Device and method for cutting out contours from planar substrates by means of a laser

The invention relates to a method for producing a contour (5) in a planar substrate (5) and for removing the contour from the substrate, in particular for producing an internal contour in a planar substrate and for removing the internal contour from the substrate, wherein in a contour definition step, by means of a laser beam (3) guided over the substrate, a plurality of individual zones (5-1, 5-2,...) of internal damage is produced along a contour line in the substrate material marking the contour (5) to be produced; in a crack definition step, by means of a laser beam guided over the substrate, a plurality of individual zones (6-1, 6-2,...) of internal damage is produced along each of a plurality of crack line segments (6a, 6b,..) in the substrate material leading, as viewed from the contour line, away at an angle alpha > 0DEG and into the contour to be removed; and in a material removal step performed after the contour definition step and after the crack definition step, by means of a material-removing las