Abstract
We investigated the laser–material interaction during the production of laser-induced subsurface modifications in silicon with a numerical model. Such modifications are of interest for subsurface wafer dicing. To predict the shape of these modifications, a two-temperature model and an optical model were combined. We compared the model results with experimental data obtained by focusing laser pulses in the bulk of silicon wafers using a microscope objective. This comparison revealed a good agreement between the simulations and the experimental results. A parameter study was performed to investigate the effect of the laser wavelength, pulse duration and pulse energy on the formation of subsurface modifications. We found that both single- and multi-photon absorption may be used to produce subsurface modifications in silicon.
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H.B. Sun, Y. Xu, S. Juodkazis, K. Sun, M. Watanabe, S. Matsuo, H. Misawa, J. Nishii, Opt. Lett. 26(6), 325 (2001)
K. Miura, J. Qiu, H. Inouye, T. Mitsuyu, K. Hirao, Appl. Phys. Lett. 71(23), 3329 (1997)
Y. Kondo, K. Nouchi, T. Mitsuyu, M. Watanabe, P.G. Kazansky, K. Hirao, Opt. Lett. 24(10), 646 (1999)
S. Juodkazis, A. Rode, E. Gamaly, S. Matsuo, H. Misawa, Appl. Phys. B, Lasers Opt. 77, 361 (2003)
A.H. Nejadmalayeri, P.R. Herman, J. Burghoff, M. Will, S. Nolte, A. Tünnermann, Opt. Lett. 30(9), 964 (2005)
E. Ohmura, F. Fukuyo, F. Fukumitsu, H. Morita, J. Achiev. Mater. Manuf. Eng. 17, 381 (2006)
J. van Borkulo, R. Evertsen, R. Hendriks, ECS Trans. 18, 837 (2009)
H.M. van Driel, Phys. Rev. B 35(15), 8166 (1987)
A.L. Smirl, I.W. Boyd, T.F. Boggess, S.C. Moss, H.M. van Driel, J. Appl. Phys. 60(3), 1169 (1986)
K. Sokolowski-Tinten, D. von der Linde, Phys. Rev. B 61(4), 2643 (2000)
E.J. Yoffa, Phys. Rev. B 21(6), 2415 (1980)
N. Bulgakova, R. Stoian, A. Rosenfeld, I. Hertel, W. Marine, E. Campbell, Appl. Phys. A, Mater. Sci. Process. 81, 345 (2005)
A. Lietoila, J. Gibbons, J. Appl. Phys. 53(4), 3207 (1982)
J. Chen, D. Tzou, J. Beraun, Int. J. Heat Mass Transf. 48(3–4), 501 (2005)
T. Monodane, E. Ohmura, F. Fukuyo, K. Fukumitsu, H. Morita, Y. Hirata, J. Laser Micro Nanoeng. 1, 231 (2006)
I.B. Bogatyrev, D. Grojo, P. Delaporte, S. Leyder, M. Sentis, W. Marine, T.E. Itina, J. Appl. Phys. 110(10), 103106 (2011)
M.I. Kaganov, I.M. Livshitz, L.V. Tanatarov, Sov. Phys. JETP 4, 173 (1957)
F. Berz, R. Cooper, S. Fagg, Solid-State Electron. 22(3), 293 (1979)
C. Bonacina, G. Comini, A. Fasano, M. Primicerio, Int. J. Heat Mass Transf. 16(10), 1825 (1973)
H.R. Shanks, P.D. Maycock, P.H. Sidles, G.C. Danielson, Phys. Rev. 130(5), 1743 (1963)
T. Sjodin, H. Petek, H.L. Dai, Phys. Rev. Lett. 81(25), 5664 (1998)
N.G. Nilsson, Phys. Scr. 8(4), 165 (1973)
W. van Roosbroeck, W. Shockley, Phys. Rev. 94, 1558 (1954)
W. Shockley, W.T. Read Jr., Phys. Rev. 87, 835 (1952)
C.G.B. Garrett, W.H. Brattain, Phys. Rev. 99, 376 (1955)
S. Sze, K.K. Ng, Physics of Semiconductor Devices, 3rd edn. (Wiley, New York, 2007)
A.E. Siegman, in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues (OSA, Washington, 1998), p. MQ1
H.H. Li, J. Phys. Chem. Ref. Data 9(3), 561 (1980)
A. Singh, in IEEE International Conference on Group IV Photonics GFP (2010), pp. 102–104
A.D. Bristow, N. Rotenberg, H.M. van Driel, Appl. Phys. Lett. 90(19), 191104 (2007)
F.N. Fritsch, R.E. Carlson, SIAM J. Numer. Anal. 17(2), 238 (1980)
Y. Chung, N. Dagli, IEEE J. Quantum Electron. 27(10), 2296 (1991)
R.E. Hummel, Electronic Properties of Materials, 3rd edn. (Springer, Berlin, 2001)
M.A. Green, Sol. Energy Mater. Sol. Cells 92(11), 1305 (2008)
Y.P. Varshni, Physica 34(1), 149 (1967)
K. Yamaguchi, K. Itagaki, J. Therm. Anal. Calorim. 69, 1059 (2002)
C.J. Glassbrenner, G.A. Slack, Phys. Rev. 134(4A), A1058 (1964)
G. Jellison Jr., D. Lowndes, Appl. Phys. Lett. 41(7), 594 (1982)
K.G. Svantesson, N.G. Nilsson, J. Phys. C 12(18), 3837 (1979)
G.E. Jellison Jr., F.A. Modine, Phys. Rev. B 27, 7466 (1983)
P. Jonsson, H. Bleichner, M. Isberg, E. Nordlander, J. Appl. Phys. 81(5), 2256 (1997)
S. Sundaram, E. Mazur, Nat. Mater. 1(4), 217 (2002)
I. Boyd, S. Moss, T. Boggess, A. Smirl, Appl. Phys. Lett. 45(1), 80 (1984)
C. Ma, W.Y. Ho, R.M. Walser, M.F. Becker, in Proc. SPIE, vol. 1848 (1993), p. 59
X. Wang, Z. Shen, J. Lu, X. Ni, J. Appl. Phys. 108(3), 033103 (2010)
J. Meyer, M. Kruer, F. Bartoli, J. Appl. Phys. 51(10), 5513 (1980)
P.C. Verburg, G.R.B.E. Römer, G.H.M. Knippels, J. Betz, A.J. Huis in ’t Veld, in Proceedings of the 13th International Symposium on Laser Precision Microfabrication, June 12–15, 2012, Washington DC, USA (2012)
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The authors would like to thank Bert Dillingh for his assistance with the initial finite element solver and Fred van Goor for providing access to a laser source.
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Verburg, P.C., Römer, G.R.B.E. & Huis in ’t Veld, A.J. Two-temperature model for pulsed-laser-induced subsurface modifications in Si. Appl. Phys. A 114, 1135–1143 (2014). https://doi.org/10.1007/s00339-013-7668-5
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DOI: https://doi.org/10.1007/s00339-013-7668-5