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Abstract
For the specific energy distribution of Gaussian laser, the obtained grooves always fall short in the sidewall verticality. To overcome this problem, the improvement of sidewall inclination in laser grooving of a CVD diamond is undertaken by the surface tilting motion control, where the insufficient material removal at the groove sidewall is relieved. Combined with finite element modelling, the influence of laser energy density, scanning speed, scanning times and scanning pitch on the inclination of sidewall are firstly analyzed, which shows that laser energy density is the main factor that dominates the sidewall inclination. The finite element simulation model (FEM) is established to achieve the contour evolution of the machining area under different tilted angles, where the generation mechanism of ‘V’ shape or ‘W’ shape at the bottom of the groove is analyzed. Finally, the inclination degree of the groove sidewall can be effectively controlled by optimizing the relative incident angle under the selected laser energy density.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
For the excellent thermal conductivity, chemical stability and wear resistance [1,2], CVD diamond is gaining wide application in optical devices, electronics and cutting tools [3–6]. However, the super hardness makes the high precision machining of diamond products great difficult. Fortunately, ultrashort pulse laser presents the advantages of high accuracy, suitability and portability [7], and the major concern of heat affected zone can be well controlled to achieve ‘cold processing’ [8,9].
However, another issue arises, that is, the processed groove usually presents a nearly ‘V’ cross-sectional profile [10–14], as far as the energy distribution characteristics of Gaussian laser is concerned. A number of researches have been conducted to eliminate the sidewall inclination, from the parameter optimization based on finite element modelling to the laser beam shaping. Cadot et al. [15] found that the groove depth was inversely proportional to the scanning speed, and a prediction model of groove profile for laser processing was built. Wu et al. [16] focused on the multiple reflection and absorption of laser inside the hole wall and built a simulation model for laser drilling, and they found that single reflection played important role on the hole depth but little effect on the diameter. In comparison, the multiple reflection has less impact on the deep-hole machining. Taking the changing ablation threshold under multi-ablation passes into consideration, Shunsuke et al. [17] proposed a three-dimensional contour simulation method in femtosecond laser ablation of polycrystalline diamond, which can be accurately applied to simulate the three-dimensional topography of the machined surface. For the influence of laser scanning trajectory, Zhang et al. [18] analyzed the Gaussian energy distribution under different laser processing trajectories and the influence of the laser parameters on the cross-sectional profile of the ‘V’ shape groove was quantified. The uneven energy distribution of Gaussian beam results in the nonuniform material removal of the ablated area. By adjusting the optical components inside the laser equipment (microlens array, diffractive optical devices and liquid crystal spatial light) [19–21], the energy distribution of the laser beam can be shaped to be the needed uniform energy distribution. For dynamic beam shaping (DBS), John et al. [22] present a new optical design to shape the pulsed laser into a ring, Gaussian or top-hat laser. Roth et al. [23] used femtosecond laser with adaptive beam shaping to process microchannels in PMMA blocks. Jia et al. [24] applied a beam shaper to convert a Gaussian laser into a top-hat laser, and the ablated pits turned to be flatter. To be mentioned, the laser incidence angle was also found to have an obvious effect on the material removal process [25]. Tokarev et al. [26] tried to polish diamond at a certain incidence angle and the roughness (Ra) reduced to be 28 nm. However, the material at the edge of the Gaussian laser spot is always incompletely removed to get an inclined sidewall, and further effort is of great necessity to achieve precision machining of the grooves.
In this paper, the evolution of the groove contour is explored by finite element modelling and experiment, where the influence of laser energy density, scanning speed, ablation times and scanning pitch on the sidewall inclination of the machined groove is investigated. To control the sidewall inclination, the tilted angle of the sample surface is selected to eliminate the ‘V’ profile caused by the Gaussian energy distribution.
2. Materials and experiments
The polycrystalline CVD (Chemical Vapor Deposition) diamond (produced by Langfang Supower Diamond Technology Co., Ltd., China) was applied for the laser ablation experiment. The surface was firstly polished with the surface roughness (Sa) of about 20 nm.
The laser ablation experiments were undertaken on a picosecond laser equipment (EdgeWave Co., Ltd., Germany), and the specifications of the laser are listed in Table 1. To control the inclination angle of the groove sidewall, the tilted angle of the sample surface was adjusted by a precision platform with an accuracy of 0.1°, as shown in Fig. 1.
Table 1. Specifications of the picosecond laser equipment
The selected experimental parameters are shown in Table 2. To obtain the dependence of sidewall inclination on the laser parameters, scanning path 1 was selected for grooving, as shown in Fig. 2, and the ablation parameters are C1, C2, C3 and C4 in Table 2. The micro grooves were ablated by laser scanning path 2, and the parameters are C5, C6 and C7 in Table 2.
Table 2. The laser ablation parameters
To remove the residual products on the surface and obtain the accurate surface morphology, the machined CVD diamond was ultrasonically cleaned for 10 min with acetone after the laser ablation. The surface topography was measured by a 3D optical profiler (Sensofar S Neox 3D, SENSOFAR-TECH, Co., Ltd., Spain) and the surface morphology was characterized by a scanning electron microscope (EM-30PLUS, COXEM, Co., Ltd., Korea).
3. Finite element simulation methods
Actually, the premise for precision machining of microstructure is to get the profile evolution rule. To achieve the changing trend of the groove profile under selected tilted angles, the simulation of the groove profiles based on the finite element method by COMSOL software is undertaken. During the laser processing, the removal rate is dependent on the laser fluence. It is assumed that the removal rate of material is linear with the surface energy density. According to Equs. (1) and (2), the laser fluence can be calculated to obtain the grid movement rate, corresponding to the material removal volume of the ablated area.
where vmesh is the grid movement velocity, n is the surface normal vector, Flux is the heat flux, ρ is the density of the material, Lv is the latent heat of vaporization, Q is the laser energy density, S is the ablated area and ΔT is the laser ablation duration. The referred material properties of CVD diamond are listed in Table 3, and the simulation is conducted based on the following simplifications and assumptions:- (1) The machined surface absorbs the laser energy completely to convert it into inward heat flux;
- (2) The material is isotropic and the influence of grain boundaries is neglected;
- (3) The influence of deposited layer on the ablated surface is neglected;
- (4) The shielding effect of plasma is not involved.
Table 3. The physical properties of CVD diamond [27]
4. Results and discussion
After a single laser ablation, the obtained groove is a nearly ‘V’ shape, corresponding to the laser energy distribution, as shown in Fig. 3. By changing the laser energy density, the scanning speed, the ablation times and the spacing pitch under the experimental parameters of C1-C4 Sets, the inclination of the obtained sidewall is explored. In order to ensure the flatness of the bottom of the processing area (Stage 1), the laser scanning path 1 is adopted, as shown in Fig. 2. As shown in Fig. 4, the area not removed is much larger than the laser spot diameter (10 µm), and the inclined sidewall contour of the groove edge is nearly a straight line.
Fig. 3. a) Laser energy distribution of the Gaussian laser, b) a typical groove profile machined by the Gaussian laser.
Fig. 4. The ablated surface under the parameters of f =400 kHz, Q = 10.18 J/cm2, v = 100 mm/s, n = 40, scanning pitch = 5 µm: a) 3D surface topography, b) the sidewall profile.
Based on the three-dimensional contour of the groove, the data points (Depth and extension length in Fig. 4) at the boundary between the sidewall and the bottom were collected, as shown in Fig. 5. The specific processing parameters, including the power, the scanning pitch, the scanning speed and the ablation times, corresponding to data points in Fig. 5, are listed in Table 2 (C1-C4). The inclination angle of the sidewall (θ) is achieved to be the included angle between the original surface and the sidewall. As shown in Fig. 5(a), when the laser power remains unchanged, the data points distribute linearly under varying scanning pitches, ablation times and scanning speeds, and the inclination angle of the fitting line is about 66.76°. Under different laser scanning pitches (C2), the recorded data points (the black squares in Fig. 5) deviate slightly from the fitting line, which is attributed to the fact that the ablated bottom becomes uneven with increasing ablation spacing, so the inclination represented by the measured junction points is inconsistent with the actual sidewall. The sidewall profiles under different scanning pitches (C2) are shown in Fig. 5(b). Without considering the bottom contour of the processed groove, the sidewalls nearly coincide, which also indicates that the scanning pitch has little effect on the sidewall inclination. Under other selected parameters, the ablation bottom is flat and the junction can still reflect the inclined sidewall. In comparison, the inclination degree of the sidewall becomes larger with increasing laser power. When the laser energy density remains unchanged, the inclination degree of the groove sidewall stays stable.
Fig. 5. a) Distribution of junction points under different processing parameters: including the laser power (C1), the scanning pitch (C2), the scanning speed (C3) and the ablation times (C4), b) the sidewall profiles under different scanning pitches.
In laser processing, the micro-groove is created by the accumulated etching of multi-pulse spots on the material surface. When the material is gradually ablated, the geometry of the pulse acting area also changes. The laser energy density Q(x, y) can be achieved by Eq. (3),
where Epulse is the energy of a single laser pulse and dS is the area differential unit of the ablation area. As shown in Fig. 6, the ablated surface is a plane at the initial stage, and the area element of the ablation area dSA can be expressed as,As the material removal continues, the ablated area becomes inclined, so the element of the ablation area can be given by Eq. (5),
According to Eq. (10), the maximum laser energy density under a laser pulse can be expressed as:
The angle between the surface normal vector (n) and the Z axis is the sidewall inclination angle (θ) in Fig. 4. With the increase of the inclination angle of the sidewall, the maximum laser energy density of the surface gradually decreases, as shown in Fig. 7(a). When the laser energy density is lower than the ablation threshold, no material is removed and the inclination angle of the sidewall does not increase.
Fig. 7. a) Maximum laser energy density at different surface tilted angles, b) comparison between theoretical and experimental sidewall inclination.
The laser energy density changes along the radial direction of the pulse spot, where a higher laser energy density contributes to a greater sidewall inclination angle. The theoretical maximum sidewall inclination can be expressed as:
where Qth is the ablation threshold of CVD diamond. In the previous work [28], the area extrapolation method was applied to calculate Qth (2.817 J/cm2). When the laser energy density remains unchanged, the inclination angle of the sidewall keeps constant.As shown in Fig. 7(b), the changing trend of the inclination by theoretical calculation corresponds to the experimental results with some deviation in the values, where the obtained sidewall inclination is lower than the theoretical one. It can be found that a higher energy density results in greater inclination angle of the sidewall theoretically. The experimentally obtained sidewall inclination is the consequence of the comprehensive action of Gaussian laser at each point. As the energy density of the Gaussian laser is not uniform, the deviation does appear for the maximum inclination of each point, and the equivalent laser energy density is actually less than the peak value. The equivalent laser energy density can be expressed as:
The approximately linear relationship between the equivalent laser energy density and the maximum laser energy density is shown in Fig. 8, and the equivalent laser energy density grows with increasing laser power.
To obtain micro grooves with improved sidewall inclination, the experimental parameters of C5-C7 Sets are selected to investigate the influence of the tilted surface angles. As shown in Fig. 9, the parameters used are given by Set C5 in Table 2. The inclination the groove right side increases significantly with the growth of the tilted angle. The width of the groove gradually increases but the depth drops. It is reported that the absorption rate of the ablated material is related to the laser incidence angle [29]. At a larger tilted angle of the sample, the projection shape of the laser spot changes from circular to be elliptical, which increases the projection area and reduces the laser energy density. Therefore, both the ablation rate and ablation depth decrease with the increase of tilted angle [30].
Fig. 9. The cross-sectional profiles and the obtained depth and width under different surface tilted angles: a) the cross-sectional profiles of the grooves, b) the depth and width of the groove, c) SEM image at the surface inclination of 0°, d) SEM image at the surface inclination of 15°.
As shown in Fig. 10, the parameters used are given by Set C7 in Table 2. The groove width does not change significantly under various laser scanning pitch, and the depth of the groove increases obviously. The inclination angle of the groove right side increases gradually. With decreasing laser scanning pitch, more energy gathers in the certain processing area, and the groove extends along the laser incidence direction. When the laser scanning pitch is 2 µm, the inclination of the right side of the groove grows to be slightly greater than 90°. When the scanning pitch dropped to 1 µm, the right sidewall of the groove obviously begins to tilt to the left, which is unfavorable for obtaining a vertical sidewall.
Fig. 10. The cross-sectional profiles and the obtained depth and width under different scanning pitches: a) the cross-sectional profiles of the grooves, b) the depth and width of the groove, c) SEM image at the scanning pitch of 3.33 µm, d) SEM image at the scanning pitch of 1 µm.
As shown in Fig. 11, the parameters used are given by Set C6 in Table 2. The groove width does not change significantly with increasing laser ablation times, but the depth increases linearly. After 30 times ablation, the inclination angle of the groove right side remains to be about 90°. Compared with the obtained results by adjusting the scanning pitch, the verticality of the right sidewall turns to be better under the selected ablation times. Therefore, the ablation times can be optimized to achieve the vertical sidewalls of different depths.
Fig. 11. The cross-sectional profiles and the obtained depth and width after different ablation times: a) the cross-sectional profiles of the grooves, b) the depth and width of the grooves, c) SEM image after 20 times of ablation, d) SEM image after 50 times of ablation.
According to the experimental results, it can be found that the tilted surface angle of workpiece has an obvious effect on the sidewall inclination of the obtained groove, but a large amount of material still remains at the other side, which requires the reverse tilting of the workpiece surface. The finite element simulation of the profile evolution can provide a basic knowledge for selecting the laser parameters, and the geometric model is shown in Fig. 12. The surface tilted angles of states A, B and C is 0°, 10° and - 10°, respectively.
To control the inclination of both sides of the groove, the simulation of the groove profile is undertaken following two steps:
- Step 1: Laser machining simulation is carried out with a tilting angle of 10° (State B);
- Step 2: The contour of the groove in Step 1 is extracted, and the simulation is then carried out at a reverse tilting angle of 10° (State C).
The laser ablation of micro groove is simplified to be a two-dimensional plane. The finite element simulation results for the original workpiece surface (State A) are shown in Fig. 13. Due to the uneven distribution of Gaussian laser energy, the edge of the processing area is inclined. According to Eq. (10), the inclination of the processing area results in decreasing value of $\cos < \textrm{n},\textrm{z} > $, and the laser energy density drops, which then leads to the decreasing material removal rate. The continuing ablation of multi-pulses finally leads to a ‘V’ shape groove. The deviation between the simulated and experimentally obtained groove contour might be partially caused by the reflection of laser beam to change the energy distribution in the processing area [16]. As the reflection phenomenon of the laser in the groove is ignored, there is a certain deviation between the experimentally obtained profiles and the simulation. As far as the simplifications and assumptions for the simulation are taken into consideration, the simulated 2D cross-sectional profiles for the original surface without tilting at the selected parameters is consistent with the experimental results.
Fig. 13. Comparison between simulated groove profiles and experimental results under different ablation times (f = 400 kHz, Q = 10.18 J/cm2, v = 100 mm/s, scanning pitch = 5 µm).
When the sample is tilted by 10° for 20 times ablation (State B) and then a reverse tilt of the surface for processing (State C), the obtained groove bottom presents a ‘V’ shape, as shown in Fig. 14(a). After changing the ablation times in Step 1 and Step 2, the bottom of the groove gradually turns into a “W” shape, which is caused by the fact that some area at the bottom is not ablated after the sample is tilted, as shown in Fig. 13(b-d). The deeper groove in Step 1, the larger remaining area in Step 2. As part of the material is removed in Step 1, the ablation times in Step 2 should be less than Step 1 to ensure a symmetrical groove, but this also leads to a worse inclination of the other side in Step 2.
Fig. 14. The simulated groove profiles under different ablation times in Step 2: a) the ablation times in Step 1 is 20, b) the ablation times in Step 1 is 30, c) the ablation times in Step 1 is 40, d) the ablation times in Step 1 is 60.
One typical cross-sectional profile of the machined groove is shown in Fig. 15, in which the number of ablation times in Step 1 is 30 and the number of ablation times in Step 2 is 20. The profile of the groove is consistent with the simulated result, and a bulge appears at the bottom. The inclination of the groove sidewall significantly improves, compared with the theoretical inclination angle of 66.76°.
Fig. 15. SEM image of cross-sectional profile of a groove under f = 400 kHz, Q = 10.18 J/cm2, v = 100 mm/s, scanning pitch = 5 µm.
The groove morphologies under different surface states are shown in Fig. 16, where the processing parameters of Fig. 16(b) are selected according to the simulation results in Fig. 14(d). By tilting the workpiece surface, the sidewall material of the groove is effectively removed. Through finite element simulation and experimental verification, it can be found that the proposed method can effectively improve the side inclination of the laser ablated microgroove. The machining parameters of grooves with different depths can be optimized through the proposed finite element simulation.
Fig. 16. Cross-sectional profiles of the laser ablated grooves under f =400 kHz, Q = 10.18 J/cm2, v = 100 mm/s, scanning pitch = 5 µm): a) at a tilted surface angle of 0°, b) at a tilted surface angle of 10° (Step 1: 60 times ablation, Step 2: 40 times ablation)
5. Conclusions
In this paper, the effects of laser energy density, scanning speed, ablation times, laser spacing and surface tilting angle on the sidewall inclination in laser processing are investigated. The laser energy density distribution is analyzed, and the finite element simulation model of the groove profile in the laser processing is established. The main conclusions of this study are as follows:
- (1) In the process of the Gaussian laser grooving, the remained material at the groove edge is much larger than the laser spot radius, and the sidewall inclination caused by the ineffectively removed material is dependent on the ablation threshold and the specific laser energy density.
- (2) Taking the changing surface tilting angle and the ablation profile into consideration, the laser energy density formula is developed and applied to the FEM simulation for profile evolution prediction, which achieves certain consistence with the experimental results.
- (3) By tilting the angle of the workpiece surface, the inclination of the groove sidewall improves significantly, where a larger tilting angle of the sample surface leads to a smaller groove depth but a greater width. The inclination of the groove sidewall can be effectively controlled by coordinating the ablation times and the tilting angle.
Funding
China Postdoctoral Science Foundation (2019TQ0151); National Natural Science Foundation of China (51805257, 52175412).
Disclosures
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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