Nanoscale measurement is an essential task of nanomanufacturing, and measurement traceability is a fundamental aspect of nanoscale measurement. High-precision nanoscale measurement instruments (e.g. atomic force microscopes (AFM) and scanning electron microscopes (SEM)) need to be calibrated by traceable standards to ensure their accuracy and reliability. However, due to the suboptimal accuracy, uniformity, and consistency of existing standards, they need to be calibrated by metrological instruments traceable to primary length standards (e.g. physical wavelength standards) before use. This results in a long traceability chain that leads to error accumulation and significantly reduces calibration efficiency. This paper proposes a novel shortened and simplified traceability chain, where the physical wavelength standard corresponding to the ⁷S₃ → ⁷P₄° transition frequency of chromium atoms is materialized into self-traceable gratings using the atom lithography technology. The self-traceable gratings can then be directly applied for calibrating measurement instruments. To verify this approach, the self-traceable gratings are calibrated using a metrological AFM of the Physikalisch-Technische Bundesanstalt. Measurement results confirmed the feasibility of the approach. Particularly, our results show that the self-traceable gratings have excellent uniformity over different measurement areas and consistency over different samples, both at 0.001 nm level. Finally, the application of the self-traceable gratings for the calibrations of a commercial AFM and SEM is demonstrated. The new traceability chain significantly simplifies the calibration process, providing a more reliable and higher efficient calibration approach for advanced nanomanufacturing than that of the state-of-the-art.

The measurement of critical dimensions in the field of integrated circuits has moved from 7 nm to 5 nm. The existing chromium atomic lithography grating has a pitch period of 4700 l mm⁻¹ and uniformity of picometer, and the interferometric signal period based on the above grating is as small as 106.4 nm, which brings new problems and challenges to the accurate processing of the signal. This paper investigates the error characteristics of ultra-high precision grating interferometric signals, establishes a Heydemann correction mathematical model for high inscribed line density grating interferometric signals, corrects the grating interferometer signals based on the random sample consensus (RANSAC), and verifies the effectiveness of the algorithm through simulation. By comparing the repeatability and linearity of the original algorithm and the self-traceable grating interferometric displacement measurement data processed by RANSAC, the conclusion that the standard deviation of the self-traceable grating interferometer repeat measurement after RANSAC is 1.60 nm in a 10 000 nm travel is obtained, and the purpose of improving the stability and uniformity of the signal solution with the algorithm of this paper is achieved, which is important for the study of laser interferometer and grating interferometer The results show that the stability and uniformity of the signal solution can be improved by the algorithm of this paper, which is of great significance for the study of the displacement solution of laser and grating interferometers.

A novel hybrid method that combines the laser-focused atomic deposition (LFAD) and extreme ultraviolet (EUV) interference lithography has been introduced. The Cr grating manufactured by LFAD has advantages of excellent uniformity, low line edge roughness and its pitch value determined directly by nature constants (i.e. self-traceable). To further enhance the density of the Cr grating, the EUV interference lithography with 13.4 nm wavelength was employed, which replicated the master Cr grating onto a Si wafer with its pitch reduced to half. In order to verify the performance of the gratings manufactured by this novel method, both mask grating (Cr grating) and replicated grating (silicon grating) were calibrated by the metrological large range scanning probe microscope (Met.LR-SPM) at Physikalisch-Technische Bundesanstalt (PTB). The calibrated results show that both gratings have excellent short-term and long-term uniformity: (i) the calibrated position deviation (i.e. nonlinearity) of the grating is below ±1 nm; (ii) the deviation of mean pitch values of 6 randomly selected measurement locations is below 0.003 nm. In addition, the mean pitch value of the Cr grating is calibrated as 212.781 ± 0.008 nm ( k = 2). It well agrees with its theoretical value of 212.7787 ± 0.0049 nm, confirming the self-traceability of the manufactured grating by the LFAD. The mean pitch value of the Si grating is calibrated as 106.460 ± 0.012 nm ( k = 2). It corresponds to the shrinking factor of 0.500 33 of the applied EUV interference lithographic technique. This factor is very close to its theoretical value of 0.5. The uniform, self-traceable gratings fabricated using this novel approach can be well applied as reference materials in calibrating, e.g. the magnification and uniformity of almost all kinds of high resolution microscopes for nanotechnology.