Correction of Interferometric High-Order Nonlinearity Error in Metrological Atomic Force Microscopy

Metrological atomic force microscopes (Met. AFMs) with built-in interferometers are one of the main workhorses for versatile dimensional nanometrology. The interferometric nonlinearity error, particularly the high-order (i.e., 3rd- and 4th-order) nonlinearity errors, is a dominant error source for further improving their metrology performance, which cannot be corrected using the conventional Heydemann correction method. To solve this problem, two new methods were developed. One uses a capacitive sensor embedded in the Met. AFM, and the other applies an external physical artifact with a flat surface. Both methods can be applied very conveniently and can effectively reduce the nonlinearity error. In this paper, the propagation of the (residual) nonlinearity error in step height calibrations is examined. Finally, the performance of the improved tool is verified in the calibration of a highly demanding industrial sample. For the measurements performed at 25 different positions and repeated six times, the standard deviation of the total 150 measured values is 0.08 nm, which includes the contributions from the reproducibility of the metrology tool and sample inhomogeneity. This research has significantly improved our dimensional nanometrology service. For instance, the extended measurement uncertainty (k = 2) is reduced from 1.0 to 0.3 nm for the step height or etching depth calibrations.