# Ablation of Copper Metal Films by Femtosecond Laser Multipulse Irradiation
## 3 Results and Discussion
The increase in the number of pulses induces a heat accumulation, where the lattice has not had enough time to cool down after each pulse, which implies a considerable increase in the lattice temperature. Therefore, the superheated liquid temperature can be enhanced and the matter can be ejected, after phase explosion, in both vapor and drop liquid forms. We suggest that in  
Figure 2: Evolution of electron and lattice temperature as a function of time during the irradiation by 10 / cm\({}^{2}\): (**a**) 5 pulses and (**b**) 10 pulses with 1.5 ps (\(\frac{2}{3}\) THz) of separation time (repetition rate). Lattice temperature (\(T_{l}\)) versus time and position into a copper sample for an absorbed fluence of 10 J/ cm\({}^{2}\): (**c**) 5 pulses and (**d**) 10 pulses with 1.5 ps (\(\frac{2}{3}\) THz) of separation time (repetition rate). d, \(t_{eq}\) and \(T_{\mathrm{c}}\) represent ablation depth, time equilibrium and critical temperature, respectively. \(T_{\mathrm{c}}=7696\) K. TTM: Two Temperature Model. the multipulse regime, the vapor rate formation is higher in comparison to single-pulse irradiation, as long as the temporal separation between pulses is short enough to build up the FTAE, in contrast with the studies done in [15; 22] with longer times between pulses. Therefore, this FTAE enhances the equilibrium temperature \(T_{eq}\), but at the same time decreases the relaxation time (equilibrium time) \(t_{eq}\), as can be seen in Figure 3, where (\(T_{eq}\)(K), \(t_{eq}\)(s)) are equal to (\(8.97\times 10^{4}\), \(14.1\times 10^{-12}\)), (\(3.07\times 10^{4}\), \(8.1\times 10^{-12}\)), corresponding to one and five pulses being indicated. Therefore, we suggest that, in addition to an enhancement of the superheated temperature, there is also an enhancement in vapor rate ejected with increasing number of pulses. Following the results discussed above, we propose that a cleaner crater can be obtained at high fluences by using femtosecond laser bursts with sufficiently low interpulse separation to minimize the liquid phase during the explosion, tailoring the temporal separation between pulses. Figure 4 shows the effect of interpulse separation time on the thermal response of the copper surface during irradiation with four pulses per burst at 1 J/cm\({}^{2}\) with \(t_{sep}\) = 0.5, 1, 1.5 and 2 ps corresponding to 2, 1, \(\frac{2}{3}\) and \(\frac{1}{2}\) THz of repetition rate, respectively. It can be seen that as the interpulse separation time is decreased, the electrons reach a higher temperature, reaching a maximum at earlier times. Although the equilibrium temperature is almost the same for all four cases under study, we see that the heating rate increases when \(t_{sep}\) decreases; for example, at 5 ps, the lattice temperature corresponding to \(t_{sep}\)= 0.5 ps is nearly twice that corresponding to \(t_{sep}\) = 2 ps. Therefore, we suggest that with decreasing the separation time, FTAE is more efficient. Finally, we fix the pulse number to four and the interpulse separation time to 1 ps (1 THz repetition rate) and vary the fluence as 1, 6, 10 and 60 J/cm\({}^{2}\). Figure 5 shows the temporal behavior of the calculated electron and lattice temperatures at different laser fluences. We observe that electrons' temperature increases with increasing laser fluence, which implies that the lattice temperature increases as well via the electron-phonon collision process. Therefore, we can deduce that the ablation depth has to increase dramatically with the laser fluence. Figure 3: Time dependence of the calculated electron (solid line) and lattice (dash line) temperature with varying pulse number at a fluence of 60 J/cm\({}^{2}\) and 1 ps (1 THz) of separation time (repetition rate). Figure 4: Time dependence of the calculated electron (solid line) and lattice (dash line) temperatures with varying separation time \(t_{sep}\) at a fluence of 1 J/cm\({}^{2}\) and four pulses.