# Transient Changes of Optical Properties in Semiconductors in Response to Femtosecond Laser Pulses
## 3 Results and Discussion
### Silicon  
The XTANT model extended for calculation of optical properties was also applied for silicon [10]. Amorphization of silicon can occur via thermal and non-thermal melting [29]. The estimated threshold dose for silicon melting is \(\sim\) 0.65 eV/atom, when solid silicon transforms into a low-density liquid (LDL). At the dose of \(\sim\) 0.9 eV/atom full amorphization of silicon occurs (to high-density liquid, HDL) [13]. Experiment investigating melting of silicon was performed by [PERSON] et al. [31]. It was similar to the experiment carried out by [PERSON] et al. for diamond. An optical pulse with 625 nm wavelength was used there. Figure 7: Optical reflectivity of diamond irradiated with the absorbed dose of 6.3 eV/atom. The dots are experimental data [30], the solid line depicts the results of the TB model with XTANT, the dashed line is Drude model. The simulations were performed with 216 atoms in the supercell. The figure is reproduced from [10]. To model this experiment, we again used soft X-ray photon energy (50 eV) for the pump pulse and 625 nm wavelength for the probe pulse. Figure 8 shows optical properties of silicon at the absorbed dose of 1.0 eV/atom (above the damage threshold). A characteristic drop of transmission and an increase of reflectivity were predicted by the simulation. The results for the reflectivity were found to be in reasonably good agreement with the experiment. In contrast to diamond, the increase of reflectivity in silicon is not so rapid. It takes a significantly longer time until it saturates, i.e., 500-600 fs after irradiation. This is the consequence of both non-thermal and thermal processes contributing to silicon amorphization. Shortly after the pulse, the non-thermal melting of the material starts and reflectivity decreases. Afterwards, the reflectivity overshoots its initial value. The dose of 1.0 eV/atom is not sufficient to amorphize silicon purely non-thermally, i.e., within a few hundreds of femtoseconds. Heating of atoms by electron-phonon coupling is necessary to accomplish the transition. This usually takes up to a few picoseconds [29]. During the material heating, its band gap starts to shrink and finally collapses, indicating a phase transition to a semi-metallic state [13]. This finding has been confirmed by the detailed simulation with XTANT in [13]. We observe in the simulations that thermal and non-thermal phase transitions can be decoupled if atoms are irradiated at a low dose (slightly above the LDL threshold), and at a very high dose (above HDL threshold). In the first case thermal melting has predominant contribution. In the latter case non-thermal melting prevails. In Figure 9 the examples for doses of 0.66 eV/atom and 1.78 eV/atom are shown, correspondingly. One can see that at the lower dose the reflectivity saturates after 1 picosecond (as thermal melting then dominates), while for high dose the saturation appears quickly (as non-thermal melting then dominates), within \(\sim\)300 fs. Also, at the dose of 1.78 eV/atom the transmission strongly decreases almost immediately after the pulse, while at the dose of 0.66 eV/atom it is still non-zero until approximately 400 fs. This again demonstrates that the optical properties are strongly linked to the atomic structure. For the non-thermal melting, the timescales of the abrupt changes of the optical properties coincide with the timescale of the phase transition. In case of thermal melting, the changes of atomic structure are triggered by the increasing atomic temperature on ps timescales. The timescale of atomic heating, i.e., electron-lattice thermalization time, is, in turn, governed by the electron-phonon coupling. As the optical properties indicate the thermally induced changes of atomic structure, by measuring those properties with a pump-probe scheme, one can estimate electron-phonon coupling rates in semiconductors. Figure 8: Optical coefficients of silicon irradiated with the absorbed dose of 1.0 eV/atom.