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Abstract
The interaction between a metal surface and multiple pulses was investigated to achieve optimal focusing conditions during ultrashort laser ablation. We report a simple theoretical expression of morphological changes in the ablated channel and demonstrate its advantage in positioning the interactive surface at the focus in real time during multiple-pulse laser ablation of a metallic material. Experimental results on the ablation depth for zinc, nickel, and copper show that the combination of a dynamic focusing system and a theoretical formula of ablation-cycle-dependent ablation depth enables one to control the shape of ablated channels. This model can be applied to a variety of high-efficiency ablation systems and may play an essential role in the development of a high-precision ablation system for the curved surfaces in highly scaled metal gravures used in printed electronics, which currently present challenges for engineers and technicians.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1 Introduction
The interaction between ultrashort pulsed lasers and materials and its related physical phenomena have been studied intensively [1–3]. Recently, the tremendous advantages of pulsed laser ablation in advanced manufacturing have been demonstrated due to the high intensity, adequate orientation, damped noise, and high versatility of this method. This cutting-edge manufacturing method has a wide variety of applications, ranging from circuit printing to nanoparticle/nanosheet synthesis [4–14]. The focusing condition of the ablation beam on a micro-sized spot at the surface of the workpiece determines the aesthetics and precision of the manufactured product. An out-of-focus laser leads to severe disadvantages in the fabricated surface, such as inhomogeneous patterns, accumulated debris, and local damage. Therefore, the ablation surface should be carefully maintained at the laser focus during processing to guarantee homogeneity and aesthetics, with the laser focus being adjusted to precisely follow variations in morphology at the interactive ablation surface throughout the entire ablation process. Reflection-based, interferometry-based, and confocal focusing methods, as well as other advanced optical methods, have been introduced [15–19]. Focusing on the applications of these advanced focusing systems, H.-S. Kim et al. and J. Jivraj employed focus stabilization to detect imperfections in broad optical surfaces [20] and surgery, respectively [21]. Nevertheless, with the majority of previous techniques, it is challenging to locate the laser focus on a non-planar surface in real time; moreover, these methods are not user-friendly in practice. A precise and versatile focusing condition requires a reliable theoretical model that depicts the interaction between the material and the ablation laser as well as the change in topography due to micro-holes produced by the ablation laser during processing.
Several scientists have developed theoretical models to describe the morphology variation in ablated patterns during pulsed-laser ablation [22–29]. M. Hashida et al. derived a relation between the ablation threshold and the pulse duration for copper [30]. O. Armbruster et al. introduced a relation among the ablation threshold, beam spot size, and number of incident laser pulses for silicon and stainless steel [31]. G. Chen and C. H. Li et al. developed a theoretical model describing the thermal effects of pulsed laser ablation on a material [32,33]. Moreover, H. Pazokian, C. Lei et al., and K. Luo et al. investigated ablated channel profile variations during laser processing [34–36]. Several scientists have developed analytical models to measure the ablation threshold under different laser ablation conditions [37–39]. Recently, T.-H. Chen et al. and A. Zemaitis et al. reported a formula for the ablation efficiency and proposed methods for increasing this parameter in ultrashort laser ablation [40–42]. While analytical models are plentiful, the combination of a precise analytical model and an experimental design for achieving tight focusing conditions during ultrashort laser ablation has not yet been proposed
In roll printed electronics, the maintenance of tight focusing conditions on the interactive surface aids in the creation of U-shaped cells, in which the ablated hole has a flat bottom, on the surface of the metal gravure. The U-shaped cells play an important role in gravure printing (Fig. 1), in contrast to V-shaped cells, which have a rounded bottom. The printing process is performed as follows. Microscopically small cells are patterned on the surface of a cylindrical gravure. The conducting ink is transferred to the cells from an ink reservoir, and the doctor blade ensures that the filled-in ink volume is exactly equal to the cell volume. The ink is completely transferred to the substrate due to the pressure applied by the impression roller to form a miniature electronic circuit. V-shaped cells are typically fabricated by fixing the ablation laser focus position [43]. Meanwhile, U-shaped cells provide a smaller ratio of surface area to volume, leading to a smaller adhesive force between the cell and fluid than in V-shaped cells; thus, U-shaped cells can be more easily emptied than V-shaped cells when the ink is transferred from the gravure cells to the substrate. In addition, when ink drops from the U-shaped cells are transferred to the substrate, they spread and coalesce to form a line on the substrate. For U-shaped cells, the drops coalesce to form a smooth continuous line; however, for V-shaped cells, in which a tight focusing condition is not maintained, the drops are more prone to form discontinuous spots or scalloped lines on the substrate [44,45]. Thus, real-time positioning of the ablation laser focus on the target surface is essential to control the cell shape on the roll gravure and consequently to optimize the filling and release of conducting ink during the printing process, thus determining the quality of printed electronics.
In this work, we analytically investigate the interaction between a metal surface and an ultrashort laser pulse to obtain the dynamical change in ablation depth during laser ablation of a metal applied in roll printed electronics. The theoretical model is then applied to a dynamic focusing system to maintain optimal focusing conditions at the workpiece surface during the ultrashort laser ablation process. The laser focus follows the evolution of the ablation depth throughout the entire ablation process. This automatic adjustment of the laser focus on an interactive surface is shown to control the ablated hole morphology and increase the ablation efficiency. This benefit is essential in printed electronics, where homogeneous patterns with U shapes on the surface of the printing gravure are needed. This paper is organized as follows. First, an experimental schematic of the dynamic focusing system is presented as a template for applying a theoretical model of ablation depth evolution during the ablation process. Secondly, the interaction between the metal sample surface and laser pulses is studied to derive the evolution of ablation depth according to the number of incident pulses and the scanning cycles of the ablation laser. Subsequently, experimental results are presented to support the reliability and applicability of the proposed theoretical model. Lastly, we provide some discussions and conclusions regarding the proposed technique. By applying the theoretical evolution of ablation depth to a dynamic focusing system, we can achieve a new generation of high-precision, high-efficiency ablation systems, offering a versatile micromachining method for highly scaled metal gravures.
2 Experimental methods
The ablation setup is shown in Fig. 2. The ablation laser is focused on the sample surface by a dynamic focusing system, which dynamically moves the focal point of the ablation laser along the z-axis. The system consists of three lenses: a negative lens ${{\boldsymbol L}_1}$ (${{\boldsymbol f}_1}$), a positive lens ${{\boldsymbol L}_2}$ (${{\boldsymbol f}_2}$), and an objective lens ${{\boldsymbol L}_3}$ (${{\boldsymbol f}_3}$). While ${{\boldsymbol L}_2}$ and ${{\boldsymbol L}_3}$ are maintained at fixed positions, ${{\boldsymbol L}_1}$ is shifted by a micro-positioning stage around the initial position, at which the beam between ${{\boldsymbol L}_2}$ and ${{\boldsymbol L}_3}$ is collimated to adjust the focal position of the ablation laser along the z-axis. The relation between the ${{\boldsymbol L}_1} - {{\boldsymbol L}_2}$ distance ${\boldsymbol h}$ and the distance ${\boldsymbol u}$ between the laser focal position and the objective lens ${{\boldsymbol L}_3}$ is expressed as follows [46]:
Accordingly, the ratio of displacement of the negative lens ${{\boldsymbol L}_1}$ to that of the laser focal position is
Fig. 2. Schematic of real-time z-scanning for multiple-pulse laser ablation on a cylindrical gravure.
In practice, the focal length of the positive lens .. should be significantly larger than that of the objective lens ${{\boldsymbol f}_3}$ because the laser focus must shift a very small distance $\Delta {\boldsymbol u}$ while the positive lens should not move by a distance $\Delta {\boldsymbol h\; }$ smaller than the limit of the micro-positioning stage. In addition, the focal spot size is found to vary only slightly, with a deviation of less than 1%; meanwhile, the lens ${{\boldsymbol L}_1}$ is shifted in the range of a few millimeters about the initial position. During the ablation process, the sample is shifted along the y-axis (Fig. 2) for a multiple-pulse laser to fabricate the channel on the surface. The channel is produced by overlapping consecutive laser pulses at the focus. After the channel is completed, the full cycle ends. The real-time z-scanning of the multiple-pulse laser is designed to maintain the laser focus on the interactive surface of the sample; in this way, after each ablation cycle along the y-axis, the laser focus is shifted a distance equal to the channel depth corresponding to the shift of the negative lens ${{\boldsymbol L}_1}$ along the z-axis. Thus, optimal focusing conditions are achieved and automatically maintained during ultrashort laser ablation. In the next section, the evolution of the ablation depth after each ablation cycle will be derived to automatically adjust the focus on the interactive surface.
3 Theoretical model
The theoretical model quantifies the general ablation process, as schematically illustrated in Fig. 2. The laser pulse is focused onto the metal surface by the dynamic focusing system described in the previous section. The distance between the laser focal position and the objective lens ${z_f} = u$ can be tuned by shifting the negative lens ${L_1}$. $w({z^{\prime}} )= {w_o}\sqrt {1 + {{\left( {\frac{{z^{\prime}}}{{{z_R}}}} \right)}^2}} $ is the beam spot size at the interactive surface (focal plane), where $z^{\prime} = z - {z_f}$ is the defocal distance from the surface to the laser focus (${z_f} = u$) and $\; {z_R} = \frac{{\pi w_o^2}}{\lambda }$ is the Rayleigh length. The laser beam is scanned along the y-axis with speed v and repetition rate f, producing an ablated channel along the y-axis with a profile of H(x). To construct a simple theoretical model for multiple-pulse laser ablation, we assume that the physical parameters of temperature, electron heat capacity, electron density, and absorption coefficient are time-independent during each pulse ($\tau $) and that only free electrons participate in heat conduction as an ideal gas $\left( {{c_e} = \frac{3}{2}} \right)$ at surface temperatures comparable to the Fermi level (free electron model). In addition, the temperature is homogeneous at the interactive surface during each pulse.
2.1. Laser penetration
Let us consider a laser pulse focused on a metal surface and penetrating into the interior region of the metal. In this process, the laser field is exponentially reduced based on the depth of laser penetration in the material due to optical absorption of the laser photons [29]. The laser electric field E(x,y,z) decreases in three directions (x, y, z) following the penetration depth into the sample:
2.2. Acceleration of electrons in metal
In this process, all laser energy absorbed by the metal is converted into kinetic energy for free electrons. Equivalently, the incident laser heats the electron gas along the propagation direction, as described by the energy conservation law [29]:
where ${n_e} = \frac{{8\sqrt 2 \pi {m^{\frac{3}{2}}}}}{{{h^3}}}\left( {\frac{2}{3}\varepsilon_F^{\frac{3}{2}}} \right)$ is the electron density of the metal and ${I_o}$ is the incident laser intensity. The thermal energy is transferred from the absorbed laser energy, which is proportional to the laser intensity ($I(z )\sim E{(z )^2}$) and the temperature-dependent absorption coefficient $a = 1 - r = \frac{{4n}}{{{{({n + 1} )}^2} + {k^2}}}$, in which n and k are the refractive index and extinction coefficient:The electron energy in Eq. (3) is calculated as
2.3. Ablation threshold
The total energy for ablation during a single pulse $\tau $ is defined as the sum of the electron work function ${\varepsilon _w}$ and the atomic binding energy or heat of evaporation of the metal ${\varepsilon _b}$. This energy is barely sufficient to eject electrons and ions from the metal surface ($z = 0$) during a single pulse:
The quantity ${I_o}$ for a single pulse is the incident intensity needed to eject electrons and ions from the metal surface. The ablation threshold fluence is then computed as follows:
To verify this model, we calculated the ablation threshold fluences of copper and gold when ablated by lasers with wavelengths of 780 and 1053 nm, respectively, and compared these values with results from previous studies. For copper, the parameters are ${n_e} = 8.45 \times {10^{28}},\; {\varepsilon _b} = 3.125\; eV,\; {\varepsilon _w} = 4.65\; eV,\; and\; \lambda = 780\; nm$. The ablation threshold fluence is calculated as ${({{F_{th}}} )_{Cu}} = 0.61\; J/c{m^2}$, which is consistent with the data shown in the experimental figure in [47], where the copper plate appears to be ablated at approximately $F = 0.6\; J/c{m^2}$. For gold, the parameters are ${n_e} = 5.9 \times {10^{28}},\; {\varepsilon _b} = 3.37\; eV,\; {\varepsilon _w} = 5.1\; eV,\; and\; \lambda = 1053\; nm$. The ablation threshold fluence is computed as ${({{F_{th}}} )_{Au}} = 0.44\; J/c{m^2},$ which is very close to the result reported in [48] (${({{F_{th}}} )_{Au}} = 0.45 \pm 0.1\; J/c{m^2}$).
2.4. Heat accumulation model
For a static laser source, according to the heat accumulation model [25,49], the ablation threshold decreases after each pulse. As more laser pulses N arrive, the threshold decreases and the surface is more easily ablated.
The absorbed flux of a moving incident laser with speed v and pulse duration $\tau $ is calculated as follows [34]:
The ablation depth after the first pulse is calculated when $x = 0$:
The laser beam moves with velocity v and repetition rate .. along the y-axis, and the number of pulses needed to cover a beam spot area along the scanning channel during the first ablation cycle is
The laser focus is positioned on the metal surface with $w({z^{\prime}} )= {w_o}$, and the depth of the laser-ablated holes after the first cycle is defined when $x = 0:$
The total depth after the Nth cycle is as follows:
Because the change in depth (a few microns) is far smaller than the focal depth (${z_R} \approx 40\; m$), the beam spot size at the interactive surface remains constant over several dozen cycles (${w_o} = w({d({1st} )} )= w({d({2nd} )} )= \ldots = w({d({N - 1th} )} )$). For this reason, the ablation depth will increase linearly with the number of cycles. In the following section, we demonstrate this linear relation by performing a laser ablation experiment on zinc, nickel, and copper.
4 Experimental results and discussion
We performed a laser ablation experiment on zinc, nickel, and copper to demonstrate the feasibility of proposed analytical model. The channels were produced with constant laser powers of $P = 0.4\; W$, $0.8\; W$, and $2\; W$, a repetition rate of $f = 400\; kHz$, a wavelength of $\lambda = 515\; nm$, and a pulse duration of $\tau = 7\; ps$. The scanning speed of the laser on the sample surface was $v = \; 1000,\; 800,\; \textrm{or}\; 400\; mm/s$, and the focal spot diameter was $2{w_o} = 3\; \mu m$. To evaluate the reliability of the proposed analytical model, the focus was fixed at the sample surface plane during the ablation process, and the evolution of the ablation depth after each scanning cycle was observed by optical microscopy. We simultaneously calculated the ablation depth after a specific number of scanning cycles based on Eq. (17). Table 1 presents parameters for the tested metals at room temperature. For these parameters, the ablation threshold fluences of zinc, nickel, and copper for the first pulse are ${({{F_{th}}} )_{Zn}} = 0.41\frac{J}{{c{m^2}}},\; {({{F_{th}}} )_{Ni}} = 1.39\frac{J}{{c{m^2}}},$ and ${({{F_{th}}} )_{Cu}} = 0.61\; J/c{m^2}$.
Table 1. The parameters for the tested metals at room temperature.
The experimentally measured ablation depth is shown in Figs. 3, 4, and 5 as a function of the scanning cycle number, and the influence of ablation cycle number on the microgroove morphology is shown for different laser powers (0.4, 0.8, and 2 W) in Figs. 6, 7, and 8. These results demonstrate the reliability and applicability of the proposed analytical model. The ablation depth increases linearly with the number of incident ablation cycles, and the microgroove surfaces become smoother and more uniform at higher cycle numbers and laser powers. The absorption coefficient ${\boldsymbol a}$ and the reflectivity ${\boldsymbol r}$ are temperature-dependent parameters; thus, the ablation threshold fluence for a specific metal is also temperature-dependent [51,52]. The parameters of ablation threshold fluence ${{\textbf F}_{{\textbf {th}}}}({{\textbf N},{\textbf w}({{\textbf z^{\prime}}} )} )$, absorbed flux of the moving incident laser ${\textbf F}({{\textbf P},{\textbf w}({{\textbf z^{\prime}}} ),{\textbf x}} )$, and effective penetration depth ${{\boldsymbol l}_{\boldsymbol s}}$ in Eq. (17) cannot be explicitly calculated from the experimental conditions because the temperature of the interactive surface changes continuously during ablation at different rates, based on the scanning speed ${\boldsymbol v}$, laser power ${\boldsymbol P}$, wavelength ${\boldsymbol \lambda }$, repetition rate ${\boldsymbol f}$, pulse duration ${\boldsymbol \tau }$, focal spot size $2{{\boldsymbol w}_{\boldsymbol o}}$, and metal type. However, the experimental findings show that the ablation depth increases linearly with the number of cycles; thus, one can fit the theoretical formula with the experimentally acquired data to achieve a robust formula of ablation-cycle-dependent depth (17) using known parameters for specific initial ablation conditions. From this formula, with each specific set of ablation conditions (${\boldsymbol v},{\boldsymbol \; P},{\boldsymbol \; \lambda },{\boldsymbol f},{\boldsymbol \tau },{{\boldsymbol w}_{\boldsymbol o}},$ metal type), we can obtain the ablation cycle dependence of ablation depth (17) applied in the specific fitting equations shown in Figs. 3, 4, and 5. By applying the proposed formulas (15), (16), and (17) with all known parameters to the micro-positioning stage, one can automate the movement of the negative lens ${{\boldsymbol L}_3}$ to maintain the ablation laser focus on the interactive surface of a highly scaled gravure during the ablation process for any initial ablation conditions. Figures 6, 7, and 8 indicate the increasing flatness of microgroove surfaces with increasing ablation cycles. The flatness reduces the adhesive force between conducting ink and microgroove surfaces. With this system, one can control the depth and flatness of the ablated holes, thus optimizing the aspect ratio (depth–diameter ratio) to achieve optimal filling and release of conducting ink. Consequently, the conducting ink can completely fill the ablated holes on the printing gravure and can be completely transferred to the substrate to form electronic structures during the gravure printing process [44,45].
Fig. 3. Laser ablation of zinc at a repetition rate of f = 400 kHz, a wavelength of λ = 515 nm, a pulse duration of τ = 7 ps, and a focal spot diameter of 2wo = $3{\boldsymbol \; \mu m}$ with scanning speed of (a) 1000 mm/s, (b) 800 mm/s, (c) 400 mm/s.
Fig. 4. Laser ablation of nickel at a repetition rate of f = 400 kHz, a wavelength of λ = 515 nm, a pulse duration of τ = 7 ps, and a focal spot diameter of 2wo = $3{\boldsymbol \; \mu m}$ with scanning speed of (a) 1000 mm/s, (b) 800 mm/s, (c) 400 mm/s.
Fig. 5. Laser ablation of copper at a repetition rate of f = 400 kHz, a wavelength of λ = 515 nm, a pulse duration of τ = 7 ps, and a focal spot diameter of 2wo = $3{\boldsymbol \; \mu m}$ with scanning speed of (a) 1000 mm/s, (b) 800 mm/s, (c) 400 mm/s.
Fig. 6. Optical microscope images of microgrooves on a zinc sample after 1, 2, or 5 ablation cycles at an incident power of 0.4 or 0.8 W and a scanning speed of 1000 mm/s.
Fig. 7. Optical microscope images of microgrooves on a nickel sample after 1, 2, or 5 ablation cycles at an incident power of 0.4 or 0.8 W and a scanning speed of 1000 mm/s.
Fig. 8. Optical microscope images of microgrooves on a copper sample after 1, 2, or 5 ablation cycles at an incident power of 0.4 or 0.8 W and a scanning speed of 1000 mm/s.
5 Conclusions
In this study, we have presented a theoretical model of the interaction between a metal surface and ultrashort laser pulses and have provided a method for controlling the morphology of ablated holes by maintaining tight focusing conditions for the interactive surface during cycle-based laser ablation. Experimental laser processing was applied to zinc, nickel, and copper surfaces to validate the derived theoretical formula. The proposed method offers substantial benefits for roll electronic printing. With versatile manipulation of the ablated cell morphology on a metal gravure, one can control the shape and size of the electronic structure on the substrate; thus, the function, homogeneity, and aesthetics of miniature electronic circuits can be significantly enhanced. Automated control of the fabrication laser focus achieved via the proposed formula can enable cost reductions and enhanced precision in ultrashort laser processing, providing important advantages for ultrashort laser-based science and technology.
Funding
National Foundation for Science and Technology Development (103.03-2020.48).
Acknowledgments
We thank the Department of Laser and Electron Beam Technologies, Korea Institute of Machinery and Materials for contributions to the study, particularly Dr Hyonkee Sohn, Dr Dongsig Shin, and Prof. Jiwhan Noh, for their helpful advice with theoretical calculation, experiment and data analysis.
Disclosures
The authors declare no conflicts of interest
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