Image Deconvolution - an Effective Tool of Crystal Structure and Defect Determination in High-Resolution Electron micros
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Image Deconvolution - an Effective Tool of Crystal Structure and Defect Determination in High-Resolution Electron microscopy Fanghua Li and Chunyan Tang* Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China * Current address: Biology Department, Brookhaven National Laboratory, NY 11973, U.S.A. ABSTRACT Image deconvolution is introduced as an effective tool to enhance the determination of crystal structures and defects in high-resolution electron microscopy. The essence is to transform a single image that does not intuitively represent the examined crystal structure into the structure image. The principle and method of image deconvolution together with the related image contrast theory, the pseudo weak phase object approximation (pseudo WPOA), are briefly described. The method has been applied to different types of dislocations, twin boundaries, stacking faults, and one-dimensional incommensurate modulated structures. Results on the semiconducting epilayers Si0.76Ge0.24/Si and 3C-SiC/Si are given in some detail. The results on other compounds including AlSb/GaAs, GaN, Y0.6Na0.4Ba2Cu2.7Zn0.3O7-δ, Ca0.28Ba0.72Nb2O6 and Bi2.31Sr1.69CuO6+δ are briefly summarized. It is also shown how to recognize atoms of Si from C based on the pseudo WPOA, when the defect structures in SiC was determined at the atomic level with a 200 kV LaB6 microscope. INTRODUCTION The development of high-resolution electron microscopy (HREM) has resulted in a powerful technique that allows for the direct observation of projected crystal structures [1, 2]. Figure 1 gives a schematic diagram of the image formation process in HREM. Passing through an object, the electron wave is modulated to form the exit wave q(r) on the bottom surface of the object. The exit wave carries the information of the object structure and becomes the object wave for the objective lens. The diffracted and image waves are then formed on the back focal plane and image plane of objective lens, respectively. The diffracted wave function Q(H) is the Fourier transform (FT) of the object wave, and the image wave ψ(r) is the inverse FT of the diffracted wave modulated by the transfer function of the objective lens. The transfer function depends on various electron-optical parameters such as the defocus, spherical and chromatic aberration of the lens, beam divergence, etc. Generally, only images taken near the Scherzer defocus (for short hereafter written as Scherzer focus) [3] represent the projected object structure faithfully when the sample is sufficiently thin, while an image taken with an arbitrary defocus does not directly reflect the structure. In addition, due to the typically limited microscope resolution, atoms may
not be resolved individually even in images that were taken at the Scherzer focus.
Object
Objective Back focal lens plane
Image plane
q(r) Q(H)
ψ (r)
Figure 1. Schematic diagram showing the image formation process. q(r), Q(H) and ψ(r) are exit wave, di
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