness of the sample, respectively.

Fig. 2
Fig. 2

Experiment setup for the temperature measurements. 1064 nm Gaussian pulse laser is operating at TEM 00 mode, laser pulse width τ = 2 ms , laser spot radius is 500 μm , energy density E = 254 J / cm 2 . Measure range of infrared pyrometer KMGA740 is 623 K - 3773 K .

Fig. 3
Fig. 3

Temperature time evolution of the laser spot center at laser fluence of 254 J / cm 2 of Si sample.

Fig. 4
Fig. 4

Temperature along r direction on the front surface at different times of Si sample obtained from calculations.

Fig. 5
Fig. 5

Temperature along z direction ( r = 0 ) at different times of Si sample obtained from calculations.

Fig. 6
Fig. 6

Von Mises stress in center on front surface of Si sample obtained from calculations.

Fig. 7
Fig. 7

Hoop stress along r axis on front surface at different times of Si sample obtained from calculations.

Fig. 8
Fig. 8

Radial stress along r axis on front surface at different times of Si sample obtained from calculations.

Fig. 9
Fig. 9

Radial stress on the z-axis at different times of the Si sample obtained from calculations.

Fig. 10
Fig. 10

Damage morphology of silicon sample induced by a single pulse laser at different energy densities. Laser pulse width τ = 2 ms . (a) Damage morphology at a laser fluence of 229 J / cm 2 ; surface layer melting without thermal stress damage. (b) Damage morphology at a laser fluence of 254 J / cm 2 ; melting damage and thermal stress damage both occur. The cracks initiate at r = 05 mm and propagate along the radial direction.

Tables (1)

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Table 1 Thermal and Mechanical Parameters of Silicon

Equations (15)

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ρ c T ( r , z , t ) t = 1 r r ( r k T ( r , z , t ) r ) + z ( k T ( r , z , t ) z ) + q ,
q = I 0 ( 1 R ) α f ( r ) g ( t ) exp ( α z ) ,
f ( r ) = exp ( 2 r 2 a 0 2 ) , g ( t ) = 1 , I ( r , t ) = I 0 exp ( 2 r 2 a 0 2 ) ,
k T ( r , z , t ) z | z = h = k T ( r , z , t ) r | r = b = 0.
T ( r , z , t ) | t = 0 = T 0 .
k T ( r , z , t ) r | r = 0 = 0.
[ C ] { T ˙ } + [ K th ] { T } = { Q } ,
( 1 Δ t [ C ] + θ [ K th ] ) { T } t = ( 1 Δ t [ C ] ( θ ) [ K th ] ) { T } t + Δ t + θ { Q } t + ( 1 θ ) { Q } t + Δ t ,
{ Δ σ } = [ D ] e p { Δ ε } ,
{ Δ σ } = [ D ] e ( { Δ ε } { Δ ε } T [ D ] e 1 T { σ } d T ) ,
{ Δ σ } = [ D ] ep ( { Δ ε } { Δ ε } T [ D ] e 1 T { σ } d T ) + [ D ] e σ ¯ { σ } H T d T H + { σ ¯ { σ } } T [ D ] e σ ¯ { σ } ,
[ D ] ep = [ D ] e [ D ] e σ ¯ { σ } { σ ¯ { σ } } T [ D ] e H + { σ ¯ { σ } } T [ D ] e σ ¯ { σ } ,
{ Δ σ } = [ D ] ep ( [ B ] { Δ U } { Δ ε } T ) ,
{ Δ R } t + Δ t = e [ B ] T [ D ] ep { Δ ε } T 2 π r d r d z .
[ K ] t + Δ t { Δ U } = { Δ R } ,

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