Drilling of Copper Using a Dual-Pulse Femtosecond Laser

Abstract

The drilling of copper using a dual-pulse femtosecond laser with wavelength of 800 nm, pulse duration of 120 fs and a variable pulse separation time (0.1–150 ps) is investigated theoretically. A one-dimensional two-temperature model with temperature-dependent material properties is considered, including dynamic optical properties and the thermal-physical properties. Rapid phase change and phase explosion models are incorporated to simulate the material ablation process. Numerical results show that under the same total laser fluence of 4 J/cm², a dual-pulse femtosecond laser with a pulse separation time of 30–150 ps can increase the ablation depth, compared to the single pulse. The optimum pulse separation time is 85 ps. It is also demonstrated that a dual pulse with a suitable pulse separation time for different laser fluences can enhance the ablation rate by about 1.6 times.

1. Introduction

Ultrashort (pico- or femto-second) lasers have been successfully demonstrated in drilling, cutting, surface structural modification and internal modification of transparent material because of their minimal heat-affected zone [1] and high peak power intensity [2]. Many theoretical and experimental works on ultrashort laser-material interactions have been reported. In the theoretical studies on femtosecond laser ablation of metal, most works have focused on two-temperature model (TTM) [1,3,4,5] or hydrodynamic model [6]. Experiments with single- or multi-shot ablation or the drilling of metal under different laser parameters have also been presented, e.g., laser fluence [7,8,9] and pulse duration [10,11,12]. For example, the ablation rate of iron can be optimized by variation of the single pulse duration in the range of 0.3–3.6 ps [12]. In our previous study, both numerical simulation and experiments was performed to investigate the femtosecond laser ablation of copper by a single-shot or multi-pulses [13,14].

Recently, numerous experiments on the enhancement of metal drilling using a dual-pulse nanosecond laser have been presented [15,16,17]. Nanosecond laser pulses separated by several tens of nanoseconds are shown that they can enhance the material removal rates while minimizing the heat-affected zone [16]. Experiments on the ultrashort dual-pulse laser drilling of copper using different wavelengths (800 nm and 532 nm) have also been investigated [18,19,20]. For a pulse separation time longer than 10 ps, the resulting plasma was found to shield the target surface and consequently decrease the ablation rate. On the other hand, the enhanced grooving of the steel when using a dual-pulse femtosecond laser was reported recently [21]. However, the optimum pulse delay time for ablation enhancement remains unclear, especially for the pulse separation time in the order of picoseconds.

In this study, the thermal ablation of copper by means of a dual-pulse femtosecond laser is investigated using a computational model, including a TTM with dynamic optical properties, two phase change models for melting and evaporation, and a phase explosion criterion for ejection of the mixture of metastable liquid droplets and vapor. The numerical results of the thermal response and the ablation depth generated by the dual-pulse femtosecond laser under different separation times and laser fluences are presented and discussed herein.

2. Modeling

In Figure 1, a copper foil is normally irradiated by a dual-pulse femtosecond laser on the front surface and the laser beam is propagated along the z-axis. The dual pulse is Gaussian in time with a full width at half maximum of t_p. The pulse separation time is t_sep. For simplicity without losing accuracy, the problem is approximated to be one dimensional since laser spot sizes are much larger than the thermally affected depth. The 1D TTM for electron and lattice temperature in a copper foil is expressed as follows [22,23]:

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

(1)

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

(2)

where t is the time, T the temperature, C the heat capacity, k the thermal conductivity, G the electron-phonon coupling factor, and S(z, t) the laser heat density. The subscripts e and l denote the electron and lattice, respectively. The k_l is usually neglected for pure metals due to the fact that it is two orders smaller than k_e. However, the heat conduction in the lattice should be considered in this model for which it includes solid-liquid and liquid-vapor phase change.

The laser heat density S for a dual pulse can be expressed in a general form as [13]:

$$\begin{array}{ll}\hfill S(z,t)=& {\displaystyle \sum _{i=1}^{2}0.94\frac{[1-R(0,t)]F_i}{t_p}\frac{1}{\delta (z,t)+{\delta }_b}}\hfill \\ & \exp \left[-{{\displaystyle {\int }_0^z\frac{1}{\delta (z,t)+{\delta }_b}dz-2.77\left(\frac{t-(i-1)t_{sep}}{t_p}\right)}}^2\right]\hfill \end{array}$$

(3)

where R(0,t) is the temperature-dependent surface reflectivity of the material at z = 0; F_i is the laser fluence of the i-pulse; δ(z, t) = 1/α(z,t) is the temperature-dependent optical penetration depth; and α(z,t) is the absorption coefficient. The electron ballistic range δ_b added to the δ(z,t) here is to take into account the effects of the hot electron diffusion that spreads the absorbed laser energy into a deeper part of electrons. In this work, a constant value of δ_b = 15 nm for copper is used [5].

In previous studies [3], constant surface reflectivity and absorption coefficient are often assumed for laser energy deposition. However, the dynamic optical properties during laser irradiation can significantly alter the irradiated laser energy absorption and influence the distribution of laser heat density, respectively. In this study, a critical point model with three Lorentzian terms is used to calculate the optical reflectivity and the absorption coefficient of copper [24].

The thermophysical properties, i.e., C, k and G, control the thermal transport and temperature distributions in the laser-irradiated material. In this study, polynomial functions are used to describe the C_e and G for the copper material over a range of electron temperatures [14,25]. At a non-equilibrium condition, the k_e used is a function of electron and lattice temperature as [24]:

$$k_e=\chi \frac{{({\mathsf{\phi }}_e^2+0.16)}^{5/4}({\mathsf{\phi }}_e^2+0.44){\mathsf{\phi }}_e}{{({\mathsf{\phi }}_e^2+0.092)}^{1/2}({\mathsf{\phi }}_e^2+\mathsf{\xi }{\mathsf{\phi }}_l)}$$

(4)

where ϕ_e = T_e/T_F and ϕ_l = T_l/T_F. T_F is Fermi temperature; χ and ξ are constants. For copper, T_F = 8.16 × 10⁴ K, χ = 377 W/(m·K), and ξ = 0.139. The bulk thermal conductivity, specific heat and mass density of copper in solid and liquid phases can be also found in [24].

If the laser fluence of a femtosecond laser pulse is sufficiently high, a solid medium can be melted and ablated through vaporization, and even by phase explosion. To accurately simulate the material removal process, the above 1D TTM is integrated with two phase change models for ultrafast melting/resolidification and evaporation, and a phase explosion model for ejection of metastable liquid and vapor. In the phase change model, the liquid-vapor interfacial velocity can be calculated from the vaporization wave model and shock wave theory [26,27]. The details of these models can be found in reference [28]. They are not described here for brevity.

For metals heated by femtosecond laser pulses, the molten material can be superheated without boiling, because the heating time is too short for the necessary heterogeneous nuclei to form. As the temperature of the superheated liquid approaches the thermodynamic equilibrium critical temperature, T_c, the tensile strength of the liquid rapidly falls to zero. Consequently, homogeneous bubble nucleation occurs at an extremely high rate. The superheated liquid thus relaxes explosively into a mixture of vapor and equilibrium liquid droplets and immediately ejected from the bulk material.

In numerical analyses of ultrafast laser ablation, it is often assumed that phase explosion takes place when the superheated liquid temperature reaches to 90% of T_c [29]. When a volume of the superheated liquid temperature reaches 0.9T_tc, that material is removed under the assumption of phase explosion. The vertical size of the corresponding volume is defined as the ablation depth.

In the numerical simulation, a copper foil with an initial temperature of 300 K is irradiated on the front surface by a dual-pulse femtosecond laser with wavelength of 800 nm, pulse duration of 120 fs and a variable pulse separation time (0.1–150 ps). For each laser pulse, the lasering starts from t = −2t_p and ends at t = 2t_p. The laser energy outside this time period is ignored, because it is too small to significantly alter the results. A number of 2500 finite volumes per µm are employed. The thermodynamic equilibrium critical temperature, T_c, is 7696 K for copper [30]. The details of the numerical iteration algorithms for modeling melting/resolidification and vaporization can be found in [31].

3. Results and Discussion

Figure 2 shows the time dependence of the calculated optical reflectivity, electron temperature and lattice temperature on the copper surface for the different laser pulses with the same total laser fluence of 4.0 J/cm², i.e., a single pulse with 4.0 J/cm² and a dual pulse of 2.0 J/cm² per pulse. The pulse separation times of the two dual-pulses, t_sep, are 10 ps and 100 ps, respectively. As shown in Figure 2a, the reflectivity decreases quickly during the laser pulse irradiation; the reflectivity at room temperature (t = −0.24 ps) is 0.962, and the minimum values for the three cases are 0.244 (t = 0.12 ps), 0.274 (t = 10.1 ps) and 0.31 (t = 100.1 ps). The time-resolved reflectivity for copper irradiated by a femtosecond laser (806 nm, 100 fs) was also presented previously [32]. The temporal reflectivity decreased from a maximum of 0.85 to a minimum of 0.23, which is similar to our single-pulse case.

For the dual-pulse cases, the minimum reflectivity after the second pulse irradiation is usually lower than that of the first pulse. For example, in the case of t_sep = 10 ps (see inset), the minimum reflectivity for the first and second pulses are 0.327 and 0.274, respectively, since the high electron temperatures (see Figure 2b) excited on the copper surface after the first pulse help decrease the reflectivity for the second pulse. It was evident that these dynamic properties could alter the thermal response.

Figure 2b shows that the highest electron temperature decreases with increases in separation time; the maximum values for the three cases are 74,229 K (t = 0.12 ps), 56,029 K (t = 10.1 ps) and 45,967 K (t = 100.1 ps), respectively. In the dual-pulse cases, however, the peak electron temperature induced by the second pulse irradiation is usually higher than that by the first pulse. For example, in the case of t_sep = 100 ps, the peak electron temperatures induced by the first and second pulses are 44,121 K and 45,967 K, respectively. It is worth noting that the surface reflectivity before the second pulse irradiation is lower than that at room temperature (Figure 2a) due to temperature rise in material. The further decrease of the reflectivity by the second pulse increases the amount of laser energy deposited from the second pulse, and thus the electron temperature is increased to a higher level than that by the first pulse.

As shown in Figure 2c, over the timescale of a few picoseconds (see inset), the lattice is heated up via the electron-phonon collisions, and the maximum lattice temperatures after the first pulse for the three cases remain at around 6,926 K, i.e., 90% of the thermodynamic equilibrium critical temperature, T_c (7696 K), which is attributed to the phase explosion. This temperature lasts for about 147 ps for the single pulse and 140 ps for the dual pulse with the pulse separation time 10 ps. However, for the dual-pulse cases with the pulse separation of 100 ps, the lattice temperature starts to drop to below 0.9 T_c at about 63 ps, and quickly reaches 0.9 T_c after the second pulse irradiation. Those time periods of temperature 0.9 T_c shown in Figure 2c indicate the occurrence of phase explosion.

The time histories of material ablation depth resulting from different laser pulses with the same total laser fluence of 4.0 J/cm² are shown in Figure 3a. For each case, there are two different ablation rates. The steep ablation rate results mainly from the phase explosion, while the flatter one in from evaporation. For the dual pulse with the separation time of 100 ps, phase explosion stops at 63 ps, followed by a vaportaion, and then re-starts when the second pulse impinges onto the material. This means that a dual pulse with a separation time shorter than 63 ps, phase explosion would continue to a time instant sooner or later than the time (178 ps here) found for the single pulse. It can be found from Figure 3a that the total ablation depths by the dual-pulse with t_sep ≤ 10 ps are smaller than that of the single-pulse case. When t_sep ≥ 30 ps, the total ablation depth is enhanced, as compared to the single pulse. The enhancement of material ablation by a dual pulse with a longer separation time can be explained as follows. Before the second laser pulse is irradiated, there is more time for the thermal energy to be conducted into the deeper part of material. The spread of energy heats more material to or near to the state of phase explosion, leading to more material ablation by the second pulse. It can be found from Figure 3a that for the case of t_sep = 100 ps, the ablation depth resulting from the first and second pulses are 52 nm and 79 nm, respectively.

The proposed method was used to predict ablation depths, as well as to compare the experimental result by [19] of two delayed femtosecond laser pulses (laser wavelength 800 nm, pulse duration 100 fs). Figure 3b shows the comparison between the simulated and experimental ablation depths with the same total laser fluence of 4.0 J/cm². The simulation results from Figure 3b demonstrate that an optimum value of the pulse separation time, t_sep, for enhancing the ablation efficiency exists. For the cases studied here with a total fluence 4.0 J/cm². The maximum ablation depth is about 150 nm for the dual pulse with the separation time 85 ps. It is noted, however, that the ablation depth by a dual pulse with t_sep < 30 ps is smaller than that by the single pulse of 125 nm.

However, the simulation ablation depths are not agreed well with those by experimental result. The simulation result for the dual pulse with t_sep < 10 ps is similar to the experimental results by [18,19]; e.g., the ablation depth is similar to that by the single pulse for t_sep < 1 ps and smaller for 1ps < t_sep < 10 ps. However, for t_sep > 10 ps, the experimental result show that the ablation depth decreases with t_sep in the range of 10–150 ps. The reason is that when t_sep > 10 ps, the plasma starts to shield the target surface and the second laser pulse is spent reheating the plasma, with no additional ablation depth resulting from the second pulse observed.

Interestingly, the study in which a dual-pulse femtosecond laser train was used to groove steel showed that the ablation depth is dramatically increased with an increase in t_sep, with a maximum ablation depth in the range of 5–30 ps obtained [21]. Recently, a dual-pulse femtosecond laser for ablation of silver foil in vacuum was presented [33]. It was also found that the ablation depth does not always decrease as the t_sep increases longer than 10 ps. For example, with a laser fluence of 106 J/cm², the ablation depth decreases for t_sep < 10 ps but increases to its maximum value for t_sep ~ 60 ps.

In the femtosecond laser material ablation process, it is desirable that the maximum ablation depth be obtained and that the temperature rise could be as low as possible to reduce the heat-affected zone and thermal stresses. Figure 4 shows the variation in the total ablation depth between the single and dual pulse for a total laser fluence of 3–8 J/cm². The ablation depth by the dual pulses with a suitable t_sep, i.e., t_sep = 80, 85, 120, 145, 170 and 190 ps, is higher than that by the single pulse. The straight lines curve-fitted from the calculated data confirm the logarithmic dependence between the ablation depth and the laser fluence. The slope of the fitted line for the dual pulse is found to be higher by about 1.64 times, as compared to that for the single pulse. It is shown that the dual femtosecond pulses with suitable pulse separation time have a potential to increase material removal rates and thereby reducing the undesired thermal effects.

4. Conclusions

This paper reports the numerical results of thermal ablation of copper foil by a single- and dual-pulse femtosecond laser for laser fluences of 3–8 J/cm². It is found that a dual pulse with a total laser fluence of 4 J/cm² and a pulse separation time around 85 ps can increase the amount of material ablated, as compared to a single pulse. It is also demonstrated that a dual pulse with a suitable pulse separation time for different laser fluences can enhance the ablation rate by about 1.6 times. The results show that a dual-pulse femtosecond laser has a potential to improve laser drilling efficiency.