Microscopy, 2015, 69–76 doi: 10.1093/jmicro/dfu098 Advance Access Publication Date: 11 November 2014

Article

Phase reconstruction in annular bright-field scanning transmission electron microscopy Takafumi Ishida1,2,*, Tadahiro Kawasaki2,3,4, Takayoshi Tanji2,3, Tetsuji Kodama5, Takaomi Matsutani6, Keiko Ogai7, and Takashi Ikuta8 1

Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan, 2Global Research Center for Environment and Energy Based on Nanomaterials Science, Furo-cho, Chikusa, Nagoya 464-8502, Japan, 3EcoTopia Science Institute, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8502, Japan, 4Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan, 5 Department of Electrical and Electronic Engineering, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tempaku, Nagoya 468-8502, Japan, 6Department of Electrical and Electronic Engineering, Faculty of Science and Technology, Kinki University, 3-4-1 Kowakae, Higashiosaka 5778502, Japan, 7APCO Ltd., 522-10 Kitano-machi, Hachioji 192-0906, Japan, and 8Department of Electrical and Electronic Engineering, Faculty of Engineering, Osaka Electro-Communication University, 18-8 Hatsu-cho, Neyagawa 572-8530, Japan *To whom correspondence should be addressed. E-mail: [email protected] Received 20 June 2014; Accepted 7 October 2014

Abstract A novel technique for reconstructing the phase shifts of electron waves was applied to Cs-corrected scanning transmission electron microscopy (STEM). To realize this method, a new STEM system equipped with an annular aperture, annularly arrayed detectors and an arrayed image processor has been developed and evaluated in experiments. We show a reconstructed phase image of graphite particles and demonstrate that this new method works effectively for high-resolution phase imaging. Key words: phase reconstruction, figure-eight-shaped Fourier filter, annular aperture, annular array of detectors

Introduction The recent development of electron optical instruments with aberration correction [1,2] has made scanning transmission electron microscopy (STEM) capable of observing the atomic column in various imaging modes [3]. In particular, annular bright-field (ABF) imaging [4] allows simultaneous visualization of light and heavy atomic columns, which is difficult for a high-angle annular dark-field imaging mode. For thin specimens, the contrast of ABF images oscillates with the amount of defocus, and there is an optimal focus

for showing the crystal structures [5,6]. This effect seems to be the same as in phase contrast images of conventional bright-field (BF) imaging in STEM. Therefore, as well as in the BF images, phase information corresponding to the projected potentials of specimens is lost or mixed with amplitude information in the ABF images. One way to reveal the phase information is to perform image processing using multiple images; this has been studied mainly in transmission electron microscopy (TEM) [7]. According to the reciprocity theorem between TEM and

© The Author 2014. Published by Oxford University Press on behalf of The Japanese Society of Microscopy. All rights reserved. For permissions, please e-mail: [email protected]

69

Microscopy, 2015, Vol. 64, No. 2

70

STEM [8–10], such image processing techniques are applicable to STEM. Ikuta and Ichihashi [11] proposed a phase reconstruction method using an annular aperture, a multichannel detector and simple image processing in STEM. We call it annular bright-field phase (ABFP) imaging because signals detected in the ABF region are used for phase reconstruction. Taya et al. [12] showed that the phase image could be reconstructed without the annular aperture. However, high-resolution phase images have not been obtained owing to lens aberrations. In this work, we realized the proposal of Ikuta using a Cs-corrected scanning transmission electron microscope equipped with an annular aperture, annularly arrayed detectors and an arrayed image processor. The effectiveness of this method was evaluated experimentally by recording and reconstructing high-resolution images of graphite particles.

Method Theory In previous papers [12–14], the theoretical background of the ABFP imaging method was explained by a threedimensional optical transfer function under tilted illumination of the TEM based on reciprocity between TEM and STEM imaging. On the other hand, we expressed it here

directly with the STEM imaging theory. Figure 1 shows a schematic illustration of the STEM optical system used to explain the ABFP imaging. According to Cowley’s expression [15], under assumption of the perfectly coherent illumination, the observed image intensity as a function of the probe position r on a two-dimensional (2D) object plane is described as Z iðrÞ ¼ Z ¼

DðkÞjΨðk; rÞj2 dk ð1Þ DðkÞjqðrÞtðrÞ expð2πik  rÞj2 dk;

where Ψðk; rÞ is the wave function on the detector plane as a function of the 2D spatial frequencies in the reciprocal space, k; DðkÞ is the detector sensitivity function; qðrÞ is the transmission function of the object; tðrÞ is the inverse Fourier transform of the transfer function of the probe-forming objective lens, TðkÞ and the symbol  represents a convolution integral. Here, the transmission function can be separated into real and imaginary parts qðrÞ ¼ 1 þ qr ðrÞ þ iqi ðrÞ:

ð2Þ

The terms qr ðrÞ and qi ðrÞ correspond to the real and imaginary components we desired to visualize, respectively. By using Eq. (2), the wave function Ψðk; rÞ can be calculated as Ψðk; rÞ ¼ð1 þ qr ðrÞ þ iqi ðrÞÞtðrÞ expð2πik  rÞ ¼TðkÞ þ ðqr ðrÞ þ iqi ðrÞÞtðrÞ expð2πik  rÞ ¼TðkÞ þ Sðk; rÞ:

ð3Þ

The first term in this equation was derived as Z 1tðrÞ expð2πik  rÞ ¼

tðrÞexp(  2πik  rÞdr

ð4Þ

¼TðkÞ: The second term in Eq. (3), Sðk; rÞ, corresponds to the wave scattered by the object. Thus the image intensity and its Fourier transform, Iðk0 Þ, becomes Z iðrÞ ¼ Z Fig. 1. Schematic illustration of (a) an ABFP-STEM optical system equipped with an annular aperture and (b) annularly arrayed detectors on the detection plane.

¼

DðkÞ  jΨðk; rÞj2 dk DðkÞfjTðkÞj2 þ T  ðkÞSðk; rÞ

þ TðkÞS ðk; rÞ þ jSðk; rÞj2 g dk;

ð5Þ

Microscopy, 2015, Vol. 64, No. 2

Iðk0 Þ ¼

Z

71

DðkÞfjTðkÞj2 δðk0 Þ

þ ðQr ðk0 Þ þ iQi ðk0 ÞÞ  Tðk0  kÞ  T  ðkÞ

ð6Þ

0

þ ðQr ðk0 Þ  iQi ðk0 ÞÞ  T  ðk þ kÞ  TðkÞ þ non-linear termsg dk; 0

0

where Qr ðk Þ and Qi ðk Þ are the Fourier transforms of qr ðrÞ and qi ðrÞ; respectively. In the braces of Eq. (5), the first term is a constant corresponding to the background of the image intensity, and so its Fourier transform is represented as the delta function in Eq. (6). The second and third terms are the linear imaging components, which enable to express the transmission function because of linear inclusion of ðqr ; qi Þ or ðQr ; Qi Þ. On the other hand, the final terms in Eqs. (5) and (6), the non-linear imaging components, are the cross terms of the transmission function and produce complicated image intensities. For an annular aperture having a width of w0 and an average radius of k0 ; the transfer function of the lens system TðkÞ has a ring-shaped distribution. When the annularly arrayed detectors (Fig. 1b) are set in the region illuminated by the transmitted beam, each off-axis detector provides a STEM image, as expressed by Eq. (5). To simplify Eq. (6), we consider an off-axial point detector located at kn ðjkn j ¼ k0 Þ; as shown in Fig. 1a. Then Dn ðkÞ ¼ δðk  kn Þ; and Eq. (6) can be written as In ðk0 Þ ¼ δðk0 Þ þ ðQr ðk0 Þ þ iQi ðk0 ÞÞTðk0  kn ÞT  ðkn Þ þ ðQr ðk0 Þ  iQi ðk0 ÞÞT  ðk0 þ kn ÞTðkn Þ þ non-linear terms :

ð7Þ

This equation indicates that the linear imaging components appear in two rings shifted by ±kn in opposite directions from the origin; this results in a figure-eight-shaped distribution (see Figs. 2 and 6). Thus, n images can be taken, whose Fourier components differ depending on the detector function Dn ðkÞ. Note that the two rings have the same shape, which is determined by the function TðkÞ; but the object information contained in the rings differs because of the opposite signs of Qi ðkÞ. In contrast, the non-linear components, which are undesired for structural analysis [16,17], are distributed over a wide area in Fourier space. Therefore, the linear components can be extracted by using a figureeight-shaped Fourier filter whose shape is consistent with the distributions of the linear term. The annularly arrayed detector of finite width provides the broader distribution of the linear components because the Fourier spectrum is derived by simple summation of spectra obtained by the point detectors located inside the detection area DðkÞ; as described in Eq. (6).

Fig. 2. Schematic diagram of the reconstruction process for amplitude and phase images.

Reconstruction of phase and amplitude images The amplitude and phase of electron waves at the exit planes of the specimens, qðrÞ; are reconstructed by numerical image processing based on the above imaging theory as follows (Fig. 2). First, multiple STEM images obtained by the annularly arrayed detectors are Fourier transformed. Second, figure-eight-shaped filters are applied to each Fourier spectrum to extract the linear components. Then the filter must be rotated in association with the center position of the detector. The rotation angle depends on the relation between the detector position and the raster-scanning direction of the STEM imaging. Here, the kx and ky coordinates in Fig. 1b are along the raster-scanning direction and in its vertical direction, respectively. When Detector A is located on the ky axis, Image A obtained with this detector is multiplied by the upright figure-eight-shaped filter, as shown in Fig. 2. For Image B, the filter is rotated 90°, corresponding to Detector B. The rotation angle of the filter should be coincident with that of the detector position. To reconstruct the real component Qr ðkÞ; only the figure-eight-shaped extraction filter is applied. On the other hand, for the imaginary

Microscopy, 2015, Vol. 64, No. 2

72

component Qi ðkÞ; the filter should have both the extraction effect and a function to make the coefficients of Qi ðkÞ equal to +1. Therefore, the extracted components are multiplied by +i or –i depending on their positions in the figure-eight-shaped filter, as shown in Fig. 2. Finally, the sum of these filtered spectra is inverse Fourier transformed to obtain the reconstructed real or imaginary components of the complex exit wave. Assuming a weak phase object approximation, the amplitude and phase images, iAmp ðrÞ and iPhase ðrÞ; that we actually desired are provided directly as the real and imaginary images, qr ðrÞ and qi ðrÞ; respectively. For thicker samples, these can be derived as follows 1

iAmp ðrÞ ¼ ½fqr ðrÞg2 þ fqi ðrÞg2 2 ;  iPhase ðrÞ ¼ atan

 qi ðrÞ : qr ðrÞ

ð8aÞ

ð8bÞ

In the ABFP imaging, the maximum spatial frequency of the transferable information is extended by up to ∼2jk0 j; which is almost twice that for the conventional BF-STEM imaging. For the correct reconstruction of the exit wave, all the spatial frequencies up to this maximum value should be collected. When the multiple spectra are summed, it is then necessary to select appropriate widths for both the annular aperture and the figure-eight-shaped filter in order to cover this range in the 2D Fourier space.

Development of the STEM imaging system A dedicated Cs-corrected scanning transmission electron microscope (Hitachi: HD-2300S) with a cold field-emission gun was operated at an accelerating voltage of 200 kV. This apparatus was also equipped with an annular aperture and the annularly arrayed detectors we newly developed. The former was installed above an objective lens to form a hollow-cone probe, and the latter was placed in a camera chamber under a fluorescent screen. The detection angles on

Fig. 3. (a) Schematic illustration of detector layout. (b) Photograph of annular array of detectors.

the detector could be changed arbitrarily by adjusting the conditions of the projection lenses installed between the objective lens and the detectors. Figure 3 shows a schematic diagram of the layout of the annularly arrayed detectors and a photograph of our developed one. The detectors have 31 channels in which 24 channels (#0–#23) are used for ABFP imaging and the others (#24–#30) are used for normal BF-STEM imaging, as shown in Fig. 3a. Each channel consists of a bare optical fiber, one end of which is coated directly by a scintillator made of P47 powders. The fiber (Mitsubishi Rayon CK20) has a core with an inner diameter of 0.485 nm and an outer diameter of 0.5 mm. The other ends of the fibers are connected to a multianode photomultiplier tube (PMT; Hamamatsu H7546B). Electrons are converted to photons without a bias potential by the scintillator. The optical fibers transfer the emitted photons to the multianode PMT. The output of the multianode PMT is amplified and fed into an interface board on a personal computer, where it is synchronized with the scanning signal in the STEM controller. This system simultaneously provides 31 images consisting of 640 × 480 pixels with a dwell time of 20 μs/pixel and a total scanning time of 8.3 s. The number of annularly arrayed detectors affects the resultant image. A smaller number of detectors provides larger detection angle for each detector, which then results in a higher signal-to-noise ratio (SNR) in the observed STEM images. On the other hand, a larger number of detectors allows the use of narrower figure-eight-shaped filters, which then results in less nonlinear components in the reconstructed image. To balance these effects, we chose to include 24 channels. Figure 4 shows scanning electron microscope images of the annular aperture fabricated with a focused ion beam (FIB) technique [18]. One side of a tantalum plate was roughly dug from 30 to ∼10 μm in thickness by FIB to shorten the process time, as shown in Fig. 4b. The aperture has three bridges that support a central obstruction plate, as indicated by the arrows in Fig. 4a. The effects of these

Fig. 4. Scanning electron microscope image of annular aperture fabricated with FIB. The two sides of the aperture plate are shown in (a) and (b).

Microscopy, 2015, Vol. 64, No. 2

73

Fig. 5. Observed STEM images of graphite particles obtained by three of the annularly arrayed detectors. Numbers k correspond to those in Fig. 3(a).

bridges on the intensity distribution of the formed electron probes were reported by Kawasaki et al. [19]. They proposed that the ratio of the area of the bridges to the transmittable area (RBA) should be