## 4 Discussion
### Double Pulse Excitation (\(t_{delay}\
eq 0\))  
To investigate the influence of irradiation with double pulses on the ultrafast dynamics Equations (1)-(7) are solved for pulse delays in the range [0,\(-\)20 ps]. In Figures 3-5, the surface carrier density, reflectivity and carrier temperature evolution, respectively, are illustrated for three representative values of \(t_{delay}\) = 0.5 ps, 0.9 ps, and 1.5 ps for \(E_{p}\) = 50 mJ/cm\({}^{2}\) and 125 mJ/cm\({}^{2}\) and both crystal orientations. Results are shown for a temporal delay between pulses smaller than \(2\tau_{p}\) (0.9 ps) where the two pulsesoverlap as well as for pulses with a larger separation (1.5 ps). According to simulations (Figure 6b,c), the maximum surface carrier density and temperature decrease gradually for short delays (\(t_{delay}<2\tau_{p}\)), reaching a minimum value that remains unchanged even at longer \(t_{delay}\). To explain this behaviour, it is important to note that the first of the constituent pulses leads to ablation; hence, the enhanced surface lattice temperature (\(\sim T_{L}^{billing}\)) of the material yields similar \(\alpha_{SPA}\) (i.e., \(\sim 10^{6}\ \times\exp\left(T_{L}^{billing}/300\right)\) cm\({}^{-1}\)) before the second pulse irradiates the material for \(t_{delay}>\sim\)2\(\tau_{p}\). Figure 6a, illustrates that \(T_{L}\sim T_{L}^{billing}\) at, approximately, \(t_{delay}=1\) ps which justifies the appearance of the minimum \(T_{L}\) at \(t_{delay}>2\tau_{p}\). This behaviour is different from the one exhibited in other laser conditions (i.e., nonablation conditions at \(\Lambda_{L}=800\) nm) for which the second pulse leads to higher carrier densities and temperatures [36,97]. Due to the substantially larger contribution of one-photon based excitation at low wavelengths and the negligent contribution of impact ionization and two-photon ionization, the fact that \(\alpha_{SPA}\) remains constant at \(t_{delay}>\sim\)2\(\tau_{p}\) leads to unchanged values for \(T_{c}\) and \(N_{c}\). The above investigation is important because it also reveals both the ultrafast dynamics and temperature evolution inside the volume of the material in ablation conditions. A detailed picture of the induced thermal effects below the surface of the material will help to model the morphological changes and surface patterning procedure. However, results show that \(T_{c}\), \(T_{L}\) and \(N_{c}\) can provide a detailed description of the laser energy distribution and thermal effects on the affected layer of the material, exploration of dynamics through analysis of the thermal changes on the surface (in ablation conditions at \(E_{p}=50\) mJ/cm\({}^{2}\) and 125 mJ/cm\({}^{2}\)) is hindered by the fact that the material remains at the isothermal \(T_{L}\ =\ T_{L}^{billing}\) for a long time and therefore, important details of the thermal effects below the surface of the material are not easily manifested. It is evident that one way to illustrate how pulse separation influences the energy absorption and thermal effects at larger depths in ablation  
Figure 3: Evolution of carrier densities for \(E_{p}=50\) mJ/cm\({}^{2}\) and 125 mJ/cm\({}^{2}\) for (001) and (100) crystal orientation at \(t_{delay}=0.5\) ps (**a**), 0.9 ps (**b**), and 1.5 ps (**c**). conditions is by presenting the affected zone characteristics (i.e., temperature distribution, volume of affected zone, position of surface after ablation). By contrast, to show the impact of the laser parameters on the induced thermal effects below the ablated region (and at depths characterized by lower energy distribution), an alternative investigation is performed; more specifically, simulations are conducted assuming excitation of the material at lower fluences (i.e., that do not cause ablation; this is equivalent to exploration of dynamical effects in places where material is excited but is not removed).