Accurate and Fast Multi-slice Simulations of HAADF Image Contrast by Parallel Computing E Carlino 1 , V. Grillo 1 , P. Palazzari 2 1 TASC-INFM-CNR National Lab., Area Science Park, S.S. 14, Km. 163.5, 34012 Trieste Italy. 2 ENEA, Casaccia Research Centre, Computing and Modelling Unit, Via Anguillarese 301, 00123 S.Maria di Galeria (Roma) Italy and Ylichron Srl, Casaccia Research Centre, Via Anguillarese 301, 00123 S.Maria di Galeria (Roma) Italy Summary: A new method for fast and accurate multi-slice calculation, in the frozen-phonon approximation, of high angle annular dark field scanning transmission electron microscopy images, is presented. The improvement with respect to the existing approaches is in a strong reduction of the time necessary for image contrast simulation, without loosing in the accuracy. The method is based on the development of optimized parallel computer codes for the multi-slice calculations in the frozen-phonon approximation. 1 Introduction Transmission electron microscopy (TEM) has been widely used in the study of the matter at the highest spatial resolution. Computer simulations of TEM experimental results have been often used to understand, and to quantify, the information contained in images and spectra. In particular, the phase contrast high resolution TEM (HRTEM), benefits of the development of fast and accurate simulation routines, allowing to understand the complex structure of the relevant interference fringes, due to the dynamical interactions of several Bloch states excited in the specimen by the primary electrons. A further direct approach to the imaging of the structure of a specimen at atomic resolution is given by scanning transmission electron microscopy (STEM) high angle annular dark field (HAADF) imaging [i]. STEM HAADF imaging gives a true structural image of the specimen, and the positions of the atomic columns in the specimen, projected on the observation plane, can be easily and intuitively interpreted by looking the typical bright spots of the atomic resolution HAADF image. Furthermore, contrary to HRTEM, the main features of the HAADF image are maintained in a large range of variation of the thickness of the STEM specimen, ranging from few nm to hundreds of nm [i]. One of the substantial differences between HRTEM and HAADF imaging, is due to the mainly incoherent nature of the image formation process of the latter. The lack of coherent effects in the image, allows one to establish the position of an interface in a material, with the highest spatial resolution, by a proper set up of the HAADF experiment [ii]. Furthermore, the intensity in the HAADF image is strongly related to the atomic number of the species contained in the specimen, allowing one to distinguish between two different atomic columns with different average atomic number [i]. For this reason HAADF imaging is also known as Z-contrast imaging. The sensitivity to the chemistry allows one to derive, at atomic resolution, the distribution of guest specie in a host matrix by properly setting the experimental HAADF conditions [iii]. Despite the capability of HAADF to give important information in a direct and intuitive way, quantitative important details of the specimen, like for example the bonds configuration at an interface [iv,v], or the quantitative chemical profiling at atomic resolution [vi], can be also achieved but requires accurate simulation of both Bragg reflections and incoherent thermal diffuse scattering (TDS) in the crystal. The importance of the TDS is recognized also in the HRTEM image formation [vii,viii] but has a definitive influence in the HAADF image formation, as most of the contribution in the image intensity is due to the further interaction of the Bragg-diffused electrons with the phonons of the specimens. In fact, the