# Ablation of Copper Metal Films by Femtosecond Laser Multipulse Irradiation
## 3 Results and Discussion
Figure 5: The time dependence of the calculated electron (solid line) and lattice (dash line) temperatures at different laser fluences with 4 pulse and 1 ps (1 THz) of separation time (repetition rate). The proposed simulation was done to predict the ablation depths at different pulse numbers, as well as to compare our results with the experimental data at a single pulse. Figure 6 shows the theoretical ablation depth of copper irradiated by 1-, 2-, 3-, 4- and 5-fs laser pulses with a 1.5-ps (\(\frac{2}{3}\) THz) separation time (repetition rate), along with experimental data from [6,11]. The ablation depth corresponding to the time equilibrium of electron-phonon relaxation \(t_{eq}\) and the condition of phase explosion \(0.9\times T_{\mathrm{c}}\) are indicated in Figure 2 by a coordinate (d, \(t_{eq}\), \(0.9\times T_{\mathrm{c}}\)). The theoretically calculated ablation depths for different pulse number are shown in (Table 1) (which correspond to the values presented in Figure 6). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fluence (J/cm\({}^{2}\))**} & **N= 1** & **N = 2** & **N = 3** & **N = 4** & **N = 5** \\ \cline{2-6}  & \multicolumn{6}{c}{**Ablation Depth (nm)**} \\ \hline
1 & 21 & 78 & 102 & 116 & 122 \\
5 & 189 & 272 & 314 & 332 & 348 \\
6 & 268 & 438 & 503 & 556 & 575 \\
10 & 357 & 532 & 611 & 664 & 671 \\
20 & 509 & 720 & 802 & 861 & 871 \\
30 & 653 & 888 & 997 & 1067 & 1070 \\
50 & 883 & 1175 & 1307 & 1394 & 1398 \\
60 & 931 & 1222 & 1357 & 1439 & 1447 \\
100 & 1080 & 1367 & 1485 & 1566 & 1575 \\
200 & 1547 & 1927 & 2096 & 2192 & 2216 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ablation depth calculated by varying the fluence at different pulses. Figure 6: Simulation of ablation depth at different pulse numbers with \(t_{sep}=1.5\) ps (\(\frac{2}{3}\) THz repetition rate), and experimental data for single-pulse ablation from [PERSON] et al. [6] and [PERSON] et al. [11]. Two different logarithmic dependences can be observed in Figure 6, as described in [3], which confirms the existence of two types of ablations, called gentle and strong ablations at low and high fluence [6], respectively. Figure 6 shows that the ablation depth in general is dramatically enhanced with fluence, but at the same total fluence, the rate of matter removal decreases as the number of pulses increases (see Figure 7) where ablation rate = (ablation depth (d))/(pulse number (N)). Therefore, we deduce that the most laser energy is deposited by the subsequent pulses reserved for the overheating of the same focal volume irradiated by the first pulse. We notice in Figure 7 that at \(F=1\,\mathrm{J/cm^{2}}\), the ablation rate is disordered, which confirms our previous proposal [32] that the physical mechanism changes when the ablation phases change [6], where at low fluence, electron-ion collision is the most dominant, implying a gentle ablation, but at high fluence, electron-phonon collision is the most dominant, implying a strong ablation. In summary, the first intense ultrashort laser pulse can produce a superheated liquid [10; 13], but because the interpulse separation is less than the thermal relaxation time, the thermal wave has no time to propagate deeper into the material. This implies a thermal accumulation effect after each pulse, i.e., there will be an overheating of the same superheated liquid induced by the first pulse at the same focal volume. Then, the evaporation rate can be enhanced during the same single-phase explosion. This will produce a reduction of the liquid phase during thermal explosion, and then, a crater with high precision can be obtained at high fluence with a multipulse femtosecond laser with a fast separation time. We see also that the calculations done using this dynamic TTM are in agreement with the experimental data reported in Figure 6.  
Figure 7: The ablation rate as a function of fluence at different pulse numbers with \(t_{sep}=1.5\) ps (\(\frac{2}{3}\) THz repetition rate).