Results and Discussion

The image degradation of present meso-scale tomography was approached with respect to the geometry, such as DOF and beam divergence, with the electron scattering in the interaction volume. DOF defines the depth of sharpness and the distance along the beam axis within, in which the object can be moved without detectable loss of the image sharpness (Williams & Carter, Reference Williams and Carter1996). The DOF originates from a two-dimensional projection of the three-dimensional image formed by an objective lens. As for STEM, which uses a convergent beam, the initial probe size (d) increases by the divergence angle for a thick specimen. The mean probe size (R) can be measured from the given convergence angle (α) and initial probe size (d) for a specimen thickness (t), as shown in equation (2). Both are inversely proportional to the spatial resolution and must exceed the virtual specimen thickness with respect to the required resolution to form a qualified image recognizable by the tomography code. Equations for DOF and R can be expressed as follows

(1)$$ {\rm DOF =\ }d{\rm /}\beta $$

(2)$$ R = (d + R_{\max } )/2 = 1.61\lambda \sin ^{ - 1} \alpha + t \times \tan \alpha $$

where d is the distance corresponding to the smallest distances that can be resolved in the object, α and β are the collection semi-angle with respect to the condenser and objective lens, and λ's for 200 and 1,250 keV equals 25.1 × 10⁻⁴ and 7.354 × 10⁻⁴ nm, respectively.

In the consideration of electron scattering, beam spread (b) and energy spread contributing to the spatial resolution are limited to the real specimen volume. b is proportional to the atomic number (Z), t ^3/2, and inversely proportional to electron beam energy (E) as shown in equation (3). The energy spread causes chromatic aberration in that the objective lens deflects electrons of lower energy more strongly, and thus the electrons from a point in the sample form a disk image (Williams & Carter, Reference Williams and Carter1996). The radius (r _ch) of the disk proportional to the losses of energy (ΔE) maintains the relationship in equation (4). EELS estimated the energy spread, and the energy loss was converted to r _ch in Figure 1:

(3)$$ b{\rm\ }\infty {\rm\ }Z/E \times t^{3/2} $$

(4)$$ r_{{\rm ch}} = C_{\rm c} (\Delta E/E_0 )\beta $$

where C _c = 0.41 cm is defined by the manufacturer and E ₀ is the energy of incident electrons.

Figure 1. Distribution of r_ch with specimen tilting angle. r_ch corresponds to the energy loss (0–1.5 keV) measured by electron energy-loss spectrometry equipped to a 1.25-MeV ultra-high-voltage transmission electron microscope. The effective specimen thickness increased from 1,500 nm (0° tilt) to 1,732 nm (60° tilt).

Good Z-contrast images were obtained from a toner section less than ~4 μm in the lateral radius, which was nearly within in-focus for the required magnification range of the STEM operated at 200 keV. Toner sections thicker than 4 μm in the lateral radius exhibited obvious image degradation at a high tilt angle, which may have originated from the geometry. Figures 2a and 2b show the Z-contrast image at 0 and 60° specimen tilt for the ~4-μm toner section. The image exhibits nearly similar noise over the whole region and clearly illustrates the surface topography of the sectioned toner with few RuO₄ particles. The wax contrast was rather dark in the Z-contrast image. The shape of the small pigment particles was also clearly distinguished. The thickness of the toner section was measured ~1,500 nm coincidentally from the tilt image and its reconstructed tomogram.

Figure 2. a,b: Z-contrast images captured with a 200-keV scanning transmission electron microscope at the specimen tilt angle of 0 and 60°. c,d: Bright-field (BF) images captured with a 1.25-MeV ultra-high-voltage TEM at the specimen tilt angle of 0 and 60°. The noticeable degradation of image quality was observed in BF image at high tilt angle.

HAADF-STEM uses highly deflected (>50 mrad) electrons to form a Z-contrast image. As it is free from the objective lens, once the incident electron is scattered the probability of the secondary collision reduces greatly by a factor of p ², where p is the scattering probability. As a result, the contribution of beam spreading in the spatial resolution (R) of the Z-contrast image is less than a BF image, which contains most of the scattered electrons. By using thickly sectioned polymer film (~1 μm), Hyun et al. (Reference Hyun, Ercius and Muller2008) illustrated that the spatial resolution of a Z-contrast image was dominated by beam divergence, and the beam spreading was negligible.

The contribution of DOF and beam divergence for image degradation increases greatly with specimen tilting. The required DOF (1,500 and 4,214 nm with respect to 0 and ±60° tilt) at a given α is proportional to sin θ, where θ is the tilt angle and α is 8 mrad measured from a 70-μm aperture. By applying the DOFs [equation (1)], d's are 12 and 34 nm for the 0 and ±60° tilt, respectively. The R values determined by beam divergence and the initial probe size were ~17 and ~38 nm, respectively. The initial probe size was determined by the Raleigh criteria. However, DOF did not contribute to the degradation of the Z-contrast image. In STEM mode, each pixel of the Z-contrast image is acquired in a serial manner using the HAADF detector, as the electron probe scans the view area sequentially. This serial nature of the image acquisition in STEM makes the DOF completely different from the DOF appearing in the parallel recording (BF images) in conventional TEM. As a result, the spatial resolution for STEM precisely fits the beam divergence (R) as in the experiment of Hyun et al. (Reference Hyun, Ercius and Muller2008).

In the case of the BF for a similar lateral-sized toner section (see Figs. 2c, 2d), application of the semi-convergence angle (β), ~0.4 mrad, produces d's of 0.7 and 9 nm with respect to the required DOFs. Related to the electron scattering, energy spread was deduced from the EELS spectrum showing distribution of energy losses (ΔE) of the incident electrons. On applying equation (4) to the recorded EELS spectrum, the distribution of r _ch shows that the BF images were mostly formed of electrons in the energy loss range of 0–300 eV (see Fig. 1). With increased tilt of the specimen, larger and broader energy loss compared with the real volume change occurred. Nevertheless, the change of r _ch restricted to 1.5 nm was not a dominant factor for the image degradation compared with the d values measured in the STEM. b was nearly negligible based on the Monte Carlo simulation using the code CASINO with respect to 0 and 60° tilt (Hovington et al., Reference Hovington, Drouin and Gauvin1997). Styrene-acrylate copolymer was used for simulation, which occupies 80–90 wt% of the toner with a density of ~1.1 g/cm (Kazuo et al., Reference Kazuo, Shinichi, Kazuhiko and Hidemi1991; Michael et al., Reference Michael, Aura, James, Joseph, Matthew and Jing2011). The beam spread from multiple scatterings produced degradation in the Z-contrast image. Equation (3) for UHV produces a six times smaller b than that of 200 keV. The b seems to consist of single scattered electrons small enough for the Z-contrast images, confirming the simulation result. Therefore, the simulated b for UHV could be real. Similarly, a previous report also produced a negligible b for an ~1-μm-thick polymer section (Hyun et al., Reference Hyun, Ercius and Muller2008).

Conclusively, the degradation was mainly caused by beam divergence for the Z-contrast image and by the combination of DOF and C _c for the BF image of UHV-TEM. Additional studies will determine the final spatial resolution from the combination of DOF and r _ch, as the quality was greater in the Z-contrast image in the medium-voltage TEM than the BF image in UHV-TEM. This difference contributes to the failure in BF tomogram. As a result, the degradation of the acquired BF images produced recognition errors by Amira. In contrast, a tomogram was successfully reconstructed from the series of Z-contrast images as shown in Figure 3. Moreover, small contrasts between wax, resin, and pigment in the BF mode were enhanced, as the Z-contrast was proportional to Z^1.7 (Kirkland et al., Reference Kirkland, Loane and Silcox1987). The scale of Z-dependent contrast for BF-TEM is known as ~Z^0.75 (Kübel et al., Reference Kübel, Voigt, Schoenmakers, Otten, Su, Tan-Chen, Carlsson and Bradley2005). Tomography simply required clear contrast (high signal-to-noise ratio) with high intensity to construct attenuation function according to the viewing angle and position (Friedricha et al., Reference Friedricha, McCartney and Busecka2005). The resultant tomogram of the Z-contrast image clearly reconstructed the distribution of wax and even the smaller pigment, as shown in Figure 3.

Figure 3. a: Reconstructed tomogram using a series of Z-contrast images acquired with a 200-keV scanning transmission electron microscope. The distribution of wax and even the smaller pigment is clearly reconstructed. b: Enlarged image of (a) showing clear distinction between the wax and the small pigment. c: The intensity map of the cross-sectioned area of the rectangle in the tomogram (a). Successive image rendering gives a color to a range of the intensity of (c) such as low, medium, and high intensity to resin, wax, and pigment in (a), respectively.