A composite strategy for high-quality and high-efficiency milling of alumina ceramic via femtosecond laser burst-mode

Industrial alumina ceramics require high surface accuracy when assembled to critical components of devices, for which high-quality milling has become an integral process. To achieve high-quality milling of alumina ceramics efficiently, this paper introduced a composite strategy based on the sequence of roughing and finishing via the femtosecond laser burst-mode. Firstly, the effects of laser parameters in the single-pulse mode such as energy fluence, spot overlap ratio, and scanning spacing on the milling quality and efficiency of alumina ceramics were investigated to provide a basis of the parameter selection for the subsequent composite strategy study. Then, the influence of the burst-mode on the optimization of the milling results was discussed, and the advantages of this mode over the single-pulse mode were revealed. Finally, a comparative investigation on the processing performance between the composite strategy and the single strategy was carried out. The results showed that milling the same structure, the roughness of the groove was reduced by 10.69% compared to the optimal processing results in a single process. At the same time, the processing efficiency was maximized with an increase of 49.91%.


Introduction
Alumina ceramics are widely used in the optoelectronics such as integrated circuits and semiconductor sensors due to their excellent properties [1,2]. However, the surface accuracy of conventional sintered and 3D-printed industrial ceramics cannot meet the requirements of increasingly sophisticated equipment. The shape and position errors will seriously affect the assembly accuracy if the assembly surface is rough [3][4][5]. Therefore, high-quality milling has become necessary to achieve functional, practical, and engineering of alumina ceramics [6,7].
For 3D-printed and sintered ceramics with complex shapes and micro-features, laser milling has been widely used to reduce the surface roughness, improve the surface quality, and increase the milling efficiency [8,9]. Kurita et al. [10] found that the femtosecond laser can eliminate microcracks and reduce heat-affected zones with higher processing accuracy than long-pulse lasers. However, femtosecond laser milling of industrial ceramics also presents specific difficulties that the apparent boundaries and voids that existed on the original surface are not filled after the milling [11]. Besides, Lin et al. [3] pointed out that femtosecond laser milling of ceramics not only does not eliminate the original voids and boundaries but also creates new ones. In response to this problem, Fan et al. [12] used a high-frequency femtosecond laser to heal voids and reduce processing defects by liquid-phase sintering unmelted particles with voids. Additionally, Zheng et al. [13,14] pointed out that femtosecond laser processing produced a significant effect of particle and debris redeposition on the machined surface, which was a major obstacle to femtosecond laser milling of ceramics. The introduction of multi-physical field processing environments such as underwater laser processing [15], water-assisted laser processing [16], ultrasonic vibration-assisted laser processing [17], and ultrasonicassisted water-confined laser processing [18] is an effective means to reduce the deposition. However, underwater laser processing would suffer from unstable processing accuracy due to the laser-induced bubbles, and the added equipment would be expensive and complex for other multi-physical field processing.
Milling efficiency is also an essential indicator of milling [19]. Lin et al. [3] noted that the milling results corresponding to the lowest machined surface roughness had a milled depth of only 0-5 μm, which did not allow for effective material removal. Zheng et al. [13,15] indicated that for underwater laser milling of ceramics, the processing efficiency was reduced due to the loss of laser energy. In recent years, the composite processing strategy provides a new solution to improve the processing efficiency of laser milling ceramics. Zheng et al. [19,20] proposed that a composite strategy can achieve high-quality and high-efficiency processing based on the results of different processing strategies and laser parameters. However, they did not carry out the experimental validation. Min et al. [21] introduced a double femtosecond laser composite strategy, where the first scanning made the alumina ceramic structurally regular and avoided deposition problems during the further process. The rough process made the milling more efficient and higher quality. For the laser milling of alumina ceramics, using the composite strategy is a great way to obtain better processing performance as well as the improvement of efficiency.
To further improve the milling performance, many scholars found that the ultrafast laser burst-mode could optimize the processing results with appropriate parameters compared to the laser single-pulse mode [22,23]. For the burst-mode, the particles and deposits present on the milled surface can be avoided, resulting in the ablation of milling more stable. Lickschat et al. [24] used different femtosecond laser burstmodes for the subsequent stainless-steel process to produce a three-dimensional structure with low surface roughness and no deposits. Additionally, the burst mode reduces the interval between adjacent pulses to the nanosecond level which will generate the thermal accumulation [23,25]. Thermal accumulation leads to a melting layer of material [26], which can smooth out typical surface microstructures, resulting in lower surface roughness [27,28]. However, suppose the laser parameters for the burst-mode were selected inaccurately, the processing results would be significantly deviated. It is because once the thermal accumulation between the burst sub-pulses is not effectively controlled, the milling results will be thermally affected seriously [29,30]. Based on the above studies, it is clear that the milling via the femtosecond laser burst-mode is feasible and the crucial point is how to select the reasonable processing parameters.
To achieve the high-quality milling of the alumina ceramics with high efficiency, this paper introduced a composite processing strategy via the femtosecond laser burst mode. The burst mode was used to optimize the milled surface of the ceramic after the rough milling via the single-pulse mode. The effects of laser parameters on milling performance and efficiency in single-pulse mode were investigated, and the influence of the burst-mode on the optimization of the roughing surface was discussed. Finally, to demonstrate the superiority of the composite strategy, a comparison experiment between the composite strategy and the single strategy using the optimal parameters was carried out.

Laser processing system
For the laser milling, a commercial ultrafast fiber laser (YSL Photonics Co. Ltd, China) with a pulse duration of ~ 400 fs and a wavelength of 1030 nm was used. The laser could be operated in single-pulse mode and burst mode. The number of sub-pulses in each burst can be set from 1 (single-pulse mode) to 5. For subsequent comparison experiments, the energy of the burst (the sum of the sub-pulses) was ensured to be equal to that of the single-pulse mode using an external power meter (Maestro, Gentec-EO, Canada). The energy of each sub-pulse in burst mode is the same, as shown in Fig. 1.
In this study, the laser was focused by an F-theta lens with a focal length of 163 mm through an optical transmission system. The laser spot diameter at the focal point was ~ 35 µm, which was obtained using D 2 -method [31]. And the laser focus was deflected on the workpiece by an XY Scanning galvanometer (hurrySCAN II 14, SCAN-LAB, Germany) with a maximum scanning speed of v scan = 1500 mm/s. The experiments were performed using a 40 × 40 × 6-mm 3 sample of normal pressure sintered alumina ceramic (Ruiming Ceramic Technology Co. Ltd, China) with an initial surface roughness of 1.6 μm. The ceramics were fixed on a motorized stage to position and adjust the focus on the sample surface. The experimental setup is shown in Fig. 2a.
During the experiment, the sample surface was processed by a series of laser pulses with different Fig. 1 The schematic diagram of the burst mode combinations of parameters to produce grooves with a size of 10 mm × 1 mm. To facilitate experiments and minimize thermal effects in single-pulse mode, all the experiments fixed the repetition frequency of 50 kHz. The laser operated in burst mode 1, 3, and 5. The energy fluence (calculated via 2E/(πw 0 2 )) was chosen by adjusting the laser energy (E). Note that the laser fluence in this paper is the sum of the fluences of the sub-pulses. As shown in Fig. 2b, the laser beam moved at a certain scanning speed, and the adjacent distance between two tracks parallel to the laser scanning direction was the scanning spacing. The spot overlap ratio (S over ), which is an important indicator in this study, is calculated in Eq. 1: where v scan is the scanning speed, f rep is the laser repetition frequency, and d f is laser spot diameter.

Single-pulse mode milling
Single-pulse mode was used to mill the alumina ceramics in this experiment. Considering the ablation threshold of the material which was obtained by the Beer-Lambert law, different energy fluences from 2.16 to 3.35 J/cm 2 were used to process the surface of the alumina ceramic. From the studies on selecting S over for planarization of industrial ceramics [3,32], S over from 70 to 99% combined with the scanning spacing from 3 to 9 μm were selected for the groove milling. Refer to other milling experiments for the choice of machined depth; the scanning number was fixed at 5 times for all the milling experimental studies. The influence of different parameter combinations on milling performance was investigated. Detailed parameters are shown in Table 1.

Optimization of the surface quality via the burst-mode
To investigate the optimization of burst mode on processing results, burst-mode optimization experiments were carried out. It was conducted on the different rough machined surfaces which were processed with two sets of processing parameters based on the single-pulse mode milling results. One of the roughing parameter selections (i.e., RP1), which is the combination of parameters that obtains the lowest roughness in the single-pulse mode, was the energy fluence of 2.68 J/cm 2 , S over of 80%, and the scanning spacing of 7 μm. The rough surfaces machined by RP1 were used to investigate whether the burst mode can further improve the processing results. Another roughing parameter selection, named RP2, was the energy fluence of 3.35 J/cm 2 , S over of 80%, and the scanning spacing of 7 μm. The high milling efficiency was obtained under the RP2. The optimal energy fluence under the single-pulse mode was also selected for the burst-mode milling. A series of different combinations of burst-mode, S over , and scanning spacing with a fixed scanning number of 5 were used for milling the rough machined surfaces to investigate the optimization of the surface quality. Detailed parameters of the burst-mode milling are shown in Table 2.

Comparison experiment between composite process and single process
To further improve the efficiency of high-quality milling, a composite processing strategy based on the sequence of roughing and finishing was proposed. A combination of parameters in single-pulse mode with high milling efficiency (PR2) was used for roughing to improve the milling efficiency. Then, a reasonable combination of parameters in burst-mode was used to finish the rough machined surface. Two sets of parameters with the lowest surface roughness during burst-mode optimization experiments were selected as finishing parameters. Meanwhile, a comparison experiment between the composite process and the single process was carried out. During the single-process experiments, the optimal parameters in single-pulse mode milling were used to mill the same structure as the composite process experiment. The processing groove size by different strategies was fixed to 10 mm × 1 mm × 40.0 μm. Detailed parameters of the comparison experiments are shown in Table 3.

Characterization and measurements
A 3D laser confocal scanning microscope (OLS-4100, Olympus, Japan) was used to observe and measure threedimensional morphologies, cross-sectional profiles, surface roughness, and machined depths. All surface roughness and depths were averaged and recorded. To assess the efficiency of laser milling of grooves, the material removal rate (MRR) was calculated as the volume of material removed divided by the processing time, as shown in Eq. 2: where A is the cross-sectional area of the machined groove, calculated from the cross-sectional profile of the groove, L is the processed length, and T is the processing time. The machined depth has a relationship with the MRR; previous studies have considered machined depth as a factor in laser milling [19]. The following studies compared the trends of machined depth and MRR with the different processing parameters.

Determination of the alumina ceramic ablation threshold
The magnitude of the energy fluence is an essential factor for the result of the laser milling. To determine that the selected energy parameters are within the appropriate range, the ablation thresholds of the alumina ceramic specimens under different burst mode were determined before the experiments.
According to the Beer-Lambert law, light absorption leads to an exponential decay of light intensity: where I is the laser energy fluence, Z is the machined depth, and α is the absorption coefficient. Since ablation only occurs when the I exceeds the fluence threshold (I th ) of the material. According to Eq. (3), the machined depth (h α ) is related to the incident laser fluence by [33,34] Figure 3 shows the relationship between the machined depth and energy fluence, where h α is plotted as a function of ln(I). From Eq. 4, it can be seen that the h α is linearly related to ln(I). After linear fitting, the alumina ablation thresholds of 1.76 J/cm 2 , 1.60 J/cm 2 , and 1.52 J/cm 2 are obtained for burst mode 1, 3, and 5, respectively. According to the thresholds of alumina ceramics under different burst

Influence of milling parameters on groove morphologies
The milling results for different laser parameters in singlepulse mode are presented in Fig , the three-dimensional morphologies and crosssectional profiles of typical S over of 70%, 80%, and 99% are selected for description and analysis. When the S over is 70%, the small S over reduces the number of pulses deposited in each area of the laser process. The bottom of the groove has a convex area, and the depth becomes shallow, as shown in Fig. 4D and (d1). As the S over increases to 80%, as shown in Fig. 4E and (e1), the profile of the groove bottom is flat. When the S over continuously increases to 99%, as presented in Fig. 4F and (f1), the deepest groove is obtained. The ablation is severe under the high S over , and the bottom profile of the groove has a concave area. The three-dimensional morphologies and cross-sectional profiles of typical scanning spacing of 3 μm, 7 μm, and 9 μm are selected for description and analysis, as shown in Fig. 4G-I, (g1)-(i1). When the scanning spacing is 3 μm, as shown in Fig. 4G and (g1), the excessive ablation is generated on the bottom surface of the milled groove, and the milling depth is deep. With the scanning spacing increases to 7 μm, as presented in Fig. 4H and (h1), the milled groove becomes shallow, and the profile is flat. At the scanning spacing of 9 μm, as shown in Fig. 4G and (g1), the shallowest groove with the fluctuation profile is obtained.
To better characterize the quality of the milled groove, the effect of different laser parameters on the quality of milled grooves in single-pulse mode is discussed by analyzing the three-dimensional morphologies of the bottom surface of the grooves. Figure 4(a2)-(c2) reflect the three-dimensional morphologies of the bottom surface of the groove for the above typical energy fluence. For the energy fluence of 2.19 J/cm 2 , since the alumina ceramics has an uneven local structure during the manufacturing, the fragments produced in the process weaken the propagation of the laser [21], resulting in the generation of convex areas in the local range of the machined surface. When the energy fluence is 2.68 J/cm 2 , the surface is flatter, and the surface roughness is minor, but there is still a small area of convex areas and voids. When the energy fluence is 3.35 J/cm 2 , the high pulse energy produces thermal stress. The generation of thermal stress leads to brittle fracture of the alumina ceramics, resulting in the phenomenon of flaking and the generation of regional voids [6]. The generation of voids is large, affecting the quality of the surface. Figure 4(d2)-(f2) reflects the three-dimensional morphologies of the bottom surface of the milled groove for the corresponding typical S over described above. As shown in Fig. 4(d2), when the S over is 70%, the total energy of the pulses deposited is low. The energy of the laser irradiation on the surface is uneven, resulting in the tendency for brittle fractures during the process. The fluctuation on the surface reduces when the S over increases to 80%, as presented in Fig. 4(e2). The mechanism of laserexcited nanoparticle generation changes and the particle aggregation is evident, leading to the significant reduction of the number and size of voids. However, as presented in Fig. 4(f2), more deep voids exist when the S over is 99%. Due to the high S over , the previous pulses influence the interaction of the subsequent pulse and the material, further affecting the laser propagation [13]. Thus, the groove bottom surface has deep voids. Meanwhile, the thermal incubation effect  where the energy fluence is 2.68 J/cm 2 and S over is 80%. The corresponding cross-sectional profiles ((a1)-(i1)) and the surface profiles of the bottom surface of the grooves((a2)-(i2)) for different laser parameters in single-pulse mode at high S over makes the process of ceramics with thermal effects. There is fracture and peeling of the surface, leading to the appearance of deeper grooves and voids [3,13]. Figure 4(g2) -(i2) show the three-dimensional morphologies of the groove bottom surface for the above typical scanning spacing. As shown in Fig. 4(g2), when scanning spacing is small, the surface is severely ablated, producing more voids on the surface and poorer surface roughness [6]. As the scanning spacing increases, the voids area decreases. When the scanning spacing is 7 μm, as presented in Fig. 4(e2), no significant processing defects exist. As shown in Fig. 4(i2), when the scanning spacing is large, the periodic structure parallel to the direction of the laser scanning path appears on the machined surface, which significantly affects the processing quality. With the larger scanning spacing, the surface of the alumina ceramics cannot be ablated due to the weak energy at the edge of the Gaussian laser spot. Periodic structure forms parallel to the direction of the laser scanning path where the material was not effectively removed.

Influence of milling parameters on groove bottom surface roughness
A further demonstration of the effects of different laser parameters on groove milling results in single-pulse mode is discussed via the surface roughness. Figure 5a shows the groove bottom surface roughness under different energy fluence. When the energy fluence is 2.19 J/cm 2 , surface roughness is 0.68 μm. With the increasing energy fluence, surface roughness decreases. At the energy fluence of 2.68 J/cm 2 , the surface roughness is the lowest at 0.52 μm. As the he energy fluence increases to 3.35 J/cm 2 , the surface roughness reaches 0.73 μm. It is important to note that the energy fluence of 2.68 J/cm 2 is the optimal energy fluence to get a better surface quality. Therefore, for all the milling experimental studies about the S over and scanning spacing, the energy fluence is fixed at 2.68 J/cm 2 . Figure 5b shows a graph of the surface roughness for a combination of parameters corresponding to S over and scanning spacing above. When the scanning spacing increases from 3 to 7 μm, the surface roughness decreases with the same S over . It is easy to find that when the scanning spacing is 7 μm, the surface roughness of each experimental group reaches the minimum value. At the S over of 70%, the surface roughness is relatively high, from 0.58 to 0.67 μm. When the S over increases to 80%, the surface roughness gets better, ranging from 0.50 μm to 0.52 μm. At the S over of 80% and the scanning spacing of 7 μm, the optimal surface roughness of 0.50 μm is obtained.
As the S over increases to 99%, the surface roughness is generally above 1 μm, as the redeposition of some of the material ejected by the thermal effect on the machined surface significantly increases the surface roughness.

Influence of milling parameters on the efficiency
Efficiency is also an essential indicator for laser milling which is characterized by the MRR. Figure 6a and b show the milling depth and MRR with the above energy fluences in single-pulse mode. The depth and MRR with energy fluence follow the same trend due to the approximately positive correlation between the ablation volume of the material and the machined depth. As the energy fluence is 2.19 J/cm 2 , the machined depth is 24.8 μm with the minimum MRR of 4.6 × 10 6 μm 3 /s. The depth and MRR increases with the increasing energy fluence. As the energy fluence increases to 3.35 J/cm 2 , the deepest groove with a depth of 40.8 μm and the maximum MRR of 7.6 × 10 6 μm 3 /s is obtained. Figure 7 shows the trends of the machined depth and MRR for the above S over and scanning spacing parameters at the energy fluence of 2.68 J/cm 2 . As shown in Fig. 7, as the scanning spacing increases, the depth of the groove decreases at different S over , but the MRR increases. Since the scanning spacing increases, the time spent processing the material decreases, which leads to a decrease in depth. Moreover, when the scanning spacing is small, the surface undergoes reheating and evaporation during the scanning. A portion of debris redeposits on the groove bottom surface, resulting in a decrease in MRR. At the S over of 70% and scanning spacing of 9 μm, the minimum machined depth of 10.3 μm is obtained with the MRR of 10.2 × 10 6 μm 3 /s. As the S over increases, the depth increases due to the increased regional pulse deposition. However, when the S over is above 80%, as the S over increases, the MRR decreases. When the S over is high, the scanning speed is low. The debris generated by material ablation cannot be effectively discharged and deposited on the groove bottom surface at low scanning speed, decreasing the MRR [35]. At the S over of 99% and scanning spacing of 3 μm, the groove reaches a maximum value of 54.4 μm, with the minimum MRR of 0.6 × 10 6 μm 3 /s. It is easy to find that S over of 80% can mill the material with the highest efficiency. At the S over of 80% and scanning spacing of 9 μm, the maximum MRR is 10.9 × 10 6 μm 3 /s. In summary, the milling quality and efficiency of singlepulse mode milling with different energy fluences, spot overlap ratios, and scanning spacing are investigated. The groove with the bottom surface roughness of 0.50 μm was obtained with the optimal parameters of energy fluence of 2.68 J/ cm 2 , S over of 80%, and the scanning spacing of 7 μm. Even with the optimal parameters, the machined surface still has small convex areas and small voids. The processing quality needs to be furtherly improved. Moreover, the milling MRR is 10.8 × 10 6 μm 3 /s, which is lower than that at high energy fluence. The milling efficiency also needs to be improved.

Optimization of the surface quality via the burst-mode
A series of milling experiments are carried out using different burst-mode processing parameters. The alumina ceramics is machined separately using two sets of parameters, i.e., PR1 and PR2 to obtain rough machined surfaces before optimization using the burst mode. Figure 8a, b, d and e show the surface roughness in different burst modes at the S over of 70% and 80%. At the low S over , the roughness of the groove surface optimized via the burst mode 5 is generally better than that of the burst mode 3. Unlike the "cold processing" of the single-pulse mode femtosecond laser, there is a particular thermal effect when using the burst mode due to the time interval between burst sub-pulses being only 25 ns. The thermal accumulation generates between the sub-pulse intervals. The laser pulses acting on the ablation of the material is different than that in the single-pulse mode due to the lower energy of the burst-mode sub-pulses. When the S over is low, the number of regional pulses deposited is relatively small. Since the lower energy of the burst sub-pulses, gentle melting of the material occurs under the action of each sub-pulse. The higher the number of sub-pulses with low pulse energy, the more heat accumulation, leading to the gentle melting via the action of multiple pulses. Moreover, the voids and unmelted particles on the machined surface can be healed by the liquid-phase sintering during the melting process. Burst mode 5 is more potent than burst mode 3 in healing the existing voids on the rough surface, resulting in a smoother surface. However, when the S over is 90%, as shown in Fig. 8c and f, the processing results at burstmode 3 are generally better than burst-mode 5. When the S over is high, the number of pulses deposited in the area becomes larger. For the same pulse deposition area, the material melts and recasts under the action of the previous pulses. As the subsequent burst sub-pulses continues to act on the already formed local liquid phase layer and recast layer, the cumulative effect of the sub-pulses would lead to the splashing of the surface material in the form of vapor droplets, which affects the processing quality. The larger the number of burst sub-pulses, the greater the effect. Also, when the number of pulses deposited is large, the area suffers more thermal accumulation which is generated via sub-pulses hitting. Excessive thermal accumulation leads to the serve thermal effect, resulting in the increase of the surface roughness. It is noticeable that for all the burst-mode milling, the surface roughness of the groove bottom is decreased as the scanning spacing increases from 5 to 7 μm. The surface suffers excessive thermal accumulation when the scanning spacing is low. The serve thermal effect affects the surface roughness. As the scanning spacing increases to the range of 7 to 11 μm, it is easy to find that the surface roughness at this range is the lowest. The particles and debris on the rough machined surface are finished by the effect of the burst pulse and the thermal accumulation between the sub-pulses. For the rough machined surface obtained by the process with the RP1 and RP2, the lowest roughness around 0.45 μm was obtained with the same combination of parameters that S over is 80%, and the scanning spacing is 9 μm using burst-mode 5. However, as the scanning spacing continues to increase, the surface roughness increases. Since the low energy of sub-pulses, the energy at the edge of the spot is even below the ablation threshold. There is still incomplete processing between the two parallel laser scanning paths when the scanning spacing is large, ultimately failing to finish the surface. Comparing the surface roughness obtained by optimizing different rough machined surfaces, it can be seen that there is only a tiny difference in the optimization effect of the burst-mode for different rough machined surfaces, and the surface roughness varies in the same trend. However, for the rough machined surface obtained with the RP1, the optimization result is better than that of the rough machined surface obtained with the RP2. This is because the rough machined surface obtained with the RP1 leaves fewer defects on the surface after processing, and the surface is more regular. Additionally, as shown in Fig. 8b and e, for the two different rough machined surfaces, the burst mode can all furtherly reduce the surface roughness compared to the optimal result obtained with the single-pulse mode as long as the selection of parameters is reasonable. By selecting the appropriate parameters, the roughness of the groove bottom is lower when optimally milled via the burst mode. The processing quality is superior compared to the single-pulse mode. Figure 9 illustrates the mechanism of the surface processed by the burst mode compared to the single-pulse mode. The reasons for the optimization of the material surface in the burst-mode under appropriate parameters can be inferred from the following:

Mechanism of the burst-mode milling
1. Reduction of the ablated particles redeposition. The deposition of removed particles during laser ablation is a typical phase explosion feature. The slowing down or suppression of the phase explosion via the burst mode can be explained on both the time and temperature scales. The characteristic time of the phase explosion after the laser reached the material surface is between picoseconds and nanoseconds [36,37]. According to the fact that the ablation particles in the non-processed area could not be covered by the second pulse, the time for the lattice to reach the critical temperature for phase explosion becomes longer due to the smaller energy of the sub-pulse in the burst mode. Since the interval between sub-pulses is on the nanosecond scale, it can be inferred that the physical process of phase explosion caused by the previous sub-pulse has partially occurred or is occurring when the subsequent sub-pulse reaches the material surface. Therefore, the burst sub-pulse is able to suppress part of the phase explosion process of the material under laser irradiation. On the temperature scale, the burst mode has lower energy of individual sub-pulses due to the same total laser power. The lower pulse energy could not bring the material lattice temperature to the critical phase explosion temperature, which inhibits the occurrence of phase explosion and results in fewer particles being obtained by ablation. The redeposition on the machined surface is reduced. 2. Transformation of the form of material removal. There are two material removal mechanisms in the strong ablation zone of ultrafast laser: phase explosion and spallation. For the phase explosion, vapor and small agglomerates are ejected from the surface violently, and melting and flow are unlikely to occur. The burst mode mentioned above partially inhibits the generation and conduct of phase explosion, transforming the material removal process into the spallation of the liquid phase layer. For the spallation, material removal occurred gently and stably, the deposition of debris on the surface from the serve ablation is significantly reduced, and the surface of the machined material is smooth [36]. 3. Removal of roughing defects. Surface debris and high surface energy nanoparticles left behind by rough process have a lower melting point than the material itself [6]. They are remelted and resolidified by thermal accumulation in the burst mode. The hydrodynamic effect causes the liquid material to flow, forming a dense and homogeneous melting layer. In addition, laser energy could not vaporize most of the material due to the low energy of burst sub-pulse. The voids and the unmelted particles of the surface would have the liquid phase sintering Fig. 9 Schematic diagram of the different mechanisms of femtosecond laser single-pulse mode and burst-mode processing material surface under the action of the laser irradiation, resulting in the healing of the voids [12].

Influence of parameters on the milling efficiency via the burst-mode
For the burst-mode milling optimization experiments under different rough machined surfaces, the machined depth and MRR follow the same trend, while the relationship between machined depth and MRR has been described in the previous discussion. Therefore, to reflect the milling efficiency of the burst mode, the MRR for the burst-mode milling optimization experiments for the rough machined surface obtained with the RP1 is selected for discussion. Figure 10 shows the MRR for the different burstmode optimization experiments. For the different burst modes, when the scanning spacing is below 7 μm, as the scanning spacing increases, the MRR increases at different S over . When the scanning spacing is low, a large amount of material vaporizes and melts, leading to the redeposition and recasting of debris on the groove bottom surface. As the scanning spacing reaches 7 to 9 μm, the MRR is high at this range. For the burst mode, the maximum MRR is 5.7 × 10 6 μm 3 /s when the S over is 80%, and the scanning spacing is 7 μm. However, as the scanning spacing continues to increase, the MRR decreases. Due to the low energy of the Gaussian spot edge, the material could not be fully processed, resulting in a decrease in MRR when the scanning spacing is above 9 μm. Additionally, as shown in Fig. 10, with the same S over and scanning spacing, the MRRs of burstmode 3 and 5 are lower than the single-pulse mode. As the number of sub-pulses increases, the MRR decreases. Since the larger number of sub-pulses, the lower the energy averaged into individual pulses while maintaining the same total laser power. The lower energy of the sub-pulses could not allow for effective material removal. Moreover, due to the nanosecond time scale between burst sub-pulses, the ablation cloud generated by the previous laser pulse interacts with another laser pulse during the laser process. The laser pulse is partially shielded, and the material generated by the ablation cloud is redeposited, resulting in a low MRR in the burst-mode process [38].
In summary, it is possible to optimize the surface roughness of the milled surface with appropriate parameters using burst mode. With the optimized parameters of S over of 80% and the scanning spacing of 9 μm using burst-mode 5, the minor surface roughness of 0.45 μm is obtained on the rough machined surface with RP1. However, the MRR is only 4.2 × 10 6 μm 3 /s. Though the appropriate burst-mode parameters can improve the milling quality, the efficiency of milling is relatively low. A reasonable processing strategy is needed for high-quality and high-efficiency milling.

Comparison experiment between the strategies of composite process and single process
To mill the alumina ceramic with high-quality and highefficiency, experiments are conducted to investigate the feasibility of milling in a composite process. The composite process is conducted based on the sequence of roughing and finishing. The RP2 is used as roughing parameters due to the high milling efficiency. The optimization of the rough machined surface with RP2 via the burst mode was discussed from above subsection. The minimum surface roughness of 0.46 µm and 0.45 µm is obtained when the S over is 90%, the scanning spacing is 7 µm for burst-mode 3, and the S over was 80%; the scanning spacing is 9 µm for burst-mode 5, respectively. Therefore, two sets of parameters are used as finishing parameters. A comparison (a) (b) (c) experiment is carried out between milling the same groove structure in the composite process and the single process to investigate the feasibility of the composite process for high-quality and high-efficiency milling. The quality and efficiency of the milling are respectively characterized by the surface roughness and MRR. Figure 11 shows the three-dimensional morphologies and cross-sectional profiles of the groove and the surface morphologies of the bottom surface of the groove for different processing strategies. Comparing Fig. 11A-C (PS1-PS3), it could be seen that in contrast to the linear propagations and concave areas due to excessive ablation that exist on the surface of the single-process milling, the surface obtained by the composite process has fewer processing defects. Figure 11 (a1)-(c1) show the crosssectional profiles of the corresponding groove bottoms. As shown in Fig. 11(a1)-(c1), the machined depths for the three different strategies are 39.9 μm, 40.3 μm, and 40.0 μm, respectively, with the error controlled to within 0.5 μm. Compared to Fig. 11(c1), the machined surfaces of Fig. 11(a1) and (b1) are more regular, and the profiles do not have large convex or concave areas, resulting in better groove profiles. Figure 11 (a2)-(c2) show the surface morphologies of the bottom surface of the groove under the corresponding processing strategies described above. As shown in Fig. 11(c2), under single-process milling, there are voids and convex areas on the bottom surface of the groove; the surface roughness is relatively poor. The processing quality needs to be improved. For the composite process, the rough machined surface has voids with excessive ablation due to the high energy fluence. After the burst-mode finishing, the rough surface particles and debris remelt and redistribute by the heat accumulation between burst sub-pulses, resulting in a certain degree of healing of voids on the rough machined surface. The deposition of debris on the machined surface reduces. As shown in Fig. 11(a2), the surface concave areas are small. The surface is smooth, with the ablation particles and debris deposition reduced due to the slowing down or suppression of phase explosion in the burst-mode. As shown in Fig. 11(b2), compared to the single process, the surface convex structures reduce, and the distribution is less concentrated. There is no significant defect, and processing quality significantly improves compared to the single process.
A comparison of processing quality and efficiency is carried out with different strategies. Figure 12 reflects the comparison of the surface roughness and MRR of the milled grooves under different processing strategies. Figure 12a shows that the bottom surface roughness of the grooves obtained from the composite process is 0.46 μm and 0.45 μm, which is significantly reduced compared to the roughness of 0.51 μm obtained from the single process, with a reduction in the roughness of up to 10.69%. Figure 12b illustrates the MRR of the milling using different strategies. The composite process significantly increases the average processing efficiency due to the higher energy fluence used in the roughing, with the MRR of 13.0 × 10 6 μm 3 /s and 12.2 × 10 6 μm 3 /s for the composite process, respectively, compared to the single process MRR of 8.6 × 10 6 μm 3 /s. The MRR increases by 49.91%, which significantly improves the processing efficiency. The results show that the composite strategy via the femtosecond Fig. 11 Three-dimensional morphologies with the strategies of PS1 (A), PS2 (B), and PS3 (C). The corresponding cross-sectional profiles ((a1)-(c1)) and the surface profiles of the bottom surface of the grooves ((a2)-(c2)) for different processing strategies laser burst-mode has higher milling quality results and a more efficient milling than the single process strategy. The composite strategy is reasonable and feasible.

Conclusion
In this study, the effects of different parameters on the threedimensional morphology, surface roughness, and MRR of laser milling ceramics were experimentally investigated using single-pulse mode and burst-mode. Subsequently, a composite strategy of roughing followed by finishing via the femtosecond laser burst-mode was introduced to achieve the high-quality milling of alumina ceramics with high efficiency. The main findings were as follows.
1. The effects of laser energy fluence, spot overlap ratio, and scanning spacing were investigated in single-pulse mode. When the energy fluence was 2.68 J/cm 2 , the spot overlap ratio was 80%, and the scanning spacing was 7 µm; the surface roughness of the grooves obtained by milling was the lowest. However, the milled groove surface still had defects, the roughness and the milling efficiency needed to be optimized. 2. Possible reasons for optimizing the quality of surface in femtosecond laser burst-mode were discussed under appropriate processing parameters: (I) slowing down or suppression of phase explosion from time and temperature scales, reducing ablation particle redeposition on the machined surface, (II) changing the form of material removal from violent phase explosion in single-pulse mode to spalling of the liquid phase layer due to gentle melting of the material, (III) reduction of defects on rough processed surface due to the thermal accumulation between sub-pulses of the femtosecond laser burstmode and the lower energy of the sub-pulses. 3. A composite laser milling strategy via the femtosecond laser burst-mode was used. After roughing process of the alumina ceramics, the milled structure was finished via the femtosecond laser burst-mode. The surface roughness of the bottom surface of the same structural groove was reduced by up to 10.69%, and processing efficiency was improved with a 49.91% increase compared to the optimal processing quality in a single process.
Funding This research was supported by the National Natural Science Foundation of China (51705258).

Data availability Not applicable.
Code availability Not applicable.

Declarations
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Competing interests
The authors declare no competing interests.