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Beam placement accuracy is fundamental to advanced lithography and patterning. As applications of focused ion beams in semiconductor manufacturing and adjacent topics become more demanding, our titular question on the unknown whereabouts of a beam becomes more pressing to answer. Such a question may seem frivolous, but in reality, is quite serious and nontrivial to answer. In a previous study, we identified micrometer-scale systematic errors of feature placement by our focused ion beam across an ultrawide patterning field. Such errors are of particular concern for machining standards that provide reference positions, such as aperture arrays for optical microscopy. , Conversely, our recent advances of localization traceability present a new opportunity to not only measure but also improve placement accuracy. In the present study, we quantitate feature positions by critical-dimension localization microscopy with ultrahigh throughput, revealing complex errors that extend to appalling values of several micrometers across a submillimeter field. We introduce a novel correction that reduces scale errors by three orders of magnitude and distortion errors by more than a factor of 40, dramatically improving the placement accuracy of our focused ion beam. Although this improvement occurs in a research laboratory context and for optical microscopy standards, our methods have broad implications for advanced lithography and patterning.
We begin by designing a square array with a lateral extent of 200 µm by 200 µm, a nominal pitch of 2502 nm, and apertures with a nominal diameter of 500 nm. This value of pitch separates aperture centers by an integer number of pixels across our wide patterning field and separates the aperture images beyond the resolution limit for optical microscopy and localization analysis. After fabrication, we trans-illuminate the aperture array, localize each aperture, and register the resulting positions with those of the design through a rigid transformation. This analysis shows total errors with magnitudes exceeding 2 µm, with root-mean-square values of 528.9 nm in the x direction and 1007.7 nm in the y direction (Figure 1a,c-d). A similarity transformation between the experimental and nominal positions distinguishes errors of uniform scale and complex distortion, returning the pitch of the experimental array as 2472.01 nm ± 0.27 nm, which is a scale error of 1.20 %, with additional systematic errors of distortion as large as approximately 1 µm and with root-mean-square values of 399.3 nm in both the x and y directions (Figure 1c-d). We report uncertainties as 68 % coverage intervals.
We modify the array design to negate these errors and improve placement accuracy, uniformly increasing the array pitch to account for the 1.20 % scale error and achieve a nominal pitch of 2500 nm. We model the distortion errors by an interpolant that adjusts the design position of each aperture and enables general correction within the extents of our sampling field. We machine and measure a new array and apply a similar analysis, registering the localization data with the new design. We measure a pitch of 2500.03 nm ± 0.27 nm, corresponding to a scale error of 0.001 %, and distortion errors of up to approximately 40 nm and with root-mean-square values of 9.0 nm in the x direction and 9.4 nm in the y direction (Figure 1b,c-d). In this way, we have found our focused ion beam, which had gone several micrometers astray, and returned it to its proper place to within a few tens of nanometers.
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