the tolerance region at a given primary beam energy and current the vc transition happens within a narrow under etch region with the thicknesses of remainders varying around the primary beam determined threshold thickness in other words the thickness of remainders of a via contact can be determined from its corresponding transition image at known beam conditions for instance if the primary electron beam is of 400 ev in energy and 60 na in current the transition region 401 represents that an equi thickness region of about 50 u00e5 remained within via contacts further calibration can turn this roughly equi thickness region into equi thickness line 402 as shown in fig4 with the x coordinate representing pattern factor and the y coordinate representing the via contact sizes other curves approximately conformal to this line exten the equi thickness line to the nearby over etch and under etch regions by doing so a process u201c fingerprint u201d image is quantified with the amount of under over etch with reference to the just etch for a given via contact design rule in the functional die region it is always possible to locate its position in this quantified u201c fingerprint u201d image and find its corresponding amount of over etch thickness with the aid of the quantified u201c fingerprint u201d image.