Precise weight measurements of stainless steel, PZT and PMMA samples were performed after groove machining with femtosecond laser pulses (150 fs, 800 nm, 5 kHz) to determine volume ablation rates and ablation threshold with good accuracy. Weighing clearly enables faster determination of such phenomenological parameters without any methodological issue compared to other methods. Comparisons of the three types of materials reveal similar monotonous trends depending on peak fluences from 0.2 to 15 J/cm2. The metallic target exhibits both the lowest volume ablation rate under the highest irradiation conditions with almost 400 µm3/pulse and the lowest ablation threshold with 0.13 J/cm2. Ceramic PZT reaches 3.103 µm3/pulse with a threshold fluence of 0.26 J/cm2 while polymer PMMA attains 104 µm3/pulse for a 0.76 J/cm2 threshold. Pros and cons of this method are also deduced from complementary results obtained on microscopic and confocal characterizations.
© 2012 OSA
Precise micromachining using ultrashort-pulses have drawn growing interest for more than a decade [1, 2]. Femtosecond lasers have demonstrated their capability of drilling [3, 4], cutting , structuring [6, 7] or marking  any kind of material, from metallic targets  to organic tissues  with good controllability and reduced collateral heat damage [11, 12]. Their main characteristic among other lasers lies in the pulse duration much shorter than the electron-phonon relaxation time  and involving high intensities even at low energies. As a consequence, ablation of usual transparent materials at certain wavelengths is possible thanks to non-linear multiphotonic absorption and impact ionization . Since laser-matter interactions are quite complex at these time scales, specific features were developed to macroscopically control the process. The ablation rate and the ablation threshold help classifying materials by quantifying the effect of the processing parameters [15, 16].
The threshold fluence is a critical parameter in laser/matter interaction for precise control of processes. Several methods were developed to determine this parameter exhibiting high discrepancies of the values .
The ablation rate, which is related to the depth per pulse, depends on both mechanical properties of the process (energy, scan speed, focusing, beam overlap, etc.) [18, 19] and properties of the material (electronic and lattice structure, thermal and optical absorptions…) . However its determination raises many issues reported in the literature which were summarized in ref . The depths of the machined features such as holes or grooves can be very difficult to estimate. Probe sensing [18, 22], optical profilometry [23, 24], coated replicas , profile observation [19, 25], tomography  are some of the methods employed for their estimation. Furthermore, in the case of dynamic machining, the analysis method for the calculation of the number of pulses which locally irradiates the material can lead to significant discrepancies in the experimental results . Until now, no clear protocol has ever been defined without any ambiguity.
The ablated volume was also studied rather than the ablated depth, which refers to the total energy absorbed by the material in 3 dimensions . On the one hand it implies that the depth is not necessarily known, but on the other hand, misleading interpretations can be avoided by considering depth, shape and impact diameter together.
But volume ablation rates are generally less considered because of their measurement methods. To our knowledge, most of the estimated volumes were deduced from long and expensive profilometric or microscopic techniques which only provide information on a very-localized area. For instance, atomic force microscopy is often used for measuring volumes of cavities [17, 22]. However such techniques are no more efficient for deep or chaotic features as it can be observed at high fluences . Other methods were imagined to measure the volume ablation rate but they were only applicable to specific cases. Gonzales et al.  estimated the ablated volume to drill metallic foils by considering a conical ablated shape whose depth was equivalent to the foil thickness. Volume and mass ablation was then deduced knowing the number of pulses and the material density.
In this study, we propose a fast and simple method based on differential weighing (DW) which allows deducing the volume ablation rate and threshold fluence with good accuracy. Such a technique was very briefly used with ranges from mg to g to determine the mass ablation rate of materials using a nanosecond laser  or the mass ablation speed using a picosecond laser  but has not been developed yet for accurate volume and threshold estimations on femtosecond processes. The consistency of the method was finally tested by comparing results with confocal and optical characterizations on a metal (stainless steel), a ceramic (PZT) and a polymer (PMMA).
2. Experimental details
Laser machining was performed using a Ti:Sapphire amplified laser which delivers 150 fs and 400 µJ pulses at a central wavelength of 800 nm. All the experiments were carried out under atmospheric conditions at a repetition rate of 5 kHz. The setup is presented on Fig. 1 . Power control was performed using a combination of a rotary half wave plate (λ/2) and a polarizing beam splitter (BS) and checked with a thermopile power meter after the focusing lens. The output beam of ~7.18 mm was diaphragmed through a 7 mm pinhole (P) to avoid edge defects. The focal plane was imaged and magnified four times on a beam analyzing camera (BA) while temporal duration was observed through an autocorrelator (AC). The waist (half width at 1/e2) of the beam was estimated to be around 34 µm with a 15% ellipticity after a 250 mm achromatic doublet (AD) lens. A long focal length was chosen for an easier groove characterization and a less critical sample positioning. The samples were set at the focal plane on XYZ translation stages and moved at a speed v of 5 mm/s. The peak fluence is defined as Fc = 2Ep/πω02.
Samples consist of 10x10 mm2 316L stainless steel plates with a 900 µm thickness (ρ = 7900 µg/cm3), 10x10 mm2 PZT plates with a 180 µm thickness (ρ = 7600 µg/cm3) and 10x10 mm2 PMMA plates with a 8 mm thickness (ρ = 1200 µg/cm3). On each sample, sixteen 8mm-long grooves were machined with 4 passes. For each material, 12 peak fluences ranging from 0.2 to 15 J/cm2 were used. It is to note that a higher number of lines can be machined close to the threshold fluence to increase mass variation according to the balance sensitivity.
Weighing was performed using a Cubis® 6202S micro-balance from Sartorius. The repetability of this device is 1 µg which allows the possibility to easily detect change in weight even close to the threshold. Confocal profilometry and profile observation were also used as comparative techniques.
3. Weighing methodology and protocol
The differential weighing (DW) method is based on a mass measurement of ablated material. The sample is weighed before and after machining. The difference Δm in the sample mass corresponds to the mass of ablated material.
But it is important to ensure that no dust or removed material is taken into account during the two weighings. This can be achieved by a specific cleaning process before each weighing. In our case, samples are immerged into two ultrasonic baths of acetone and ethanol successively for three minutes. Acetone removes organic material and ethanol helps diluting acetone and residual traces. Special care should be taken to avoid temperature difference between the sample and the weighing pan which can lead to significant drift in the measurement. The samples were finally dried in ambient air and left several hours next to the micro-balance to ensure temperature equilibrium and consequently, reduce the error on mass measurement. Some materials such as polymers can react with acetone or ethanol. For PMMA samples, acetone and ethanol were replaced by soapy distilled water and distilled water respectively. In this case, the ultrasonic cleaning was preceded by a hand cleaning with soft paper and soapy water. To test the repeatability of the whole weighing process (cleaning + weighing + temperature influence), a 500 mg stainless steel sample was cleaned and weighed 10 times within a day showing a maximal mass variation of 3 µg which will be considered as the measurement error on the mass.
Knowing the volume density ρ of the material, the ablated volume ΔV can be deduced as:Eq. (3) in Eq. (2) gives the experimental expression of the number of pulses used to machine the sample:Eq. (1) and Eq. (4):
The differential weighing method permits to easily determine volume ablation rates by measuring the mass of ablated material during laser machining. The higher the ablated mass is, the more accurate the ablation rate is. In the meantime, laser machining must not be too long and the sample surface can be limited for several reasons (smallness, cost, etc.). Thus, it is necessary to adjust the ablated mass according to the balance characteristics, to the machining time and to the available amount of material.
The ablated mass Δm can be adjusted by changing the number of pulses during laser machining. The laser/matter interaction depending on the process properties (scan speed, repetition rate, number of passes, beam size and average power, etc.) [18, 19], the best way to increase the ablated mass is to increase the grooves length Lpath.
To test the reliability and the accuracy of this method, results were compared to confocal optical profilometry. Such microscopes were already used for measuring depths in the order of tenths of microns as demonstrated in previous studies for mineral materials [30, 31]. In our set-up, confocal optical microscopy was performed using a commercial setup (Leica SP2) mount with a x63 water immersion objective for stainless steel and PZT and a x40 immersion objective for PMMA. A HeNe laser at 543 nm was used as the illumination source. This optical sectioning microscopy allows us to acquire images of a thin x-y slice at different depths of a sample by removing the out of focus light in each image plane. The z-stack representing the surface of the sample is then computed for topographic representation and the volume of the groove could be reached. Confocal optical microscope has a better resolution than conventional optical microscope, and was estimated in our set-up at 200 nm in lateral direction and 1µm in the axial one . For these resolutions, the field is limited to 240 µm for stainless steel and PZT (Np = 950 pulses) and 375 µm for PMMA (Np = 1500 pulses).
4. Results and discussion
Results for stainless steel are first presented in Fig. 2 . Mass variations were measured, ranging from 26 µg at a fluence of 0.2 J/cm2 to 1628 µg at a fluence of 14.6 J/cm2 with a measurement error of ± 6 µg. Volume ablation rates were deduced by both differential weighing and confocal methods according to (5). DW and confocal measurements are in good agreement. The volume ablation rate varies from 7 µm3/pulse at 0.2 J/cm2 to 400 µm3/pulse at 14.6 J/cm2. A linear regression on the DW volume ablation rate curve at low fluence leads to a peak fluence threshold of 0.13 J/cm2, close to the 0.14 J/cm2 presented in ref . within roughly the same laser parameters.
It is to note that the DW curve is very smooth while an unexpected step appears around 3.5 J/cm2 on the confocal one. Moreover, the difference between DW and confocal results increases with fluence.
Figures 3(a) and 3(b) present 3D topographic views of stainless steel samples at 0.8 and 4.1 J/cm2 obtained with confocal microscopy and the mean resulting profiles. Moreover, these samples were cut orthogonally to the grooves direction, molded in a KM-U polymer and mirror-polished to enable the observation of the 16 grooves cross-sections. Three of them are shown on Figs. 3(c) and 3(d) to compare the results. Profiles are very similar for low fluences. At fluences higher than 4.1 J/cm2, profiles exhibit strong roughness and vary significantly from one cross-section to another. This trend is amplified with increasing fluence. Such chaotic profiles involve troubles for confocal characterizations and induce under-estimations of the ablated volumes. The error is hardly predictable since it depends on both the resolution of the profilometric technique and the roughness of the machined zone. In the case of cross-section observations, errors can also be made by considering only one profile as representative of the whole machined area. Time consuming analyses of multiple profiles are necessary to get correct mean estimations of the ablated volume. Nevertheless, this method has the advantage to be the only way to see recast in a groove at the expense of destructing the sample.
The same study was performed on both PZT (Fig. 4 ) and PMMA (Fig. 5 ), except for the profile observation part, to test the robustness of the DW method. Mass measurements Δm vary from 144 µg to 11370 µg for PZT and from 6 µg to 6161 µg for PMMA on the same fluence range. According to Eq. (6), both materials are ablated faster than stainless steel, with maximum volume ablation rates of 2900 µm3/pulse and 10200 µm3/pulse for PZT and PMMA respectively. The ablation threshold of PZT is estimated to be around 0.26 J/cm2, less than the two values of 0.38 and 0.29 J/cm2 obtained in ref .
As compared to stainless steel, confocal measurements systematically underestimate the ablated volumes for all tested fluences. The upper surface roughness is around 3 µm, which can imply this systematic error on the volume estimations. However, DW and confocal curves look very similar even at high fluences despite features deeper than in stainless steel. This smaller discrepancy can be explained by the smoother and more regular bottoms of the ceramic grooves.
For PMMA, the threshold fluence is around 0.59 J/cm2, higher than the two other materials while ablated volumes are much higher. Intensities have to be high enough to generate non-linear absorptions in a material usually transparent at this wavelength. Depths increase so quickly that confocal microscopy cannot detect bottoms after 4 J/cm2, revealing the limits of most of the profiling techniques. As compared to DW, deep features can easily be used for ablation estimations.
It has to be noted that saturation was never observed in the studied range of fluence with mass measurements. DW seems efficient enough to be used for any regime of ablation since it is not based on profiling. Even next to the ablation threshold, an increase in the machined features can lead to a sufficient mass measurement to deduce ablation.
We presented a new method for determining the volume ablation rate characterizing the interaction between the laser process and the machined material. This method is based on a differential weighing of the sample before and after machining. The weight difference corresponds to the amount of material which has been removed during laser machining.
Demonstration was made on three different types of material: a metal (stainless steel), a ceramic (PZT) and a polymer (PMMA). For each material, a comparison was led between differential weighing and confocal microscopy. Results were similar, and differences were correlated to the inhomogeneity of the groove profile thanks to a microscopic line section analysis.
Fast, user-friendly and affordable, DW method allows a quasi-real-time optimization of a process. But it also presents physical advantages. The first one is that measuring the ablated mass leads to a precise volume ablation rate averaged on a very high number of pulses and to an accurate detection of material removal corresponding to the definition of the ablation threshold. Secondly, DW method does not depend on the machined groove profile or roughness of the sample compared to other microscopic or profilometric techniques. It is applicable for both industrial processes and fundamental researches since mass detection is independent of the studied range of fluences. Of course, differential weighing gives no information concerning the shapes of the features and profilometric techniques remain necessary to check the quality of machining. Moreover, knowing the total ablated volume and the total time of machining, DW method can be used to estimate the processing time of any machining under the same experimental conditions.
This paper deals with the application of differential weighing method for volume ablation rate in the case of femtosecond laser/matter interaction. But the method can be applicable to any pulsed laser machining.
Authors are gratefully thanking Aurelie Mourgues from Sartorius who gives us the possibility to freely perform weighings on a Cubis® 6202S micro-balance.
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