TraceableX,Yself-calibration at single nm level of an optical microscope used for coherence scanning interferometry

Abstract

Coherence scanning interferometry used in optical profilers are typically good for Z-calibration at nm-levels, but the X,Y accuracy is often left without further notice than typical resolution limits of the optics, i.e. of the order of ~1 µm. For the calibration of metrology tools we rely on traceable artefacts, e.g. gauge blocks for traditional coordinate measurement machines, and lithographically mask made artefacts for microscope calibrations. In situations where the repeatability and accuracy of the measurement tool is much better than the uncertainty of the traceable artefact, we are bound to specify the uncertainty based on the calibration artefact rather than on the measurement tool. This is a big drawback as the specified uncertainty of a calibrated measurement may shrink the available manufacturing tolerance. To improve the uncertainty in X,Y we can use self-calibration. Then, we do not need to know anything more than that the artefact contains a pattern with some nominal grid. This also gives the opportunity to manufacture the artefact in-house, rather than buying a calibrated and expensive artefact. The self-calibration approach we present here is based on an iteration algorithm, rather than the traditional mathematical inversion, and it leads to much more relaxed constrains on the input measurements. In this paper we show how the X,Y errors, primarily optical distortions, within the field of view (FOV) of an optical coherence scanning interferometry microscope, can be reduced with a large factor. By self-calibration we achieve an X,Y consistency in the 175 × 175 µm2 FOV of ~2.3 nm (1σ) using the 50× objective. Besides the calibrated coordinate X,Y system of the microscope we also receive, as a bonus, the absolute positions of the pattern in the artefact with a combined uncertainty of 6 nm (1σ) by relying on a traceable 1D linear measurement of a twin artefact at NIST.

Uncertainty analysis of two-dimensional self-calibration with hybrid position using the GUM and MCM methods

“…For to resolve problems concerning calibration in electron-beam lithography. The main approaches are the Fourier transform [9,10], rigid motion estimation [11,12], least squares method [13][14][15][16], and optimisation [17,18]. By measuring the coordinates of each point when a grid plate is in different positions on a stage and substituting them into a 2D self-calibration model, the system errors of the stage can be separated from the measurements.…”

Characterization and Correction of the Geometric Errors Using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

“…For optical confocal microscopes, the Z-calibrations at nm levels are typically good, while the X-and Y-accuracies are often left, without further notice than resolution limits of the optics [10,11]. Among the investigations of lateral calibrations, many studies focus on the optical system [12].…”

“…B. Daemi et al designed a comprehensive verification test by using a high precision metrology method based on subpixel resolution image analysis [17]. The calibration of confocal microscopes usually relies on traceable standard artefacts, which are commonly made up of regular patterns [10]. This paper describes the experimental studies based on the kinematic modeling and algorithms for the correction of the geometric errors developed in Part I [18].…”

Self-calibration for the 2D stage based on weighted least squares

“…Wang et al explored the performance of the self-calibration method when the grid plate was placed in eight positions [19]. Ekberg attained many achievements in the research on self-calibration [20][21][22]. He introduced a new general approach for self-calibration that continually optimizes the stage to a perfect state.…”