Ablation depth enhancement on a copper surface using a dual-color double-pulse femtosecond laser

Zhaohui Liu; Yuexin Wan; Xiaolong Li; Botao Fu; Zhen Yi; Wei Chen; Wei Chen; Jia Qi; Jia Qi; Ya Cheng; Ya Cheng; Ya Cheng

doi:10.1364/OE.497612

1. Introduction

Ultrafast pulsed lasers have become increasingly crucial for metal ablation during the past decades for its non-thermal ablation and high accuracy capabilities. Recently, some efforts were performed to improve the laser material processing efficiency and quality by optimizing the laser pulse duration [1,2], repetition rate [3,4], wavelength [5], fluence [2,6], and ablation environments [1,7–10]. Since the early 2000s, a strategy of bursts consisting of two [11–13] or more pulses [3,14–17] has been widely investigated. However, it was found that the ablated volume by double-pulse ablation can be suppressed at the inter-pulse delay from tens of picoseconds to several nanoseconds on many materials, such as copper [12,15–17], nickel [11], silver [18], and steel [14–17]. The suppression of double-pulse ablation can be attributed to many factors. At the inter-pulse delay times of a few picoseconds to hundreds of picoseconds, interference between the rarefaction wave and shock wave generated by the first and second pulse is the main reason. The second pulse can also be shielded by the ablation cloud induced by the first pulse when the delay is beyond tens of picoseconds. For a longer inter-pulse delay between a hundred picoseconds to hundreds of nanoseconds, the shielding of subsequent pulses and re-deposition of material takes place [13,19].

The ablation of copper, one of the most essential industrial metallic materials, has been widely studied to increase throughput for materials processing [4,17,20,21]. For example, Andrius et al. found that the milling ablation efficiency of copper can be increased by 20% for three pulses per burst with an intra-burst pulse repetition rate of 64.5 MHz compared to a non-burst regime [20]. Another research demonstrates that the biburst mode processing, consisting of GHz bursts inside of MHz bursts, had a higher drilling ablation efficiency than the single-pulse drilling [4]. The author revealed that GHz processing seems to be inefficient for both milling and drilling compared to single-pulse processing. However, the ablation efficiency of MHz burst was highly dependent on the odd and even number of pulses per burst, which also was mentioned in other studies [16,17].

In our previous study, we achieved a higher ablation depth and lower surface roughness on stainless steel by using the dual-color double-pulse ablation strategy with the two pulses operating at wavelengths of 515 nm and 1030 nm [22]. In this paper, we choose copper as target to improve the ablation process by the dual-color double-pulse ablation. The time scale for the energy transferring from electron to phonon, electron–phonon coupling time, is about 8∼12 ps for copper [23] compared to a shorter relaxation time of about 1 ps for steel [24]. A longer electron–phonon coupling time means that we have enough inter-pulse delay time, before the interaction between two subsequent pulses, to alter the optical properties, in turn, the laser energy deposition. Winter et al. reported that the surface reflectivity of copper at a wavelength of 515 nm is approximately 59%, which is significantly lower than the reflectivity at a wavelength of 1030 nm, which stands at about 97% [25]. With lower surface reflectivity, more energy is absorbed by the material instead of reflected in the air. Moreover, the interband absorption induced by 515 nm can excite more electrons from d-band above Fermi level because of a higher single photon energy of 515 nm. These electrons contribute to the electron–electron scattering frequency and alter the optical properties. Therefore, we adopt 515 nm as the first pulse instead of 1030 nm in the double pulse ablation to increase the light absorption by the material. The optical properties change of reflectivity (R) and absorption coefficient ($\alpha$) for copper can be described by a critical point model with three Lorentzian terms for interband transition, which was proposed by Ren et al. [26]. The well-known two-temperature model (TTM) is widely used to describe laser-metal interaction. In this article, we combine the critical point model and TTM to analyze the optical properties of copper during the dual-color double-pulse ablation process.

2. Material and methods

The experimental setup can be seen in our previous study [22]. Briefly, a laser pulse with wavelength of 1030 nm and a pulse duration of about 200 fs generated by a commercial Light Conversion laser system is split into two parts through a polarization beam splitter (PBS). One of the pulses passes through a BBO (β-BaB₂O₄) crystal to generate 515 nm wavelength through a nonlinear process. While the other one passes through a delay line to adjust the delay between two paths by optical path difference. Two beams are focused on the surface of copper film by a focusing lens with a focal length of 150 mm. The spot size of 515 nm pulse is halved by a telescope system to match the focused spot size as 1030 nm on the focusing surface. The fluence of 1030 nm is set to be 1.0 J/cm², which is around our experiment's maximum ablation efficiency. Meanwhile, the fluence of 515 nm varied from 0.1 and 0.5 to 1.0 J/cm². The delay between two pulses t_delay = t₁₀₃₀ - t₅₁₅ ranges from -5 ∼ 30 ps, where t₅₁₅ and t₁₀₃₀ are the arriving time of the respective pulse on the ablated surface, respectively. Grooves are machined on the X-Y motion stage at a scanning speed of 50 mm/s. The ablation depth of grooves is measured by using commercial confocal microscope (ZEISS-LSM-800).

3. Modeling and simulation

The dielectric permittivity can be evaluated by the critical point model with three Lorentzian terms proposed by Ren et al. [26].

(1)$$\varepsilon (\omega ) = {\varepsilon _\infty } - \frac{{\omega _D^2}}{{{\omega ^2} + i\gamma \omega }} + \sum\limits_{p = 1}^3 {{B_p}{\Omega _p}(\frac{{{e^{i{\phi _p}}}}}{{{\Omega _p} - \omega - i{\Gamma _p}}} + \frac{{{e^{ - i{\phi _p}}}}}{{{\Omega _p} + \omega + i{\Gamma _p}}})} = {\varepsilon _1}(x,t) + i{\varepsilon _2}(x,t),$$

where ${\varepsilon _\infty }$ is dielectric constant, $\omega _D^{}$ plasma frequency, $\omega$ laser frequency, B weighting factor, $\Omega $ energy of gap, $\phi$ phase, and $\Gamma $ broadening. Those parameters can be found in [26]. $\gamma$ is damping coefficient which is reciprocal of electron relaxation time ${\tau _e}$ which can be calculated by:

(2)$${\tau _e} = \frac{1}{{{B_l}{T_l} + {A_e}T_e^2}} \approx \frac{1}{{3.54{\upsilon _{e,ph}} + {A_e}T_e^2}},$$

in which ${B_l}{T_l}$ represents the electron-phonon collision rates ${\upsilon _{e,ph}}$, and ${A_e}T_e^2$ the electron-electron collision rates. At room temperature with the electron relaxation time of 10 fs, ${B_l}{T_l}$ can be approximated as 3.54${\upsilon _{e,ph}}$. The electron-phonon collision rate ${\upsilon _{e,ph}}$ at room temperature and above can be written as [27]:

(3)$${\upsilon _{e,ph}} = \frac{{{\Xi ^2}}}{{8\pi {\varepsilon _F}{k_F}\rho s}}\frac{{{m_{opt}}}}{{{m_e}}}\left\{ {{q_b}\frac{{{e^{{\varphi_l}}} + {e^{{\varphi_e}}}}}{{({e^{{\varphi_l}}} - 1)({e^{{\varphi_e}}} + 1)}}\frac{{{{(2{k_F})}^4} - {q_b}^4}}{4} - 4\eta {q_b}^2{k_F}^2\frac{{{e^{{\varphi_l}}} - {e^{{\varphi_e}}}}}{{({e^{{\varphi_l}}} - 1)({e^{{\varphi_e}}} + 1)}}} \right\},$$

where ${\varphi _l} = {\beta _l}\hbar {q_b}s$, ${\varphi _e} = {\beta _e}\hbar {q_b}s$, ${\beta _l} = {({T_l}{k_B})^{ - 1}}$, ${\beta _e} = {({T_e}{k_B})^{ - 1}}$, T_e and T_l are the electron and lattice temperature, k_B Boltzmann constant, $\hbar$ reduced Planck Constant, s longitudinal sound velocity, ${\varepsilon _F}$ Fermi energy, ${k_F}$ radius of the Fermi sphere, $\rho$ density, ${m_{opt}}$ effective electron mass, $\eta = 2{m_{opt}}s/\hbar$. $\Xi = 3.99$eV, ${q_b} = \textrm{ 8}.\textrm{97} \times \textrm{1}{\textrm{0}^9}$m^-1, and ${m_{opt}} = 1.39{m_e}$ for copper [26].

By using the Fresnel function, the optical properties reflectivity R and absorption coefficient $\alpha$ can be expressed as:

(4)$$R = \frac{{{{({f_1} - 1)}^2} + f_2^2}}{{{{({f_1} + 1)}^2} + f_2^2}},$$

(5)$$\alpha = \frac{{2\omega {f_2}}}{c},$$

where c is the light speed in vacuum, the refractive index f₁ and the extinction coefficient f₂ are functions of real and imaginary parts of the dielectric function ${\varepsilon _1}$ and ${\varepsilon _2}$:

(6)$${f_1} = \sqrt {\frac{{{\varepsilon _1} + \sqrt {\varepsilon _1^2 + \varepsilon _2^2} }}{2}} ,$$

(7)$${f_2} = \sqrt {\frac{{ - {\varepsilon _1} + \sqrt {\varepsilon _1^2 + \varepsilon _2^2} }}{2}} ,$$

The optical properties of R and $\alpha$ depending on both electron and lattice temperature. For metals like copper, the evolution of the electron and lattice temperature after short-pulse laser irradiation can be generally described by the two-temperature model (TTM) [28]:

(8)$${C_e}\frac{{\partial {T_e}}}{{\partial t}} = \frac{\partial }{{\partial x}}({k_e}\frac{{\partial {T_e}}}{{\partial x}}) - G({T_e} - {T_l}) + S(x,t),$$

(9)$${C_l}\frac{{\partial {T_l}}}{{\partial t}} = \frac{\partial }{{\partial x}}({k_l}\frac{{\partial {T_l}}}{{\partial x}}) + G({T_e} - {T_l}),$$

in which C_e, C_l, k_e, and k_l are the heat capacity and thermal conductivity of electron and lattice respectively, G is the electron-phonon coupling factor. The expression of C_e, C_l, k_e, k_l, and G can be found in [26]. x is spatial coordinate, t is time, and S laser source term which can be expressed as [29]:

(10)$$\begin{array}{l} S(x,t) = 0.94\frac{{[{1 - R(0,t)} ]{J_0}}}{{{t_p}}}\alpha (x,t)\exp \left[ { - \int_0^x {\alpha (x,t)dx - 2.77{{(\frac{t}{{{t_p}}})}^2}} } \right],\\ \end{array}$$

where $R(0,t)$ is the surface reflectivity, t_p is the pulse width with full width at half maximum (FWHM), J₀ the laser pulse fluence.

The time zero t = 0 is defined as when the pulse peak of 515 nm reaches the ablated surface. And the initial boundary condition can be written as follows:

(11)$${T_e}(x, - 2{t_p}) = {T_l}(x, - 2{t_p}) = 300K,$$

(12)$$\frac{{\partial {T_e}(0,t)}}{{\partial x}} = \frac{{\partial {T_e}(L,t)}}{{\partial x}} = \frac{{\partial {T_l}(0,t)}}{{\partial x}} = \frac{{\partial {T_l}(L,t)}}{{\partial x}} = 0,$$

where L is the thickness of the copper film. The Eqs. (8) and (9) can be solved by using a finite difference method [30]. The detailed solution procedure can be found in [31].

4. Results and discussion

Figure 1 displays the relative ablation depth change $\Delta d/({d_{515}} + {d_{1030}})$ as a function of delay time between inter-pulse delay t_delay at different fluence of 515 nm. The corresponding ablation depth of the grooves can be found in Fig. S1. (see Supplement 1). $\Delta d = {d_{515 + 1030}} - ({d_{515}} + {d_{1030}})$, where ${d_{515 + 1030}}$ is the ablation depth of dual-color double-pulse, and ${d_{515}} + {d_{1030}}$ is the sum of ablation depth for individual wavelengths, which also can be regarded as the ablation for dual-color double-pulse at infinite inter-pulse delay. The error bars for $\Delta d/({d_{515}} + {d_{1030}})$ represent measurement errors. The error bars for the time delay are about 500 fs. The dashed-lines in Fig. 1(b) and (c) represent the ablation depth of dual-color double-pulse equal to the total ablation depth of 515 nm and 1030 nm pulses. The fluence of 515 nm pulse in Fig. 1(a) is 0.1 J/cm², a little lower than the ablation threshold, bringing zero ablation depth for 515 nm pulse (that is ${d_{515}}$=0). By using the dual-color double-pulse, the maximum ablation depth increased by about 40% at the inter-pulse delay of 3∼10 ps compared to the total ablation depth of both the 515 nm and 1030 nm pulses. Beyond the inter-pulse delay of 10 ps, the ablation depth of dual-color double-pulse decreased slowly, but is still larger than the single pulse ablation of 1030 nm even at the inter-pulse delay of 30 ps. When the fluence of 515 nm increases to 0.5 J/cm², half of the fluence of 1030 nm, the maximum ablation depth appears at the inter-pulse delay of 0∼2 ps with an increment of about 50%, as shown in Fig. 1(b). With the inter-pulse delay increase, the ablation depth dual-color double-pulse decreased. By the inter-pulse delay beyond 10 ps, the ablation depth appears to be smaller than the sum ablation depth of 515 nm and 1030 nm pulses. As can be seen in Fig. 1(c), there is a very narrow inter-pulse delay time window of about 0∼1.5 ps where the value of $\Delta d/({d_{515}} + {d_{1030}})$ is slightly bigger than 0 at the fluence of 1.0 J/cm² for 515 nm. The maximum ablation depth is only about 0.05% at 0 delays, almost equal to the total ablation depth of both the 515 nm and 1030 nm pulses. The depth drops rapidly with the time delay, as shown both in Fig. 1(b) and (c), meaning the dual-color double-pulse suppress the ablation process, which was observed in previous study with single-color double-pulse ablation [12,13,32,33].

Figure 2 displays the calculated evolution of the surface temperature of electrons for copper irradiated by 515 nm pulse at the fluence of 0.1, 0.5, and 1.0 J/cm². The normalized Gaussian laser pulse with black-dash lines in Fig. 2 is the pulse of 515 nm with pulse width of 200 fs and peak power at t = 0. As shown in Fig. 2, the peak electron temperature is about 10.3 kK, 21.6 kK, and 35.2 kK at the fluence of 0.1, 0.5, and 1.0 J/cm², respectively. The temperature of the electron begins to decrease due to thermal diffusion as well as the energy exchange between the electron and lattice. To analyze the behavior of dual-color double-pulse ablation on copper film, Fig. 3 demonstrates the calculated surface reflectivity and absorption coefficient of copper as a function of the inter-pulse delay for 1030 nm after the irradiation of 515 nm pulse at various fluence. Figure 3 (c) and (d) show more details of Fig. 3(a) and (b) at the inter-pulse delay from -400 to 400 ps. As is shown in Fig. 3(a) and (b), both surface reflectivity and absorption coefficient for 1030 nm decreases rapidly after the irradiation by 515 nm and reach its lowest point (Fig. 3(c) and (d)) by the time the electron temperature comes to the highest (Fig. 2). Subsequently, the reflectivity and absorption coefficient for 1030 nm remains steady with a slow increase in the following time delay. Lower surface reflectivity means the material absorbs more laser energy, while a smaller absorption coefficient means larger optical penetration depth. Hence, the first pulse of 515 nm can alter the optical property for 1030 nm by interband transmission as well as increasing the temperature of electron and lattice, leading to more effective energy deposition for the subsequent pulse.

Fig. 1. The relative ablation depth changes $\Delta d/({d_{515}} + {d_{1030}})$ as a function of delay time between inter-pulse delay t_delay at fluence for 515 nm of (a) 0.1 J/cm², (b) 0.5 J/cm², and (c) 1.0 J/cm². The fluence of 1030 nm is kept to be 1.0 J/cm². The dashed-lines in (b) and (c) stand for the ablation depth for dual-color double-pulse equal to the total ablation depth of both the 515 nm and 1030 nm pulses.

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Fig. 2. The calculated evolution of the surface temperature of electron temperature for copper irradiated by 515 nm pulse at the fluence of 0.1, 0.5, and 1.0 J/cm². The black dashed-lines are the pulse of 515 nm with pulse width of 200 fs as well as peak power at t = 0.

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Fig. 3. The calculated surface reflectivity (a), (c) and absorption coefficient (b), (d) of copper as a function of the inter-pulse delay for 1030 nm after the irradiation of 515 nm at a fluence of 0.1, 0.5, and 1.0 J/cm². The black dashed-lines in Fig. 3(c) and (d) are the same as in Fig. 2.

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The increase of the ablation depth by the dual-color double-pulse ablation in Fig. 1(a) can then be explained. For example, the pulse of 515 nm at the fluence of 0.1 J/cm² increases the temperature of electron in the material to about 10 kK (blue lines in Fig. 2), which enhance the electron-electron and electron-phonon collision frequency and influences the optical property by the Drude part in the dielectric function. The surface reflectivity for 1030 nm drops from 97% to 67% by 30%, while the absorption coefficient decreases from 8.42 μm^-1 to 5.6 μm^-1 by 33.5%. The subsequent 1030 nm pulse absorbs more energy from the subsequent 1030 nm pulse, leading to a more effective ablation process. One may notice that the enhancement still exists at the inter-pulse delay of -5∼0 ps. The arrival time for 1030 nm pulse is earlier than 515 nm at the inter-pulse delay of -5∼0 ps. Although the fluence of 515 nm at 0.1 J/cm² is lower than the ablation threshold, the former pulse of 1030 nm may reduce the ablation threshold for 515 nm leading to the nonzero of the ablation depth. By increasing the pulse energy of 515 nm from 0.1 J/cm² to 0.5 J/cm², the maximum temperature of electron rises to 22 kK (red lines in Fig. 2). With higher electron temperature, the surface reflectivity and absorption coefficient become smaller (40% and 2.4 μm^-1, respectively), which leading to a higher ablation depth, as is shown in Fig. 1(b). The surface reflectivity and absorption coefficient can still be lowered by increasing the fluence of 515 nm to 1.0 J/cm². The maximum electron temperature can be heated up to 35 kK (violet lines in Fig. 2), leading to surface reflectivity for 1030 nm drop to 28% and the absorption coefficient decline to 1.2 μm^-1. However, the ablation enhancement by the dual-color double-pulse isn’t obvious with the energy increment of 515 nm pulse as expected. The reason can be explained by the compensation of the rarefaction and shock waves generated by the first and subsequent laser pulses. The energy of 515 nm pulse at 1.0 J/cm² is high enough to induce an extremely severe interaction between two pulses which would weaken the enhancement of the dual-color double-pulse process induced by the first pulse of 515 nm. The situation might be different when the fluence of 515 nm is 0.1 J/cm². There is no rarefaction wave generated by the first pulse of 515 nm because the fluence is below the ablation threshold. When the fluence of 515 nm increase to 0.5 J/cm², the electron absorbs the laser energy and transports it to the lattice leading to the homogeneous melting at the time scale of electron-ion relaxation time (about 8∼12 ps [23]). At this time, the shock and rarefaction wave occurred. However, the suppression by rarefaction interference of two pulses is too weak to counteract the enhancement before the inter-pulse delay of 10 ps because there is no enough time for the energy to transfer from electron to lattice to generate rarefaction interference. A higher temperature of electrons can be induced at higher energy of 515 nm pulse of 1.0 J/cm². The lattice’s temperature is heated faster because the electron-phonon coupling factor G positively correlates with electron temperature. Hence, the suppression happened sooner for 1.0 J/cm² than 0.5 J/cm². The higher the energy of 515 nm pulse, the stronger the interaction between two pulses and the faster the decline of the value $\Delta d/({d_{515}} + {d_{1030}})$ as a function of delay time.

5. Conclusion

Femtosecond laser ablation of copper is investigated by dual-color double-pulse ablation. With the optimal choice of the 515 nm pulse energy, the ablation depth can be enhanced by at least 50% compared to total ablation depth of both the 515 nm and 1030 pulses at the inter-pulse delay within the range of the electron–phonon coupling time. The reason for ablation enhancement of the dual-color double-pulse ablation can be explained by the increasing temperature of electrons induced by the first pulse of 515 nm leading to the decrease of surface reflectivity and absorption coefficient for 1030 nm. The changes in the optical properties could alter the laser energy deposition, in turn, the amount of material ablation. While at a higher fluence of 515 nm (such as 1.0 J/cm²), the rarefaction interference between two pulses is so strong that the suppression effect counteracts the promotion of the dual-color double-pulse ablation.

Funding

Shanghai Municipal Science and Technology Major Project; National Key Research and Development Program of China (2019YFA0705000); Science and Technology Commission of Shanghai Municipality (21DZ1101500).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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Ablation depth enhancement on a copper surface using a dual-color double-pulse femtosecond laser

Abstract

1. Introduction

2. Material and methods

3. Modeling and simulation

4. Results and discussion

5. Conclusion

Funding

Disclosures

Data availability

Supplemental document

References

Supplementary Material (1)

Data availability

Cited By

Figures (3)

Equations (12)

Optics Express