The simulation of high angle annular dark field (HAADF) images can be tackled by multi-slice and Bloch wave methods. , , , The HAADF image formation is due to the mainly incoherent interaction of the highly focused electron probe along the zone axis atomic columns of the specimen. The origin of the incoherent nature of the interaction along each column resides in the electron-phonon scattering process. Hence, the thermal diffuse scattering is of particular importance in the HAADF image formation. Within the multi-slice method the role of the thermal diffuse scattering can be treated in the most direct way by applying the so-called frozen phonon approximation. This approach is based on the assumption that the high-energy electrons are so fast that each electron sees a snapshot of the atomic thermal movement. The calculated intensity is therefore the incoherent superposition of the images formed for each atomic configuration in the range of positions given by the Debye-Waller factors. According to our test simulations, and in agreement with literature, 20 configurations are at least necessary to converge to a precision better than 2% in simulating HAADF image contrast. This means that the multi-slice simulation must be repeated for each atomic configuration and for each point of the image. Calculation time depends critically on sample thickness, scan size and frequency of the potential and the wave-function sampling in both direct and reciprocal space.2 Even with a small scan size (12x16 pixels) the calculation of a single cell image for a GaAs cell in a 10 nm thick sample requires more than 5 hours of computing time. Hence, multi-slice approach produces very accurate and reliable results for the HAADF image simulation but at a cost of very large computer-time. Here we present a program for HAADF image multi-slice calculation based on the routines developed by Kirkland. The program has a user-friendly interface and allows a direct access to the parameters necessary for the calculation. Furthermore, a parallelisation of the calculation has been implemented allowing a strong reduction of the time necessary for the HAADF calculations.
STEM_CELL:COMPUTER SIMULATION FOR HAADF SIMULATION AND ANALYSIS
2005
Abstract
The simulation of high angle annular dark field (HAADF) images can be tackled by multi-slice and Bloch wave methods. , , , The HAADF image formation is due to the mainly incoherent interaction of the highly focused electron probe along the zone axis atomic columns of the specimen. The origin of the incoherent nature of the interaction along each column resides in the electron-phonon scattering process. Hence, the thermal diffuse scattering is of particular importance in the HAADF image formation. Within the multi-slice method the role of the thermal diffuse scattering can be treated in the most direct way by applying the so-called frozen phonon approximation. This approach is based on the assumption that the high-energy electrons are so fast that each electron sees a snapshot of the atomic thermal movement. The calculated intensity is therefore the incoherent superposition of the images formed for each atomic configuration in the range of positions given by the Debye-Waller factors. According to our test simulations, and in agreement with literature, 20 configurations are at least necessary to converge to a precision better than 2% in simulating HAADF image contrast. This means that the multi-slice simulation must be repeated for each atomic configuration and for each point of the image. Calculation time depends critically on sample thickness, scan size and frequency of the potential and the wave-function sampling in both direct and reciprocal space.2 Even with a small scan size (12x16 pixels) the calculation of a single cell image for a GaAs cell in a 10 nm thick sample requires more than 5 hours of computing time. Hence, multi-slice approach produces very accurate and reliable results for the HAADF image simulation but at a cost of very large computer-time. Here we present a program for HAADF image multi-slice calculation based on the routines developed by Kirkland. The program has a user-friendly interface and allows a direct access to the parameters necessary for the calculation. Furthermore, a parallelisation of the calculation has been implemented allowing a strong reduction of the time necessary for the HAADF calculations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
