Practicable model for phonon spectroscopy at atomic resolution in scanning transmission electron microscopy for thick crystalline specimens

We generalize a recently proposed theory for atomic resolution phonon spectroscopy in scanning transmission electron microscopy, which explicitly includes the dependence of the spectrum on probe position, to apply to thick specimens, where probe channeling is important. We also take into account anisotropy due to atoms of the same species exhibiting different vibrational modes. This approach considers the contribution from individual atoms to the spectrum. Simulations to explore the dependence of the spectrum, in particular of its shape, on the probe position and thickness are carried out for the perovskite <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>SrTiO</a:mi><a:mn>3</a:mn></a:msub></a:math>, which has recently been experimentally investigated, and computational efficiency is discussed.