Method and apparatus for the determination of laser correcting tool parameters

A method for determining at least one unknown laser beam parameter of a laser beam used for correcting registration errors of a photolithographic mask, the method comprising:

• a. inducing a first persistent modification in a substrate in the photolithographic mask by an interaction of the substrate of the photolithographic mask with the laser beam having a first set of laser beam parameters, wherein the first persistent modification introduces a local density variation in the substrate of the photolithographic mask;
• b. measuring the first persistent modification induced in the substrate of the photolithographic mask;
• c. calculating a second persistent modification in the substrate of the photolithographic mask using a deformation model describing persistent modifications that introduce local density variations in the substrate of the photolithographic mask with a second set of laser beam parameters, wherein the first set of laser beam parameters comprises the second set of laser beam parameters and the at least one unknown laser beam parameter;
• d. setting up a target functional comprising the first persistent modification induced in the substrate of the photolithographic mask and the second persistent modification;
• e. determining the at least one unknown laser beam parameter by minimizing the target functional;
• and
• f. after determining the at least one unknown laser beam parameter, using the deformation model to control the laser beam to correct registration errors of one or more photolithographic masks.