Abstract

An experimental setup is presented to measure and interpret the solid phase crystallization of amorphous silicon thin films on glass at very high temperatures of about 800°C. Molybdenum-SiO2-silicon film stacks were irradiated by a diode laser with a well-shaped top hat profile. From the relevant thermal and optical parameters of the system the temperature evolution can be calculated accurately. A time evolution of the laser power was applied which leads to a temperature constant in time in the center of the sample. Such a process will allow the observation and interpretation of solid phase crystallization in terms of nucleation and growth in further work.

© 2013 OSA

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2012 (3)

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express20(S6), A856–A863 (2012).
[CrossRef]

2011 (1)

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

2010 (1)

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

2008 (2)

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5(10), 3221–3228 (2008).
[CrossRef]

2006 (2)

D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett.27(7), 564–566 (2006).
[CrossRef]

A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth287(2), 386–390 (2006).
[CrossRef]

2004 (1)

A. Matsuda, “Microcrystalline silicon. Growth and device application,” J. Non-Cryst. Solids338-340, 1–12 (2004).
[CrossRef]

2002 (2)

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells72(1-4), 551–558 (2002).
[CrossRef]

1998 (1)

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998).
[CrossRef]

1997 (1)

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997).
[CrossRef]

1994 (1)

T. Chaki, “Solid-phase-epitaxy – Effects of irradiation, dopant, and pressure,” Phys. Status Solidi A142(1), 153–166 (1994).
[CrossRef]

1989 (1)

S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci.36(1-4), 1–11 (1989).
[CrossRef]

1988 (1)

G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep.3(1), 1–77 (1988).
[CrossRef]

1983 (1)

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys.16(5), L97–L100 (1983).
[CrossRef]

1978 (1)

U. Köster, “Crystallization of amorphous silicon films,” Phys. Status Solidi A48(2), 313–321 (1978).
[CrossRef]

1967 (1)

1966 (1)

Aberle, A.

A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth287(2), 386–390 (2006).
[CrossRef]

Andrä, G.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express20(S6), A856–A863 (2012).
[CrossRef]

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5(10), 3221–3228 (2008).
[CrossRef]

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

Aoucher, M.

G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells72(1-4), 551–558 (2002).
[CrossRef]

Barnes, B. T.

Becker, C.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

Bergmann, J.

J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express20(S6), A856–A863 (2012).
[CrossRef]

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

Brixner, B.

Chaki, T.

T. Chaki, “Solid-phase-epitaxy – Effects of irradiation, dopant, and pressure,” Phys. Status Solidi A142(1), 153–166 (1994).
[CrossRef]

de Unamuno, S.

S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci.36(1-4), 1–11 (1989).
[CrossRef]

Detavernier, C.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

Egan, R.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Falk, F.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

J. Bergmann, M. Heusinger, G. Andrä, and F. Falk, “Temperature dependent optical properties of amorphous silicon for diode laser crystallization,” Opt. Express20(S6), A856–A863 (2012).
[CrossRef]

G. Andrä and F. Falk, “Multicrystalline silicon films with large grains on glass: preparation and applications,” Phys. Status Solidi C5(10), 3221–3228 (2008).
[CrossRef]

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

Farhi, G.

G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells72(1-4), 551–558 (2002).
[CrossRef]

Fazio, E.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Fisicaro, G.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Fogarassy, E.

S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci.36(1-4), 1–11 (1989).
[CrossRef]

Gawlik, A.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

Grigoropoulos, C.

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997).
[CrossRef]

Heusinger, M.

Hoeger, I.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

Klimm, C.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

Knaepen, W.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

Köster, U.

U. Köster, “Crystallization of amorphous silicon films,” Phys. Status Solidi A48(2), 313–321 (1978).
[CrossRef]

Kunz, O.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

La Magna, A.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Lavoie, C.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

Lombardo, S.

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998).
[CrossRef]

Mannino, G.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Matsuda, A.

A. Matsuda, “Microcrystalline silicon. Growth and device application,” J. Non-Cryst. Solids338-340, 1–12 (2004).
[CrossRef]

Mohammed-Brahim, T.

G. Farhi, M. Aoucher, and T. Mohammed-Brahim, “Study of the solid phase crystallization behavior of amorphous sputtered silicon by X-ray diffraction and electrical measurements,” Sol. Energy Mater. Sol. Cells72(1-4), 551–558 (2002).
[CrossRef]

Neri, F.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Olson, G.

G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep.3(1), 1–77 (1988).
[CrossRef]

Ose, E.

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

Ouyang, Z.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Priolo, F.

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998).
[CrossRef]

Privitera, V.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Rech, B.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

Roth, J.

G. Olson and J. Roth, “Kinetics of solid phase crystallization in amorphous silicon,” Mater. Sci. Rep.3(1), 1–77 (1988).
[CrossRef]

Ruggeri, R.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Scherf, S.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

Schmidt, T.

T. Schmidt, I. Hoeger, A. Gawlik, G. Andrä, and F. Falk, “Solid phase epitaxy of silicon thin films by diode laser irradiation for photovoltaic applications,” Thin Solid Films520(24), 7087–7092 (2012).
[CrossRef]

Sinh, N.

N. Sinh, G. Andrä, F. Falk, E. Ose, and J. Bergmann, “Optimization of layered laser crystallization for thin-film crystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells74(1-4), 295–303 (2002).
[CrossRef]

Soderstrom, T.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Sontheimer, T.

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

Spinella, C.

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998).
[CrossRef]

Sun, Y.

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997).
[CrossRef]

Sweet, J. J.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

Tao, Y.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Toyoda, T.

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys.16(5), L97–L100 (1983).
[CrossRef]

Van Meirhaeghe, R.

W. Knaepen, C. Detavernier, R. Van Meirhaeghe, J. J. Sweet, and C. Lavoie, “In-situ X-ray Diffraction study of Metal Induced Crystallization of amorphous silicon,” Thin Solid Films516(15), 4946–4952 (2008).
[CrossRef]

Varlamov, S.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Wolf, M.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Wong, J.

Y. Tao, S. Varlamov, O. Kunz, Z. Ouyang, J. Wong, T. Soderstrom, M. Wolf, and R. Egan, “Effects of annealing temperature on crystallization kinetics, film properties and cell performance of silicon thin-film solar cells on glass,” Sol. Energy Mater. Sol. Cells101, 186–192 (2012).
[CrossRef]

Wong, M.

D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett.27(7), 564–566 (2006).
[CrossRef]

Yabe, M.

T. Toyoda and M. Yabe, “The temperature dependence of the refractive indices of fused silica and crystal quartz,” J. Phys. D Appl. Phys.16(5), L97–L100 (1983).
[CrossRef]

Zhang, D.

D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett.27(7), 564–566 (2006).
[CrossRef]

Zhang, X.

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

G. Mannino, C. Spinella, R. Ruggeri, A. La Magna, G. Fisicaro, E. Fazio, F. Neri, and V. Privitera, “Crystallization of implanted amorphous silicon during millisecond annealing by infrared laser irradiation,” Appl. Phys. Lett.97(2), 022107 (2010).
[CrossRef]

Appl. Surf. Sci. (1)

S. de Unamuno and E. Fogarassy, “A thermal description of the melting of c-silicon and a-silicon under pulsed excimer lasers,” Appl. Surf. Sci.36(1-4), 1–11 (1989).
[CrossRef]

IEEE Electron Device Lett. (1)

D. Zhang and M. Wong, “Three-mask polycrystalline silicon TFT with metallic gate and junctions,” IEEE Electron Device Lett.27(7), 564–566 (2006).
[CrossRef]

Int. J. Heat Mass Tran. (1)

Y. Sun, X. Zhang, and C. Grigoropoulos, “Spectral optical functions of silicon in the range of 1.13-4.96 eV at elevated temperatures,” Int. J. Heat Mass Tran.40(7), 1591–1600 (1997).
[CrossRef]

J. Appl. Phys (1)

T. Sontheimer, S. Scherf, C. Klimm, C. Becker, and B. Rech, “Characterization and control of crystal nucleation in amorphous electron beam evaporated silicon for thin film solar cells,” J. Appl. Phys. 110, 063530 (2011).

J. Appl. Phys. (1)

C. Spinella, S. Lombardo, and F. Priolo, “Crystal grain nucleation in amorphous silicon,” J. Appl. Phys.84(10), 5383–5414 (1998).
[CrossRef]

J. Cryst. Growth (1)

A. Aberle, “Progress with polycrystalline silicon thin-film solar cells on glass at UNSW,” J. Cryst. Growth287(2), 386–390 (2006).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Scheme of experimental setup for laser crystallization.

Fig. 2
Fig. 2

Layout of the used samples.

Fig. 3
Fig. 3

Measured intensity distribution of the diode laser in the focal plane.

Fig. 4
Fig. 4

Controlling voltage together with laser power output.

Fig. 5
Fig. 5

Typical TRR signal of a sample irradiated with a diode laser for 35 ms. The appropriate calculated temperature is shown in blue. Tmc marks the melting temperature of crystalline silicon whereas tmc stands for time at which the silicon melting was measured.

Fig. 6
Fig. 6

Power for a constant temperature in the center of the sample surface. The power and temperature scale are normalized.

Fig. 7
Fig. 7

TRR signal of a sample irradiated by different power levels following the function shown in Fig. 6. The irradiation starts at 0 s and ends at 1.5 s.

Tables (1)

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Table 1 Optical and thermal parameters used in the simulation. T R =289 K . Tis in K.

Equations (2)

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ρ(T) c p (T) T t =(κ(T)T)
d ρ f (T) c p,f (T) T t t ( κ f (T) t T)= n (κ(T)T)+I

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