2-D Self-Calibration for Scale Based Metrology in Nanolithography

Abstract Two-dimensional precision stages for semiconductor lithography require sub-nm-level accuracy. Current ultraprecision stage metrology based on heterodyne laser interferometers with a 632.8-nm HeNe laser and interpolation to λ/2048 provide resolution of 0.3 nm. Unfortunately, the refractive index of air varies with CO2 and water vapor content, as well as with air turbulence. Without expensive atmospheric compensation, the actual accuracy may only be subμm for operation in air. In our approach two scale based metrology system (OPTRA NanoGrid) are used. The NanoGrid greatly reduces possible effects from air turbulence and Abbe offsets from using separate X and Y scales. However, the metrology is based on an physical artifact, and the accuracy of the metrology is limited to the accuracy of the grid artifact itself: about 1μm. Physical scales may provide greater precision, but not always greater accuracy. Real-time selfcalibration is implemented to improve the accuracy of stage to the level limited by repeatability of stage. Fourier transform is used to decouple the distortion of artifact metrology and stage metrology at sampling points from 3 measurement view. Based on feedback principle high accuracy translation and rotation is implemented to minimize misalignment error. Square reversal is used to calculate rotation error δγ. Iterative algorithm is developed to isolate the rotation error δγ in self-calibration.