## 4 Discussion
### Single Pulse Excitation (\(t_{delay}=0\))
Nevertheless, for the sake of completeness and aiming to present a general theoretical framework that describes processes that also take place in other semiconductors, even at higher photon energies, a full model is considered assuming a nonzero \(\beta_{TPA}\) and \(\theta\) (Equation (3)). Simulation results that represent the maximum surface lattice temperature also show that \(T_{L}\) evolution rises faster for (001) and therefore, the crystal orientation plays an important role (Figure 2c). To avoid confusion, it is noted that the maximum value of \(T_{L}\) (\(\sim\)3245 K) occurs at different depths of the irradiated material because ablation is more intense at higher fluences and therefore a larger volume is ablated. More specifically, the size of the ablated volume should be larger at higher fluences as the absorbed energy is distributed at larger depths. Nevertheless, the approach followed in the current analysis takes into account the fact that the temperatures attained are high enough to induce evaporation of the material and therefore, to avoid an overestimation of the material surface temperature in the calculations, a correction to the simulation scheme is required. Hence, becausethe boiling temperature is assumed to be the condition for evaporation, in the simulations, all points which exceed that temperature are removed. Thus, the region which is simulated at each timepoint varies dynamically and upon removal of all points with \(T_{L}>T_{L}^{bolling}\), the depth of the induced morphology increases. It is noted that the constant temperature (\(T_{L}~{}=~{}T_{L}^{bolling}\)) in Figure 1c is due to the fact that energy relaxation between the lattice and carrier subsystems is not been reached for some picoseconds; this indicates that until the moment of equilibration between \(T_{L}\) and \(T_{c}\), the carrier subsystem will continue to give energy to the lattice system which might rise above the \(T_{L}^{bolling}\) even if the surface points dynamically change. Hence, the surface continues to reach the boiling temperature and it evaporates leading to ablation while this elevating high temperature remains constant until relaxation processes start to become stronger. By contrast, a cutoff in the temporal decay of the carrier density or the reflectivity is not observed in the simulations. This results from the fact that the carrier density drops slowly after the end of the pulse due to an Auger recombination. Other processes that influence the variation of carrier density (see third equation in Equation (1)) such as the single photon absorption process that is dependent on the lattice temperature has ended before the lattice reaches \(T_{L}^{bolling}\). Similarly, for the same \(E_{p}\), the enhanced \(T_{c}\) for (001) yields a larger \(T_{L}\) which, in turn, implies a larger ablation compared to the mass removal for (100). Special attention is also required to the behaviour of the reflectivity evolution. In previous studies, it was reported that at longer wavelengths and other semiconductors (i.e., silicon), the reflectivity initially drops below the value at 300 K before it starts rising towards reaching a peak as the carrier density increases [26, 66, 94]. Then, as the Auger recombination becomes important and the pulse switches off, the number of carrier drops which forces the reflectivity to fall before relaxing to the initial value. A similar behaviour is also present for both orientations of rutile TiO\({}_{2}\) (Figure 2d). Notably, although the shape of the reflectivity curves is similar for both crystal orientations, the different value of the initial reflectivity for (100) and (001) causes variation in the energy absorption. On the other hand, for the same crystal orientation, irradiation with higher fluences increases the _metallisation_ process of the material. This leads to a rapidly enhanced carrier density followed by a larger peak value of the reflectivity of the excited material. The latter is attributed the generation of an increased number of carriers at higher fluences (Figure 2a).