Abstract¶
Accurate interpretation of data on the atomic scale obtained by S/TEM requires robust simulation methods. The most common method to achieve this is the multislice. The conventional multislice (CMS) algorithm relies on scattering physics assumptions which break down at lower accelerating voltages. This thesis presents an implementation of two improved versions of the multislice algorithm into the TEM simulation package abTEM written in Python. These are the Propagator Corrected Multislice (PCMS) and the Fully Corrected Multislice (FCMS). The former uses higher order terms to more accurately describe the spherical curvature of the Ewald Sphere, contrary to the parabolic approximation used in CMS. The Fully Corrected MS starts from the same Schrödinger equation as the other methods but makes fewer approximations concerning electron energy and simultaneously accounts for backscattering effects. All three methods are compared for a sample of SrTiO3 for various thicknesses and electron energies. The obtained results agree with previous literature, highlighting that the effects are negligible for high electron energies (∼200 keV) and start to appear around (∼50 keV). The Propagator corrected and Fully corrected MS agree until the energy drops approximately below 10 keV, where they begin to diverge. Additionally, the reconstructed backscattered signal follows the expected theoretical dependence on the square of the electron wavelength, showing significantly weaker signals at higher energies.
Transmission electron microscopy (TEM) is a powerful method for imaging the atomic scale Williams & Carter (2009), leveraging the much smaller wavelength of electrons compared to ordinary light, where diffraction causes a limit to resolution.
Computer simulation of the scattering process can be a powerful tool to interpret the complex scattering patterns of the electron beam. To simulate the complex interactions of the electrons with the sample, various techniques exist. This paper will focus on the multislice algorithm Cowley & Moodie (1957), which works by dividing potential of the sample into many discrete slices and calculating the scattering for each slice, followed by a propagation through vacuum. The multislice algorithm, in its conventional and most common form, works by assuming that the electrons move very fast. While this is a valid assumption to make since commonly, high accelerating voltages are used for TEM, there are situations where lower voltages are required. For example if the sample is radiation sensitive and higher energy beams would damage the sample Kaiser et al., 2011Egerton et al., 2004. Another reason for simulating with lower voltages is the use of STEM in SEM, where a TEM measurement is performed inside a SEM which typically operates at a lower voltage Sun et al. (2018). These situations have sparked an increased interest in low voltage TEM. Therefore, being able to accurately model TEM even for these lower voltages is of great importance.
In order to accurately simulate this, better models are required. Two recently-proposed extensions to the multislice method will be implemented into python and added to the python package abTEM: the propagator corrected multislice (PCMS) and the fully corrected multislice (FCMS) Ming & Chen (2013). abTEM is an open-source software written in Python which makes performing multislice simulations very easy. The improved methods will be benchmarked compared to the conventional multislice (CMS).
CMS, as it exists in abTEM, assumes that all electron scattering happens in the forward direction, meaning every electron entering the sample will exit it on the other side. In reality however, there is a chance of the electrons scatter- ing back to the electron source. This thesis adds this functionality to abTEM as well as the ability to reconstruct the total backscattered wave which might be valuable to SEM simulation Schweizer et al. (2020).
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