High efficiency GHz laser processing with long bursts

Bursts of GHz repetition rate pulses involve more ablation mechanisms than single femtosecond pulses. Efficient ablation by GHz laser pulses is a multi-step process, consisting of a first thermal incubation phase, followed by a highly efficient ablation phase. GHz ablation therefore combines thermal and non-thermal ablation mechanisms. With an optimal choice of the burst duration, the ablation efficiency can be highly enhanced. Long bursts, comprising tens of pulses to hundreds of pulses, are needed to take full advantage of the increase in ablation efficiency.


Introduction
Femtosecond lasers have seen significant development over the past 10 years as a flexible tool for high quality material processing. The unique laser-matter interaction mechanism offers both a unique precision and quality, as well as the capability to process virtually any type of material. Current applications, for instance in the display and semiconductor industries, in refractive and cataract eye surgery, or high precision mechanical parts manufacturing require only a moderate ablation efficiency, compatible with current laser and beam handling technology. Increasing the ablation efficiency would improve existing applications, as well as enable new processes through a better economic return on investment. A higher ablation efficiency would, for instance, open the way for large area surface texturing applications.
Normalized ablation efficiency is traditionally expressed by the specific ablation rate, expressed in cubic millimeters of ablated matter, per minute, per Watt of laser average power or in µm 3 µJ −1 (1 mm 3 min −1 W −1 = 16.7 µm 3 µJ −1 ). As an example for metallic materials, ablation efficiency is in the * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. order of 0.4 mm 3 min −1 W −1 . Such a value is typical of many femtosecond laser processes [1].
A possible approach is to increase the average power of the laser to achieve a higher ablation rate in mm 3 min −1 . This approach is actively pursued worldwide, both in terms of laser development [2] and processing technology [3].
A key feature of GHz laser processing is the combination of sub-threshold heat accumulation, localized thermal melting, and laser ablation. Understanding the interplay between these components is key to optimizing ablation efficiency. In this publication, we present a possible phenomenological model for GHz laser ablation. We show, both with the help of this model and experimental results, that the number of pulses in each individual burst is an important parameter, and resolve previously diverging results. Finally, we offer guidelines for the optimization of the efficiency of GHz laser processing.

GHz laser ablation
Femtosecond lasers typically operate with trains of laser pulses at repetition rates ranging from tens of kHz to several MHz. Burst mode operation, where each individual pulse in the train is split into a burst of lower energy pulses, modifies the temporal sequence of the energy distribution in the material. The typical repetition rate of pulses within the burst is in the MHz to GHz range. With these repetition rates, the temporal separation between the laser pulses is less than the material thermal relaxation time and thermal accumulation occurs in the target material [33]. Managing thermal accumulation is an important factor in burst mode femtosecond laser processing. For example, a low number of pulses in the burst can limit thermal effects due to thermal accumulation. In the case of short bursts, the fluence of each burst sub-pulse must be higher than the single pulse ablation threshold to initiate the ablation from the first pulse. In such conditions, there is only a modest increase in ablation efficiency compared to single pulse operation. This result has been reported for MHz bursts with only a few pulses and additional limiting mechanisms such as plasma shielding have been recorded [29]. The same behavior has also been reported with GHz bursts consisting of a low number of pulses [27].
The main interest of GHz bursts is to use individual pulse fluences below the ablation threshold as shown in early work from the Ilday group [4,5], and subsequently confirmed by several other studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In this case, a refined approach of ablation mechanisms is needed, both thermal and non-thermal, to understand the high increase in ablation efficiency. We suggest defining GHz ablation in two distinct phases: an initial heating phase, followed by a second very efficient ablation phase, with both thermal and non-thermal contributions to the ablation process.

Heating
The laser matter interaction in femtosecond mode cannot be described by defining a single lattice temperature. As in the case of single pulse ablation [34], a two-temperature model (electronic temperature and lattice temperature) is also used to account for the temperature increase during exposure of the material to a burst of pulses [16,24,29,35]. The role of the material temperature increase is experimentally highlighted for surface treatment, such as polishing, associated with a thermal smoothing of the surface. Surface polishing with bursts is well known in the case of MHz bursts [29] and has been recently extended to GHz bursts [17]. To perform simulations of thermal effects induced by GHz bursts, it is necessary to build a scenario of thermophysical processes following electron excitation by the laser electromagnetic field. Several processes are involved, including electron thermalization, electron heat conduction, electron-phonon coupling on thermal transfer and atomic motion. Povarnitsyn et al [16] propose new possible thermodynamic paths to reach ablation with GHz bursts, which are different from those usually described for single pulse ablation [36]. Simulations with GHz bursts [16,37] highlight the role of fluences below the ablation threshold for material heating by successive pulses.
In our description of the ablation scenario with GHz bursts, a first step is induced by the first pulses of the burst, having individual fluences below the single pulse ablation threshold. No ablation occurs, but an efficient heating of the material is initiated. An illustration of this heating phase is shown in figure 1, in the case of silicon. This material is very thermally sensitive and heating leads to the appearance of a bump in the center of the affected area [38], which has also recently been observed in the case of GHz bursts [8]. As reported in [8], the length of the heat affected zone in this heating phase is in the order of the characteristic heat diffusion length l D , estimated by the simple formula: l D = √ Dh.τ where Dh is the thermal diffusivity and τ the total burst duration. In silicon, the thermal diffusivity is Dh = 0.87 cm 2 s −1 at room temperature. The heat diffusion length l D value is 3.1 µm for burst configuration with 0.88 GHz intra burst repetition rate and 100 pulses. In these specific conditions, a bump appears for a total fluence (fluence of the whole burst) higher than 1.2 J cm −2 , meaning that the fluence of each individual sub-pulse is then 0.012 J cm −2 , far below the single pulse ablation threshold of silicon 0.43 J cm −2 [39].
This heating phase will obviously create significant changes in material morphology, which has to be taken into account in the following phases.

Highly efficient ablation
The following phase of the ablation process is deducted from the analysis of a large number of experimental results, performed for a wide range of laser parameters [8][9][10][11], rarely considered in most published results. In particular, in the 'static' case of single crater realization, a precise study was conducted by Mishchik et al [8] to determine a fluence crater threshold, defined as the total fluence (or the fluence of the whole burst) needed to observe the first crater ablation. For the previously mentioned example (silicon, 0.88 MHz intra-burst repetition rate and 100 pulses, figure 1), while the bump threshold is 1.2 J cm −2 , the crater threshold is 1.9 J cm −2 . The large depth of the first crater obtained for fluences just above the threshold is a significant result, that can be generalized for all observations performed [8][9][10][11]. The measured crater depth is 2.5 µm in the case shown in figure 1 (middle). This depth is close to the value of the afore-mentioned thermal length l D calculated at 3.1 µm. Our hypothesis is thus that a strong ablation occurs when a thermal threshold is reached, leading to the sudden ejection of a large part of the previously heated material. This description accounts for the link between ablated depth and thermal diffusion length, when the total fluence of the burst is close to the crater threshold, and also for the observation of ablated material around the crater (figure 1). The existence of phase explosion mechanisms has been invoked to describe ablation [36,[40][41][42] for metals and semiconductors, and can support the formulated hypothesis.
Nevertheless, even if this thermal ablation phase is very efficient, it can hardly evacuate all the matter of the heated volume. Matter ejection mechanisms can also confine ablated materials on the irradiated surface [36] and a reasonable hypothesis is that a layer of initially heated material remains on the material surface. The thickness of this remaining hot layer is labeled l rh in figure 1.
At this step in the ablation process, the first burst pulses have heated the irradiated material up to a thermal threshold, leading to ablation by matter ejection. If the burst contains more pulses, these can act in a new ablation phase, which is just as efficient but non-thermal. To understand why such a process can occur, let us consider the consequences of the temperature rise on the remaining hot layer. It is well known that a temperature rise leads to a decrease in the ablation threshold [43]. For GHz bursts, however, the physical processes following absorption and contributing to ablation are not well understood. Moreover, the role of different absorption mechanisms, creating electron excitation, has also to be considered. For instance, for band gap materials, pulse-to-pulse incubation phenomena can occur [44,45]. This incubation phenomena can strongly modify the material laser absorption. In the case of silicon, Caballero et al [32] suggest striking a balance of between one and three-photon absorption. While the hypothesis of a multi-photon absorption is usually preferred for a single pulse, single photon absorption could have a higher probability in the case of a burst. GHz bursts could generate a significantly higher number of free electrons, which will promote subsequent mechanisms leading to ablation. Several physical mechanisms can thus give rise to the ablation threshold lowering for a hot layer. To summarize these hypotheses, we introduce an 'effective' ablation threshold, characterized by a much lower value than the single pulse ablation threshold of the cold material.
The last phase of the ablation process is an efficient ablation mechanism, occurring when the 'effective' ablation threshold reaches the fluence of the burst sub-pulses. Subpulses can thus ablate this layer. The ablation is performed at a pulse fluence close to the ablation threshold. It is known as the most efficient case of ablation with a single pulse [29]. Moreover, as previously mentioned by Ilday and coll. [4], the hypothesis of a 'self-sustaining' ablation mechanism is then plausible. After the hot layer ablation, a new heating phase occurs with subsequent pulses, inducing the lowering of the ablation threshold, and allowing a new start of the single pulse ablation process. The optimal regime is achieved when the depth of the heated layer is comparable to the ablation depth of a single pulse [10]. In our example of silicon, the average ablation depth by a single fs pulse is around 40 nm [46]. This depth can be compared with the thermal length value of 33 nm obtained for 800 pluses at 0.88 GHz and for a value of Dh = 0.12 cm 2 s −1 taken at 1400 • C [47]. In summary, an 'ablation cooling' mechanism should not be understood as a cooling mechanism that affects the whole material temperature, no experimental signature of this type has been highlighted in dedicated experiments [48], but rather as a local self-sustaining heating/ ablation mechanism that leaves the temperature of the material constant.
After this very efficient phase of non-thermal ablation, greater crater depths are obtained, as shown in figure 1, again in the case of silicon with 0.88 GHz bursts. From 50 to 100 pulses, the crater depth increases from 2.5 to 5 µm. The ablation process carried out to this end, leads to a high ablation depth. The essential condition to achieve high ablation efficiency is to take advantage of the self-sustaining mechanism by using long bursts with a high number of pulses, typically in the range of 50 to several 100.

GHz laser technology flexibility
Laser design is a key factor in optimizing the processing parameters for GHz laser bursts. It is important to be able to control the number of pulses in the bursts up to several 100, as well as to optimize burst morphology. Apart from the initial design in [4,5], few published works have so far met this criterion.
We have developed a specific GHz laser system, compatible with most commercial ultrafast amplifiers, based on a high repetition rate solid-state oscillator [6][7][8][9][10][11]. The oscillator is passively mode-locked and generates soliton-like pulses of 310 fs pulse duration at 1030 nm center wavelength. The short cavity length (17 cm) gives access to a repetition rate of 0.88 MHz. One or two optional subsequent 50/50 laser couplers enable laser operation at 1.76 GHz or 3.52 GHz. An acousto-optic modulator (AOM), operating as a pulse-picker, allows the selection of an arbitrary number of pulses in the GHz train.
The low energy, low power pulse train is then seeded in a standard chirped pulse amplification laser system, consisting of a pulse stretcher, a fiber or solid-state amplifier, and a pulse compressor. In contrast to other techniques [26][27][28], this linear amplification process does not limit the number of pulses per burst.
It should be noted however, that due to gain depletion, the shape of the burst envelope is naturally distorted after amplification. To compensate for this effect, the AOM pulse-picker is driven by a compensating waveform generated by an arbitrary waveform generator. The output burst then consists of individual pulses with constant pulse energy (cf figure 2), with the exception of the first and last few pulses, due to the non-zero rise time of the AOM. If needed, an additional electro-optic modulator with faster rise time can eliminate these pulses and further improve the overall burst shape. In practice, and especially when using long bursts, this effect is often negligible.
With this flexible laser system, it is therefore possible to vary the intra-burst repetition rate, burst shape and length, in addition to the adjustable parameter of the ultrafast laser amplifier (energy per intra-burst pulse, laser repetition rate, pulse duration, etc.). When coupling the GHz seed laser to a solid-state amplifier (Tangor model from Amplitude), we obtained in excess of 100 W of average power, with a typical repetition rate of 100 kHz and a total energy up to 1 mJ per burst.

Ablation efficiency
We present in the following section, selected results from an existing database on GHz ablation on silicon, copper, aluminum, and stainless steel for craters, lines, and cavities machining [11]. The experimental protocol is described in detail in [10,11]. The beam-diameter is adjusted with a set of lenses. A 1/e 2 beam diameter of 38.3 µm at the focal point is used for the experiments at 0.88 GHz repetition rate, and 39.5 µm for the experiments at 1.76 and 3.52 GHz repetition rate, respectively. The scan speed is 2 m s −1 , leading to 47.8% pulse overlap.
The profile of each crater was measured with a confocal microscope. For line scribing, the 3D profile is divided into a series of 2D sections for which the depth and width of the line, the ablated section (below z = 0) and the section of redeposited material (above z = 0) are measured. The Sa roughness of the samples before machining were respectively 0.15 µm for silicon, 0.35 for copper, 0.33 for aluminum and 0.54 for stainless steel. Figure 3 shows an example of the ablation efficiency evolution with the total burst fluence, for a 100 kHz burst repetition rate and a 1.76 GHz intra-burst repetition rate in the case of line scribing in copper. In previously published results [10], it was shown that changing the intra-burst repetition rate from 0.88 to 1.76 or 3.52 GHz does not modify the ablation efficiency if the burst duration remains constant. This observation is consistent with our interpretation of the ablation process. It also highlights the fact that the ablation mechanisms combining thermal and non-thermal ablation applies throughout the intra-burst repetition rate range that we have studied (0.88-3.52 GHz). Figure 3 shows our results for three different burst lengths: 57 ns (100  pulses in the burst), 227 ns (400 pulses in the burst) and 908 ns (1600 pulses in the burst). The curves show a maximum efficiency with fluence, as is generally the case for ablation curves. The results clearly show an increase in ablation efficiency with the length of the burst, highlighting the interest of optimizing the burst pulse number for GHz machining. Looking at the ablation curves, one can see that the first points just above the threshold are obtained for an individual fluence of the burst sub-pulses ranging from 0.03 to 0.2 J cm −2 , far below the single pulse ablation threshold of copper 0.4 J cm −2 [1].

Experimental results with long bursts.
For optimizing burst length, it is also necessary to consider the quality of the machining. In order to define an objective quality criterion, in the case of line scribing, the crosssections of redeposited and ablated matter, using ablation profiles, are evaluated first. A quality factor Q is defined as 1−((redeposited section)/(ablated section)). A value close to 1 for the quality factor Q indicates a high quality, where the amount of redeposited matter is negligible compared to the amount of matter removed from the ablation crater. Figure 4(a) presents results of ablated and redeposited matter evolution with fluence and figure 4(b) shows the Q factor evolution with fluence for results of line engraving on copper presented in figure 3, with three different numbers of pulses per burst (100, 400 and 1600) at an intra-burst repetition rate of 1.76 GHz. We kept the same color code for all figures. The Q factor curves show the same trend for the three different burst durations. The longest bursts present a strong increase of the ablated matter cross-sections, while redeposited matter increases slowly, leading to the highest Q factor for longer bursts. This observation is consistent with our interpretation of the GHz ablation process. The amount of redeposited material is associated with the thermal ablation phase, that only happens once, while the self-sustaining non-thermal ablation phase occurs for each pulse following the initial ablation phase. Despite a Q value next to 1 for line scribing, the inspection of surface rugosity for cavities milling shows higher values for long pulses, depending on the material [10]. As can be seen in the surface rugosity results presented in ref. 10, surface rugosity increases with the total fluence, and thus too long bursts can have a detrimental effect on surface quality. A compromise between quality and efficiency is to be identified for each specific application.
The ablation efficiency in the case of craters depends on spot size [10,23]. As the spot size modifies the irradiated volume, it also affects thermal ablation efficiency. In the case of lines or cavities processing, the different role played by the pulse overlap in GHz or single pulse ablation has been reported by several authors [10,23]. This optimal overlap decreases to 50% in the GHz case compared to 70% in the single pulse case. In published results [10,23], the efficiency of GHz ablation depends somewhat on the experimentally chosen process: percussion drilling (crater realization), cutting (line realization) or milling (cavity realization). This dependance does not occur for single pulse ablation. Dependency on the process and optimal pulse overlap can be linked to the role of thermal ablation mechanisms, whose contribution is greater in the GHz case.

Discussion.
A comparison of ablation efficiency for single femtosecond pulses, MHz and GHz bursts, and single nanosecond pulses [10][11][12]29], shows the interest of long GHz bursts. Table 1 shows the ablation efficiency for short and long GHz-bursts compared with single fs pulses and nanosecond pulses corresponding to a similar long burst duration, around 200 ns in the case of cavities milling for silicon, copper and stainless steel. GHz-bursts are significantly more efficient than single fs pulses, but only for bursts with a long duration. Table 1 also illustrates the close proximity of long GHz bursts to single ns pulses. This similar behavior has been also reported in theoretical results [16,24]. The specificity of GHz processing is to enable an adjustment of the burst duration with a ns precision. This is a key advantage of GHz processing leading to a possible optimization of the processing quality.  figure 3 with the same color legend: 100 pulses per burst and duration 57 ns (blue curve), 400 pulses per burst and duration 227 ns (green curve) and 1600 pulses per burst and duration 908 ns (red curves). From [11], the dashed lines are guides to the eyes. Reproduced from [10]. CC BY 4.0. (b). Machining quality obtained for line scribing of copper, corresponding to ablation results presented in figures 3 and 4. The inset in the graph schematically presents how the quality factor Q is computed. The color legend is the same as in figure 3. Hundred pulses per burst and duration 57 ns (blue curve), 400 pulses per burst and duration 227 ns (green curve) and 1600 pulses per burst and duration 908 ns (red curves). From [11], the dashed lines are guides to the eyes. Table 1. Comparison of maximal specific ablation rates (in mm 3 −1 min −1 W) reached in milling, for silicon, copper and stainless steel. Values are given for single femtosecond-pulses [49], GHz-bursts [10,27] and single nanosecond pulses [49].

Method for pulse number and pulse duration optimization
As shown in this study, optimizing the burst duration is essential to achieve an optimum result both in ablation efficiency and quality of GHz femtosecond laser ablation.
The simple physical approach presented in section 2 can help in the determination of experimental laser and processing parameters.
The achievement of optimal experimental results, for a given material, is based on the adjustment of many experimental parameters: on the one hand, we can consider all the parameters associated with the laser and the experimental set up, leading to a given fluence on the sample: pulse energy, spot size, beam scan speed and pulse overlap, and on the other hand the parameters setting temporal sequence of energy distribution to the material: pulse duration, burst repetition rate, intra-burst repetition rate and pulse number in the burst.
It can be difficult and time consuming to simultaneously optimize the fluence on the material and number of pulses in the burst. To simplify this optimization process, we have developed an iterative method [9] based on the physical understanding and experimental results presented.
We want to simultaneously optimize the pulse number N and the total fluence F of a long burst. We define FI = F/N the individual fluence of the burst sub-pulses. The optimization is done at a given laser repetition rate and intra-burst repetition rate (labeled f ). The aim is to maximize the ablation depth L. A first estimation of the pulse number N 1 can be made if the diffusivity D of the material is known, by choosing a test value for L. According to the initial phase in the ablation process, we can estimate at the ablation threshold, the ablation depth L as being equal to the thermal diffusion length value. The number N 1 of pulses is then: Starting from a burst with this pulse number N 1 , the method then proposes to experimentally determine the optimal value of F, denoted F opt1 for the initial configuration. Figure 5 shows examples of ablation efficiency evolution with fluence. These curves show a maximum in the ablation efficiency, corresponding to the optimal fluence.
We can estimate this optimal fluence without having to measure all data points in the curve. We know that this optimal fluence is always close to the ablation threshold, which we will note F t . This fluence is easy to determine experimentally, looking for the smallest fluence needed to visualize an ablation. The optimal fluence F opt is then estimated by multiplying F t by a factor close to 1, for example between 1.5 and 3. For this first burst configuration, the first ablation phase process takes place and the thermal ablation occurs. A heated layer remains on the ablated surface. At the same time, the material ablation threshold for a single pulse is lowered to an unknown 'effective' value, which we call F t2 . As soon as this threshold reaches the sub-pulse fluence, ablation by additional pulses starts. It is therefore relevant to increase the number of pulses to obtain greater ablation depths. Let us choose to increase the pulse number by a value N a , defining N 2 = N 1 + N a . This increase is done by maintaining the same fluence FI for the added pulses, and can be calculated as follows: Indeed, a constant FI value for all couples (N, F t ) during optimization is consistent with maintaining the same set of physical mechanisms involved. From equation (2) we can thus determine a threshold fluence of a longer burst by: To complete the optimization procedure, we estimate the fluence of the optimal burst F opt2 in the same way as F opt1 , thus multiplying F t2 by a factor close to 1, for example between 1.2 and 2. In this way, we obtain the parameter couple (N 2 , F opt2 ) for a burst more efficient than N 1 , F opt1 .
We can apply this procedure to the example used throughout this paper, using a 0.88 GHz burst for silicon drilling. If we start from a burst of 100 pulses, whose threshold fluence was measured at 1.8 J cm −2 [11], we can optimize the drilling efficiency by doubling the number of pulses (N a = N 1 ). Equation (3) is used to estimate the threshold fluence of the more efficient burst at 2 × 1.9 = 3.6 J cm −2 . Figure 5 shows the experimental efficiency curve from [8] for 200 pulses burst, with a measured threshold of 3.3 J cm −2 . This value is consistent with the estimated value. In this example, the method used allows for an increase from the optimal fluence for 100 pulses burst (red points on the figure 5) to the optimum of 200 pulses burst (blue points on the figure 5) without the need to carry out extensive measurements of ablation efficiency and to draw the curves, only by measuring the value of the crater threshold of a first test burst.

Conclusion
GHz burst mode operation of femtosecond lasers has shown a significant potential to increase the ablation efficiency of ultrafast laser processing. Over the past several years, several studies have shown varying results, ranging from an order of magnitude to only a modest increase in ablation efficiency. Due to the short pulse duration of each individual pulse, as well as the short temporal spacing between pulses in the GHz burst, the laser-matter interaction process is complex and involves physical mechanisms at different scales, coupling for instance a two temperatures model of the laser-matter interaction with thermal processes. We have presented a two-phase model for the GHz interaction process, which resolves the discrepancy in existing literature. We find that the number of pulses in the burst, at a given GHz repetition rate, is a key parameter, and that long bursts, i.e. comprising tens of pulses to hundreds of individual pulses, are essential to obtain a significant increase in ablation threshold. The ablation efficiency of GHz pulses is indeed comparable to the ablation efficiency of ns pulses. Experiments comparing ablation with single ns pulses and GHz bursts, carried out under comparable experimental conditions, would be useful in establishing more precise and quantitative results. The precise control of thermal effects by the key laser parameters enables us to maintain a high quality of the process and opens the way to new applications such as micro-welding of dissimilar components or high precision surface polishing.