Exit Wave Function Retrieval from Diffraction Patterns ...

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data collection for thin [110]GaAs-film using a Gatan multipixel-CCD camera in ... Here 64=8x8 single NAED patterns (c) from 4D-Data cube (b) were used for ...
780 DOI: 10.1017/S1431927608088156

Microsc Microanal 14(Suppl 2), 2008 Copyright 2008 Microscopy Society of America

Hardware and Software for Nano-Area Diffractive Imaging in S/TEM V.V. Volkov1, J. Wall2 and Y. Zhu1 1 2

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973, USA Biology Department, Brookhaven National Laboratory, Upton, NY 11973, USA

Nano-Area Electron Diffraction (NAED) is a novel characterization tool suited for diffraction studies of individual nanoparticles and catalysts, including low-dimensional objects at nanoscale such as quantum dots, nanowires and nanotubes, due to high sensitivity of NAED patterns to local structure of the object [1]. In practice, the collimated e-beam for NAED patterns recorded with near-paraxial illumination can be reduced down to few nanometers size, typical for Convergent Beam Electron Diffraction (CBED) patterns. However, the NAED pattern remains similar to conventional diffraction patterns (DPs) and therefore retains structure information about the object down to diffraction-limited resolution. To overcome a sub-Angström resolution limit set by lens aberrations for modern (scanning) transmission electron microscopes (S/TEM), we suggest a novel solution for diffractive (“lensless”) imaging [2] by using NAED patterns recorded for non-periodic or arbitrarycomplex objects. The procedure requires the two following steps: - A sequence of NAED patterns from the object can be recorded in raster mode in modified STEM, for which both of the bright field (BF) and annual dark field (ADF) detectors should be replaced with single 2D-multipixel detector. In Fig. 1 (a,b) we show a practical example of such 8x8=64 NAEDs data collection for thin [110]GaAs-film using a Gatan multipixel-CCD camera in discrete-scanning mode. Such a CCD in final STEM hardware setup will be replaced with a new active matrix 2Dmultipixel detector (of size 32x32 pix and speed ~10000 frames/s) developed at BNL and optimized for diffractive imaging [3]. The replacement of BF/ADF detectors with 2D-multipixel detector allows direct use of rich nano-area diffraction data (Fig.1 c-e) usually lost by signal integration with BF/ADF detectors. Notice that procedure used in Fig.1 for acquisition of NAED patterns is already sufficient to realize the so-called “Diffraction Imaging” method (Fig. 1 c-e), which may have several useful applications for real-space mapping of diffraction features at nanoscale resolution limited by the tunable beam size. For instance, dark-field images in Fig.1 e, obtained by digital processing of NAED patterns, indeed, follow different diffraction data variations versus (X,Y) beam positions. Resolution of Diffraction Imaging will be limited by the beam size and beam scan properties. - If all NAED patterns used above were recorded with partial overlapping (see also Fig.1d), then the next step of appropriate phasing and unique inversion of all NAED patterns [4,5] into one global real-space solution can be realized. Such procedure known as “Diffractive Imaging”, transforms all NAED patterns into object’s exit-wave function with diffraction-limited resolution. Calculated results shown in Fig.2 clearly demonstrate that robust, unique and very fast diffractive imaging solution can be obtained, if the effect of overlapping patterns [4] breaking duality of diffractive solution is utilized along with our Automatic Chaining Diffraction (ACD) algorithm [5]. [1] J. M. Zuo, I.A. Vartanyants, M. Gao, R. Zhang, and L.A. Nagahara, Science 300 (2003) 1419. [2] J.R. Fienup, Appl. Opt. 21 (1982) 2758. [3] W. Chen et al. Nucl. Instrum. & Methods in Phys. Research, Sec.A, 512 (2003) 368-377. [4] H.M.L. Faulkner and J.M. Rodenburg, Phys. Rev. Lett. 93 (2004) 023903; J.M. Rodenburg et al. Phys. Rev. Lett. 98 (2007) 034801. [5] V. Volkov, J. Wall and Y. Zhu, Ultramicroscopy (2008), doi:10.1016/j.ultramic.2007.11.007 [6] Work was supported by the US DOE, BES (DE-AC02-98CH10886).

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Microsc Microanal 14(Suppl 2), 2008

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Fig.1 Practical example of Diffaction Imaging presented by 4-Dimensional NAED Data cube (b) recorded in STEM mode at the edge of thin [110]GaAs film (d) with ~20 nm focused paraxial beam (a). Here 64=8x8 single NAED patterns (c) from 4D-Data cube (b) were used for flexible DPs processing and direct digital construction of several “spectral” 8x8-images, including conventional ADF and new additional (e) dark-field images DF(200), DF(111) and DF(200) in pre-selected (HKL) reflections shown in (c). The trace of ~20 nm focused beam scan in real space is shown by a composite image (d). Communication interface with microscope (JEOL 3000F) can be further upgraded to improve “pixel resolution” and quality of Diffraction Imaging process.

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Fig.2 Experimental setup (a) for Diffractive Imaging with paraxial nano-beam. Here synthetic exit wave presented by the amplitude (carbon nanotubes: c) and phase (C540 fullerene: d) was used to create several NAED patterns (b) similar to real patterns in Fig.1. Then all NAED patterns (b) were used to create in hardware BF(e) and ADF(f) images in STEM with resolution ~2.7 A. In contrast to BF/ADF (e,f) images spoiled by mixed (c,d) exit-wave components, our diffractive images obtained by novel ACD algorithm [5] from the same NAED data (b) with resolution improvement down to ~0.33A produce much better quality for exit-wave amplitude and phase (g, h) free from artefacts and nearly identical to input (c,d) data.

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