Quantitative scanning transmission electron microscopy is widely used for structural and chemical analysis nowadays. Experimental data can be directly compared with simulations by normalizing raw intensities J with respect to the incoming beam intensity J₁-J_o [1]. J₁ is usually determined by scanning the electron beam in image mode over the detector. From the detector region the intensity J₁ and from regions beside the detector an offset intensity J₀^det is determined that has to be subtracted from J and J₁. The normalized intensity I can be derived by I=(J-J₀^det)/(J₁-J₀^det). However, typical detector scans exhibit a non-circular shape and non-uniform sensitivity. These effects are usually taken into account by a radial sensitivity curve in simulations [1,2].

In this contribution we present several further instrumental imperfections and characterize how they affect quantitative STEM using the example of measurement of specimen thickness:

1. The effect of centering of the diffration pattern and the anisotropy of the ADF detector was studied as follows: A 2-D sensitivity map was generated from a detector scan and then used to derive the average ADF intensity in a unit cell of GaAs. The sensitivity map was rotated or shifted with respect to simulated diffraction patterns. Then the relative intensity to the perfectly centered case was calculated. The error in the ADF intensity caused by different rotations was found to be only 0.5 %, whereas a decentering of only 7 mrad causes an error of about 6 %.

2. A cut-off and distortions of the diffraction pattern due to an image corrector have been found (Fig. 1a). These effects can be taken into account by a detector scan procedure, where the beam is scanned over the detector in diffraction mode by tilting the incoming electron beam. The advantage of this procedure is that cut-off and distortions are directly embedded in an effective sensitivity (Fig. 1b). We found the most severe deviation of the sensitivity map for a camera length of 102 mm. The respective radial sensitivity is compared in Fig. 1c with the conventional one. At this camera length an error of about 15 nm specimen thickness for 50 nm GaAs would be found, if cut-off and distortions would be neglected by using a conventional detector scan procedure.

3. Intense illumination, as e.g. a zero beam positioned accidentally on the detector, might cause a local sensitivity enhancement as shown in the inset of Fig. 2a. This results in a modification of the sensitivity curve (Fig. 2a). The modification of the sensitivity may cause an error of about 1 nm for thickness measurement of 50 nm GaAs.

4. We found that the measured incoming beam intensity J₁ depends on the dwell time and is overestimated for long dwell times (Fig. 2b), independently on the previous history of the detector. This effect can lead to a thickness underestimation of about 4 nm for 50 nm thick GaAs.

5. An afterglow of the detector with a typical decay time of about 260 μs was found (Fig. 3a). This afterglow results in an overestimation of the bias of the amplifier from a detector scan, if J₀^det is determined by averaging over a region beside the detector. This overestimation leads to negative normalized intensities in an image from a vacuum region. Histograms of detector scans (Fig. 3c) reveal a sharp peak at an intensity J₀^amp that is attributed to the bias level of the amplifier, suggesting the usage of J₀^amp.

6. The usage of J₀^amp results in a positive normalized intensity in vacuum regions. Histograms of such regions revealed that accidental electrons hit the detector (Fig. 3b) [3,4] and therefore the mean value of the intensity in a vacuum image J₀^vac must be used for J₀^det. Effects 5 and 6 together may result in an error of about 2.3 nm for a 5 nm thick Si specimen, which is a significant error in an atom counting experiment.

The reported instrumental imperfection have been investigated using our FEI Titan80-300 ST microscope equipped with an corrector for the aberrations of the imaging lens and a Fischione HAADF detector. 

[1] J.M. LeBeau, S. Stemmer, Ultramicroscopy 108 (2008) 1653.

[2 ] A. Rosenauer, et al., Ultramicroscopy 111 (2011), 1316.

[3] R. Ishikawa, et al., Microsc. Microanal. 20 (2014) 99.

[4] F.F. Krause, M. Schowalter et al., Ultramicroscopy 161 (2016), 146.

Figures:

Fig. 1: a) Diffraction pattern exhibiting a cut-off and distortions due to the imaging corrector. b) Effective detector sensitivity including cut-off, distortions by a corrector, non-circularity and non-uniformity for a camera length of 102 mm. c) Comparison of the respective radial sensitivies with the conventional one.

Fig. 2: a) Radial sensitivity for a normal situation and a situation, where the detector was exposed for a long time (inset). b) Incident beam intensity as a function of dwell time for different beam currents.

Fig. 3: a) Linescans within detector scan images taken along the primary scan direction. An afterglow of the detector with a typical decay time of 0.260 ms was found. b) Histograms of intensities of images taken in a vacuum region. Beside the amplifier peak additional peaks are observed, that are attributed to single electrons.

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