Quantitative annular dark‐field imaging at atomic resolution
Authors: Yamashita Shunsuke , Koshiya Shogo , Ishizuka Kazuo , Kimoto Koji 
Published: December 2016

Quantitative annular dark‐filed (ADF) imaging in scanning transmission electron microscopy (STEM) enables us to identify the type and number of atoms of local crystal structures. A quantification procedure of ADF images was proposed by LeBeau and Stemmer, in which the signal at each pixel is placed on an absolute scale by normalizing the current reaching an ADF detector by the incident probe current [1]. Their procedure made possible a direct comparison between experimental and simulated ADF images without any arbitrary scaling parameters. In this study we acquired quantitative ADF images of a graphene and compared with simulated images to investigate how accurately the scattering intensities match between experiments and simulations.

We used a Titan
3
microscope (FEI) equipped with spherical aberration correctors (DCOR and CETCOR, CEOS) operating at an acceleration voltage of 80 kV. An ADF detector (Model 3000, Fischione) and an analog‐to‐digital (A/D) converter (DigiScan II, Gatan) were used. We evaluated a nonlinear response of the ADF signal detection system, which had not been analyzed. Relationship between an ADF detector current (

I
ADF

[pA]) and an ADF image signal (

S
ADF

[count]) was measured as shown in Fig. 1. Quantitative contrasts

Q
ADF

[%], i.e.

I
ADF

normalized by the incident probe current

I
0

, were calculated from

S
ADF

using the nonlinear response. The quantification procedure was performed using an in‐house DigitalMicrograph (Gatan) scripts.

The range of ADF detection angle was experimentally measured. The ADF inner angle (48.4 mrad) was measured by scanning an incident probe on the ADF detector. We found that the ADF outer angle (200 mrad) is limited by the aperture in the microscope column above the ADF detector, and the actual outer angle was measured by observing the shadow of the objective aperture [2]. The STEM image simulation was performed using a multislice program (xHREM with STEM Extension, HREM), in which defocus spread and residual aberrations (up to 5th order) were taken into account.
Figure 2 shows (a) a quantitative ADF image of graphene with 1–4 layers and (b) the histogram of the quantitative ADF image. The mean contrast, which was measured by averaging the value in areas including several unit cells, was 0.054% at a single‐layer region. Since the mean value of a simulated image was 0.053%, the mean quantitative contrast exhibited excellent agreement between experimental and simulated images. We can instantly decide the number of graphene layers based on the quantitative ADF image.
Next we examined atomic‐resolution ADF images of a single layer graphene, as shown in Fig. 3. To reproduce atomic ADF image profiles, an effective source distribution, which corresponds to a demagnified source image on the specimen, should be implemented in STEM simulation. Although a Gaussian function has been often utilized as the effective source distribution, we found that the linear combination between Gaussian and Lorentzian (G+L in Fig. 3c) well reproduces experimental results. We also found that there is a small systematic deviation, which is probably due to time‐dependent aberrations (e.g., coma). Highly‐stable microscope system and/or real‐time aberration assessment are required for the advanced quantitative STEM imaging at atomic resolution.