Ultramicroscopy 96 (2003) 323–333 Layer-doubling method in ADF-STEM image simulation K. Mitsuishi*, M. Takeguchi, Y. Toda, K. Furuya National Institute for Materials Science, 3-13 Sakura, Tsukuba 305-0003, Ibaraki, Japan Received 11 July 2002; accepted 11 November 2002 Abstract A layer-doubling method developed in LEED calculation is applied to the ADF-STEM image simulation. This approach makes it possible to simulate image intensities of systems having a repeated slab structure, such as embedded precipitates or defects, with a much higher efficiency because it does not require the diagonalization of repeated slabs. As a simple example of this method, channeling effects are calculated for a system with embedded crystalline displaced slabs for various different slab thicknesses. r 2003 Elsevier Science B.V. All rights reserved. PACS: 07.78.+s; 61.14.Dc; 61.16.Bg Keywords: Scanning transmission electron microscopy (STEM); Electron diffraction and elastic scattering theory; Image simulation 1. Introduction Recent progress in the technique of annular dark-field scanning transmission electron microscopy (ADF- STEM) [1–3] has enabled analysis of small changes in impurity atom concentrations in matrices, surfaces, interfaces and precipitates [4–8]. Now the technique is becoming quantitative rather than a qualitative. However, ADF-STEM images cannot be interpreted directly due to the channeling effect of the incident electrons [9–11]. Therefore, for evaluation of small changes in image intensity it is still necessary to perform image simulations for various experimental parameters and structural models. For this purpose, the efficiency of the calculation must be optimized, because the simulation of ADF-STEM images requires much longer computation times than for image simulation in standard high-resolution electron microscopy (HREM). Here, we apply the layer-doubling method [12] to calculate with higher efficiency ADF-STEM images of systems containing repeated structures. By using this approach, the diagonalization process, whichconsumesalargeportionofcomputationtime,hastobeperformedonlyonceforeachrepeatedslab. And the combination of the different thickness of each slab can be calculated simply by multiplying matrices. This approach is not only effective for larger systems of precipitates or faults embedded in a crystalline matrix, but also for the systems with single unit cell thick atomic displacements and/or reconstruction layer at interfaces or defects where various surrounding layer thicknesses must be calculated to fit the images. ARTICLE IN PRESS *Corresponding author. Tel.:+81-298-59-5053; fax:+81-298-59-5054. E-mail address: mitsuishi.kazutaka@nims.go.jp (K. Mitsuishi). 0304-3991/03/$-see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-3991(03)00097-4