The importance of thermal stresses and strains induced in laser processing with focused Gaussian beams

The thermoelastic equations are solved for laser heating of a semi-infinite elastic medium by a focused TEM00 Gaussian beam. Single integral expressions are derived for stresses and strains, which are analytically evaluated on axis at the surface and far from the laser-heated region (for a laser spot size≫absorption depth), and numerically evaluated for the example of laser heating of a silicon substrate. This analysis is extended to the case of laser heating of thin films on substrates. Use of these stress and strain profiles suggests that dislocations may form at the surface during high-temperature laser processing of silicon at scan speeds typically used in direct laser writing. Also the elastic strains induced during laser heating shift phonon frequencies from their thermal equilibrium values, thereby complicating the use of Raman scattering as an optical probe of temperature. This is shown to be particularly significant for laser heating of silicon thin films on fused silica substrates and not very important for laser processing of silicon substrates or silicon thin films on sapphire.