# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 3 Results and Discussion
### Gallium Arsenide  
Such estimation has been performed for GaAs in [32], however, not with the code XTANT. The current version of XTANT cannot treat properly the relaxation of X-ray excited GaAs. This is due to the specific band properties of GaAs which, in particular, imply that the effective masses of electrons and holes differ by a factor of \(\sim\)10. As a consequence, there is no fast global thermalization of electrons and holes in both valence and conduction bands [32]. Instead, electrons and holes thermalize separately within the conduction and the valence band, respectively, at the timescale of a few hundred fs. The equilibration of electron and hole temperatures occurs much later, at \(\sim\)10 ps. The XTANT code uses currently the assumption of simultaneous thermalization of electrons and holes. It cannot then be applied in this case. Optical properties of GaAs were studied experimentally in [9; 33] with VUV/soft X-ray (40 eV) in [33], and with X-rays (800 eV) in [9]. The absorbed doses were not sufficient to induce neither non-thermal nor thermal melting. X-ray photoabsorption triggers secondary electron cascading and production of electron-hole pairs. As soon as the energetic photoelectrons appear, also electron-lattice energy exchange starts. This process lasts for a few picoseconds. Due to the atomic heating, the band gap shrinks, as discussed above. Including the temperature dependence of the band gap into a two-temperature model (combined with an extended Drude-model), and fitting the model to the experimental data, allowed us to extract the electron-lattice thermalization time in FEL-excited GaAs [32]. Since the excitation level here is low, we expected the Drude model to be applicable. However, it was not the case. Only after the Drude model was extended to include the effects of: (i) interband transitions, and (ii) the thermally-induced band gap shrinkage, it could reproduce the overshooting effect. It should also be mentioned that radiative electron-hole recombination time is on the order of 100 ns [34], thus, it does not give an additional contribution to the optical properties on the considered timescales. Both experimental results and theory predictions show reflectivity overshooting (Figure 10). This specific effect appears only if the energy of probe photon is comparable with the band gap width, which makes the optical coefficients to be very sensitive to the changes of the band gap width. For probe-photon energies far above the band gap, this effect is not observable, see the case of 400 nm probe in Figure 10.  
For comparison, we show the reflectivity change obtained with XTANT, assuming a fast global thermalization of carriers between valence and conduction bands (at a timescale of a few hundred fs) at 800 eV FEL pump photon energy and 40 mJ/cm\({}^{2}\) pulse fluence (Figure 11). As expected, the predictions are in a clear disagreement with the experimental data. This indicates that a modification of XTANT, going beyond the assumption of fast global equilibration, is required to properly model GaAs. This is a topic of our on-going investigation. Note that for Si and diamond the effective m  
Figure 9: Optical coefficients of silicon irradiated with a dose of 0.66 eV/atom (**left**) and with a dose of 1.78 eV/atom (**right**) calculated with XTANT. conduction and valence band are comparable, therefore, the approximation of the unified Fermi-Dirac distribution for both bands holds already within a few femtoseconds after their irradiation [10]. Since the band gap width is a function of the lattice temperature, the theoretical and experimental data on reflectivity can be used to extract the electron-phonon thermalization time or the electron-phonon coupling parameter. In case of GaAs irradiated with X-rays below the melting threshold, we extracted the electron-lattice thermalization time from the data and found it to be in the order of 2-3 ps. This technique can also be applied for other narrow band gap semiconductors.