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Symmetries in transmission electron microscopy imaging of crystals with strain
2022, Koprucki, Thomas, Maltsi, Anieza, Mielke, Alexander
Transmission electron microscopy (TEM) images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries, we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process, we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.
On the Darwin--Howie--Whelan equations for the scattering of fast electrons described by the Schrödinger equation
2020, Koprucki, Thomas, Maltsi, Anieza, Mielke, Alexander
The Darwin-Howie-Whelan equations are commonly used to describe and simulate the scattering of fast electrons in transmission electron microscopy. They are a system of infinitely many envelope functions, derived from the Schrödinger equation. However, for the simulation of images only a finite set of envelope functions is used, leading to a system of ordinary differential equations in thickness direction of the specimen. We study the mathematical structure of this system and provide error estimates to evaluate the accuracy of special approximations, like the two-beam and the systematic-row approximation.
Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes
2020, Maltsi, Anieza, Niermann, Tore, Streckenbach, Timo, Tabelow, Karsten, Koprucki, Thomas
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin–Howie–Whelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for model-based geometry reconstruction of semiconductor QDs, involving machine learning techniques.
Symmetries in TEM imaging of crystals with strain
2022, Koprucki, Thomas, Maltsi, Anieza, Mielke, Alexander
TEM images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion that might affect the image. For the imaging process we prove mathematically that the intensities are invariant under specific transformations. A combination of these invariances with specific properties of the strain profile can then explain symmetries observed in TEM images. We demonstrate our approach to the study of symmetries in TEM images using selected examples in the field of semiconductor nanostructures such as quantum wells and quantum dots.
Correction to: Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes
2021, Maltsi, Anieza, Niermann, Tore, Streckenbach, Timo, Tabelow, Karsten, Koprucki, Thomas
Correction to: Optical and Quantum Electronics (2020) 52:257 https://doi.org/10.1007/s11082-020-02356-y
Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes
2020, Maltsi, Anieza, Niermann, Tore, Streckenbach, Timo, Tabelow, Karsten, Koprucki, Thomas
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the Darwin-Howie-Whelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for model-based geometry reconstruction of semiconductor QDs, involving machine learning techniques.