{"id":{"repo_id":"tu-berlin","oai_identifier":"oai:depositonce.tu-berlin.de:11303/27118"},"canonical_url":"https://search.dev.ndltd.org/etd/tu-berlin/oai:depositonce.tu-berlin.de:11303/27118","repository":{"repo_id":"tu-berlin","name":"Technische Universität Berlin","base_url":"https://api-depositonce.tu-berlin.de/server/oai/request"},"display":{"title":"Strain relaxation in TEM lamellae probed by 4D-STEM: from projected strain to dynamical-diffraction-based reconstruction of composition","abstract":"Scanning Transmission Electron Microscopy (STEM) provides the spatial resolution necessary to determine material composition from strain measurements on the nanoscale, but it relies on thin, electron-transparent lamellae. In such lamellae, the tetragonal distortion established during epitaxial growth partially relaxes at the free surfaces created during specimen preparation. The resulting three-dimensional strain field breaks the direct link between measured strain and composition, and intensity distribution within diffraction discs associated with dynamic diffraction varies, hindering precise evaluation of the strain state from locally recorded diffraction patterns. Rather than mereley suppressing these effects, this thesis explicitly investigates how surface strain-relaxation in thin TEM lamellae causes deviations from bulk assumptions in 4D-STEM measurements across strained interfaces, and how these deviations can be exploited to recover, among other quantities, information about the bulk strain state. First, electron scattering from strain fields that vary along the beam direction due to surface relaxation is discussed within both the kinematical approximation and a dynamical description. A continuum-mechanical model is derived that predicts the strain state of a thin lamella based on growth assumptions. The model captures the evolution of the strain state with decreasing specimen thickness from the biaxially strained bulk limit toward the uniaxially strained infinitely thin lamella limit. Using narrow (Al,Ga)N layers embedded in GaN as a model system, the impact of relaxation on STEM-based strain measurements is investigated experimentally. A patterned illumination aperture is employed to enable precise measurements robust to variations in dynamic diffraction conditions, and implications for the interpretability of the resulting strain maps using these apertures are discussed. Relaxation-induced intensity redistributions within diffraction discs are examined systematically by comparing simulations based on the relaxed strain field with simulations enforcing a bulk-like strain distribution. The analysis reveals distinct impacts of the three parameters: lamella thickness, layer width, and layer composition on dynamic diffraction. Additionally, a general thickness-dependent sensitivity to relaxation is observed. Finally, a method is presented to determine these three parameters from the observed dynamical-diffraction variations. Experimental datasets are matched to simulations, and the parameters are extracted by minimizing the discrepancy between the two under systematic parameter variation. The reconstructed values agree well with reference methods (X-ray diffraction and STEM-EDS), despite remaining challenges, particularly when assumptions of the employed strain models (e.g., sharp material interfaces) are violated. The proposed method remains applicable over a broad range of lamella thicknesses, reducing the need for precise thickness control during specimen preparation, and it requires no additional instrumentation beyond a state-of-the-art STEM.","abstract_html":"Scanning Transmission Electron Microscopy (STEM) provides the spatial resolution necessary to determine material composition from strain measurements on the nanoscale, but it relies on thin, electron-transparent lamellae. In such lamellae, the tetragonal distortion established during epitaxial growth partially relaxes at the free surfaces created during specimen preparation. The resulting three-dimensional strain field breaks the direct link between measured strain and composition, and intensity distribution within diffraction discs associated with dynamic diffraction varies, hindering precise evaluation of the strain state from locally recorded diffraction patterns. Rather than mereley suppressing these effects, this thesis explicitly investigates how surface strain-relaxation in thin TEM lamellae causes deviations from bulk assumptions in 4D-STEM measurements across strained interfaces, and how these deviations can be exploited to recover, among other quantities, information about the bulk strain state. First, electron scattering from strain fields that vary along the beam direction due to surface relaxation is discussed within both the kinematical approximation and a dynamical description. A continuum-mechanical model is derived that predicts the strain state of a thin lamella based on growth assumptions. The model captures the evolution of the strain state with decreasing specimen thickness from the biaxially strained bulk limit toward the uniaxially strained infinitely thin lamella limit. Using narrow (Al,Ga)N layers embedded in GaN as a model system, the impact of relaxation on STEM-based strain measurements is investigated experimentally. A patterned illumination aperture is employed to enable precise measurements robust to variations in dynamic diffraction conditions, and implications for the interpretability of the resulting strain maps using these apertures are discussed. Relaxation-induced intensity redistributions within diffraction discs are examined systematically by comparing simulations based on the relaxed strain field with simulations enforcing a bulk-like strain distribution. The analysis reveals distinct impacts of the three parameters: lamella thickness, layer width, and layer composition on dynamic diffraction. Additionally, a general thickness-dependent sensitivity to relaxation is observed. Finally, a method is presented to determine these three parameters from the observed dynamical-diffraction variations. Experimental datasets are matched to simulations, and the parameters are extracted by minimizing the discrepancy between the two under systematic parameter variation. The reconstructed values agree well with reference methods (X-ray diffraction and STEM-EDS), despite remaining challenges, particularly when assumptions of the employed strain models (e.g., sharp material interfaces) are violated. The proposed method remains applicable over a broad range of lamella thicknesses, reducing the need for precise thickness control during specimen preparation, and it requires no additional instrumentation beyond a state-of-the-art STEM.","abstract_has_math":false,"creators":["Otto, Frederik"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Lehmann, Michael"],"committee_chairs":[],"committee_members":[],"year":2026,"date_issued":"2026","date_published":"2026","updated_at":"2026-07-27T21:28:47Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":["https://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://doi.org/10.14279/depositonce-25952"],"render_values":[{"text":"https://doi.org/10.14279/depositonce-25952","href":"https://doi.org/10.14279/depositonce-25952","code":true}]}]},"links":{"outbound_url":"https://depositonce.tu-berlin.de/handle/11303/27118","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Lehmann, Michael"]},{"key":"dc:creator","label":"Author","values":["Otto, Frederik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-05-28T07:33:14Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-28T07:33:14Z"]},{"key":"dc:date.issued","label":"Date","values":["2026"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights.uri","label":"Rights URI","values":["https://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://depositonce.tu-berlin.de/handle/11303/27118","https://doi.org/10.14279/depositonce-25952"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Scanning Transmission Electron Microscopy (STEM) provides the spatial resolution necessary to determine material composition from strain measurements on the nanoscale, but it relies on thin, electron-transparent lamellae. In such lamellae, the tetragonal distortion established during epitaxial growth partially relaxes at the free surfaces created during specimen preparation. The resulting three-dimensional strain field breaks the direct link between measured strain and composition, and intensity distribution within diffraction discs associated with dynamic diffraction varies, hindering precise evaluation of the strain state from locally recorded diffraction patterns. Rather than mereley suppressing these effects, this thesis explicitly investigates how surface strain-relaxation in thin TEM lamellae causes deviations from bulk assumptions in 4D-STEM measurements across strained interfaces, and how these deviations can be exploited to recover, among other quantities, information about the bulk strain state. First, electron scattering from strain fields that vary along the beam direction due to surface relaxation is discussed within both the kinematical approximation and a dynamical description. A continuum-mechanical model is derived that predicts the strain state of a thin lamella based on growth assumptions. The model captures the evolution of the strain state with decreasing specimen thickness from the biaxially strained bulk limit toward the uniaxially strained infinitely thin lamella limit. Using narrow (Al,Ga)N layers embedded in GaN as a model system, the impact of relaxation on STEM-based strain measurements is investigated experimentally. A patterned illumination aperture is employed to enable precise measurements robust to variations in dynamic diffraction conditions, and implications for the interpretability of the resulting strain maps using these apertures are discussed. Relaxation-induced intensity redistributions within diffraction discs are examined systematically by comparing simulations based on the relaxed strain field with simulations enforcing a bulk-like strain distribution. The analysis reveals distinct impacts of the three parameters: lamella thickness, layer width, and layer composition on dynamic diffraction. Additionally, a general thickness-dependent sensitivity to relaxation is observed. Finally, a method is presented to determine these three parameters from the observed dynamical-diffraction variations. Experimental datasets are matched to simulations, and the parameters are extracted by minimizing the discrepancy between the two under systematic parameter variation. The reconstructed values agree well with reference methods (X-ray diffraction and STEM-EDS), despite remaining challenges, particularly when assumptions of the employed strain models (e.g., sharp material interfaces) are violated. The proposed method remains applicable over a broad range of lamella thicknesses, reducing the need for precise thickness control during specimen preparation, and it requires no additional instrumentation beyond a state-of-the-art STEM.","Scanning Transmission Electron Microscopy (STEM) liefert die nötige Ortsauflösung, um Materialzusammensetzungen auf der Nanoskala aus Verspannungsmessungen zu bestimmen, erfordert hierfür allerdings dünne, elektronentransparente Lamellen. Für diese relaxiert die, im Wachstum ausgebildete tetragonale Verspannung teilweise an den freien Oberflächen. Durch das resultierende dreidimensionale Verspannungsfeld lässt sich die Kompositionsverteilung nicht mehr direkt aus gemessenen Verspannungen rückschließen. Zusätzlich variieren Muster der dynamischen Beugung innerhalb von Beugungsscheiben, wodurch eine präzise Auswertung des Verspannungszustandes aus lokal aufgenommenen Beugungsbildern erschwert wird. Anstatt diese Effekte zu unterdrücken, widmet sich diese Arbeit ganz explizit den durch Verspannungsrelaxation an den Oberflächen dünner TEM-Lamellen verursachten Abweichungen von der Volumenannahme. Durch 4D-STEM-Messungen an verspannten Grenzflächen können unter anderem, Informationen über den Volumenverspannungszustand gewonnen werden. Zunächst wird die Elektronenstreuung an in Strahlrichtung variierenden Verspannungsfeldern, die aus Oberflächenrelaxation resultieren, sowohl in kinematischer Näherung als auch in dynamischer Beschreibung diskutiert. Anschließend wird ein kontinuummechanisches Modell hergeleitet, welches den Verspannungszustand einer dünnen Lamelle basierend auf Wachstumsannahmen beschreibt. Dieses zeigt die Evolution des Verspannungszustandes mit abnehmender Probendicke vom biaxial verspannten Volumenlimit zum uniaxial verspannten Grenzfall für unendlich dünne Lamellen. Am Modellsystem schmaler (Al,Ga)N-Schichten in GaN werden die Auswirkungen der Relaxation auf Verspannungsmessungen im STEM experimentell untersucht. Hierzu wird eine strukturierte Beleuchtungsblende für präzise Messungen trotz dynamischer Beugungsbedingungen genutzt und deren Auswirkungen auf die Interpretierbarkeit der Messungen diskutiert. Die durch Relaxation bedingten Intensitätsveränderungen innerhalb der Beugungsscheiben werden systematisch untersucht. Hierzu werden Strahl-Simulationen auf Basis des relaxierten Verspannungsfeldes mit Simulationen unter Bulk-Annahme verglichen. Die Analyse zeigt einzigartige Einflüsse der drei Parameter: Lamellendicke, Schichtbreite und Schichtkomposition auf dynamische Beugung, sowie eine dickenabhängige Sensitivität dynamischer Beugung auf Relaxation. Es wird eine Methode zur Bestimmung dieser drei Parameter aus beobachteten Veränderungen der dynamischen Beugung vorgestellt. Dazu werden experimentelle Datensätze mit Simulationen verglichen. Die Parameter ergeben sich aus der Minimierung der Abweichung zwischen Experiment und Simulation bei systematischer Parametervariation. Trotz verbleibender Herausforderungen, etwa in Fällen, in denen die Annahmen der Strain-Modelle über scharfe Materialübergänge verletzt werden, stimmen die rekonstruierten Werte gut mit Referenzmethoden (Röntgendiffraktometrie und STEM-EDS) überein. Die neu etablierte Methode ist über einen breiten Bereich von Lamellendicken anwendbar, reduziert so die Anforderungen an eine strenge Dickenkontrolle in der Probenpräparation und benötigt keine zusätzliche Instrumentierung über ein modernes STEM hinaus."]},{"key":"dc:title","label":"Title","values":["Strain relaxation in TEM lamellae probed by 4D-STEM: from projected strain to dynamical-diffraction-based reconstruction of composition"]}]}],"canonical_facts":{"dc:contributor.advisor":["Lehmann, Michael"],"dc:creator":["Otto, Frederik"],"dc:date.accessioned":["2026-05-28T07:33:14Z"],"dc:date.available":["2026-05-28T07:33:14Z"],"dc:date.issued":["2026"],"dc:description.abstract":["Scanning Transmission Electron Microscopy (STEM) provides the spatial resolution necessary to determine material composition from strain measurements on the nanoscale, but it relies on thin, electron-transparent lamellae. In such lamellae, the tetragonal distortion established during epitaxial growth partially relaxes at the free surfaces created during specimen preparation. The resulting three-dimensional strain field breaks the direct link between measured strain and composition, and intensity distribution within diffraction discs associated with dynamic diffraction varies, hindering precise evaluation of the strain state from locally recorded diffraction patterns. Rather than mereley suppressing these effects, this thesis explicitly investigates how surface strain-relaxation in thin TEM lamellae causes deviations from bulk assumptions in 4D-STEM measurements across strained interfaces, and how these deviations can be exploited to recover, among other quantities, information about the bulk strain state. First, electron scattering from strain fields that vary along the beam direction due to surface relaxation is discussed within both the kinematical approximation and a dynamical description. A continuum-mechanical model is derived that predicts the strain state of a thin lamella based on growth assumptions. The model captures the evolution of the strain state with decreasing specimen thickness from the biaxially strained bulk limit toward the uniaxially strained infinitely thin lamella limit. Using narrow (Al,Ga)N layers embedded in GaN as a model system, the impact of relaxation on STEM-based strain measurements is investigated experimentally. A patterned illumination aperture is employed to enable precise measurements robust to variations in dynamic diffraction conditions, and implications for the interpretability of the resulting strain maps using these apertures are discussed. Relaxation-induced intensity redistributions within diffraction discs are examined systematically by comparing simulations based on the relaxed strain field with simulations enforcing a bulk-like strain distribution. The analysis reveals distinct impacts of the three parameters: lamella thickness, layer width, and layer composition on dynamic diffraction. Additionally, a general thickness-dependent sensitivity to relaxation is observed. Finally, a method is presented to determine these three parameters from the observed dynamical-diffraction variations. Experimental datasets are matched to simulations, and the parameters are extracted by minimizing the discrepancy between the two under systematic parameter variation. The reconstructed values agree well with reference methods (X-ray diffraction and STEM-EDS), despite remaining challenges, particularly when assumptions of the employed strain models (e.g., sharp material interfaces) are violated. The proposed method remains applicable over a broad range of lamella thicknesses, reducing the need for precise thickness control during specimen preparation, and it requires no additional instrumentation beyond a state-of-the-art STEM.","Scanning Transmission Electron Microscopy (STEM) liefert die nötige Ortsauflösung, um Materialzusammensetzungen auf der Nanoskala aus Verspannungsmessungen zu bestimmen, erfordert hierfür allerdings dünne, elektronentransparente Lamellen. Für diese relaxiert die, im Wachstum ausgebildete tetragonale Verspannung teilweise an den freien Oberflächen. Durch das resultierende dreidimensionale Verspannungsfeld lässt sich die Kompositionsverteilung nicht mehr direkt aus gemessenen Verspannungen rückschließen. Zusätzlich variieren Muster der dynamischen Beugung innerhalb von Beugungsscheiben, wodurch eine präzise Auswertung des Verspannungszustandes aus lokal aufgenommenen Beugungsbildern erschwert wird. Anstatt diese Effekte zu unterdrücken, widmet sich diese Arbeit ganz explizit den durch Verspannungsrelaxation an den Oberflächen dünner TEM-Lamellen verursachten Abweichungen von der Volumenannahme. Durch 4D-STEM-Messungen an verspannten Grenzflächen können unter anderem, Informationen über den Volumenverspannungszustand gewonnen werden. Zunächst wird die Elektronenstreuung an in Strahlrichtung variierenden Verspannungsfeldern, die aus Oberflächenrelaxation resultieren, sowohl in kinematischer Näherung als auch in dynamischer Beschreibung diskutiert. Anschließend wird ein kontinuummechanisches Modell hergeleitet, welches den Verspannungszustand einer dünnen Lamelle basierend auf Wachstumsannahmen beschreibt. Dieses zeigt die Evolution des Verspannungszustandes mit abnehmender Probendicke vom biaxial verspannten Volumenlimit zum uniaxial verspannten Grenzfall für unendlich dünne Lamellen. Am Modellsystem schmaler (Al,Ga)N-Schichten in GaN werden die Auswirkungen der Relaxation auf Verspannungsmessungen im STEM experimentell untersucht. Hierzu wird eine strukturierte Beleuchtungsblende für präzise Messungen trotz dynamischer Beugungsbedingungen genutzt und deren Auswirkungen auf die Interpretierbarkeit der Messungen diskutiert. Die durch Relaxation bedingten Intensitätsveränderungen innerhalb der Beugungsscheiben werden systematisch untersucht. Hierzu werden Strahl-Simulationen auf Basis des relaxierten Verspannungsfeldes mit Simulationen unter Bulk-Annahme verglichen. Die Analyse zeigt einzigartige Einflüsse der drei Parameter: Lamellendicke, Schichtbreite und Schichtkomposition auf dynamische Beugung, sowie eine dickenabhängige Sensitivität dynamischer Beugung auf Relaxation. Es wird eine Methode zur Bestimmung dieser drei Parameter aus beobachteten Veränderungen der dynamischen Beugung vorgestellt. Dazu werden experimentelle Datensätze mit Simulationen verglichen. Die Parameter ergeben sich aus der Minimierung der Abweichung zwischen Experiment und Simulation bei systematischer Parametervariation. Trotz verbleibender Herausforderungen, etwa in Fällen, in denen die Annahmen der Strain-Modelle über scharfe Materialübergänge verletzt werden, stimmen die rekonstruierten Werte gut mit Referenzmethoden (Röntgendiffraktometrie und STEM-EDS) überein. Die neu etablierte Methode ist über einen breiten Bereich von Lamellendicken anwendbar, reduziert so die Anforderungen an eine strenge Dickenkontrolle in der Probenpräparation und benötigt keine zusätzliche Instrumentierung über ein modernes STEM hinaus."],"dc:identifier.uri":["https://depositonce.tu-berlin.de/handle/11303/27118","https://doi.org/10.14279/depositonce-25952"],"dc:language.iso":["en"],"dc:rights.uri":["https://creativecommons.org/licenses/by/4.0/"],"dc:title":["Strain relaxation in TEM lamellae probed by 4D-STEM: from projected strain to dynamical-diffraction-based reconstruction of composition"],"dc:type":["Doctoral Thesis"]},"updated_at":"2026-07-27T21:28:47Z"}