Abstract

The formation of near-wavelength laser-induced periodic surface structures (LIPSS) on silicon upon irradiation with sequences of Ti:sapphire femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied theoretically. For this purpose, the nonlinear generation of conduction band electrons in silicon and their relaxation is numerically calculated using a two-temperature model approach including intrapulse changes of optical properties, transport, diffusion and recombination effects. Following the idea that surface plasmon polaritons (SPP) can be excited when the material turns from semiconducting to metallic state, the “SPP active area” is calculated as function of fluence and double-pulse delay up to several picoseconds and compared to the experimentally observed rippled surface areas. Evidence is presented that multi-photon absorption explains the large increase of the rippled area for temporally overlapping pulses. For longer double-pulse delays, relevant relaxation processes are identified. The results demonstrate that femtosecond LIPSS on silicon are caused by the excitation of SPP and can be controlled by temporal pulse shaping.

© 2013 OSA

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2013 (5)

T. J.-Y. Derrien, T. E. Itina, R. Torres, T. Sarnet, and M. Sentis, “Possible surface plasmon polariton excitation under femtosecond laser irradiation of silicon,” J. Appl. Phys.114, 083104 (2013).
[CrossRef]

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Area dependence of femtosecond laser-induced periodic surface structures for varying band gap materials after double pulse excitation,” Appl. Surf. Sci.278, 7–12 (2013).
[CrossRef]

S. Höhm, M. Rohloff, A. Rosenfeld, J. Krüger, and J. Bonse, “Dynamics of the formation of laser-induced periodic surface structures on dielectrics and semiconductors upon femtosecond laser pulse irradiation sequences,” Appl. Phys. A110, 553–557 (2013).
[CrossRef]

M. Huang, Y. Cheng, F. Zhao, and Z. Xu, “The significant role of plasmonic effects in femtosecond laser-induced grating fabrication on the nanoscale,” Ann. Phys.S25, 74–86 (2013).
[CrossRef]

J. Bogdanowicz, M. Gilbert, N. Innocenti, S. Koelling, B. Vanderheyden, and W. Vandervorst, “Light absorption in conical silicon particles,” Opt. Express21, 3891–3896 (2013).
[CrossRef] [PubMed]

2012 (2)

G. Tsibidis, M. Barberoglou, P. Loukakos, E. Stratakis, and C. Fotakis, “Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in subablation conditions,” Phys. Rev. B86, 115316 (2012).
[CrossRef]

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl.24, 042006 (2012).
[CrossRef]

2011 (2)

U. Chakravarty, R. Ganeev, P. Naik, J. Chakera, M. Babu, and P. Gupta, “Nano-ripple formation on different band-gap semiconductor surfaces using femtosecond pulses,” J. Appl. Phys.109, 084347 (2011).
[CrossRef]

A. Vorobyev and C. Guo, “Antireflection effect of femtosecond laser-induced periodic surface structures on silicon,” Opt. Express19, A1031–A1036 (2011).
[CrossRef] [PubMed]

2010 (5)

J. Bonse and J. Krüger, “Pulse number dependence of laser-induced periodic surface structures for femtosecond laser irradiation of silicon,” J. Appl. Phys.108, 034903 (2010).
[CrossRef]

T. Crawford, G. Botton, and H. Haugen, “Crystalline orientation effects on conical structure formation in femtosecond laser irradiation of silicon and germanium,” Appl. Surf. Sci.256, 1749–1755 (2010).
[CrossRef]

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

T. J.-Y. Derrien, T. Sarnet, M. Sentis, and T. E. Itina, “Application of a two-temperature model for the investigation of the periodic structure formation on Si surface in femtosecond laser interactions,” J. Optoelectron. Adv. Mater.12, 610–615 (2010).

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron.40, 966–985 (2010).
[CrossRef]

2009 (3)

J. Bonse, A. Rosenfeld, and J. Krüger, “ On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys.106, 104910 (2009).
[CrossRef]

D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited - a comparative study on ZnO,” J. Appl. Phys.105, 034908 (2009).
[CrossRef]

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano3, 4062–4070 (2009).
[CrossRef] [PubMed]

2008 (1)

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

2007 (3)

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci.253, 8075–8079 (2007).
[CrossRef]

R. Wagner and J. Gottmann, “Sub-wavelength ripple formation on various materials induced by tightly focused femtosecond laser radiation,” J. Phys. Conf. Ser.59, 333–337 (2007).
[CrossRef]

D. Korfiatis, K. Thoma, and J. Vardaxoglou, “Conditions for femtosecond laser melting of silicon,” J. Phys. D Appl. Phys.40, 6803–6808 (2007).
[CrossRef]

2006 (2)

J. Bonse, “All-optical characterization of single femtosecond laser-pulse-induced amorphization in silicon,” Appl. Phys. A84, 63–66 (2006).
[CrossRef]

M. Harb, R. Ernstorfer, T. Dartigalongue, C. T. Hebeisen, R. E. Jordan, and R. J. D. Miller, “Carrier relaxation and lattice heating dynamics in silicon revealed by femtosecond electron diffraction,” J. Phys. Chem. B110, 25308–25313 (2006).
[CrossRef] [PubMed]

2005 (2)

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, W. Marine, and E. E. B. Campbell, “ A general continuum approach to describe fast electronic transport in pulsed laser irradiated materials - the problem of coulomb explosion,” Appl. Phys. A81, 345–356 (2005).
[CrossRef]

J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys.97, 013538 (2005).
[CrossRef]

2004 (2)

A. L. Magna, P. Alippi, V. Privitera, G. Fortunato, M. Camalleri, and B. Svensson, “A phase-field approach to the simulation of the excimer laser annealing process in Si,” J. Appl. Phys.95, 4806–4814 (2004).
[CrossRef]

F. Costache, S. Kouteva-Arguirova, and J. Reif, “Sub-damage-threshold femtosecond laser ablation from crystalline Si: surface nanostructures and phase transformation,” Appl. Phys. A79, 1429–1432 (2004).
[CrossRef]

2003 (1)

A. Borowiec and H. K. Haugen, “Subwavelength ripple formation on the surfaces of compound semiconductors irradiated with femtosecond laser pulses,” Appl. Phys. Lett.82, 4462–4464 (2003).
[CrossRef]

2002 (4)

J. Reif, F. Costache, M. Henyk, and S. V. Pandelov, “Ripples revisited - non-classical morphology at the bottom of femtosecond laser ablation craters in transparent dielectrics,” Appl. Surf. Sci.197–198, 891–895 (2002).
[CrossRef]

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phys. A74, 19–25 (2002).
[CrossRef]

A. Sabbah and D. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B66, 165217 (2002).
[CrossRef]

S. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater.1, 217–224 (2002).
[CrossRef]

2000 (3)

D. von der Linde and K. Sokolowski-Tinten, “The physical mechanisms of short-pulse laser ablation,” Appl. Surf. Sci.154–155, 1–10 (2000).
[CrossRef]

W.-K. Rhim and K. Ohsaka, “Thermophysical properties measurement of molten silicon by high-temperature electrostatic levitator: density, volume expansion, specific heat capacity, emissivity, surface tension and viscosity,” J. Cryst. Growth208, 313–321 (2000).
[CrossRef]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B61, 2643–2650 (2000).
[CrossRef]

1998 (1)

T. Sjodin, H. Petek, and H.-L. Dai, “ Ultrafast carrier dynamics in silicon: A two-color transient reflection grating study on a (111) surface,” Phys. Rev. Lett.81, 5664–5667 (1998).
[CrossRef]

1992 (1)

A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. A. Trubaev, “ Surface electromagnetic waves in optics,” Opt. Eng.31, 718–730 (1992).
[CrossRef]

1990 (1)

A. Esser, W. Kütt, M. Strahnen, G. Maidorn, and H. Kurz, “Femtosecond transient reflectivity measurements as a probe for process-induced defects in silicon,” Appl. Surf. Sci.46, 446–450 (1990).
[CrossRef]

1988 (1)

J. E. Sipe and H. V. Driel, “Laser induced periodic surface structure: an experimental and theoretical review,” Proc. SPIE1033, 302–318 (1988).
[CrossRef]

1987 (1)

H. V. Driel, “Kinetics of high-density plasmas generated in Si by 1.06- and 0.53-μm picosecond laser pulses,” Phys. Rev. B35, 8166–8176 (1987).
[CrossRef]

1986 (1)

P. Desai, “Thermodynamic properties of iron and silicon,” J. Phys. Chem. Ref. Data15, 967–983 (1986).
[CrossRef]

1983 (2)

C. Shank, R. Yen, and C. Hirlimann, “Time-resolved reflectivity measurements of femtosecond-optical-pulse-induced phase transitions in silicon,” Phys. Rev. Lett.50, 454–457 (1983).
[CrossRef]

J. E. Sipe, J. F. Young, J. Preston, and H. V. Driel, “ Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B27, 1141–1154 (1983).
[CrossRef]

1980 (1)

E. J. Yoffa, “Dynamics of dense laser-induced plasmas,” Phys. Rev. B21, 2415–2425 (1980).
[CrossRef]

Alippi, P.

A. L. Magna, P. Alippi, V. Privitera, G. Fortunato, M. Camalleri, and B. Svensson, “A phase-field approach to the simulation of the excimer laser annealing process in Si,” J. Appl. Phys.95, 4806–4814 (2004).
[CrossRef]

Audouard, E.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci.253, 8075–8079 (2007).
[CrossRef]

Babu, M.

U. Chakravarty, R. Ganeev, P. Naik, J. Chakera, M. Babu, and P. Gupta, “Nano-ripple formation on different band-gap semiconductor surfaces using femtosecond pulses,” J. Appl. Phys.109, 084347 (2011).
[CrossRef]

Bajt, S.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Barberoglou, M.

G. Tsibidis, M. Barberoglou, P. Loukakos, E. Stratakis, and C. Fotakis, “Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in subablation conditions,” Phys. Rev. B86, 115316 (2012).
[CrossRef]

Barty, A.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Baudach, S.

J. Bonse, S. Baudach, J. Krüger, W. Kautek, and M. Lenzner, “Femtosecond laser ablation of silicon-modification thresholds and morphology,” Appl. Phys. A74, 19–25 (2002).
[CrossRef]

Bäuerle, D.

D. Bäuerle, Laser Processing and Chemistry (Springer, 2011), 4th ed.
[CrossRef]

Bogan, M.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Bogdanowicz, J.

Bonch-Bruevich, A. M.

A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. A. Trubaev, “ Surface electromagnetic waves in optics,” Opt. Eng.31, 718–730 (1992).
[CrossRef]

Bonse, J.

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Area dependence of femtosecond laser-induced periodic surface structures for varying band gap materials after double pulse excitation,” Appl. Surf. Sci.278, 7–12 (2013).
[CrossRef]

S. Höhm, M. Rohloff, A. Rosenfeld, J. Krüger, and J. Bonse, “Dynamics of the formation of laser-induced periodic surface structures on dielectrics and semiconductors upon femtosecond laser pulse irradiation sequences,” Appl. Phys. A110, 553–557 (2013).
[CrossRef]

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl.24, 042006 (2012).
[CrossRef]

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K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Marine, W.

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, W. Marine, and E. E. B. Campbell, “ A general continuum approach to describe fast electronic transport in pulsed laser irradiated materials - the problem of coulomb explosion,” Appl. Phys. A81, 345–356 (2005).
[CrossRef]

Martsinovskii, G. A.

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

Mazur, E.

S. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater.1, 217–224 (2002).
[CrossRef]

Miller, R. J. D.

M. Harb, R. Ernstorfer, T. Dartigalongue, C. T. Hebeisen, R. E. Jordan, and R. J. D. Miller, “Carrier relaxation and lattice heating dynamics in silicon revealed by femtosecond electron diffraction,” J. Phys. Chem. B110, 25308–25313 (2006).
[CrossRef] [PubMed]

Möller, T.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Munz, M.

J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys.97, 013538 (2005).
[CrossRef]

Naik, P.

U. Chakravarty, R. Ganeev, P. Naik, J. Chakera, M. Babu, and P. Gupta, “Nano-ripple formation on different band-gap semiconductor surfaces using femtosecond pulses,” J. Appl. Phys.109, 084347 (2011).
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Ohsaka, K.

W.-K. Rhim and K. Ohsaka, “Thermophysical properties measurement of molten silicon by high-temperature electrostatic levitator: density, volume expansion, specific heat capacity, emissivity, surface tension and viscosity,” J. Cryst. Growth208, 313–321 (2000).
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E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

Pandelov, S. V.

J. Reif, F. Costache, M. Henyk, and S. V. Pandelov, “Ripples revisited - non-classical morphology at the bottom of femtosecond laser ablation craters in transparent dielectrics,” Appl. Surf. Sci.197–198, 891–895 (2002).
[CrossRef]

Petek, H.

T. Sjodin, H. Petek, and H.-L. Dai, “ Ultrafast carrier dynamics in silicon: A two-color transient reflection grating study on a (111) surface,” Phys. Rev. Lett.81, 5664–5667 (1998).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 2007).

Preston, J.

J. E. Sipe, J. F. Young, J. Preston, and H. V. Driel, “ Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B27, 1141–1154 (1983).
[CrossRef]

Privitera, V.

A. L. Magna, P. Alippi, V. Privitera, G. Fortunato, M. Camalleri, and B. Svensson, “A phase-field approach to the simulation of the excimer laser annealing process in Si,” J. Appl. Phys.95, 4806–4814 (2004).
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H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1986).

Redlin, H.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Reif, J.

F. Costache, S. Kouteva-Arguirova, and J. Reif, “Sub-damage-threshold femtosecond laser ablation from crystalline Si: surface nanostructures and phase transformation,” Appl. Phys. A79, 1429–1432 (2004).
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J. Reif, F. Costache, M. Henyk, and S. V. Pandelov, “Ripples revisited - non-classical morphology at the bottom of femtosecond laser ablation craters in transparent dielectrics,” Appl. Surf. Sci.197–198, 891–895 (2002).
[CrossRef]

Rhim, W.-K.

W.-K. Rhim and K. Ohsaka, “Thermophysical properties measurement of molten silicon by high-temperature electrostatic levitator: density, volume expansion, specific heat capacity, emissivity, surface tension and viscosity,” J. Cryst. Growth208, 313–321 (2000).
[CrossRef]

Riffe, D.

A. Sabbah and D. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B66, 165217 (2002).
[CrossRef]

Rohloff, M.

S. Höhm, M. Rohloff, A. Rosenfeld, J. Krüger, and J. Bonse, “Dynamics of the formation of laser-induced periodic surface structures on dielectrics and semiconductors upon femtosecond laser pulse irradiation sequences,” Appl. Phys. A110, 553–557 (2013).
[CrossRef]

Rosandi, Y.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Rosenfeld, A.

S. Höhm, A. Rosenfeld, J. Krüger, and J. Bonse, “Area dependence of femtosecond laser-induced periodic surface structures for varying band gap materials after double pulse excitation,” Appl. Surf. Sci.278, 7–12 (2013).
[CrossRef]

S. Höhm, M. Rohloff, A. Rosenfeld, J. Krüger, and J. Bonse, “Dynamics of the formation of laser-induced periodic surface structures on dielectrics and semiconductors upon femtosecond laser pulse irradiation sequences,” Appl. Phys. A110, 553–557 (2013).
[CrossRef]

J. Bonse, J. Krüger, S. Höhm, and A. Rosenfeld, “Femtosecond laser-induced periodic surface structures,” J. Laser Appl.24, 042006 (2012).
[CrossRef]

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron.40, 966–985 (2010).
[CrossRef]

D. Dufft, A. Rosenfeld, S. K. Das, R. Grunwald, and J. Bonse, “Femtosecond laser-induced periodic surface structures revisited - a comparative study on ZnO,” J. Appl. Phys.105, 034908 (2009).
[CrossRef]

J. Bonse, A. Rosenfeld, and J. Krüger, “ On the role of surface plasmon polaritons in the formation of laser-induced periodic surface structures upon irradiation of silicon by femtosecond-laser pulses,” J. Appl. Phys.106, 104910 (2009).
[CrossRef]

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, W. Marine, and E. E. B. Campbell, “ A general continuum approach to describe fast electronic transport in pulsed laser irradiated materials - the problem of coulomb explosion,” Appl. Phys. A81, 345–356 (2005).
[CrossRef]

Sabbah, A.

A. Sabbah and D. Riffe, “Femtosecond pump-probe reflectivity study of silicon carrier dynamics,” Phys. Rev. B66, 165217 (2002).
[CrossRef]

Sanner, N.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci.253, 8075–8079 (2007).
[CrossRef]

Sarnet, T.

T. J.-Y. Derrien, T. E. Itina, R. Torres, T. Sarnet, and M. Sentis, “Possible surface plasmon polariton excitation under femtosecond laser irradiation of silicon,” J. Appl. Phys.114, 083104 (2013).
[CrossRef]

T. J.-Y. Derrien, T. Sarnet, M. Sentis, and T. E. Itina, “Application of a two-temperature model for the investigation of the periodic structure formation on Si surface in femtosecond laser interactions,” J. Optoelectron. Adv. Mater.12, 610–615 (2010).

Schulz, J.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Seibert, M.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Sentis, M.

T. J.-Y. Derrien, T. E. Itina, R. Torres, T. Sarnet, and M. Sentis, “Possible surface plasmon polariton excitation under femtosecond laser irradiation of silicon,” J. Appl. Phys.114, 083104 (2013).
[CrossRef]

T. J.-Y. Derrien, T. Sarnet, M. Sentis, and T. E. Itina, “Application of a two-temperature model for the investigation of the periodic structure formation on Si surface in femtosecond laser interactions,” J. Optoelectron. Adv. Mater.12, 610–615 (2010).

Shandybina, G. D.

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

Shank, C.

C. Shank, R. Yen, and C. Hirlimann, “Time-resolved reflectivity measurements of femtosecond-optical-pulse-induced phase transitions in silicon,” Phys. Rev. Lett.50, 454–457 (1983).
[CrossRef]

Shymanovich, U.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Sipe, J. E.

J. E. Sipe and H. V. Driel, “Laser induced periodic surface structure: an experimental and theoretical review,” Proc. SPIE1033, 302–318 (1988).
[CrossRef]

J. E. Sipe, J. F. Young, J. Preston, and H. V. Driel, “ Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B27, 1141–1154 (1983).
[CrossRef]

Sjodin, T.

T. Sjodin, H. Petek, and H.-L. Dai, “ Ultrafast carrier dynamics in silicon: A two-color transient reflection grating study on a (111) surface,” Phys. Rev. Lett.81, 5664–5667 (1998).
[CrossRef]

Smirnov, D. S.

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

Soder, H.

M. Guillermin, F. Garrelie, N. Sanner, E. Audouard, and H. Soder, “Single and multi-pulse formation of surface structures under static femtosecond irradiation,” Appl. Surf. Sci.253, 8075–8079 (2007).
[CrossRef]

Sokolowski-Tinten, K.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B61, 2643–2650 (2000).
[CrossRef]

D. von der Linde and K. Sokolowski-Tinten, “The physical mechanisms of short-pulse laser ablation,” Appl. Surf. Sci.154–155, 1–10 (2000).
[CrossRef]

Stoian, R.

N. M. Bulgakova, R. Stoian, and A. Rosenfeld, “Laser-induced modification of transparent crystals and glasses,” Quantum Electron.40, 966–985 (2010).
[CrossRef]

N. M. Bulgakova, R. Stoian, A. Rosenfeld, I. V. Hertel, W. Marine, and E. E. B. Campbell, “ A general continuum approach to describe fast electronic transport in pulsed laser irradiated materials - the problem of coulomb explosion,” Appl. Phys. A81, 345–356 (2005).
[CrossRef]

Stojanovic, N.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Strahnen, M.

A. Esser, W. Kütt, M. Strahnen, G. Maidorn, and H. Kurz, “Femtosecond transient reflectivity measurements as a probe for process-induced defects in silicon,” Appl. Surf. Sci.46, 446–450 (1990).
[CrossRef]

Stratakis, E.

G. Tsibidis, M. Barberoglou, P. Loukakos, E. Stratakis, and C. Fotakis, “Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in subablation conditions,” Phys. Rev. B86, 115316 (2012).
[CrossRef]

Sturm, H.

J. Bonse, M. Munz, and H. Sturm, “Structure formation on the surface of indium phosphide irradiated by femtosecond laser pulses,” J. Appl. Phys.97, 013538 (2005).
[CrossRef]

Sundaram, S.

S. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater.1, 217–224 (2002).
[CrossRef]

Svensson, B.

A. L. Magna, P. Alippi, V. Privitera, G. Fortunato, M. Camalleri, and B. Svensson, “A phase-field approach to the simulation of the excimer laser annealing process in Si,” J. Appl. Phys.95, 4806–4814 (2004).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 2007).

Thoma, K.

D. Korfiatis, K. Thoma, and J. Vardaxoglou, “Conditions for femtosecond laser melting of silicon,” J. Phys. D Appl. Phys.40, 6803–6808 (2007).
[CrossRef]

Timoshenko, V. Y.

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

Tobey, R.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Torres, R.

T. J.-Y. Derrien, T. E. Itina, R. Torres, T. Sarnet, and M. Sentis, “Possible surface plasmon polariton excitation under femtosecond laser irradiation of silicon,” J. Appl. Phys.114, 083104 (2013).
[CrossRef]

Treusch, R.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Trubaev, V. A.

A. M. Bonch-Bruevich, M. N. Libenson, V. S. Makin, and V. A. Trubaev, “ Surface electromagnetic waves in optics,” Opt. Eng.31, 718–730 (1992).
[CrossRef]

Tsibidis, G.

G. Tsibidis, M. Barberoglou, P. Loukakos, E. Stratakis, and C. Fotakis, “Dynamics of ripple formation on silicon surfaces by ultrashort laser pulses in subablation conditions,” Phys. Rev. B86, 115316 (2012).
[CrossRef]

Urbassek, H. M.

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Vanderheyden, B.

Vandervorst, W.

Vardaxoglou, J.

D. Korfiatis, K. Thoma, and J. Vardaxoglou, “Conditions for femtosecond laser melting of silicon,” J. Phys. D Appl. Phys.40, 6803–6808 (2007).
[CrossRef]

Versteeg, H.

H. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dynamics - The Finite Volume Method (Pearson Education, 2007).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing (Cambridge University, 2007).

von der Linde, D.

K. Sokolowski-Tinten and D. von der Linde, “Generation of dense electron-hole plasmas in silicon,” Phys. Rev. B61, 2643–2650 (2000).
[CrossRef]

D. von der Linde and K. Sokolowski-Tinten, “The physical mechanisms of short-pulse laser ablation,” Appl. Surf. Sci.154–155, 1–10 (2000).
[CrossRef]

Vorobyev, A.

Wagner, R.

R. Wagner and J. Gottmann, “Sub-wavelength ripple formation on various materials induced by tightly focused femtosecond laser radiation,” J. Phys. Conf. Ser.59, 333–337 (2007).
[CrossRef]

Xu, N.

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano3, 4062–4070 (2009).
[CrossRef] [PubMed]

Xu, Z.

M. Huang, Y. Cheng, F. Zhao, and Z. Xu, “The significant role of plasmonic effects in femtosecond laser-induced grating fabrication on the nanoscale,” Ann. Phys.S25, 74–86 (2013).
[CrossRef]

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano3, 4062–4070 (2009).
[CrossRef] [PubMed]

Yen, R.

C. Shank, R. Yen, and C. Hirlimann, “Time-resolved reflectivity measurements of femtosecond-optical-pulse-induced phase transitions in silicon,” Phys. Rev. Lett.50, 454–457 (1983).
[CrossRef]

Yoffa, E. J.

E. J. Yoffa, “Dynamics of dense laser-induced plasmas,” Phys. Rev. B21, 2415–2425 (1980).
[CrossRef]

Young, J. F.

J. E. Sipe, J. F. Young, J. Preston, and H. V. Driel, “ Laser-induced periodic surface structure. I. Theory,” Phys. Rev. B27, 1141–1154 (1983).
[CrossRef]

Zabotnov, S. V.

G. A. Martsinovskii, G. D. Shandybina, D. S. Smirnov, S. V. Zabotnov, L. A. Golovan, V. Y. Timoshenko, and P. K. Kashkarov, “ Ultrashort excitations of surface polaritons and waveguide modes in semiconductors,” Opt. Spectrosc.105, 67–72 (2008).
[CrossRef]

Zhao, F.

M. Huang, Y. Cheng, F. Zhao, and Z. Xu, “The significant role of plasmonic effects in femtosecond laser-induced grating fabrication on the nanoscale,” Ann. Phys.S25, 74–86 (2013).
[CrossRef]

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano3, 4062–4070 (2009).
[CrossRef] [PubMed]

ACS Nano (1)

M. Huang, F. Zhao, Y. Cheng, N. Xu, and Z. Xu, “Origin of laser-induced near-subwavelength ripples: Interference between surface plasmons and incident laser,” ACS Nano3, 4062–4070 (2009).
[CrossRef] [PubMed]

AIP Conf. Proc. (1)

K. Sokolowski-Tinten, A. Barty, S. Boutet, U. Shymanovich, H. Chapman, M. Bogan, S. Marchesini, S. Hau-Riege, N. Stojanovic, J. Bonse, Y. Rosandi, H. M. Urbassek, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, H. Redlin, M. Frank, S. Bajt, J. Schulz, M. Seibert, J. Hajdu, R. Treusch, C. Bostedt, M. Hoener, and T. Möller, “Short-pulse laser induced transient structure formation and ablation studied with time-resolved coherent xuv-scattering,” AIP Conf. Proc.1278, 373–379 (2010).
[CrossRef]

Ann. Phys. (1)

M. Huang, Y. Cheng, F. Zhao, and Z. Xu, “The significant role of plasmonic effects in femtosecond laser-induced grating fabrication on the nanoscale,” Ann. Phys.S25, 74–86 (2013).
[CrossRef]

Appl. Phys. A (5)

J. Bonse, “All-optical characterization of single femtosecond laser-pulse-induced amorphization in silicon,” Appl. Phys. A84, 63–66 (2006).
[CrossRef]

S. Höhm, M. Rohloff, A. Rosenfeld, J. Krüger, and J. Bonse, “Dynamics of the formation of laser-induced periodic surface structures on dielectrics and semiconductors upon femtosecond laser pulse irradiation sequences,” Appl. Phys. A110, 553–557 (2013).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Scheme of typical free-carrier density distribution at the surface of silicon during laser pulse irradiation. The hatched circular zone corresponds to the area on which surface plasmon polaritons (SPP) can be excited while the free-carrier density Ne is greater than the threshold density for SPP excitation N t h S P P at the interface between air and silicon.

Fig. 2
Fig. 2

Evolution of the free-carrier density (left ordinates) at the surface of silicon irradiated by a femtosecond double-pulse with a delay of Δt = 0.5 ps and single pulse fluence of F0 = 0.2, 0.3 and 0.5 J/cm2 (pulse duration τ = 150 fs, laser wavelength λ = 800 nm). (a) Short timescales up to 1 ps. (b) Long timescales up to 5 ps. For comparison, the temporal double-pulse intensity profile is shown (right ordinates). The horizontal lines indicate the threshold density N t h S P P for SPP excitation. The maximum values of the carrier density N e max are marked in (b).

Fig. 3
Fig. 3

Maximum free-carrier density as a function of laser fluence F0 and double-pulse delay Δt. The black isoline represents the SPP threshold density N t h S P P. The three crosses indicate the parameters used in Fig. 2. (Irradiation parameters: τ = 150 fs, λ = 800 nm). The vertical dashed line corresponds to the data displayed in Fig. 4.

Fig. 4
Fig. 4

Maximum free-carrier density N e max as a function of the double-pulse delay Δt (red solid line). The dashed blue and dotted green represent N e t max calculated for ζ = 50% and 99%, respectively. Model parameters: F0 = 0.25 J/cm2, τ = 150 fs, λ = 800 nm. The dotted horizontal line indicates the threshold density N t h S P P for SPP excitation.

Fig. 5
Fig. 5

Calculated SPP active area ��SPP as a function of the double-pulse delay Δt for three different values of ζ = 50%, 90% and 99%) (a). The blue data points of the LSFL rippled area ��SPP are taken from [22] for comparison. Model parameters: F0 = 0.40 J/cm2, τ = 150 fs, λ = 800 nm, w0 = 16.5 μm. In (b), representative scanning electron micrographs for delays up to 2 ps are shown. The LSFL rippled area is marked at Δt = 0.7 ps.

Tables (1)

Tables Icon

Table 1 Material parameters used in numerical simulations of femtosecond laser-irradiated silicon (wavelength λ = 800 nm, pulse duration τ = 150 fs).

Equations (12)

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e [ ε Si * ] < 1
ε Si * ( N e ) = ε Si ω p 2 ( N e ) ω 2 ( 1 + i ν ω ) ,
r j , k = r j , j + 1 + r j + 1 , k e 2 i ϕ j + 1 1 + r j , j + 1 r j + 1 , k e 2 i ϕ j + 1 ,
N e t = ( k B T e μ e N e ) + G e R e .
d I d z = ( σ 1 I + σ 2 I 2 ) .
I 0 ( t ) = F 0 τ 4 ln 2 π [ e 1 2 ( t t 1 σ τ ) 2 + e 1 2 ( t t 2 σ τ ) 2 ] .
C e T e t = ( κ e T e ) γ ( T e T Si ) + Q e ,
C Si T Si t = ( κ Si T Si ) + γ ( T e T Si ) .
r ( F ) = w 0 1 2 ln ( F 0 F )
N e t max ( r ( F ) , Δ t ) = N t h S P P
N t h S P P = m e * ε 0 ( e [ ε Si ] + 1 ) e 2 ( ω 2 + ν 2 )
𝒜 S P P ( Δ t ) = π r S P P 2 ( Δ t ) .

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