Reliability of parameters of associated base straight line in step height samples: Uncertainty evaluation in step height measurements using nanometrological AFM

Step height is widely used as one of the important nanometrological standards for the calibration of nanometrological instruments. In the calculation of step height, a method of determining a base straight line as a reference line is very important. In nanometrology, which is a field of dimensional metrology, an associated feature (Gaussian associated feature), such as a base straight line, is normally calculated from a measured dataset of a metrological instrument on a real feature using the least squares method. The reliability of a base straight line varies depending on the position and number of measured points for the line and the uncertainty in step height calibration also varies depending on the reliability of the base straight line. In this study, we carried the out step height measurement of micropatterned thin films (10, 7, 5, and 3 nm) using an atomic force microscope (AFM) equipped with a three-axis laser interferometer (nanometrological AFM) and evaluated the uncertainty in these measurements. From the uncertainty evaluation results, the uncertainty derived from the reliability of the parameters of the base straight line was one of the major sources of uncertainty when the measured points for the base straight line were varied. An expanded uncertainty (k = 2) of less than 0.4 nm was obtained. Furthermore, the reliable range of an associated base straight line in a single step height, such as that in an atomic step sample, was calculated and in importance of the calculation of the reliable range was shown in the uncertainty evaluation and in determining the measurement strategy.