A closed form solution for laser drilling of silicon nitride and alumina ceramics

A closed form solution has been obtained for laser drilling of silicon nitride (Si3N4) and alumina ceramics (Al2O3). The drilling of workpiece is performed by using a TEM00 10 ns pulse Nd:YAG laser. It is assumed that the phase transition from solid to vapor occurs without melting. Considering the absorption of plasma plume formed on the surface of the ceramics, the one-dimensional thermal model is developed in order to describe the drilling process. The governing equation of heat-diffusion is solved analytically using a Laplace transformation method. Erosion depth per laser pulse obtained from the closed form solution agrees with the available experimental data.