# Ablation of Copper Metal Films by Femtosecond Laser Multipulse Irradiation
## 3 Results and Discussion  
The numerical simulations were carried out for copper films irradiated by single and multipulse femtosecond laser irradiation with varying fluence, number of pulses and separation times. The choice of copper as a target and these specific parameters of the laser was to be able to compare our results with those available in the literature [15; 16; 29]. Figure 1 shows the calculated reflectivity \(R\) and absorption coefficient \(\alpha\), from Equations (11) and (12), as a function of temperature at an 800-nm wavelength. This figure indicates that \(R\) and \(\alpha\) decrease dramatically with temperature. The decrease in \(R\) causes the target to absorb more laser energy, while the decrease in \(\alpha\) changes the distribution of the laser's heat density \(S\) inside the target. It is obvious that these properties influence the amount of laser energy deposition and distribution during the irradiation and then affect the thermal response (ablation rate) of the material. This is why the optical dynamics must be taken into account during the simulation. [PERSON] et al. [14], [PERSON] et al. [21] and [PERSON] et al. [30] considered \(R\) and \(\alpha\) as constants, which may be valid only at low temperatures. Figure 2 shows the time evolution of the calculated electron and lattice temperatures of copper at a fluence of 10 J/cm\({}^{2}\) and the contour of lattice temperature versus time and position, calculated from the TTM Equations (1) and (2). We see in Figure 2a that the lattice temperature is dramatically increased when the number of pulses increases, and it is important to mention that there is no thermal relaxation (no thermal explosion) until the last pulse, which can enhance the lattice temperature via fast thermal accumulation process. Therefore, despite laser fluence being greater than 10 J/cm\({}^{2}\), the laser-plume interaction has a negligible effect during the irradiation. However, when the separation time between pulses is greater than the relaxation time, the laser-plume interaction must be taken into account. We notice also that the lattice temperature continues increasing more when the pulse number increase as well (Figure 2b). However, on the other hand, we observed immediately in Figure 2d that the lattice is more heated in the same focal volume than in Figure 2c, with some dissipation into the deeper material, for the 10 th pulse's irradiation. This considerable enhancement of temperature is attributed to the heat accumulation effects, which can be called the FTAE because the separation time between pulses is less than the thermal relaxation time. Therefore, we suggest that an overheating of the same  
Figure 1: Reflectivity and absorption coefficient versus electron temperature. Note that the x-axis starts at 300 K.  
superheated liquid was induced by the first pulse, which implies a reduction in ablation rate after each subsequent pulse. Figure 2c,d shows also that the lattice remains cold for the first few picoseconds, because the phonons carry little energy, and it takes many electron-phonon scattering processes, and therefore several picoseconds, before the electrons and the lattice reach thermal equilibrium [31]. To understand the advantage of metal ablation by fast multipulses per burst fully, we must study all the factors that can improve the results in comparison with a single-pulse irradiation. Figure 3 shows the effect of pulse number with 1 ps (1 THz) of separation time (repetition rate) on heating the surface during irradiation. We observe that electron's temperature increases when the number of pulses increases (see Figure 3), which implies a rapid decrease in reflectivity (Figure 1). Therefore, the surface absorption can be enhanced. After each femtosecond laser pulse, the electrons transfer some of their energy to the lattice via electron-phonon collision [31], which implies a pseudo-escalation of the lattice temperature (see Figure 3); as the same remarks mentioned in [19], until the final thermal relaxation is reached.