## 4 Discussion
### Double Pulse Excitation (\(t_{delay}\
To emphasise on the significant role of the one-photon excitation and at conditions that do not induce ablation (i.e., \(T_{L}<T_{L}^{boiling}\)) before the second pulse irradiates the material, simulations have been performed for irradiation with \(E_{p}\) = 10 mJ/cm\({}^{2}\) for \(t_{delay}\) = 0.7 ps, 1.5 ps, 4 ps and 10 ps (Figure 7). Interestingly, the carrier density is higher for (001) than for (100) (Figure 7a-d) unlike the behaviour for ablation conditions. This can be attributed to the almost insignificant variation of reflectivity at low fluences and the fact that energy absorption (due to lower reflectivity) is higher for (001) than for (100) at low carrier densities (Figure 4). Results for the carrier density and lattice temperature will help to understand the thermal response of the material at larger depths when high temperatures (but not equal to the boiling point are generally reached). Another interesting issue that is revealed by comparing the carrier density evolution in the two regimes (i.e., ablative and nonablative regimes) is the drop of \(N_{c}\) as a function of time. In contrast to the pronounced smoother gradual decrease in the carrier density value at lower fluences (part of the curve in Figure 7b-d due to the first pulse) for which the maximum attained value for \(N_{c}\) is low, there is a substantially steeper decrease when a substantially peak value of \(N_{c}\) has been reached (Figures 2a, 3 and 7a-d (after exposure to the second pulse)). It is noted that the smooth decrease in \(N_{c}\) for small carrier densities has also been reported in previous works [26; 56; 57; 94; 95]. Figure 4: Evolution of reflectivity 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). Figure 5: Evolution of carrier temperature 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**). Figure 6: (**a**) Lattice temperature at \(t_{delay}\) = 0.9 ps. (**b**) Maximum carrier density and (**c**) maximum carrier temperature for \(t_{delay}\) in the range [0–10 ps] (\(E_{p}\) = 50 mJ/cm\({}^{2}\) and 125 mJ/cm\({}^{2}\) for (001) and (100) crystal orientation. Figure 7: Evolution of maximum carrier density (first row) lattice temperature (second row)) for \(t_{delay}\) = 0.7 ps (**a**,e**), 1.5 ps (**b**,f**), 4 ps (**c**,g**) and 10 ps (**d**,h**), respectively. (\(E_{p}\) = 10 mJ/cm\({}^{2}\)) for (001) and (100) crystal orientation. On the other hand, given that the single photon absorption coefficient is essentially unchanged within the first of the double pulse sequence (because \(T_{L}\) has not started to increase), any change in the carrier density is predominantly caused from the contribution of \(I\) and secondly to the Auger recombination. At low fluences (\(\sim\)10 mJ/cm\({}^{2}\)), no sharp increase in the carrier density is computed because it occurs at higher fluences (Figures 2a and 3). By contrast, when the second constituent pulse irradiates the material, the energy of the lattice system is sufficiently high (Figure 7e-h) to lead to high levels of excitation as \(\alpha_{SPA}\) increases rapidly. Thus, a large number of excited carriers is produced. Results show that for subablation conditions, the maximum \(T_{L}\) increases as the temporal delay becomes larger. This can be attributed to the enhanced one-photon absorption (\(\alpha_{SPA}\) attains large values during the first pulse, but it is about two orders higher when the second pulse irradiates the material due to its \(T_{L}\) dependence (Figure 7e-h)) and free carrier absorption while the influence of impact ionisation appears to be minimal. According to Figure 7, the second pulse irradiates an already hot material (at increasing \(T_{L}\)) that further increases the single photon absorption that leads to a higher carrier density which affects eventually \(T_{L}\) through electron-phonon scattering.