Three-dimensional conduction effects during scribing with a CW laser

Abstract

A three-dimensio nal conduction model has been developed to predict the shape of the groove formed by partially evaporating the surface of a semi-infinite body using a moving Gaussian laser beam. The full three-dimensional conduction equation with relevant nonlinear boundary conditions is solved using the boundaryelement method, and results for groove depth and shape are compared for a variety of laser and solid parameters with a one-dimensional conduction model where conduction losses were treated in an approximate fashion using a simple integral method. As expected, it is observed that when thermal losses due to conduction are minor, the approximate one-dimensional conduction solution is very close to the three-dimensional solution (large laser scanning speeds, low thermal conductivity). The three-dimensional model is always able to predict the correct smooth groove shape along the centerplane TJ = 0. This cannot be predicted by the one-dimensional conduction model because of the neglected sideways conduction, leading to serious errors in the prediction of maximum groove depths.