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Author: Mielke, Alexander × Author: Koprucki, Thomas ×

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    Symmetries in TEM imaging of crystals with strain
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    On the Darwin--Howie--Whelan equations for the scattering of fast electrons described by the Schrödinger equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    Symmetries in transmission electron microscopy imaging of crystals with strain
    (London : [Verlag nicht ermittelbar], 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.
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    Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Kantner, Markus; Höhne, Theresa; Koprucki, Thomas; Burger, Sven; Wünsche, Hans-Jürgen; Schmidt, Frank; Mielke, Alexander; Bandelow, Uwe
    Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.