Modeling of Surface Structure Formation after Laser Irradiation

Abstract

The Stefan problem in a semi-infinite media under laser irradiation is considered. It is related to the melting and solidification processes, resulting in certain surface structure after the solidification. A simple model, as well as a more sophisticated one is proposed to describe this process. The latter model allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. It has to be found as a solution of two-phases Stefan problem. The results of example calculations by the fourth-order Runge-Kutta method are presented, assuming that the solid-liquid interface has a parabolic shape. The calculated crossection of the surface structure shows a characteristic cone in the center, in agreement with experimental observations.

Analytic-Numerical Modeling and Investigation of Nanostructures' Dynamics on Material Surfaces After Laser Irradiation

“…Varying  during the numerical experiment, we can indirectly simulate the formation of nanostructures in various conditions whose presence in the analytical model is not yet possible to specify in any explicit analytical way. Thus, the 1D equation in the model is more general than the classical equation of mass and heat transfer and diffusion considered, for example, in [2]. The opportunity to study the processes of formation of nanostructures in a numerical experiment which more realistically reproduces the conditions of laboratory experience is the motivation for the inclusion of the term ( , )…”

“…C. The main properties of the constructed difference schemes  The developed explicit difference scheme (4) -( 7), which approximates the mathematical model (2), is easier to implement with a computer than the developed implicit difference scheme (9) -( 12) approximating the same mathematical model;  The order of convergence of the two difference schemes is the same. The two difference schemes' estimate in the energy norm is…”