Self-calibration of microscopes based on 3D micro standards

A 2D self-calibration method based on orthogonal vector polynomials is presented and applied for the first time to measurements of a 3D micro standard by the PTB's Nanometer Comparator (NMC) and a scanning electron microscope (SEM). The method separates the reproducible machine error field and the object errors by use of measurements in different orientations and locations of the object. The determination of the object displacements with the interferometer of the NMC provides a traceable scaling of the object. The 3D object used has markers on two different planes with a vertical distance of 1.2 µm, and its layout allows the rotation and shift of the object to be precisely identified. The maximum standard deviations of the marker positions in the X/Y direction were below 4 nm on the NMC. However, the residuals of the 2D equation system with a size of approx. 10 nm show a systematic difference between the markers on the upper and lower plane. This indicates that the machine error field of the NMC was not continuous in three dimensions. Therefore, the markers on the upper and lower planes were treated independently, thus the 2D error separation was performed separately for both planes. After the separate solutions with two different machine error fields for the two planes, the residuals of the equation systems did not contain significant systematic effects. Their standard deviation was below 2.2 nm for both planes. The traceable marker positions determined with the NMC were used to calibrate the SEM. Despite the larger depth of focus of the SEM, the vertical position of the markers also has an influence on the error field of the machine. The residua of the equation system for both planes don’t show systematic effects while their standard deviation was below 31 nm.