Incoherence/Rutherford (Elastic) Scattering/Thermal Diffuse
(Quasi-Elastically) Scattering (TDS)/Z-Contrast in HAADF-STEM
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In STEM mode, each element of the electron source can be assumed to emit electrons incoherently and thus results in an incoherent broadening of the probe [5]. Atomic number- (Z-) contrast imaging can provide qualitative and quantitative two-dimensional (2-D) information on the chemical composition. Such images are obtained by the detection of elastically and quasi-elastically scattered electrons using a high-angle annular dark-field (HAADF) detector. To form Z-contrast images, the STEM objective aperture must be inserted to cut out high-angle electron rays, and an annular detector must be inserted after the projector lens system.

As discussed in page 2579, a collection angle higher than 50 mrad allows acquisition of mainly incoherent electrons in the HAADF image [1]. Lakner et al. used angular range between 60 and 180 mrad for mapping structure of GaAs/GaInP semiconductor heterostructures. They suggested that scattering in this range is dominated by Rutherford (elastic) scattering and thermal diffuse (quasi-elastically) scattering (TDS). Note that TDS was previously considered as “background intensity”. In HAADF imaging, such high-angle scattering is very sensitive to the atomic number (Z) of the scattering atoms and therefore provides information of the local chemical composition [2]. In many applications, we can consider the high angle scattering follows Rutherford’s law only, i.e. the scattering cross section is proportional to effective scattering potential or to Zα (α = 1.2~ 2) [7-11] (see Rutherford cross-section). The physical mechanism for this Z-dependent behavior is that high-angle scattering is mostly from the electrons scattered by the inner cores of atoms. The partial screening of the atomic nucleus by the inner shell electronic charges is responsible for the value of n to be less than 2 for a pure Rutherford scattering. Z-contrast technique has further been used for high-resolution STEM (HRSTEM) imaging. In this case, the use of a HAADF-STEM signal removes the complexity of conventional bright-field scattering in HRTEM and the associated diffraction complications and the incoherent images are directly interpretable. However, in many cases the purity of Z-contrast in HAADF images is still a question (See page2582).

Due to its unique performances, ADF-STEM has been applied in many fields:
         i) Identification of the presence of nanostructures with high signal-to-noise ratio. For instance, the empty space or carbon film on Cu grid represents as ‘dark area’ in the images and nanostructures present bright dots.
         ii) Elemental identification of amorphous materials based on Z-contrast theory.
         iii) Elemental identification in crystals based on Z-contrast theory if all the elements are in the same crystal structure (e.g. in Figure 4788a).

Voyles et al [3] analyzed Sb (antimony) doped Si (silicon) in the <110> zone-axis orientation using ADF-STEM (annular dark-field scanning transmission electron microscopy) operated at 200 kV, directly observed individual Sb atoms at atomic-resolution, and identified the Sb clusters in Si responsible for the saturation of charge carriers. The size, structure, and distribution of these clusters were determined with a Sb-atom detection efficiency of almost 100%. The brightest dots on the left in the ADF-STEM image in Figure 4788a are atomic columns containing at least one Sb atom and the undoped region on the right shows no such very bright dots. Regarding the quality of the TEM sample, their simulations showed that for a Si column containing a single Sb atom to be more than 25% brighter than a pure Si column, the sample must be less than 50 Å thick. Random variations in thickness must be less than the contrast of one Sb atom, and the surfaces must be free from native amorphous SiO2 layers and amorphized bulk Si layers.

HAADF-STEM image of a cross section of highly Sb-doped Si

Figure 4788a. ADF-STEM image of a cross section of highly Sb-doped Si. [3]

Figure 4788b (a) shows a HAADF-STEM image of single-layered h-BN (hexagonal boron-nitride) and Figure 4788b (b) is a corresponding atomic model where a EELS linescan has been recorded, shown in (c) and (d). The STEM contrast of the N and B locations is determined by the atomic number, called Z-contrast. Figure 4788b (c) and (d) shows the EELS profiles of the boron K-edge and nitrogen K-edge signals, respectively.

(a) A HAADF-STEM image of single-layered h-BN (hexagonal boron-nitride), (b) A corresponding atomic model where a EELS linescan has been recorded, and (c) and (d) shows the EELS profiles of the boron K-edge and nitrogen K-edge signals.

Figure 4788b. (a) A HAADF-STEM image of single-layered h-BN (hexagonal boron-nitride), (b) A corresponding atomic model where a EELS linescan was recorded, and (c) and (d) the EELS profiles of the boron K-edge and nitrogen K-edge signals. Adapted from [4]

In Figure 4788c, the intensities of the Nb and Ni atom columns in [010] direction shows the -Ni-Nb-Nb- ordering in Ba3NiNb2O9 in P-3m1 (164) space group. Its lattice parameters are a = b = 5.7550(5) Å and c = 7.0656(2) Å.

HAADF Z-contrast of Ba3NiNb2O9

Figure 4788c. HAADF intensities of the Nb and Ni atom columns in [010] direction showing the -Ni-Nb-Nb- ordering. Brightest contrast: Ba (Z=88); brighter contrast: Nb (Z = 73); weak contrast: Ni (Z=46). [14]

Generally speaking, the formation of bright-field and dark-field TEM/STEM images normally obeys the principle of the monotonic increase of cross sections σ(Z) for  thermal diffuse, elastic, and inelastic scatterings. For instance, the high-angle scattered electrons in HAADF measurements are predominantly those electrons which have undergone thermal scattering. Therefore, if there is no diffraction effects, darker (lighter) contrasts in bright-field (dark-field) images, respectively, are associated with heavier elements, for instance, as shown in Figure 4788d for a Pt/Cr interface with ZCr = 24 and ZPt=78.

Contrast of Pt/Cr interface in bright-field and dark-field TEM/STEM images

Figure 4788d. Contrasts of Pt/Cr interface in dark-field (a) and bright-field (b) TEM/STEM images. Adapted from [6]

Some other factors can also affect the HAADF contrast of the atoms. For many complex compounds, one need to carefully select the observation direction for HAADF-STEM imaging in order to correctly analyze the Z-contrast of different elements with closer atomic numbers. In such cases, they need to first study the crystalline structure with simulators to figure out the crystal orientation in which each atomic column contains a single type of elements only. The number of atoms in a single atomic column may also need to be taken into account. For instance, the observation of <1-10> direction for double perovskite (DP) Sr2FeMoO6 structures is a good choice. Figure 4788e (a) presents an HAADF-STEM observation of elemental ordering in a DP Sr2FeMoO6 film and a schematic projection drawing of the lattice along the <1-10> direction. Each lattice site becomes a column of pure Sr (Z=38), Fe (Z=26), or Mo (Z=42) atoms, respectively, and thus each site gives its unique brightness in the HAADF-STEM image, originated from their atomic numbers. The bright Sr-Mo-Sr triplets separated by a darker Fe atom. Table 4788a list the comparison between the theoretical Z-contrast and experimental intensity. We can know that the ratios of the normalized intensities of Sr and Mo atoms are slightly greater than the ratios of their normalized Z-contrast factors (Z1.7). For Sr atom columns, their intensity is not constant and they have an intensity variation of about 5%, which is in the range of common systematic errors. In this experiment, an aberration-corrected HAADF STEM system in a FEI Titan TEM is operated at 300 kV. The specimen thickness is ~50 nm and the specimen preparation was finalized by Argon (Ar) milling.

(a) HAADF-STEM image and schematic projection drawing of the DP Sr2FeMoO6 lattice along the <1-10> direction (a) HAADF-STEM image and schematic projection drawing of the DP Sr2FeMoO6 lattice along the <1-10> direction
(a) (b)

Figure 4788e. (a) HAADF-STEM image and schematic projection drawing of the DP Sr2FeMoO6 lattice along the <1-10> direction. Each triplet is a bright Sr-Mo-Sr chain (e.g. the dashed yellow box). Adapted from [16]. And (b) Brightness (intensity) plot of a Fe-Sr-Mo-Sr chain along the green arrow in (a).

Table 4788a. Comparison between the theoretical Z-contrast and experimental intensity.

Elements Atomic number (Z) Theoretical Z1.7 Normalized Z1.7 Experimental intensity Normalized intensity
Fe 26 254.4 1.00 107 1.00
Sr1 38 484.9 1.91 212 1.98
Mo 42 574.8 2.26 246 2.30
Sr2 38 484.9 1.91 222 2.07

In Figure 4788f, multislice simulation presents the total cross section of Au (gold) as a function of the number of atoms in a Au column.[12] In other words, the HAADF intensity depends on the atomic number (Z-contrast) as well as the number of atoms in the column. Without the need for a calibration standard, LeBeau et al. [13] were able to quantify the number and location of the atoms in the specimen from 4 to 33 atom column height when the experimental images taken from a wedge-shaped Au thin foil was compared directly with theory.

HAADF intensity as a function of the  number of atoms along the Au column, obtained by multislice simulation

Figure 4788f. HAADF intensity as a function of the number of atoms along the Au column, obtained by multislice simulation. [12]

Table 4788b lists some examples of elemental groups which had been studied by researchers and had been suggested whether the elements are experimentally distinguishable within each group by HAADF technique. Assuming ZA > ZB, in general, the elements can be distinguished at atomic scale if A1.7/B1.7 > 5 with very thin specimens, and the elemental layers can be separated at low magnifications of 2 < A1.7/B1.7 < 5 (e.g. Nb/Ni) with "thick" specimens. The elements cannot be distinguished at all at any magnifications if A1.7/B1.7 < 2. However, for a well-aberration-corrected HAADF STEM, the distinguishability is much greater, e.g. one even was able to seperate the Mo and Sr atom columns (Mo1.7/Sr1.7=1.19).

Table 4788b. Examples of elemental groups studied by researchers.

Group Symbol Elements Atomic number (Z) Z1.7 A1.7/B1.7 Distinguishability Reference
1 A Sb 51 799.6 9.0 Yes [3]; also see Figure 4788a
B Si 14 88.8
2 A Cr 78 1,646.5 7.4 Yes [6]; also see Figure 4788d
B Pt 24 222.0
3 A Ni/Cu 28/29 ~288.5 3.69 Yes [15]; also see Al87Ni7Cu3Ce3 in page1437
B Al 13 78.29
4 A Ce 58 995.0 ~3.45 Yes [15]; also see Al87Ni7Cu3Ce3 in page1437
B Ni/Cu 28/29 ~288.5
5 A Nb 73 1,471.1 2.2 Yes [14]; also see Figure 4788c
B Ni 46 670.9
6 A Y 39 506.8 1.6 Not [15]
B Zn 30 324.4
7 A Mo 42 574.8 1.19 Yes [16]; also see Figure 4788e or Table 4788a (with aberration-correction)
B Sr 38 484.9
8 A Cu 29 306.3 ~1.06 Not  
B Ni 28 288.5
9   O 8 34.3   Invisible by HAADF  






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