# On the Melting Thresholds of Semiconductors under Nanosecond Pulse Laser Irradiation
## 3 Results and Discussion
### Gallium Arsenide  
For simulations of the laser heating of GaAs, we used the same values of the thermophysical properties as in Ref. [8]. For the temperature dependence of \(c_{\mathrm{p}}\), the data from [52] were used, which are also in a good agreement with the data reported in [53]. Optical properties were taken from measurements [54], which are also in a good agreement with [55]. The absorption and reflection coefficients were calculated from the refractive index and the extinction coefficient and taken as temperature-independent. The material properties used in the simulations are presented in Tables A9-A12 of Appendix A. Several regimes of laser irradiation of GaAs corresponding to available experimental and theoretical data were investigated in our modelling, with the laser wavelengths ranging from 308 to 694 nm and pulse duration ranging from 15 to 70 ns. For all the conditions, the melting thresholds calculated here with our unified model are in good agreement with the values reported in the literature (Table 1). Below we discuss each irradiation regime in more detail. \(\lambda\) = _308 nm_, \(\tau\) = _30 ns_. Our model implements the same optical and temperature-dependent material properties as in the model presented by [PERSON] et al. [8]. For the solid-state reflectivity and the optical absorption, the data used for simulations in [8] are in agreement with the measured data for solid GaAs [53]. As the parameters of the model [8] and ours are very similar, we take this comparison as a validation for our model that gives a deviation of only \(\sim\)6% (see Table 1). \(\lambda\) = _694 nm_, \(\tau\) = _15 ns_. [PERSON] et al. [12] carried out simulations for a ruby laser with a 15 ns pulse duration using an explicit numerical scheme. The melting threshold was identified at a laser fluence of 300 mJ/cm\({}^{2}\), which corresponded to the situation when a \(\sim\)65-nm-thick surface layer was molten [12]. In our simulations, this fluence of 300 mJ/cm\({}^{2}\) results in a melting depth of 13 nm, while the melting threshold corresponding to reaching the melting point on the sample surface is 265 mJ/cm\({}^{2}\) (see Figure 2 for comparison). The difference in the melting depth can be attributed to two factors. First, the authors [12] extrapolated the temperature-dependent absorption coefficient for the solid-state GaAs from the room temperature util the melting point, which appears to be questionable. In our simulations, we use constant but reliable data on the optical absorption and reflectivity of molten GaAs at the wavelength of the ruby laser [48]. The reflectivity coefficient of liquid GaAs in both Ref. [12] and this work was adopted from [13], \(R\) = 0.67. The second factor may be related to using an explicit numerical scheme in Ref. [12], whose approximation to the initial equations often represent a challenge. Figure 2: Comparison of the results obtained by modelling in Ref. [12] and in this work for GaAs irradiated by 694-nm, 15-ns laser pulses. (**a**) The depth of molten material as a function of time for several laser fluences (reprinted with permission from Ref. [12]). (**b**) The results of the present modeling for laser fluences of 265 mJ/cm\({}^{2}\) (corresponding to the defined melting threshold) and 300 mJ/cm\({}^{2}\). The temporal evolution of the melt depth at 300 mJ/cm\({}^{2}\) is also given to compare with Ref. [12]. The laser pulse is shown by the dashed line. \(\lambda=694~{}nm\), \(\tau=20~{}ns\). [PERSON] et al. [13] presented two sets of measurements. Using a HeNe probe laser, the temperature-dependent reflectivity was investigated. The second set of data gives time-of-flight measurements of particles evaporated from the GaAs surface (Figure 3a). Comparison of their experimental data and our simulations is given in Table 1, which are in reasonable agreement.