## 4 Discussion
### Single Pulse Excitation (\(t_{delay}=0\))  
Firstly, to highlight the role of crystal orientation, single pulses are used. More specifically, double pulses of zero delay (\(t_{delay}=0\)) with no interference effect are considered and the ultrafast dynamics are investigated. Two sets of the equal laser pulses with \(E_{p}=50\) mJ/cm\({}^{2}\) and \(E_{p}=125\) mJ/cm\({}^{2}\), respectively, lead to a total pulse fluence on the solid sample of 100 mJ/cm\({}^{2}\) and 250 mJ/cm\({}^{2}\), respectively. The evolution of the carrier density, carrier temperature and the lattice temperatures on the surface of the material (at the centre of the Gaussian pulse where the energy absorption is maximal) are illustrated in Figure 2a-c, respectively, for the aforementioned fluences and (100) and (001) crystal orientation. Results illustrate that the maximum carrier densities are higher for (100) than for (001) which highlights the important role of the value of the optical mass. A similar monotonicity is followed by the maximum carrier temperature and simulations show that the maximum value is acquired shortly after the time the carrier density reaches the peak value which agrees with results in previous reports for other semiconductors [26; 56; 57; 94; 95]. We note there is an initial rise of the carrier temperature (Figure 2b) during the first moments of irradiation due to the significantly large heat capacity of the carrier system with respect to that of the lattice. The main processes of energy increase from the electron system are through a (linear) one-photon and free-carrier energy absorption. After a short period, \(T_{c}\) rises rapidly with an increase in the pulse energy. The initial increase can be explained through the examination of the contribution of the competing mechanisms indicated by the various components in the \"source term\" (see an enlarged region in Figure A1 in Appendix A). Similarly, this behaviour is followed by a small decrease. At large fluences, larger amounts of carriers are produced and (given the fact that one-photon absorption and Auger recombination are the two predominant factors that alter carrier density) Auger recombination becomes significant because it varies as \(N_{c}^{3}\). Hence, the enhanced Auger recombination [94] converts carrier ionization energy into kinetic energy that results in an increase in the carrier temperature. It is noted that \(T_{c}\) attains very high values and this could potentially influence the energy band-gap response. Certainly, a more rigorous approach (e.g., based on first principles [96]) should also be considered to estimate a possible \(E_{g}\) variation for large \(T_{c}\). Nevertheless, without loss of generality, it is assumed that substantial qualitative and quantitative changes (that yields different morphological changes) do not occur if \(E_{g}\) is considered constant. Results indicate that differences of the maximum values of \(T_{c}\) and \(N_{c}\) for (001) and (100) at \(E_{p}=125\) mJ/cm\({}^{2}\) are not very distinct compared to those at lower fluences due to the fact that this energy value rapidly yields maximum value of \(N_{c}\) close to \(N_{v}\) (thus, the upper value of available carriers for excitation is nearly reached). Furthermore, it is noted  
Figure 2: Evolution of values of carrier density (**a**), carrier temperature (**b**), lattice temperature (**c**) and reflectivity (**d**) for \(E_{p}=50\) mJ/cm\({}^{2}\) and \(125\) mJ/cm\({}^{2}\) for (001) and (100) crystal orientation at \(x=y=0\) and on the surface of the material. that although longer wavelengths and other semiconductors both impact ionization and two-photon absorption play an important role in the carrier dynamics and lattice response, for TiO\({}_{2}\) and \(\Lambda_{L}\) = 248 nm (that yield energies well above \(E_{g}\)) the latter processes appear to yield insignificant changes in \(N_{c}\) and \(T_{c}\) (see Appendix B).