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An effective focusing setting in femtosecond laser multiple pulse ablation
Optics & Laser Technology 54 (2013) 30–34
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Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
An effective focusing setting in femtosecond laser multiple pulse ablation Gang Chang, Yiliu Tu n Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4
art ic l e i nf o
a b s t r a c t
Article history: Received 20 July 2012 Received in revised form 23 January 2013 Accepted 17 April 2013 Available online 30 May 2013
Most of reported works on laser micro-machining have been carried out under ‘tight-focusing’ arrangement. However, defocusing has to be considered when dealing with depth evolution in multiple pulse ablation. In this paper, we show that laser intensity distribution is very sensitive to defocusing and, in multiple pulse ablation, defocusing is unavoidable even under the ‘tight focusing’. Both theoretic analysis and experimental result indicate that convergent defocusing is a better option for some micromachining purposes. The optimal defocusing arrangement not only results in a maximum material removal rate (MRR) and maximum depth evolution, but also prevents harmful heat damage caused by extreme high intensity at the focal center. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Ultrafast pulse laser micro-machining Material removal rate (MRR) Defocusing
1. Introduction The conventional optical arrangement used in laser ablation process is ‘tight-focusing’ method [1], i.e., laser beam is focused on target surface. Most of the researchers [2,3] believe that crater depth of the single pulse ablation has a square–logarithm relationship with laser intensity. ‘Tight focusing’ is one of the common ways to enhance laser intensity. The diameter of the crater, which determines the resolution of machining result, also has similar square–logarithm relationship with laser pulse energy [4]. Under ‘tight focusing’ arrangement, the laser intensity at center of focal spot is the highest while the diameter of the focal spot is the smallest. Matsumura et al. [5] have analyzed the laser deep drilling process and showed that the laser power is not the only parameter involved. In a hole drilling process, the final depth and shape of the hole after ablation are also affected by beam diameter, penetration coefficient of the target material, total number of pulses and the parameters of the optical delivery system, etc. For a focal laser delivery system, the defocusing is a crucial factor, not only because laser intensity is prominently affected by the focusing, but also because multiple pulse ablation introduces defocusing into laser machining process even under the initial ‘tightfocusing’ arrangement. The laser intensity profile, shown in Fig. 1, changes after the ablation. For example, in a laser drilling process, the surface is modified by laser ablation and, as a consequence, laser intensity distribution is deviated from its initial distribution under ‘tight-focusing’ situation. Another concern about the
n
Corresponding author. Tel.: +1 403 220 4142; fax: +1 403 282 8406. E-mail address: [email protected] (Y. Tu).
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.04.025
defocusing is that the ‘tight focusing’ arrangement is not spontaneously the optimal focal arrangement for all laser machining purposes [6,7]. The laser milling process [8] is a good example, in which the ablation efficiency is associated with the total material removal rate (MRR) instead of the depth increment at individual point. Ablation under suitable defocusing has a higher total MRR than that under the ‘tight-focusing’. In the following section, a theoretic analysis shows that, based on the purpose of the machining, an optional focal position other than the ‘tight focusing’ results in higher MRR, deeper hole or more uniformly surface. The inference is verified by simulation and experimental results.
2. Theory The theory is based on two basic assumptions. The first one is that the laser used is a Gaussian laser beam TEM00 [9,10]. The intensity (I) under focusing situation, as shown in Fig. 2, can be expressed as Iðρ; zÞ ¼
2 2 E e−ρ =2ωðzÞ 2πω2ðzÞ
In which, the beam radius ωðzÞ follows: ! z2 z2 λ2 ω2ðzÞ ¼ ω20 n 1 þ 2 ¼ ω20 þ 2 2 zr π ω0
ð1Þ
ð2Þ
where z is the defocusing distance alone beam incident direction; ρ is the polar distance from beam axis (Z-axis). The origin of coordinates is at the focal center; E is the fluence of the laser
G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
pulse; λ is the wavelength of laser; and ω0 and zr ¼ πω20 =λ are Gaussian beam waist and Rayleigh length separately [9]. The second assumption is about ablation development on z direction or depth of the crater caused by laser ablation which, similar as the penetrate depth, has an exponential relationship with laser intensity ! I E κρ2 Δz ¼ κ ln ð3Þ ¼ κ ln − 2 I th 2πω2ðzÞ I th 2ωðzÞ Here, Ith is ablation threshold intensity and κ is a material parameter which is related with crater depth in the ablation. From Eq. (3), it is clear that laser ablation is limited in a range in which the laser intensity is larger than the ablation threshold intensity. The laser affected volume [11], as shown in Fig. 3, is defined as the volume in which laser intensity is over the ablation threshold intensity (Ith). ρboundary is used to represent the boundary of laser affected volume where laser intensity equals to Ith ! E 2 2 ρboundary ¼ 2ωðzÞ ln ð4Þ 2πω2ðzÞ I th At the top of the laser affected volume, where ρboundary ¼ 0, z is denoted as ztop 2πω2ðztop Þ I th ¼ E
the objective lens of the optical system ω2ðz Þ ω2ðf Þ ω2ðzÞ ω20 ¼ 2 ¼ 2 ¼ 2 top 2 2 2 zr z þ zr ztop þ zr f þ z2r
ð6Þ
To simply equations, we define ζ¼
z2top þ z2r z2 þ z2r
¼
ω2ðztop Þ ω2ðzÞ
¼
E 2πω2ðzÞ I th
Eq. (3) is changed as ! I E κρ2 κρ2 ζ Δz ¼ κ ln ¼ κ ln − 2 ¼ κ ln ζ− 2 I th 2πω2ðzÞ I th 2ωðztop Þ 2ωðzÞ
ð7Þ
And radius of the laser affected volume ρboundary is expressed as ρ2boundary ¼
2ω2ðztop Þ ζ
ln ζ
ð8Þ
The material removal rate (MRR) is the integral of depth ðΔzÞ over the crater and it is expressed as Z ρboundary Δz2πρ dρ MRR ¼ 0
"
¼ κπ ρ2 ln ζ−
ð5Þ
According to the definition of ωðzÞ in Eq. (2), the following equation presents the relationship between ω and z, especially at focal center ðz ¼ 0Þ, objective lens plane ðz ¼ f Þ and the peak point of the laser affected volume ðz ¼ ztop Þ. Here f is the focal distance of
31
¼
κπω2ðztop Þ ζ
ρ4 ζ 4ω2ðztop Þ
#ρboundary 0
ðln ζÞ2
ð9Þ
The maximum MRR appears at where dðMRRÞ=dz ¼ 0 or dðMRRÞ=dζ ¼ 0. It is where ln ζ ¼ 2 or ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e2 . Let us compare it with the position where ρboundary has its maximum value, i.e. ln ζ ¼ 1 or ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e.
Fig. 1. The laser intensity distribution changes after every pulse.
Fig. 2. Defocusing arrangement.
Fig. 3. Laser affected volume.
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G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
Average MRR over the crater or MRR ¼
MRR MRR κ ¼ 2 ¼ ln ζ Area of crater 2 πρboundary
ð10Þ
So MRR ¼ κ at where MRR gets to its maximum value. At the focal center where z ¼0 ζ¼
z2top þ z2r z2r
¼
z2top z2r
ρ2boundary ¼ 2ω20 ln "
þ1¼
ω2ðztop Þ ω20
ω2ðztop Þ ω20
ω2ðztop Þ
ð12Þ
#2
MRR ¼
κπω20
MRR ¼
" # ω2ðztop Þ MRR κ κ ln ¼ ¼ ln ζ 2 2 πρ2boundary ω20
ln
ð11Þ
ω20
ð13Þ
ð14Þ
In the center of the focal point, Δz ¼ κ lnðE=2πω20 I th Þ ¼ κ ln ζ. Above analysis leads to several interesting conclusions about single pulse ablation. (A) The depth increment Δz, diameter of the crater and MRR of each pulse are affected by defocusing position. In a deep hole drilling process, the largest Δz appears at the ‘tight focusing’ point (focal center) and the crater diameter is the minimum. However, the total MRR is the minimum. (B) Optimal focal position is associated with the purpose of the machining. The maximum total MRR under a fixed laser power appears at where ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e2 . It is the optimal focal position for milling and grooving processes to achieve the highest machining efficiency. The maximum crater diameter appears when ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e. The special advantage of this position is the mildest intensity deviation between center and boundary. So that when higher laser power is set to save the processing time of milling or grooving, the laser intensity on Z axis keeps only e times of the ablation threshold intensity. It is useful to ensure machining quality since it avoid the harmful extra heat damage. (C) In most cases, z⪢zr , the focal position of the maximum MRR and the maximum diameter are at 0:37ztop and 0:61ztop , respectively.
3. Simulation for multiple pulses ablation The laser machining process always involves multiple pulse ablation. As mentioned in the Introduction section, it will induce the defocusing in the process. (A) Simulation result, according to Eqs. (1), (3) and (7), can provide the detail of depth evolution under the different focusing arrangements. Fig. 4 shows the simulation results of the deep drilling process. The depth increment of single pulse under ‘tight focusing’ arrangement drops due to the defocusing which indicates the machining efficiency decreases and more energy of the laser is converted to heat directly rather than contributed to ablation. Two typical focal positions are convergent defocusing and divergent defocusing. The result in Fig. 4 also shows that the depth increment of each pulse under the convergent defocusing situation increases gradually to its maximum when the modified surface falls into focal zone. (B) There is a limit for the final depth evolution. It is not surprise to find that the final depth after numerous pulses, as shown in Fig. 5, is associated with the focusing position and the size of the laser affected volume. Compared with the results of
Fig. 4. Depth increment per pulse is changed by the defocusing situation. The maximum value appears at the ‘tight focusing’ position.
Fig. 5. Final relative hole depth depends on the initial defocusing position. The maximum depth is not at the ‘tight focusing’ position but on the convergent side.
defocusing arrangement, the diameter of the hole under ‘tight focusing’ arrangement is the smallest but final depth of the hole is not the deepest. Under defocusing arrangement, the diameter of the hole is enlarged to its maximum on both convergent side and divergent side. (C) In term of total MRR, the optimal focal position appears on the convergent side. The maximum MRR means the highest ablation efficiency and the highest percentage of the ablation energy converting rate. Though the depth increment of a single pulse is less than that under ‘tight-focusing’ arrangement, the total MRR over the whole process and the final depth are maximized. According to Eq. (9), if the ablation is in the open environment, such as in milling or grooving, the optimal focusing arrangement is at where ζ ¼ ðz2top þ z2r Þ=ðz2 þ Z 2r Þ ¼ e2 . In practice, the part of the beam may be blocked when the hole goes deeper. The plasma plume developed in the deeper hole introduces stronger ‘selffocusing’ effect than that in open space. Since the effects of these two factors are opposite, the optimal defocusing distance is not far from the position. Above simulation does not include the effect of debris which re-deposits on the new modified surface. Though some authors claim that ultrashort pulse laser ablation is a ‘debris free’ process
G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
[12], there are evidences that the removed particles under the intensive laser power will coat on the surface [13] and change the profile of the new surface [14]. The threshold intensity differs with or without debris [15]. In practice, compressed gas, water jet and special coating [16,17] have been used to remove debris from surface. Since the mild power laser focused above the surface can be used to clean debris [18], the optional defocusing arrangement, which limits the maximum intensity under e times of Ith, is a good option to avoid the accumulation of debris.
4. Experiment The ultra short pulse laser system used in this paper is Ti: Sapphire Libra-S femtosecond laser from Coherent Ltd. The pulse duration of the laser is 100 fs at 1 KHz repetition rate. The wavelength is 800 710 nm. The objective lenses are Mitutoyo Ltd's Apo NiR series. The measurement instruments used in experiment include a scanning electronic microscope (SEM) Phillips XL30 ESEM, a laser power meter, (Newport 2935-c) and an optical microscopy. The experimental ablation samples are silicon chip and bulk aluminum. First group of experiments is drilling series of holes along a line under different defocusing conditions, using the 10 objective lens which focal length is 20 mm. The pulse energy is 30 μJ. The process time of each hole is fixed at 5 s which is 5000 shots. The sample is a silicon chip with 250 μm thickness. After ablation, the chip is broken along the drilling line to exposure the holes so that depth of holes can be measured. Second group of the experiments is to compare results of grooving under different focusing conditions. Three typical defocusing positions are chosen, i.e. ‘tight focusing’, convergent side and divergent side. The pulse energy is fixed on 30 μJ for both silicon and aluminum samples. The groove ablation is under fixed scanning speed. Not only the depth but also the profiles of the groove are measured. The average MRR of total grooving process is calculated and the average MRR of the first 20 scanning circles is used as initial MRR, as shown in Fig. 6. The laser used in experiment is low repetition rate (1 KHz). With heat accumulation effect, according to the Gamaly [15], high repetition rate (5 MHz) radiation will lower ablation threshold intensity Ith. The plasma may block and interact with the following pulses. Therefore, the theory as verified at 1 kHz repetition rate in this paper cannot be indisputably applied in the case of high repetition rate, e.g. at MHz level. Further experiment is necessary to extend the conclusion to the high repetition rate laser.
Fig. 6. Material removal rate is affected by the defocusing. Both convergent and divergent side have the maximum initial MRR while only the convergent side has the maximum average MRR over the whole machining process.
33
5. Conclusion and discussion (A) For the so-called ‘cold ablation’ [19] such as ultra-short laser ablation [13], large portion of the laser energy should contribute to ablation without causing significant temperature rising outside of the target area. The simulation and experimental results demonstrate the fact that the ‘tight focusing’ arrangement is not the optimal setting in all multiple pulses ablation. The shortcoming of the ‘tight-focusing’ arrangement is that laser intensity at the spot center is much higher than that on the edge of the spot. When the laser energy increases, the intensity at the center of the spot can be tremendously higher than the threshold intensity. Eq. (7) suggests that the higher the intensity is, the more portion of the energy is directly converted to the heat. Cavalleri et al. [20] have showed that there are several different damage stages under different laser intensities, from phase change to lattice disassembly, and melting eventually. The large intensity deviation inside of the spot will cause mixed changes in the crater. Under the defocusing arrangement, the discrepancy of the intensity is moderate so that the damage is at same stage. For example, at the defocusing position where the maximum diameter happens, the intensity at center is only e times higher than threshold intensity. The intensity uniformity inside of the spot is the warranty of the ablation quality. Taking advantage of this feature, the laser power can be set higher to save machining time. It is especially useful in milling or grooving. For the 10 lens used in the experiment, Rayleigh length zr is 3:2 μm while the final depth can easily go up to several hundred microns, close to ztop. The defocusing is unavoidable after z≥zr . Therefore, even if the initial ‘tight focusing’ is used during the micro-machining process, it is still not rare that the laser works at the defocusing position. ζ is very sensitive with z near the focal center. For example when ztop ¼ 100 μm, ζ ¼ 978 where z ¼0 while ζ ¼ 489 where z ¼ zr ¼ 3:2 μm. The optimal defocusing position is at 0:37ztop which is much larger than zr. Comparing with the ‘tightfocusing’ situation, the laser intensity under defocusing is not very sensitive to the change of z. (B) Instead of using the ‘tight focusing’ arrangement, the defocusing on convergent side can achieve the highest MRR and deepest final depth evolution. The result in Fig. 7 suggests that the optimal focal arrangement should be chosen according to the machining purpose. If the maximum depth is the purpose and the laser power is fixed, the optimal focal position is the defocusing position on the convergent side. If the shortest machining time is the purpose and laser power can be higher, such as in the milling
Fig. 7. Experimental result and simulation. The left is groove under the divergent defocusing arrangement and the right one is that under the convergent defocusing arrangement. The depth of latter is 50% deeper than that under ‘tight-focusing’ condition.
34
G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
process, the maximum diameter position with the highest laser power is the best option. In either case, the optimal defocusing distance is proportional to the square root of the laser energy. 6. Summary Defocusing is a crucial factor in the laser micro-machining because the laser intensity can be disturbed tremendously by the defocusing. The optimal focal arrangement should be chosen according to the machining purpose. Both theoretic analysis and experimental result demonstrate that the defocusing arrangement has profound advantages over the conventional ‘tight focusing’ arrangement in multiple pulse ablation process. To achieve higher material removal rate (MRR), which means higher efficiency in grooving process, defocusing on the convergent side is the optimal. The final depth in this way is greater than that under ‘tight-focusing’ arrangement. The machining precision is affected by defocusing, too. Acknowledgments It is hereby to acknowledge the financial support of the project from Canada Foundation for Innovation (CFI).
References [1] Herbstman JF, Hunt AJ, Yalisove SM. Applied Physics Letters 2008;93:011112. [2] Nolte S, Momma C, Jacobs H, Tünnermann A, Chichkov BN, Wellegehausen B, et al. Journal of the Optical Society of America B 1997;14:2716–22. [3] Ma S, McDonald J, Tryon B, Yalisove S, Pollock T. Metallurgical and Materials Transactions A 2007;38:2349–57. [4] Liu JM. Optics Letters 1982;7:196–8. [5] Matsumura T, Nakatani T, Yagi T. Applied Physics A 2007;86:107–14. [6] Wang W, Mei X, Jiang G, Lei S, Yang C. Applied Surface Science 2008;255:2303–11. [7] Nath A, Laha S, Khare A. Applied Surface Science 2011;257:3118–22. [8] Tsai C-H, Chen H-W. Journal of Materials Processing Technology 2003;136: 158–65. [9] Karimi E, Zito G, Piccirillo B, Marrucci L, Santamato E. Optics Letters 2007;32: 3053–5. [10] Ng T, Tan H, Foo S. Optics & Laser Technology 2007;39:1098–100. [11] Chang G, Tu Y. Optics and Lasers in Engineering 2012;50:767–71. [12] Guo X, Li R, Hang Y, Xu Z, Yu B, Dai Y, et al. Applied Physics A 2009;94:423–6. [13] Singh AP, Kapoor A, Tripathi K, Kumar G. Optics & Laser Technology 2002;34: 37–43. [14] Semaltianos N, Perrie W, Vishnyakov V, Murray R, Williams C, Edwardson S, et al. Materials Letters 2008;62:2165–70. [15] Gamaly E. Physics Reports 2011;508:91–243. [16] Perrottet D, Green S, Richerzhagen B. In: The 17th Annual SEMI/IEEE advanced semiconductor manufacturing conference, 2006. ASMC 2006, p. 233–6. [17] Shin DS, Lee JH, Suh J, Kim TH. Materials Science and Engineering: A 2006;416:205–10. [18] Kim T, Lee J, Cho S, Kim T. Optics and Lasers in Engineering 2005;43:1010–20. [19] Nowak K, Baker H, Hall D. Applied Physics A 2006;84:267–70. [20] Cavalleri A, Sokolowski-Tinten K, Bialkowski J, Schreiner M, von der Linde D. Journal of Applied Physics 1999;85:3301–9.
Contents lists available at SciVerse ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
An effective focusing setting in femtosecond laser multiple pulse ablation Gang Chang, Yiliu Tu n Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Dr. NW, Calgary, Alberta, Canada T2N 1N4
art ic l e i nf o
a b s t r a c t
Article history: Received 20 July 2012 Received in revised form 23 January 2013 Accepted 17 April 2013 Available online 30 May 2013
Most of reported works on laser micro-machining have been carried out under ‘tight-focusing’ arrangement. However, defocusing has to be considered when dealing with depth evolution in multiple pulse ablation. In this paper, we show that laser intensity distribution is very sensitive to defocusing and, in multiple pulse ablation, defocusing is unavoidable even under the ‘tight focusing’. Both theoretic analysis and experimental result indicate that convergent defocusing is a better option for some micromachining purposes. The optimal defocusing arrangement not only results in a maximum material removal rate (MRR) and maximum depth evolution, but also prevents harmful heat damage caused by extreme high intensity at the focal center. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Ultrafast pulse laser micro-machining Material removal rate (MRR) Defocusing
1. Introduction The conventional optical arrangement used in laser ablation process is ‘tight-focusing’ method [1], i.e., laser beam is focused on target surface. Most of the researchers [2,3] believe that crater depth of the single pulse ablation has a square–logarithm relationship with laser intensity. ‘Tight focusing’ is one of the common ways to enhance laser intensity. The diameter of the crater, which determines the resolution of machining result, also has similar square–logarithm relationship with laser pulse energy [4]. Under ‘tight focusing’ arrangement, the laser intensity at center of focal spot is the highest while the diameter of the focal spot is the smallest. Matsumura et al. [5] have analyzed the laser deep drilling process and showed that the laser power is not the only parameter involved. In a hole drilling process, the final depth and shape of the hole after ablation are also affected by beam diameter, penetration coefficient of the target material, total number of pulses and the parameters of the optical delivery system, etc. For a focal laser delivery system, the defocusing is a crucial factor, not only because laser intensity is prominently affected by the focusing, but also because multiple pulse ablation introduces defocusing into laser machining process even under the initial ‘tightfocusing’ arrangement. The laser intensity profile, shown in Fig. 1, changes after the ablation. For example, in a laser drilling process, the surface is modified by laser ablation and, as a consequence, laser intensity distribution is deviated from its initial distribution under ‘tight-focusing’ situation. Another concern about the
n
Corresponding author. Tel.: +1 403 220 4142; fax: +1 403 282 8406. E-mail address: [email protected] (Y. Tu).
0030-3992/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.optlastec.2013.04.025
defocusing is that the ‘tight focusing’ arrangement is not spontaneously the optimal focal arrangement for all laser machining purposes [6,7]. The laser milling process [8] is a good example, in which the ablation efficiency is associated with the total material removal rate (MRR) instead of the depth increment at individual point. Ablation under suitable defocusing has a higher total MRR than that under the ‘tight-focusing’. In the following section, a theoretic analysis shows that, based on the purpose of the machining, an optional focal position other than the ‘tight focusing’ results in higher MRR, deeper hole or more uniformly surface. The inference is verified by simulation and experimental results.
2. Theory The theory is based on two basic assumptions. The first one is that the laser used is a Gaussian laser beam TEM00 [9,10]. The intensity (I) under focusing situation, as shown in Fig. 2, can be expressed as Iðρ; zÞ ¼
2 2 E e−ρ =2ωðzÞ 2πω2ðzÞ
In which, the beam radius ωðzÞ follows: ! z2 z2 λ2 ω2ðzÞ ¼ ω20 n 1 þ 2 ¼ ω20 þ 2 2 zr π ω0
ð1Þ
ð2Þ
where z is the defocusing distance alone beam incident direction; ρ is the polar distance from beam axis (Z-axis). The origin of coordinates is at the focal center; E is the fluence of the laser
G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
pulse; λ is the wavelength of laser; and ω0 and zr ¼ πω20 =λ are Gaussian beam waist and Rayleigh length separately [9]. The second assumption is about ablation development on z direction or depth of the crater caused by laser ablation which, similar as the penetrate depth, has an exponential relationship with laser intensity ! I E κρ2 Δz ¼ κ ln ð3Þ ¼ κ ln − 2 I th 2πω2ðzÞ I th 2ωðzÞ Here, Ith is ablation threshold intensity and κ is a material parameter which is related with crater depth in the ablation. From Eq. (3), it is clear that laser ablation is limited in a range in which the laser intensity is larger than the ablation threshold intensity. The laser affected volume [11], as shown in Fig. 3, is defined as the volume in which laser intensity is over the ablation threshold intensity (Ith). ρboundary is used to represent the boundary of laser affected volume where laser intensity equals to Ith ! E 2 2 ρboundary ¼ 2ωðzÞ ln ð4Þ 2πω2ðzÞ I th At the top of the laser affected volume, where ρboundary ¼ 0, z is denoted as ztop 2πω2ðztop Þ I th ¼ E
the objective lens of the optical system ω2ðz Þ ω2ðf Þ ω2ðzÞ ω20 ¼ 2 ¼ 2 ¼ 2 top 2 2 2 zr z þ zr ztop þ zr f þ z2r
ð6Þ
To simply equations, we define ζ¼
z2top þ z2r z2 þ z2r
¼
ω2ðztop Þ ω2ðzÞ
¼
E 2πω2ðzÞ I th
Eq. (3) is changed as ! I E κρ2 κρ2 ζ Δz ¼ κ ln ¼ κ ln − 2 ¼ κ ln ζ− 2 I th 2πω2ðzÞ I th 2ωðztop Þ 2ωðzÞ
ð7Þ
And radius of the laser affected volume ρboundary is expressed as ρ2boundary ¼
2ω2ðztop Þ ζ
ln ζ
ð8Þ
The material removal rate (MRR) is the integral of depth ðΔzÞ over the crater and it is expressed as Z ρboundary Δz2πρ dρ MRR ¼ 0
"
¼ κπ ρ2 ln ζ−
ð5Þ
According to the definition of ωðzÞ in Eq. (2), the following equation presents the relationship between ω and z, especially at focal center ðz ¼ 0Þ, objective lens plane ðz ¼ f Þ and the peak point of the laser affected volume ðz ¼ ztop Þ. Here f is the focal distance of
31
¼
κπω2ðztop Þ ζ
ρ4 ζ 4ω2ðztop Þ
#ρboundary 0
ðln ζÞ2
ð9Þ
The maximum MRR appears at where dðMRRÞ=dz ¼ 0 or dðMRRÞ=dζ ¼ 0. It is where ln ζ ¼ 2 or ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e2 . Let us compare it with the position where ρboundary has its maximum value, i.e. ln ζ ¼ 1 or ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e.
Fig. 1. The laser intensity distribution changes after every pulse.
Fig. 2. Defocusing arrangement.
Fig. 3. Laser affected volume.
32
G. Chang, Y. Tu / Optics & Laser Technology 54 (2013) 30–34
Average MRR over the crater or MRR ¼
MRR MRR κ ¼ 2 ¼ ln ζ Area of crater 2 πρboundary
ð10Þ
So MRR ¼ κ at where MRR gets to its maximum value. At the focal center where z ¼0 ζ¼
z2top þ z2r z2r
¼
z2top z2r
ρ2boundary ¼ 2ω20 ln "
þ1¼
ω2ðztop Þ ω20
ω2ðztop Þ ω20
ω2ðztop Þ
ð12Þ
#2
MRR ¼
κπω20
MRR ¼
" # ω2ðztop Þ MRR κ κ ln ¼ ¼ ln ζ 2 2 πρ2boundary ω20
ln
ð11Þ
ω20
ð13Þ
ð14Þ
In the center of the focal point, Δz ¼ κ lnðE=2πω20 I th Þ ¼ κ ln ζ. Above analysis leads to several interesting conclusions about single pulse ablation. (A) The depth increment Δz, diameter of the crater and MRR of each pulse are affected by defocusing position. In a deep hole drilling process, the largest Δz appears at the ‘tight focusing’ point (focal center) and the crater diameter is the minimum. However, the total MRR is the minimum. (B) Optimal focal position is associated with the purpose of the machining. The maximum total MRR under a fixed laser power appears at where ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e2 . It is the optimal focal position for milling and grooving processes to achieve the highest machining efficiency. The maximum crater diameter appears when ζ ¼ ðz2top þ z2r Þ=ðz2 þ z2r Þ ¼ e. The special advantage of this position is the mildest intensity deviation between center and boundary. So that when higher laser power is set to save the processing time of milling or grooving, the laser intensity on Z axis keeps only e times of the ablation threshold intensity. It is useful to ensure machining quality since it avoid the harmful extra heat damage. (C) In most cases, z⪢zr , the focal position of the maximum MRR and the maximum diameter are at 0:37ztop and 0:61ztop , respectively.
3. Simulation for multiple pulses ablation The laser machining process always involves multiple pulse ablation. As mentioned in the Introduction section, it will induce the defocusing in the process. (A) Simulation result, according to Eqs. (1), (3) and (7), can provide the detail of depth evolution under the different focusing arrangements. Fig. 4 shows the simulation results of the deep drilling process. The depth increment of single pulse under ‘tight focusing’ arrangement drops due to the defocusing which indicates the machining efficiency decreases and more energy of the laser is converted to heat directly rather than contributed to ablation. Two typical focal positions are convergent defocusing and divergent defocusing. The result in Fig. 4 also shows that the depth increment of each pulse under the convergent defocusing situation increases gradually to its maximum when the modified surface falls into focal zone. (B) There is a limit for the final depth evolution. It is not surprise to find that the final depth after numerous pulses, as shown in Fig. 5, is associated with the focusing position and the size of the laser affected volume. Compared with the results of
Fig. 4. Depth increment per pulse is changed by the defocusing situation. The maximum value appears at the ‘tight focusing’ position.
Fig. 5. Final relative hole depth depends on the initial defocusing position. The maximum depth is not at the ‘tight focusing’ position but on the convergent side.
defocusing arrangement, the diameter of the hole under ‘tight focusing’ arrangement is the smallest but final depth of the hole is not the deepest. Under defocusing arrangement, the diameter of the hole is enlarged to its maximum on both convergent side and divergent side. (C) In term of total MRR, the optimal focal position appears on the convergent side. The maximum MRR means the highest ablation efficiency and the highest percentage of the ablation energy converting rate. Though the depth increment of a single pulse is less than that under ‘tight-focusing’ arrangement, the total MRR over the whole process and the final depth are maximized. According to Eq. (9), if the ablation is in the open environment, such as in milling or grooving, the optimal focusing arrangement is at where ζ ¼ ðz2top þ z2r Þ=ðz2 þ Z 2r Þ ¼ e2 . In practice, the part of the beam may be blocked when the hole goes deeper. The plasma plume developed in the deeper hole introduces stronger ‘selffocusing’ effect than that in open space. Since the effects of these two factors are opposite, the optimal defocusing distance is not far from the position. Above simulation does not include the effect of debris which re-deposits on the new modified surface. Though some authors claim that ultrashort pulse laser ablation is a ‘debris free’ process
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[12], there are evidences that the removed particles under the intensive laser power will coat on the surface [13] and change the profile of the new surface [14]. The threshold intensity differs with or without debris [15]. In practice, compressed gas, water jet and special coating [16,17] have been used to remove debris from surface. Since the mild power laser focused above the surface can be used to clean debris [18], the optional defocusing arrangement, which limits the maximum intensity under e times of Ith, is a good option to avoid the accumulation of debris.
4. Experiment The ultra short pulse laser system used in this paper is Ti: Sapphire Libra-S femtosecond laser from Coherent Ltd. The pulse duration of the laser is 100 fs at 1 KHz repetition rate. The wavelength is 800 710 nm. The objective lenses are Mitutoyo Ltd's Apo NiR series. The measurement instruments used in experiment include a scanning electronic microscope (SEM) Phillips XL30 ESEM, a laser power meter, (Newport 2935-c) and an optical microscopy. The experimental ablation samples are silicon chip and bulk aluminum. First group of experiments is drilling series of holes along a line under different defocusing conditions, using the 10 objective lens which focal length is 20 mm. The pulse energy is 30 μJ. The process time of each hole is fixed at 5 s which is 5000 shots. The sample is a silicon chip with 250 μm thickness. After ablation, the chip is broken along the drilling line to exposure the holes so that depth of holes can be measured. Second group of the experiments is to compare results of grooving under different focusing conditions. Three typical defocusing positions are chosen, i.e. ‘tight focusing’, convergent side and divergent side. The pulse energy is fixed on 30 μJ for both silicon and aluminum samples. The groove ablation is under fixed scanning speed. Not only the depth but also the profiles of the groove are measured. The average MRR of total grooving process is calculated and the average MRR of the first 20 scanning circles is used as initial MRR, as shown in Fig. 6. The laser used in experiment is low repetition rate (1 KHz). With heat accumulation effect, according to the Gamaly [15], high repetition rate (5 MHz) radiation will lower ablation threshold intensity Ith. The plasma may block and interact with the following pulses. Therefore, the theory as verified at 1 kHz repetition rate in this paper cannot be indisputably applied in the case of high repetition rate, e.g. at MHz level. Further experiment is necessary to extend the conclusion to the high repetition rate laser.
Fig. 6. Material removal rate is affected by the defocusing. Both convergent and divergent side have the maximum initial MRR while only the convergent side has the maximum average MRR over the whole machining process.
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5. Conclusion and discussion (A) For the so-called ‘cold ablation’ [19] such as ultra-short laser ablation [13], large portion of the laser energy should contribute to ablation without causing significant temperature rising outside of the target area. The simulation and experimental results demonstrate the fact that the ‘tight focusing’ arrangement is not the optimal setting in all multiple pulses ablation. The shortcoming of the ‘tight-focusing’ arrangement is that laser intensity at the spot center is much higher than that on the edge of the spot. When the laser energy increases, the intensity at the center of the spot can be tremendously higher than the threshold intensity. Eq. (7) suggests that the higher the intensity is, the more portion of the energy is directly converted to the heat. Cavalleri et al. [20] have showed that there are several different damage stages under different laser intensities, from phase change to lattice disassembly, and melting eventually. The large intensity deviation inside of the spot will cause mixed changes in the crater. Under the defocusing arrangement, the discrepancy of the intensity is moderate so that the damage is at same stage. For example, at the defocusing position where the maximum diameter happens, the intensity at center is only e times higher than threshold intensity. The intensity uniformity inside of the spot is the warranty of the ablation quality. Taking advantage of this feature, the laser power can be set higher to save machining time. It is especially useful in milling or grooving. For the 10 lens used in the experiment, Rayleigh length zr is 3:2 μm while the final depth can easily go up to several hundred microns, close to ztop. The defocusing is unavoidable after z≥zr . Therefore, even if the initial ‘tight focusing’ is used during the micro-machining process, it is still not rare that the laser works at the defocusing position. ζ is very sensitive with z near the focal center. For example when ztop ¼ 100 μm, ζ ¼ 978 where z ¼0 while ζ ¼ 489 where z ¼ zr ¼ 3:2 μm. The optimal defocusing position is at 0:37ztop which is much larger than zr. Comparing with the ‘tightfocusing’ situation, the laser intensity under defocusing is not very sensitive to the change of z. (B) Instead of using the ‘tight focusing’ arrangement, the defocusing on convergent side can achieve the highest MRR and deepest final depth evolution. The result in Fig. 7 suggests that the optimal focal arrangement should be chosen according to the machining purpose. If the maximum depth is the purpose and the laser power is fixed, the optimal focal position is the defocusing position on the convergent side. If the shortest machining time is the purpose and laser power can be higher, such as in the milling
Fig. 7. Experimental result and simulation. The left is groove under the divergent defocusing arrangement and the right one is that under the convergent defocusing arrangement. The depth of latter is 50% deeper than that under ‘tight-focusing’ condition.
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process, the maximum diameter position with the highest laser power is the best option. In either case, the optimal defocusing distance is proportional to the square root of the laser energy. 6. Summary Defocusing is a crucial factor in the laser micro-machining because the laser intensity can be disturbed tremendously by the defocusing. The optimal focal arrangement should be chosen according to the machining purpose. Both theoretic analysis and experimental result demonstrate that the defocusing arrangement has profound advantages over the conventional ‘tight focusing’ arrangement in multiple pulse ablation process. To achieve higher material removal rate (MRR), which means higher efficiency in grooving process, defocusing on the convergent side is the optimal. The final depth in this way is greater than that under ‘tight-focusing’ arrangement. The machining precision is affected by defocusing, too. Acknowledgments It is hereby to acknowledge the financial support of the project from Canada Foundation for Innovation (CFI).
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