# Drilling of Copper Using a Dual-Pulse Femtosecond Laser

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}, 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

## 2. Modeling

_{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]:

_{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.

_{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].

_{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]:

_{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 × 10

^{4}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].

_{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.

_{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.

_{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

^{2}, i.e., a single pulse with 4.0 J/cm

^{2}and a dual pulse of 2.0 J/cm

^{2}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.

_{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.

_{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.

_{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.

^{2}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.

^{2}. 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/cm

^{2}. 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.

_{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.

_{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/cm

^{2}, the ablation depth decreases for t

_{sep}< 10 ps but increases to its maximum value for t

_{sep}~ 60 ps.

^{2}. 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

^{2}. It is found that a dual pulse with a total laser fluence of 4 J/cm

^{2}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.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Time dependence of calculated (

**a**) optical reflectivity; (

**b**) electron temperature and (

**c**) lattice temperature on the copper surface for different laser pulses with the same total laser fluence of 4.0 J/cm

^{2}.

**Figure 3.**(

**a**) Time history of ablation depth resulting from different laser pulses and (

**b**) ablation depth as a function of separation time, with a total laser fluence of 4.0 J/cm

^{2}.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Cheng, C.-W.; Chen, J.-K. Drilling of Copper Using a Dual-Pulse Femtosecond Laser. *Technologies* **2016**, *4*, 7.
https://doi.org/10.3390/technologies4010007

**AMA Style**

Cheng C-W, Chen J-K. Drilling of Copper Using a Dual-Pulse Femtosecond Laser. *Technologies*. 2016; 4(1):7.
https://doi.org/10.3390/technologies4010007

**Chicago/Turabian Style**

Cheng, Chung-Wei, and Jinn-Kuen Chen. 2016. "Drilling of Copper Using a Dual-Pulse Femtosecond Laser" *Technologies* 4, no. 1: 7.
https://doi.org/10.3390/technologies4010007