- Email: [email protected]
Calculations and experiments of material removal and kinetic energy during pulsed laser ablation of metals
surfacescience ELSEVIER
Applied Surface Science 96-98 ( 1996)61-65
Calculations and experiments of material removal and kinetic energy during pulsed laser ablation of metals Sebastian l%hler lnstitur ftir Metallphysik and So~erforschungsbereich
*, Hans-Ulrich
Krebs
345, Uniuersitiit Gb’ttingen,HospitalstraJe 3-7, 37073 Gijtttingen, Germany
Received 22 May 1995
Abstract Numerical calculations are presented, which describe the processes of target heating and ablation of pure metals (for instance Fe) during irradiation by 30 ns laser pulses at 248 nm. The following effects are taken into account: the absorption of the laser radiation and the heat conduction within the target, the evaporation of material from the target surface, the cooling of the target surface by the heat of evaporation and the partial absorption of the incident laser beam in the evaporated material. As results of the calculations, the temperature profile in the target and the ablated material can be obtained. Furthermore, by energy balance, an energy of the ablated material of up to some 100 eV is obtained. Experiments performed concerning the threshold energy of ablation, the removed mass from the target and the kinetic energy of the deposited ions (by time-of-flight measurements) are in good agreement with the performed calculations.
1. Introduction Many model calculations in the literature describe the target heating during laser annealing [l]. In the case of metals, different mechanisms for the ablation, including the ablation rate and the kinetic energy of the atoms and ions are discussed [2,3]. But often free parameters are used in these models or a significant difference exists to the experimentally observed ablation rates and kinetic energies of the deposited particles [4-61. In this paper, we describe model calculations of the target heating and material removal, which include the absorption of the incident
* Corresponding author.
laser radiation by the ablated material, and compare the calculations with measured ablation rates and experimentally observed kinetic energies of the ablated material and their dependence from the laser energy.
2. Model calculations Because the laser spot size (3 mm X 0.5 mm) on the target surface is much larger than the thermal diffusion length (some pm), a one-dimensional explicit finite element method was used to determine the temperature profile in the target during and after the laser pulse. The time dependence is described by the following thermal conduction equation, including
0169-4332/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0169-4332(95)00466-l
62
S. Fiihler, H.-V. Krebs/Applied
time dependent specific heat sources Q(t) (absorption of the incoming laser radiation) and sinks s(t) (heat of evaporation)
+
Q(t)-s(f),
(1)
with the temperature T, time t, depth n, density p. thermal conductivity k(T) and heat capacity c,(T). In this model, the ablation mechanism is simply described as thermal evaporation from a hot surface (e.g. [2]). The vapor pressure p,,(T) rapidly increases at temperatures well above the evaporation temperature leading to an evaporated depth z,,(t) according to
with the atomic mass m,, the Boltzmann constant k, and the surface temperature T,. The evaporating material causes a heat sink S, at the surface by cooling the surface by the heat of evaporation q,,(T,) according to as, -=-
at
Wt) at
.P.%“(TS).
The ablated depth is in the same order as the absorption length at 248 nm and, therefore, a significant amount of energy is absorbed in the removed material. Because it is difficult to describe the local and temporal density and temperatures of the ablated atoms, ions and electrons, and because the optical properties are not known precisely, in this paper the absorption in the so-called Knudsen layer [7] is simply described with the same optical properties as the bulk material. The heat source is the incident laser intensity I, reduced by the part of the reflected light. This intensity is partially absorbed in the removed material of thickness z,,(t), while the remaining laser intensity is heating the target, with P(x) being the energy density in the depth x. qx)
= (1 - R) .I. ,-~G~zeJ~). e-a.fi,x.
(4)
(Note that in the case of an incident angle of 45”, the absorption coefficient (Y has to be corrected by a geometric factor of a.1 Then, by calculating the total ablated mass and the total energy absorbed by
Surface Science 96-98 (1996) 61-6S
the ablated material, the average energy per atom can be deduced. In the case of Fe, data for the temperature dependence of k(T) [81as well as analytic expressions for c(T), p,(T) and q,,(T) [9] were available for the crystalline phases and even above the melting point. For the optical properties, only room temperature data were used (reflectivity 51%, absorption coefficient 6.4 . 10’ cm- ’ [lo]). The weak temperature dependence of the density was neglected.
3. Experimental
procedures
All experiments were performed in an UHV system with a base pressure of less than 10m7 mbar. An excimer laser (Lambda Physik LPX 11Oi) with KrF (248 nm, 300 mJ, 30 ns) was used. The laser beam was focused onto a rotating metal target at an incident angle of 45” as earlier described [l 11.In order to determine the ablated mass (in the range of mg/lOOOO shots), the weight of the target was measured before and after irradiation. The kinetic energy of the ions was determined at a distance of 73 cm perpendicular to the target surface by time-offlight (TOF) measurements. At a distance of about 20 cm from the target a fine Ni net was used to strip off the electrons. In the ion multiplier the intense radiation of the plume was also detected and used as the starting signal. The ion current was measured with a storage oscilloscope connected to a PC to analyze the data.
4. Results The calculated temperature profiles in the target obtained for iron are depicted in Fig. 1. At energy densities below the threshold energy for ablation (e.g. 2 J/cm2), the temperature increases during the laser pulse continuously up to 4000 K. At this temperature, the vapor pressure is not high enough to remove a significant amount of material. Significant ablation of material starts at a surface temperatures of about 5000 K, reached at a laser fluence of 4 J/cm’. Then, the evaporation of material cools the surface and the removed material is shielding the surface from the laser beam so that the surface
S. Fiihler, H.-U. Krebs/Applwd
Surface Science 96-98
63
(19961614S
20 z 2 g
1612-
Y 0 ,i’ Oy’
Model .o. -z
4 J/cm2
B
E f?!
8m
0
a
/Y
.oo
Experiment
4-
4
2
Laser Fluence (J/cm2)
Fig. 3. Calculated ablation rate for Fe in dependence of the laser fluence. For comparison, measured values of stainless steel are shown.
Depth
(elm)
Fig. 1. Calculated temperature profiles in the Fe target during irradiation by 30 ns laser pulses at 248 nm with different laser fluences.
temperature does not further increases. At an energy density of 8 J/cm* the surface temperature reaches 6000 K within about 5 ns and cools down again to about 4000 K already during the pulse, due to the absorption of the incoming laser intensity by the
&
6000
End of Pulse
t
evaporated material (see Fig. 2). For the same reason, the ablation rate is limited at higher laser fluences. By neglecting the absorption in the evaporated material, much higher surface temperatures occur causing an ablation rate that is about one order higher than the experimentally observed values. In Fig. 3 the ablation rate of Fe obtained by the model is compared with the measured ablation rate of stainless steel. The threshold energy as well as the absolute rate are in good agreement. The difference in the curvature is probably caused by the simplification of the absorption by the evaporated material and the neglection of plasma effects. The energy absorbed in the plasma is not wasted, because it leads to the plasma formation and high kinetic energy of the deposited particles. In order to measure the kinetic energy of the ions, modified Maxwell-Boltzmann velocity distributions of the type, .Gz)aG.exP
i
OO
10
20 Time (ik!)
40
50
Fig. 2. Time dependence of the calculated surface temperatures at different laser fluences. At high fluences the absorption in the evaporated material causes a temperature maximum.
%+Jz-%)’ 2,k .T B
(5) eff
i
were fitted to the TOF-measurements (Fig. 41, with the velocity uz calculated from the arrival time, the effective temperature T,.,, and the average velocity u cm. It was assumed that the ions are single charged and of unit atomic mass, as has been found in other studies 1121. As shown in Fig. 5, the calculated average energy per atom is comparable with the measured kinetic energy of the ions. Model and
S. Fiihler, H.-U. Krebs/Applied Surface Science 96-98 (1996) 61-65
order of magnitude higher and kinetic energies significant less than in our experiments. The same discrepancy is found for the ablation of Cu by Lunney and coworkers [12,13].
10 J/cm2 9 J/cm2 ii;?
\ 8 J/cm2 5. Conclusions
I Fig. 4. Time-of-flight spectra of Fe taken at 73 cm distance from the target at different laser fluences.
experiment both show an almost linear increase of the energy with the laser fluence up to more than 100 eV. Also, the absolute values of the curves are very similar. But, it should be noted that the described energy balance does not give any information about the mechanism, how the energy in the plasma is converted into kinetic energy of the deposited particles. Often the pulsed laser deposition (PLD) is compared with the scaling model of Phipps et al. [4] describing the absorption mechanism in the plasma by inverse bremsstrahlung. But, as Phipps pointed out, this model is only valid at much higher intensities. At the low intensities commonly used for PLD, the model of Phipps predicts ablation rates about one 200
From our calculations for ns ablation it can be concluded that, unlike fs laser pulses, the thermal conduction and the absorption in the plasma cannot be neglected. On the other hand, the process is not only controlled by the plasma as with p,s and longer laser pulses. As we have shown, the ablation of metals by ns UV laser pulses can be described by our model in good agreement with respect to the threshold energy, the ablation rate and the kinetic energy. At this, the primary process of laser ablation, which certainly includes athermal processes due to the high heating rate of the target during the pulse, was simply described as a thermal evaporation. But, due to the high instantaneous ablation rate, a Knudsen layer is formed [7] causing a much stronger forward peaking [ 141. Additionally, the absorption in the dense plasma leads to non-thermal high kinetic energies of the ions of up to a few 100 eV. These secondary processes hide the original evaporation processes and cause the special structural properties of the pulsed laser deposited metallic films described in 1151.
References Fe 0
0
.u z .E Y
0
50-
3
h
ma
Experiment
6I,
81,
0 ‘0
0 P 2 8.
4I.
101
Energy Density (Jlcm2) Fig. 5. The calculated average energy per ablated atom and the measured average kinetic energy of the ions (Fe). versus the laser fluence.
[l] M. van Allmen, Laser Beam Interactions (Springer, Berlin, 1987). [2] R. Kelly and J.E. Rothenberg, Nucl. Instr. Meth. Phys. Res. B 7/S (1985) 755. [3] R. Kelly, A. Miotello, B. Baren, A. Gupta and K. Casey, Nucl. Instr. Meth. Phys. Res. B 65 (1992) 197. [4] C.R. Phipps, T.P. Turner, R.F. Harrison, G.W. York, W.Z. Osborne, G.K. Anderson, X.F. Corlis, L.C. Haynes, H.S. Steele, K.C. Spicochi and T.R. King, J. Appl. Phys. 64 (1988) 1083. [5] R.K. Singh and J. Narayan, Phys. Rev. B 41 (1990) 3174. [6] A. Kar and I. Mazumder, Phys. Rev. E 49 (1994) 410. [7] R. Kelly and R.W. Dreyfus, Nucl. Instr. Meth. Phys. Res. B 32 (1988) 341. [8] Y.S. Touloukian, Ed., Thermophysical properties of Matter, Vol. 1 (Plenum, New York, 1970) p. 169.
S. Fiihler, H.-O; Krebu/Applied Surface Science 96-98 (1996161-65 [9] 0. Knacke, 0. Kubaschewski and K. Hesselmann, Eds., Thermochemical Properties of Inorganic Substances. 2nd ed. (Springer, Berlin, 1991) p. 664. [lo] K.-H. Hellwege and 0. Mandelung, Eds., Landolt-BSmstein, Neue Setie III 15b (1985) p. 223 and p. 252. [ll] H.U. Krebs and 0. Bremert, Appl. Phys. Len. 62 (1993) 2341.
65
1121 R. Jordan, C. Cole, J.G. Lunney, K. Mackay and D. Givord, Appl. Surf. Sci. 86 (1995) 24. [13] J.G. Lunney, Appl. Surf. Sci. 86 (1995) 79. ]14] H.U. Krebs, S. El-tier and 0. Bremert, Appl. Surf. Sci. 86 (19951 86. 1151 M. StGrmer and H.U. Krebs, _I.Appl. Phys. 76 (1995) 7080.
Applied Surface Science 96-98 ( 1996)61-65
Calculations and experiments of material removal and kinetic energy during pulsed laser ablation of metals Sebastian l%hler lnstitur ftir Metallphysik and So~erforschungsbereich
*, Hans-Ulrich
Krebs
345, Uniuersitiit Gb’ttingen,HospitalstraJe 3-7, 37073 Gijtttingen, Germany
Received 22 May 1995
Abstract Numerical calculations are presented, which describe the processes of target heating and ablation of pure metals (for instance Fe) during irradiation by 30 ns laser pulses at 248 nm. The following effects are taken into account: the absorption of the laser radiation and the heat conduction within the target, the evaporation of material from the target surface, the cooling of the target surface by the heat of evaporation and the partial absorption of the incident laser beam in the evaporated material. As results of the calculations, the temperature profile in the target and the ablated material can be obtained. Furthermore, by energy balance, an energy of the ablated material of up to some 100 eV is obtained. Experiments performed concerning the threshold energy of ablation, the removed mass from the target and the kinetic energy of the deposited ions (by time-of-flight measurements) are in good agreement with the performed calculations.
1. Introduction Many model calculations in the literature describe the target heating during laser annealing [l]. In the case of metals, different mechanisms for the ablation, including the ablation rate and the kinetic energy of the atoms and ions are discussed [2,3]. But often free parameters are used in these models or a significant difference exists to the experimentally observed ablation rates and kinetic energies of the deposited particles [4-61. In this paper, we describe model calculations of the target heating and material removal, which include the absorption of the incident
* Corresponding author.
laser radiation by the ablated material, and compare the calculations with measured ablation rates and experimentally observed kinetic energies of the ablated material and their dependence from the laser energy.
2. Model calculations Because the laser spot size (3 mm X 0.5 mm) on the target surface is much larger than the thermal diffusion length (some pm), a one-dimensional explicit finite element method was used to determine the temperature profile in the target during and after the laser pulse. The time dependence is described by the following thermal conduction equation, including
0169-4332/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI 0169-4332(95)00466-l
62
S. Fiihler, H.-V. Krebs/Applied
time dependent specific heat sources Q(t) (absorption of the incoming laser radiation) and sinks s(t) (heat of evaporation)
+
Q(t)-s(f),
(1)
with the temperature T, time t, depth n, density p. thermal conductivity k(T) and heat capacity c,(T). In this model, the ablation mechanism is simply described as thermal evaporation from a hot surface (e.g. [2]). The vapor pressure p,,(T) rapidly increases at temperatures well above the evaporation temperature leading to an evaporated depth z,,(t) according to
with the atomic mass m,, the Boltzmann constant k, and the surface temperature T,. The evaporating material causes a heat sink S, at the surface by cooling the surface by the heat of evaporation q,,(T,) according to as, -=-
at
Wt) at
.P.%“(TS).
The ablated depth is in the same order as the absorption length at 248 nm and, therefore, a significant amount of energy is absorbed in the removed material. Because it is difficult to describe the local and temporal density and temperatures of the ablated atoms, ions and electrons, and because the optical properties are not known precisely, in this paper the absorption in the so-called Knudsen layer [7] is simply described with the same optical properties as the bulk material. The heat source is the incident laser intensity I, reduced by the part of the reflected light. This intensity is partially absorbed in the removed material of thickness z,,(t), while the remaining laser intensity is heating the target, with P(x) being the energy density in the depth x. qx)
= (1 - R) .I. ,-~G~zeJ~). e-a.fi,x.
(4)
(Note that in the case of an incident angle of 45”, the absorption coefficient (Y has to be corrected by a geometric factor of a.1 Then, by calculating the total ablated mass and the total energy absorbed by
Surface Science 96-98 (1996) 61-6S
the ablated material, the average energy per atom can be deduced. In the case of Fe, data for the temperature dependence of k(T) [81as well as analytic expressions for c(T), p,(T) and q,,(T) [9] were available for the crystalline phases and even above the melting point. For the optical properties, only room temperature data were used (reflectivity 51%, absorption coefficient 6.4 . 10’ cm- ’ [lo]). The weak temperature dependence of the density was neglected.
3. Experimental
procedures
All experiments were performed in an UHV system with a base pressure of less than 10m7 mbar. An excimer laser (Lambda Physik LPX 11Oi) with KrF (248 nm, 300 mJ, 30 ns) was used. The laser beam was focused onto a rotating metal target at an incident angle of 45” as earlier described [l 11.In order to determine the ablated mass (in the range of mg/lOOOO shots), the weight of the target was measured before and after irradiation. The kinetic energy of the ions was determined at a distance of 73 cm perpendicular to the target surface by time-offlight (TOF) measurements. At a distance of about 20 cm from the target a fine Ni net was used to strip off the electrons. In the ion multiplier the intense radiation of the plume was also detected and used as the starting signal. The ion current was measured with a storage oscilloscope connected to a PC to analyze the data.
4. Results The calculated temperature profiles in the target obtained for iron are depicted in Fig. 1. At energy densities below the threshold energy for ablation (e.g. 2 J/cm2), the temperature increases during the laser pulse continuously up to 4000 K. At this temperature, the vapor pressure is not high enough to remove a significant amount of material. Significant ablation of material starts at a surface temperatures of about 5000 K, reached at a laser fluence of 4 J/cm’. Then, the evaporation of material cools the surface and the removed material is shielding the surface from the laser beam so that the surface
S. Fiihler, H.-U. Krebs/Applwd
Surface Science 96-98
63
(19961614S
20 z 2 g
1612-
Y 0 ,i’ Oy’
Model .o. -z
4 J/cm2
B
E f?!
8m
0
a
/Y
.oo
Experiment
4-
4
2
Laser Fluence (J/cm2)
Fig. 3. Calculated ablation rate for Fe in dependence of the laser fluence. For comparison, measured values of stainless steel are shown.
Depth
(elm)
Fig. 1. Calculated temperature profiles in the Fe target during irradiation by 30 ns laser pulses at 248 nm with different laser fluences.
temperature does not further increases. At an energy density of 8 J/cm* the surface temperature reaches 6000 K within about 5 ns and cools down again to about 4000 K already during the pulse, due to the absorption of the incoming laser intensity by the
&
6000
End of Pulse
t
evaporated material (see Fig. 2). For the same reason, the ablation rate is limited at higher laser fluences. By neglecting the absorption in the evaporated material, much higher surface temperatures occur causing an ablation rate that is about one order higher than the experimentally observed values. In Fig. 3 the ablation rate of Fe obtained by the model is compared with the measured ablation rate of stainless steel. The threshold energy as well as the absolute rate are in good agreement. The difference in the curvature is probably caused by the simplification of the absorption by the evaporated material and the neglection of plasma effects. The energy absorbed in the plasma is not wasted, because it leads to the plasma formation and high kinetic energy of the deposited particles. In order to measure the kinetic energy of the ions, modified Maxwell-Boltzmann velocity distributions of the type, .Gz)aG.exP
i
OO
10
20 Time (ik!)
40
50
Fig. 2. Time dependence of the calculated surface temperatures at different laser fluences. At high fluences the absorption in the evaporated material causes a temperature maximum.
%+Jz-%)’ 2,k .T B
(5) eff
i
were fitted to the TOF-measurements (Fig. 41, with the velocity uz calculated from the arrival time, the effective temperature T,.,, and the average velocity u cm. It was assumed that the ions are single charged and of unit atomic mass, as has been found in other studies 1121. As shown in Fig. 5, the calculated average energy per atom is comparable with the measured kinetic energy of the ions. Model and
S. Fiihler, H.-U. Krebs/Applied Surface Science 96-98 (1996) 61-65
order of magnitude higher and kinetic energies significant less than in our experiments. The same discrepancy is found for the ablation of Cu by Lunney and coworkers [12,13].
10 J/cm2 9 J/cm2 ii;?
\ 8 J/cm2 5. Conclusions
I Fig. 4. Time-of-flight spectra of Fe taken at 73 cm distance from the target at different laser fluences.
experiment both show an almost linear increase of the energy with the laser fluence up to more than 100 eV. Also, the absolute values of the curves are very similar. But, it should be noted that the described energy balance does not give any information about the mechanism, how the energy in the plasma is converted into kinetic energy of the deposited particles. Often the pulsed laser deposition (PLD) is compared with the scaling model of Phipps et al. [4] describing the absorption mechanism in the plasma by inverse bremsstrahlung. But, as Phipps pointed out, this model is only valid at much higher intensities. At the low intensities commonly used for PLD, the model of Phipps predicts ablation rates about one 200
From our calculations for ns ablation it can be concluded that, unlike fs laser pulses, the thermal conduction and the absorption in the plasma cannot be neglected. On the other hand, the process is not only controlled by the plasma as with p,s and longer laser pulses. As we have shown, the ablation of metals by ns UV laser pulses can be described by our model in good agreement with respect to the threshold energy, the ablation rate and the kinetic energy. At this, the primary process of laser ablation, which certainly includes athermal processes due to the high heating rate of the target during the pulse, was simply described as a thermal evaporation. But, due to the high instantaneous ablation rate, a Knudsen layer is formed [7] causing a much stronger forward peaking [ 141. Additionally, the absorption in the dense plasma leads to non-thermal high kinetic energies of the ions of up to a few 100 eV. These secondary processes hide the original evaporation processes and cause the special structural properties of the pulsed laser deposited metallic films described in 1151.
References Fe 0
0
.u z .E Y
0
50-
3
h
ma
Experiment
6I,
81,
0 ‘0
0 P 2 8.
4I.
101
Energy Density (Jlcm2) Fig. 5. The calculated average energy per ablated atom and the measured average kinetic energy of the ions (Fe). versus the laser fluence.
[l] M. van Allmen, Laser Beam Interactions (Springer, Berlin, 1987). [2] R. Kelly and J.E. Rothenberg, Nucl. Instr. Meth. Phys. Res. B 7/S (1985) 755. [3] R. Kelly, A. Miotello, B. Baren, A. Gupta and K. Casey, Nucl. Instr. Meth. Phys. Res. B 65 (1992) 197. [4] C.R. Phipps, T.P. Turner, R.F. Harrison, G.W. York, W.Z. Osborne, G.K. Anderson, X.F. Corlis, L.C. Haynes, H.S. Steele, K.C. Spicochi and T.R. King, J. Appl. Phys. 64 (1988) 1083. [5] R.K. Singh and J. Narayan, Phys. Rev. B 41 (1990) 3174. [6] A. Kar and I. Mazumder, Phys. Rev. E 49 (1994) 410. [7] R. Kelly and R.W. Dreyfus, Nucl. Instr. Meth. Phys. Res. B 32 (1988) 341. [8] Y.S. Touloukian, Ed., Thermophysical properties of Matter, Vol. 1 (Plenum, New York, 1970) p. 169.
S. Fiihler, H.-O; Krebu/Applied Surface Science 96-98 (1996161-65 [9] 0. Knacke, 0. Kubaschewski and K. Hesselmann, Eds., Thermochemical Properties of Inorganic Substances. 2nd ed. (Springer, Berlin, 1991) p. 664. [lo] K.-H. Hellwege and 0. Mandelung, Eds., Landolt-BSmstein, Neue Setie III 15b (1985) p. 223 and p. 252. [ll] H.U. Krebs and 0. Bremert, Appl. Phys. Len. 62 (1993) 2341.
65
1121 R. Jordan, C. Cole, J.G. Lunney, K. Mackay and D. Givord, Appl. Surf. Sci. 86 (1995) 24. [13] J.G. Lunney, Appl. Surf. Sci. 86 (1995) 79. ]14] H.U. Krebs, S. El-tier and 0. Bremert, Appl. Surf. Sci. 86 (19951 86. 1151 M. StGrmer and H.U. Krebs, _I.Appl. Phys. 76 (1995) 7080.