FEM calculations on laser bending of silicon with a moving laser source

Abstract

In this paper we are going to present FEM calculations applied for laser bending of silicon microstructures and compare them with our experimental results. According to the mechanisms in plastic deformation of metals with laser radiation we performed calculations to find out, if there are similar mechanisms in forming of silicon. To model the laser heating up mechanism we have to take into account several physical effects like heat radiation or reflection of silicon for the used laser radiation. To transform the laser bending process into a FE model the boundary conditions include compromises and simplifications of the geometry and the energy input. In our calculations we modelled the laser beam as a moving heat source in order to get information about the temperature distribution, the temperature gradient and the heat flow in dependence on the position on the sample and the time. The calculated essentially higher temperatures at the edges of the structure compared to the middle of the structure, exceeding the melting point there, are in very good agreement to the melting areas observed at the edges in the experi-ments. After a number of consecutive scans we reach a balanced temperature field moving with the laser beam across the surface. The calculations revealed that there is a steep temperature gradient in the depth of the structure indicating a similar temperature gradient mechanism observed in forming of metals with laser radiation. Additionally we carried out temperature field calculations to determine the influence of the process parameters like the laser power, the velocity of the heat source, the material thickness or the position of laser treatment on the temperature field generated in the material. The results of the calculations are in very good agreement with our experiments. Next time stress field calculations are intended. At the moment there are not enough data on the plastic behaviour of silicon available to the authors in order to get reliable results.