Local sample thickness determination via scanning transmission electron microscopy defocus series

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The usable aperture sizes in (scanning) transmission electron microscopy ((S)TEM) have significantly increased in the past decade due to the introduction of aberration correction. In parallel with the consequent increase of convergence angle the depth of focus has decreased severely and optical sectioning in the STEM became feasible. Here we apply STEM defocus series to derive the local sample thickness of a TEM sample. To this end experimental as well as simulated defocus series of thin Si foils were acquired. The systematic blurring of high resolution high angle annular dark field images is quantified by evaluating the standard deviation of the image intensity for each image of a defocus series. The derived dependencies exhibit a pronounced maximum at the optimum defocus and drop to a background value for higher or lower values. The full width half maximum (FWHM) of the curve is equal to the sample thickness above a minimum thickness given by the size of the used aperture and the chromatic aberration of the microscope. The thicknesses obtained from experimental defocus series applying the proposed method are in good agreement with the values derived from other established methods. The key advantages of this method compared to others are its high spatial resolution and that it does not involve any time consuming simulations.

Lay description

In (scanning) transmission electron microscopy (S)TEM the local sample thickness is a crucial parameter. Any quantitative evaluation of a sample's structure or composition relies on a precise knowledge of the amount of material viewed in projection. Larger apertures can be used in STEM due to the progress in instrumentation. Therefore the depth of focus decreases and the signal becomes depth sensitive. This allows optical sectioning in analogy to light microscopy.

Lay description

Here we propose a method to determine the local sample thickness from a STEM defocus series utilizing high angle annular dark field imaging. Thereto we investigate the systematic blurring of high resolution STEM images of thin Si foils when changing the defocus away from its optimum value.

Lay description

We measure the standard deviation of the image intensity (STDI) as a function of defocus to quantify this blurring. At optimum defocus the images exhibit a high contrast, as the atomic columns appear bright in a dark background, accordingly the standard deviation shows a maximum. Away from the optimum defocus the contrast vanishes and the STDI drops to a background value. The width of the STDI versus defocus curve is directly proportional to the local sample thickness. Roughly speaking this means as long as the focus of the electron beam lies inside the sample, the image exhibits non negligible contrast. Therefore by measuring this width from an experimental defocus series, the local sample thickness can be derived.

Lay description

Our derived thickness values are in excellent agreement with other established techniques. In contrast to these established techniques our method does not involve any time consuming simulations.

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