Analytical and numerical calculations of the temperature distribution in Si and Ge targets irradiated by excimer lasers

The calculations of the temperature distribution induced by excimer lasers in silicon and germanium by using different mathematical approaches are presented. In this work, the heat conduction differential equation is solved by: (i) conventional analytical method, where the thermal parameters, i.e., thermal conductivity, specific heat and density are temperature independent; (ii) the Kirchhoff transformation method, that incorporates the dependence of the thermal conductivity with the temperature through a polynomial function; (iii) a numerical approach, by using the finite elements method (ANSYS program), which allows the incorporation of all temperature dependent parameters and the phase changes of the material using the enthalpy function. A comparison of the temperature profile versus depth obtained for semi-infinite amorphous germanium and crystalline silicon materials when irradiated with an ArF excimer laser (193 nm, 20 ns) is presented. The melting depth for a given energy density is also evaluated by the different mathematical methods. The validity of these results and the reliability and advantages of the numerical methods is discussed.