EFFICIENCY ASPECTS IN PROCESSING OF METALS WITH HIGH-REPETITION-RATE ULTRA-SHORT-PULSE LASERS Paper M403

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1 EFFICIENCY ASPECTS IN PROCESSING OF METALS WITH HIGH-REPETITION-RATE ULTRA-SHORT-PULSE LASERS Paper M43 Gediminas Raciukaitis, Marijus Brikas, Mindaugas Gedvilas Laboratory for Applied Research, Institute of Physics, Savanoriu Ave. 31, LT-3 Vilnius, Lithuania Abstract Production time and quality are main concerns in competition of laser technologies in microfabrication with other diverse methods. Ultra-short pulse lasers can offer extraordinary precision on a nanometer scale when laser fluence is close to the ablation threshold. High pulse energies or high repetition rate are usually proposed to be used for an increase in productivity of the system. We discuss experimental and modeling results on effects of both laser and material parameters to the ablation threshold, energy coupling and heating of the workpiece in case of metals. Optimal focusing of the laser beam facilitates an enhancement in the material removal rate but the comparatively large beam spot does not allow achieving a high lateral accuracy. High repetition rate is favorable for the ablation threshold. The threshold decreases with irradiation due to defect formation and modification of the surface causing better energy coupling to material. On the other hand, considerable portion of energy from the laser pulse is converted to heat even when ultra-short pulses are applied. The heat is dissipated in surrounding material causing rise in temperature of the workpiece. Plasma which is formed in picosecond time domain well absorbs laser energy in the whole spectral range and affects an energy coupling to the workpiece. Thermal management of the specimen could be a problem at high repetition rates because of the laser energy wasted in the bulk. Balancing between the rate of energy introduction and accompanying alterations in material and surrounding requires new strategies for effective use of the laser energy. Introduction Requirements of modern micro- and nanotechnologies for the material processing can be fulfilled by laser fabrication. It offers versatile methods for cutting, drilling, ablation, internal modification of a variety of engineering materials. Laser microfabrication has particular benefits compared to other fabrication technologies (chemical wet etching, electro-erosion, etc.) because it is a non-contact process with high accuracy, repeatability and flexibility. Most of engineering materials can be processed with lasers, especially of ultra-short pulse duration. Using ultrashort pulse lasers, the ablation process can be easily controlled because the material is removed in small quantities. A lot of laser pulses are required to remove a considerable amount of the material. The typical method of machining with ultra-short laser pulses is realized by raster scanning, or the machining of sequentially overlapping linear trenches [1]. The fabrication speed might be increased with the mean laser power and / or pulse repetition rate []. Both ways have their own benefits and drawbacks. Efficient use of the laser energy in microfabrication is discussed below. The ratio of the actual laser fluence to the ablation threshold is a measure of the material excitation. As the fluence of the pulse with fixed energy depends on the beam spot, it can be easily controlled by variation in focusing. A simple model of [1] has shown that geometrical optimization of the ablation efficiency is possible. The model is valid for fluences close to the ablation threshold as the energy coupling might be affected by products of the ablation itself. At high energy densities, laser radiation ignites plasma, and typical time for the process is 5-1 ps [3]. Therefore, plasma might have an effect on energy coupling to the target when picosecond lasers are applied. The ablation without the plasma generation took place when laser fluence was below 5F th [4]. Introduction of laser energy to the material at short intervals leads to a multi-pulse processing. Intensive laser radiation affects properties of the material surface in such a way that the material becomes more sensitive to laser radiation and energy density required for material removal decreases several times. The reason for alteration is the accumulation of structural defects on the metal surface formed by irradiation with a laser of the sub-threshold fluence. Accumulation of defects is related to chemical and structural changes in the material [5], [6]. Defects, which require the incubation period, facilitate evaporation of the material by next

2 coming laser pulses. Using high-repetition-rate lasers the effects should be more evident. The heat accumulation is another feature of laser processing with high-repetition-rate lasers. Short pulses of laser radiation trigger rapid evaporation of the material. An escape of the coupled energy from the absorption area within the pulse duration is negligible. Therefore, high accuracy of processing can be achieved. However, even when femtosecond lasers are applied, at least as much as 3% of absorbed energy remains in a specimen near the ablation region [3][7]. Heating of the specimen takes place with highrepetition-rate lasers because the excess energy is not dissipated during a short time between pulses. Heat accumulation was significant starting with 1 khz using nanosecond lasers for paint removal [8]. Thermal cycling disappeared and cumulative heating was noted in glass when it was irradiated with the femtosecond laser with the pulse repetition rate above khz [9]. The laser with the repetition rate of 133 MHz permitted a rise in efficiency of the metal foil drilling. At such a high repetition rate, laser radiation caused a quasi-continuous preheating and an accurate evaporation of the material with ultra-short pulses [1]. Effects related to the use of high power and repetition rate lasers in ablation of metals (aluminum, copper, stainless steel) and silicon were investigated. Numeric simulation and experiments were performed to find out conditions of the efficient use of laser energy. Experimental set-up & procedures Two types of commercially available lasers, emitting 164 nm radiation, were used in experiments. The picosecond laser PL11 (Ekspla) was generating 1 ps-long pulses at repetition rates from 5 to 1 khz. The output power was up to 1 W. Another laser used in the experiment was the nanosecond laser NL64 (Ekspla), generating 6-13 ns long pulses depending on the pulse repetition rate from to 4 khz with an average power of up to 6 W. The laser beam was expanded to the diameter of 4 mm (1/e ) and directed to the galvoscanner ScanGine 14 (ScanLab). Laser radiation was focused on the sample by telecentric lens with the focal length of 16 mm. The spot size was µm. The scanner was controlled using SAM Light software (Scaps). The experiments were performed on the silicon wafer and sheets of metals: aluminum, copper and stainless steel 34. Craters were formed on the surface when laser fluence was above the ablation threshold. A different number of laser pulses at various pulse energies were applied to create the craters. A single laser pulse as well as 1, 1 or 1 pulses were applied to make a crater. The pulse repetition rate was reduced down to 1 khz in order to eliminate the effects related to plasma shielding and thermal phenomena. The required pulses were selected with Pockel s cell from the outgoing pulse train at repetition rates up to 1 khz. The diameters of craters were measured and plotted versus laser pulse energy used to ablate the crater. The threshold was estimated from the relationship between the laser fluence F and the diameter D of a crater etched with a pulse: F D = ω ln, (1) Fth where ω denotes the beam waist and F th is the threshold fluence. Linear fitting of the data was performed according to the relation D ~ln(e p ). The waist radius (a laser spot) was estimated at the first step from a slope of the fitting line, and the pulse energies E p were converted to the laser fluence [11]. The ablation rate was estimated in bulk metal specimens. Rectangular cavities with the lateral dimension of 1x1 mm were milled in the metals with multiple laser pulses. The laser power was varied between the experiments, while the scanning speed, hatch and the number of scans were kept constant. 8 million pulses with the pulse energy in the range of 1-5 μj (3-16 J/cm ) were applied. The depth of lasermilled holes was measured using an optical microscope, and an ablated volume was calculated. The impact of the pulse repetition rate on heat deposition during multi-pulse ablation and cutting of metals was evaluated from melt expulsion and surface coloration. Modeling with FEMLAB software was performed to estimate cumulative heating of the target by the rest of coupled laser energy. Results & Discussions Optimisation of laser beam focusing In case of ultra-short pulses, the laser energy is coupled at an absorption depth of the specimen. Modeling and experiments were performed to establish relations between the laser ablation efficiency in terms of the material removal rate with parameters of the laser beam: the spot size, pulse energy or fluence. The modeling is based on the work of Furmanski et al. [1]. The model is a simplified view to the laser ablation. It does not take into account any reflection from the surface, including tilted crater walls. The whole laser energy is coupled in a narrow layer of the material

3 according to the Beer law. Any energy losses due to heat conduction and plasma absorption are excluded. The assumption is valid quite well in case of ultrashort pulses when the heat diffusion during pulse duration is less than the absorption depth. The analysis was performed in order to determine relations between the laser and material parameters as well as the efficient and precise laser fabrication by ablation. The maximum depth of the crater z, ablated with a single laser pulse, can be found as [1]: 1 F F z = ln =δ ln, () αeff Fth Fth where δ is the scaling parameter which represents an effective absorption depth; F th is the ablation threshold, F is laser fluence. The diameter of the crater near the surface is fluence dependent as in equation (1) if the Gaussian beam is applied. Laser fluence is related to the pulse energy and the beam waist as: Ep F =, (3) π w where E p is the laser pulse energy. The volume of the crater can be calculated by integrating the crater profile: w F V = π δ ln 4. (4) Fth It is maximal when the laser beam is focused to an optimal spot with the waist, which depends on the pulse energy and the ablation threshold: Ep wmax =. (5) e π Fth Laser microfabrication is based on the use of multiple laser pulses to ablate the material. When a burst of laser pulses is applied together with scanning, every new pulse hits the workpiece surface at a different place. The scanning can be expressed by a shift between centers of laser spots Δx or by a beam overlap in % as follows (w - Δx)/w. If a shift between every two laser pulses is Δx, the laser fluence of the n - th pulse at the initial point can be written as: (, ) exp n Δ x F x y F y = =. (6) w w The depth of the final crater (trench) is increased by applying the n - th laser pulse (taking into account its shift) by amount of z n : F nδx y zn ( y) = δ ln. (7) Fth w w The profile of the trench made by partially overlapping laser pulses can be calculated by using the formula: N Δxδ F y w F y. Z( y) = z ( y) = ln ln 1 n N 3w Fth w Δ x Fth w (8) Summation is taken for the shifted pulses with the fluence above the ablation threshold at the initial place. The depth of the resulting trench depends on the pulse energy and the beam focusing when the shift between pulses is kept constant. Cross-section of the trench might be used as a measure of the laser ablation efficiency: δπ 3 ln F w ln F S = Δx. (9) 6Δx Fth Fth The evaporation rate (volume per time) can be estimated when the pulse repetition rate and the shift between pulses are taken into account: dv δπ 3 rep rep ln F w ln F = R SΔ x= R Δx. (1) dt 6 Fth Fth The evaporation rate increases with the laser pulse energy and fluence, but the dependence is non-linear. By varying focusing of the beam it is possible to reach a maximum in the evaporation of the material (Fig.1). dv/dt, mm 3 /s μj 1 μj 3 μj E p =5 μj 4 μj w, μm Fig. 1 Material removal rate at ablation of the trench with a burst of laser pulses depending on the laser beam waist at fixed pulse energies. F th =.6 J/cm, δ=.38, R rep =5 khz, dx=.1 μm. For every given set of laser pulse energy E p, the ablation threshold F th and the distance between subsequence laser pulses Δx, we can define the beam waist when the evaporation rate is maximal. If the shift between subsequent laser pulses is much less than the beam radius ( Δx << w ), the optimal beam waist is the same as in case of single pulse ablation (6). The most efficient material removal takes place when the laser fluence is equal to: F = ef 7.4F. (11) max th th

4 The expression for the maximal evaporation rate at the optimal laser beam focusing can be written by substitution of equation (6) into equation (1): dv δ E p Δx δ Ep = Rrep 1 R. (1) rep dt max ef th w max efth The evaporation rate depends on material properties (absorption depth and ablation threshold) and parameters of the laser beam (pulse energy, repetition rate). The pulse energy and the repetition rate linearly affect the evaporation rate. Therefore, these laser parameters are topmost important for scaling the efficiency of laser microfabrication. Experimental verification of the modeling results was performed by ablating trenches in stainless steel at variable focusing. The depth profiles of the trenches were measured with a stylus profiler. At a given scanning speed, the evaporation rate dv/dt was calculated and it is shown as a function of the beam waist at the constant pulse energy (Fig. ). Volume ablation rate, μm 3 /s 3k k 1k SS Beam waist, μm Fig. Volume removal rate in mm 3 /s of stainless steel as a function of beam waist. Pulse energy was 8 µj at 5 khz. F th =.6 J/cm ; δ =.38; Δx =.1 µm. Good correlation between calculated and experimental data was found when the beam waist was large enough or the laser fluence was not too high. Deviations of the experimental data from estimations occurred in an opposite case and could be related to the limitation of the stylus profiler to measure deep and narrow trenches which were formed at the tide focusing and the high laser fluence. The geometrical limitation of the stylus led to the underestimated value of the trench crosssection. Effect of plasma shielding on the ablation rate The ablation rate was estimated in the bulk metal specimens using both lasers. Rectangular cavities with the lateral dimension of 1x1 mm were milled in the metals with multiple (8 millions) laser pulses. The depth of the holes was measured using an optical microscope, and an ablated volume was calculated. The depth of laser milled cavities varied from 35 to 3 µm. The mean ablation rate in µm/pulse was estimated dividing the cavity volume by the pulse number and the laser spot area. As the milled area was large compared to a laser spot, the shielding effects of a confined crater [1] had no impact on the results. The ablation rate increased with the laser pulse energy and power but deviation from linearity was remarkable (Fig. 3). A slower rise of the ablation rate at higher pulse energies was observed. Total ablation rate, mm/s 8 1, SS34 PL11 1 Mean laser power, W NL64 Fig. 3 Ablation rate of the stainless steel 34 as a function of laser pulse energy. PL11 laser. Dot lines represent linear approximation. Results of ablation with the nanosecond Q-switched laser (NL64) are presented for comparison. The repetition rate was kept constant (5 khz), while the pulse energy and average power were controlled simultaneously by an attenuator. Saturation in the rise of the total ablation rate revealed at higher laser power. The ablation efficiency was limited by phenomena that were excited at the high intensity of laser radiation. The results were transformed into the energetic ablation efficiency in µm 3 /mj, the volume of the material ablated with a portion of energy. Both parameters are mean value of action of more than a million laser pulses and represent the real efficiency of laser processing. Fig. 4 shows the energetic ablation efficiency in µm 3 /mj as a function of the mean laser power. Since every milijoule of the NL64 laser energy was able to remove more material at a higher average power of the laser (higher repetition rate), a significant fall in energetic efficiency was found using the picosecond laser at a higher power. The intensity of absorbed laser radiation was estimated for both lasers

5 and it was compared to the intensity of plasma ignition of metals (*1 13 W/m ) [13]. Energetic efficiency, μm 3 /mj PL11 plasma NL64, 1,, 3, Laser power, W SS Laser intensity, W/m Fig. 4 Energetic efficiency of laser ablation of stainless steel with the picosecond and nanosecond lasers. Dotted lines show intensity of laser radiation absorbed in the specimen. The plasma formation threshold is indicated. Fig. 5 shows experimental data of the energetic ablation efficiency of steel, nickel and aluminum with the picosecond laser. Energetic efficiency, μm 3 /mj 8 6 4,,,4,6 pulse energy, mj steel Ni Al Fig. 5 Ablation efficiency in metals with the picosecond laser at the 5 khz (filled dots) and 1 khz (open dots) repetition rate. The data were evaluated at two different pulse repetition rates and are plotted versus pulse energy. A significant fall in the energetic efficiency occurred using the picosecond laser at a higher power. The evaporation efficiency in µm 3 /mj was higher for the pulse repetition rate of 5 khz (filled dots) compared to 1 khz (open dots) at the same pulse energy in case of all examined metals, except aluminum. The repetition rate had no effect on the energetic ablation efficiency in aluminum. Nickel showed a high drop in the efficiency in a narrow range of pulse energies. Accumulation effects versus ablation threshold The ablation threshold for stainless steel, copper, silicon and aluminum by irradiation with the PL11 picosecond laser was investigated using 1, 1, 1 and 1 pulses to make a crater at a different laser pulse energy. Diameters of craters were measured and used for analysis. The approximation according to equation (1) was performed using experimental data. Results of the evaluation are given in Table 1. Table 1 Ablation threshold of metals for the 1 ps pulse duration. Material Ablation threshold, J/cm [14] [15] 1 pulse 1 pulses 1 pulses 1 pulses SS Al Cu We used the incident laser power (pulse energy) instead of the absorbed one in evaluations. It is not correct regarding parameters of the material because most of the energy was reflected by the metal surface. Metals reflect about 7-99% of laser radiation in the near infrared range. It is technically difficult to measure the laser energy coupled to the workpiece but in our case the ablation threshold is sensitive to surface finishing conditions. No special attempts were made to prepare the surface of specimens before experiments, such as chemical or electro-chemical polishing [16]. According to the accumulation model of Jee et al. [16], the ablation threshold and the number of laser pulses are related by an equation: S 1 F th ( N) = Fth (1) N, (13) where < S 1 is the accumulation coefficient, which describes incubation of defects after laser irradiation. S = 1 means that no incubation appears and the ablation threshold does not depend on the number of laser pulses. A typical value for metals is S = If the parameter S is larger than 1, the specimen surface is hardened by laser irradiation. The ablation threshold is affected by the initial state of the surface. The surface roughness and contamination increase absorption, and therefore the energy input to the material. Heat accumulation The high pulse repetition rate is often assumed as the only way to increase productivity of laser processing. The open question is about heating the target with laser energy which has been absorbed by the target but not

6 removed with vapor, plasma and particulates. Even at the kilohertz repetition rate, the coupled laser energy is not dissipated until the next laser pulse arrives. Joule heating of the target should be more problematic when the repetition rate of the laser reaches hundreds of kilohertz and even megahertz. Heating of workpieces during laser ablation with the high power and repetition rate laser is a fact that can be easily recognized. Surface coloration of metals is a typical example and appears in processing of thin metal foils with geometrically limited head conduction. Experimental qualification of the specimen heating is a complicated task and we applied various methods of modeling to solve the heat conduction equation in 3D and time in order to determine how temperature is distributed inside the specimen during ablation with single and multiple laser pulses. The equation was T αz ρcp = ( κ T ) + ( 1 R) α Ie, (14) t where T(x,y,z,t) is temperature, which is a function of time and coordinates; I is the external heat source (laser radiation with Gaussian distribution in space and time); α is the absorption coefficient; R is the reflectivity; κ is the heat conductivity; ρ is the density; C p is the heat capacity of the specimen. Using the finite element analysis of the 3D heat conduction equation, the ablation with a single nanosecond (1 1/e ) and picosecond pulse (1 1/e ) was modeled. The latter was used instead of 1 ps in order to be in the validity range of the one-temperature approach. If temperature of an element of the material exceeded the evaporation temperature, it was removed, creating a crater. Melting heat and heat of vaporization were included into consideration. Temperature distributions at the end of both laser pulses are shown in Fig. 6. Energetic efficiency of the ablation was 5% in case of the nanosecond pulse. The rest of the absorbed laser energy was dissipated into bulk or removed by particulates leaving the specimen in liquid or solid phase with a steam of vapor. The melted layer exceeded as much as 3 nm. The heat spread over a few µm during the pulse of the 1 ns length. In case of the pulse with the duration of 1 ps, the melted layer was as small as 8 nm and the ablation efficiency was higher due to lower losses by head conduction. When the burst of laser pulses is applied, the energy dissipated into bulk of the specimen is accumulated. Gamali et al. [17] modeled a variation in surface temperature of the target irradiated by a quence of laser pulses. Thermal cycling together with cumulative heating was found to be dependent on the pulse repetition rate. Experimentally, no cycling was observed in processing glass with lasers at the repetition rate exceeding khz [16]. We used a mean laser power to estimate the cumulative heating of a target by the rest of laser energy coupled to the specimen but not removed with vapor. The FEMLAB software was used to model 3D temperature distribution, when the focused laser beam irradiated a target. Aluminum foil as large as 1 x 1 cm with the thickness of 1 µm was one-side embedded into a holder with fixed temperature of o C. The laser beam was absorbed at the depth of 1 nm. Calculation of the thermal profile was performed at an incident laser power of 1 W, the mean power which can be generated by the most popular nowadays highrepetition-rate ultra-fast lasers. We assumed that 1% of the coupled laser power was converted to heat. Modeling results are shown in Fig. 7. Fig. 6 Crater ablated in silicon with a single laser pulse and temperature distribution in the specimen at the end of the laser pulse. Pulse energy 1 µj; spot size 5 1/e ; pulse duration 1 ns (left) and 1 ps (right). Coordinates x and z are in µm. The thin black line represents an interface between solid and liquid phases. The temperature as high as 45 o C was achieved in a few tens of seconds close to the laser incident area while the side of the specimen without contact with the holder was heated to a temperature lower by 1 o C. Non-homogeneous heating of the specimen may cause its deformation due to thermal expansion. Good

7 thermal contact should be secured in experiments on laser microfabrication with small specimens. Fig. 7 Heating of the aluminum foil by the rest of laser energy left in the material after ablation. Time spent from the moment when laser irradiation started and the maximum temperature nearby the ablation place are shown. Discussion The ablation rate increased with the laser fluence. For the same pulse energy, the fluence can be varied by changing focusing of the beam. Therefore, simple geometrical modeling on how focusing might affect the material removal efficiency was carried out. Any effects that could had influence on the energy coupling to the material or its removal were not taken into account. The situation was realized when low fluences just above the ablation threshold were applied and the aspect ratio of the trench was small. The optimal focusing conditions for stainless steel were estimated. The best results for laser pulses with energy of 8 µj were achieved when the beam was around µm in radius (1/e ). The optimal beam diameter increases with the pulse energy. The efficient material removal requires moderate laser fluences. When the pulse energy is high, the spot size becomes large. It can be too large in order to achieve the required precision of fabrication in the range of 1- µm or below. Two solutions might be applied: 1. Low pulse energies can be used to machine small features. The excessive laser energy can be applied by splitting the beam and using multi-beam parallel processing;. Fabrication process can be organized with variable focusing and the pulse energy control. The initial rough fabrication is performed at the maximal pulse energy and the optimal beam focusing in order to achieve the most efficient material removal rate. Later, the reduced pulse energy and focusing to a small spot can be used to tune the shape to the required precision. High intensity of laser radiation facilitates heating of the material to very high temperatures, when ionized atoms are transformed into plasma. Plasma effectively absorbs laser radiation shielding the specimen [3]. It starts to form with delay of 5-1 ps after the irradiation start from the evaporated material. Even for the laser pulses as short as 1 ps, the plasma can have an impact on the energy transfer from the beam to the material. The intensity of the absorbed laser radiation used in experiments was estimated and compared to the intensity of plasma ignition of metals (*1 13 W/m ) [13]. In case of the picosecond laser, the intensity was much higher than the plasma ignition limit in the whole range of laser power, and the rise in intensity was synchronous with a fall in the ablation efficiency. Therefore, we suppose that the limiting factor in the energetic ablation efficiency of the picosecond laser was plasma formation at the specimen surface. Every investigated metal had a specific pulse energy when the ablation efficiency was maximal. The pulse energy in Fig. 7 corresponds to the incident laser energy. Aluminum has reflectivity of 91% at the 164 nm wavelength, while that of nickel and steel is about 7%. Therefore, aluminum required a three times higher incident pulse energy to absorb the same amount than nickel. Adjustment of the efficiency of lasers according to the absorbed laser energy might lead to a close range of laser parameters for the optimal use of the laser power. The laser milling was performed on a large enough area by scanning the laser beam. Therefore, the remaining ablation products in the air should not absorb the laser beam significantly as in case of percussion drilling [3]. Plasma itself is an energy source that returns energy to the specimen by heating it. The direct increase in the pulse energy can be an inefficient way to reach a higher ablation rate. Splitting the beam into a few beams might be a solution with high pulse energy lasers. Every laser pulse, even with the energy below the evaporation threshold, induced structural alterations. The deformations of the metal surface occurred under irradiation with the laser pulse. Defects on the surface

8 were accumulated at the fluences below the singlepulse threshold. Therefore, the lower laser pulse energy was required for initiation of the material removal in the multi-shot regime. As a result, the ablation threshold decreased with the increase in the number of pulses. The ablation threshold of metals was investigated by Gamali et al. in [15], using a laser with the pulse duration of 1 ps and the pulse repetition rate of 4. MHz. They estimated that the ablation threshold increased twice in vacuum compared to that in the air. Their values of.17 J/cm for aluminum,.3 J/cm for copper and.19 J/cm for steel are close to our values when a large number of pulses (N=1) was applied. The single pulse ablation threshold of copper and stainless steel was found to be.58 J/cm and.1 J/cm, respectively, when the laser pulse duration was 15 fs [18]. The thresholds fell down to.55 J/cm and.13 J/cm, respectively, when 1 pulses were applied. The values are close to those estimated in this work with the picosecond laser. A significant change in the ablation threshold was observed for all investigated metals when the picosecond laser was applied. We did not use any preparation of the specimens in experiments, while electro-polishing was applied in [15]. Accumulation effects depended on the initial condition of the surface. Apparently, the surface of the rolled metal sheet in our case was in a meta-stable state and irradiation with a sequence of laser pulses triggered the defect formation. Lowering of the ablation threshold might be useful in laser material processing using high-repetition-rate lasers which usually generate lower pulse energies. Apart from the defect generation with high-repetitionrate lasers, a significant amount of absorbed energy remains in the material. The heat accumulation is another feature of laser processing with highrepetition-rate lasers. Even when femtosecond lasers are applied, at least as much as 3% of absorbed energy remains in a specimen near the ablation region [3], [7]. The excess energy is not dissipated during a short time between pulses. Conclusions Effects related to the use of high power and repetition rate lasers in ablation of metals which had the influence on the material removal rate and thus on the laser processing efficiency were investigated: the beam focusing, defect as well as heat accumulation and plasma shielding. The volume ablation rate is a non-linear function of the pulse energy. Numerical simulation of the ablation efficiency was performed using simple relations between the laser and material parameters. An optimum beam waist was estimated for a certain pulse energy to maximize the ablation. However, the beam size was large and did not allow achieving high accuracy. Variation of the beam focusing is required for coarse but efficient as well as fine but slow laser processing. The ablation threshold of metals and silicon depended on the number of pulses affecting the same area. The reduction in the ablation threshold by irradiation with a series of laser pulses can be useful in application of the high-repetition-rate lasers with the low pulse energy in order to increase the processing efficiency. At a constant scanning speed, the beam overlap increases with the repetition rate. As a consequence, the reduced ablation threshold is able: to make the material removal with the lower energy pulses that are usually generated with high repetition rate lasers easier; to remove more material by one laser pulse of the same fluence because the ablation rate depends on the above-threshold fluence. The energy efficiency of the laser processing fell down when the fluence was above the limit which depended on the material. The density of absorbed laser energy was close to the plasma formation threshold. The limiting factor in the energy efficiency of ablation with the picosecond laser was plasma formation at the specimen surface. The direct increase in the pulse energy can be an inefficient way to reach a higher ablation rate. Splitting the beam into a few beams might be a solution with high-pulse-energy lasers. Intelligent control of process parameters is required to keep optimal conditions for the material removal by laser ablation. Acknowledgments The work was supported by the Lithuanian State Science and Studies Foundation under project No V- 38/8. References [1] J. Furmanski, A.M. Rubenchik, M.D. Shirk, B.C. Stuart (7) Deterministic processing of alumina with ultrashort laser pulses, J. Appl. Phys., 1, [] Zhang, W., Azer, M., Benicewicz, P., Jones, M.L., Que, L., Industrial applications of laser micro/nano material processing, Proc. of International Congress on Applications of Lasers & Electro- Optics, ICALEO 6, Scottsdale, USA, October 3- November, 6, #M41.

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