Institut für Physik und Astronomie
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Institute
Für die Entwicklung professioneller Handlungskompetenzen angehender Lehrkräfte stellt die Unterrichtsreflexion ein wichtiges Instrument dar, um Theoriewissen und Praxiserfahrungen in Beziehung zu setzen. Die Auswertung von Unterrichtsreflexionen und eine entsprechende Rückmeldung stellt Forschende und Dozierende allerdings vor praktische wie theoretische Herausforderungen. Im Kontext der Forschung zu Künstlicher Intelligenz (KI) entwickelte Methoden bieten hier neue Potenziale. Der Beitrag stellt überblicksartig zwei Teilstudien vor, die mit Hilfe von KI-Methoden wie dem maschinellen Lernen untersuchen, inwieweit eine Auswertung von Unterrichtsreflexionen angehender Physiklehrkräfte auf Basis eines theoretisch abgeleiteten Reflexionsmodells und die automatisierte Rückmeldung hierzu möglich sind. Dabei wurden unterschiedliche Ansätze des maschinellen Lernens verwendet, um modellbasierte Klassifikation und Exploration von Themen in Unterrichtsreflexionen umzusetzen. Die Genauigkeit der Ergebnisse wurde vor allem durch sog. Große Sprachmodelle gesteigert, die auch den Transfer auf andere Standorte und Fächer ermöglichen. Für die fachdidaktische Forschung bedeuten sie jedoch wiederum neue Herausforderungen, wie etwa systematische Verzerrungen und Intransparenz von Entscheidungen. Dennoch empfehlen wir, die Potenziale der KI-basierten Methoden gründlicher zu erforschen und konsequent in der Praxis (etwa in Form von Webanwendungen) zu implementieren.
Cosmic rays (CRs) constitute an important component of the interstellar medium (ISM) of galaxies and are thought to play an essential role in governing their evolution. In particular, they are able to impact the dynamics of a galaxy by driving galactic outflows or heating the ISM and thereby affecting the efficiency of star-formation. Hence, in order to understand galaxy formation and evolution, we need to accurately model this non-thermal constituent of the ISM. But except in our local environment within the Milky Way, we do not have the ability to measure CRs directly in other galaxies. However, there are many ways to indirectly observe CRs via the radiation they emit due to their interaction with magnetic and interstellar radiation fields as well as with the ISM.
In this work, I develop a numerical framework to calculate the spectral distribution of CRs in simulations of isolated galaxies where a steady-state between injection and cooling is assumed. Furthermore, I calculate the non-thermal emission processes arising from the modelled CR proton and electron spectra ranging from radio wavelengths up to the very high-energy gamma-ray regime.
I apply this code to a number of high-resolution magneto-hydrodynamical (MHD) simulations of isolated galaxies, where CRs are included. This allows me to study their CR spectra and compare them to observations of the CR proton and electron spectra by the Voyager-1 satellite and the AMS-02 instrument in order to reveal the origin of the measured spectral features.
Furthermore, I provide detailed emission maps, luminosities and spectra of the non-thermal emission from our simulated galaxies that range from dwarfs to Milk-Way analogues to starburst galaxies at different evolutionary stages. I successfully reproduce the observed relations between the radio and gamma-ray luminosities with the far-infrared (FIR) emission of star-forming (SF) galaxies, respectively, where the latter is a good tracer of the star-formation rate. I find that highly SF galaxies are close to the limit where their CR population would lose all of their energy due to the emission of radiation, whereas CRs tend to escape low SF galaxies more quickly. On top of that, I investigate the properties of CR transport that are needed in order to match the observed gamma-ray spectra.
Furthermore, I uncover the underlying processes that enable the FIR-radio correlation (FRC) to be maintained even in starburst galaxies and find that thermal free-free-emission naturally explains the observed radio spectra in SF galaxies like M82 and NGC 253 thus solving the riddle of flat radio spectra that have been proposed to contradict the observed tight FRC.
Lastly, I scrutinise the steady-state modelling of the CR proton component by investigating for the first time the influence of spectrally resolved CR transport in MHD simulations on the hadronic gamma-ray emission of SF galaxies revealing new insights into the observational signatures of CR transport both spectrally and spatially.
Control over spin and electronic structure of MoS₂ monolayer via interactions with substrates
(2023)
The molybdenum disulfide (MoS2) monolayer is a semiconductor with a direct bandgap while it is a robust and affordable material.
It is a candidate for applications in optoelectronics and field-effect transistors.
MoS2 features a strong spin-orbit coupling which makes its spin structure promising for acquiring the Kane-Mele topological concept with corresponding applications in spintronics and valleytronics.
From the optical point of view, the MoS2 monolayer features two valleys in the regions of K and K' points. These valleys are differentiated by opposite spins and a related valley-selective circular dichroism.
In this study we aim to manipulate the MoS2 monolayer spin structure in the vicinity of the K and K' points to explore the possibility of getting control over the optical and electronic properties.
We focus on two different substrates to demonstrate two distinct routes: a gold substrate to introduce a Rashba effect and a graphene/cobalt substrate to introduce a magnetic proximity effect in MoS2.
The Rashba effect is proportional to the out-of-plane projection of the electric field gradient. Such a strong change of the electric field occurs at the surfaces of a high atomic number materials and effectively influence conduction electrons as an in-plane magnetic field. A molybdenum and a sulfur are relatively light atoms, thus, similar to many other 2D materials, intrinsic Rashba effect in MoS2 monolayer is vanishing small. However, proximity of a high atomic number substrate may enhance Rashba effect in a 2D material as it was demonstrated for graphene previously.
Another way to modify the spin structure is to apply an external magnetic field of high magnitude (several Tesla), and cause a Zeeman splitting, the conduction electrons.
However, a similar effect can be reached via magnetic proximity which allows us to reduce external magnetic fields significantly or even to zero. The graphene on cobalt interface is ferromagnetic and stable for MoS2 monolayer synthesis. Cobalt is not the strongest magnet; therefore, stronger magnets may lead to more significant results.
Nowadays most experimental studies on the dichalcogenides (MoS2 included) are performed on encapsulated heterostructures that are produced by mechanical exfoliation.
While mechanical exfoliation (or scotch-tape method) allows to produce a huge variety of structures, the shape and the size of the samples as well as distance between layers in heterostructures are impossible to control reproducibly.
In our study we used molecular beam epitaxy (MBE) methods to synthesise both MoS2/Au(111) and MoS2/graphene/Co systems.
We chose to use MBE, as it is a scalable and reproducible approach, so later industry may adapt it and take over.
We used graphene/cobalt instead of just a cobalt substrate because direct contact of MoS2\ monolayer and a metallic substrate may lead to photoluminescence (PL) quenching in the metallic substrate. Graphene and hexagonal boron nitride monolayer are considered building blocks of a new generation of electronics also commonly used as encapsulating materials for PL studies. Moreover graphene is proved to be a suitable substrate for the MBE growth of transitional metal dichalcogenides (TMDCs).
In chapter 1,
we start with an introduction to TMDCs. Then we focus on MoS2 monolayer state of the art research in the fields of application scenario; synthesis approaches; electronic, spin, and optical properties; and interactions with magnetic fields and magnetic materials.
We briefly touch the basics of magnetism in solids and move on to discuss various magnetic exchange interactions and magnetic proximity effect.
Then we describe MoS2 optical properties in more detail. We start from basic exciton physics and its manifestation in the MoS2 monolayer. We consider optical selection rules in the MoS2 monolayer and such properties as chirality, spin-valley locking, and coexistence of bright and dark excitons.
Chapter 2 contains an overview of the employed surface science methods: angle-integrated, angle-resolved, and spin-resolved photoemission; low energy electron diffraction and scanning tunneling microscopy.
In chapter 3, we describe MoS2 monolayer synthesis details for two substrates: gold monocrystal with (111) surface and graphene on cobalt thin film with Co(111) surface orientation.
The synthesis descriptions are followed by a detailed characterisation of the obtained structures: fingerprints of MoS2 monolayer formation; MoS2 monolayer symmetry and its relation to the substrate below; characterisation of MoS2 monolayer coverage, domain distribution, sizes and shapes, and moire structures.
In chapter~4, we start our discussion with MoS2/Au(111) electronic and spin structure. Combining density functional theory computations (DFT) and spin-resolved photoemission studies, we demonstrate that the MoS2 monolayer band structure features an in-plane Rashba spin splitting. This confirms the possibility of MoS2 monolayer spin structure manipulation via a substrate.
Then we investigate the influence of a magnetic proximity in the MoS2/graphene/Co system on the MoS2 monolayer spin structure.
We focus our investigation on MoS2 high symmetry points: G and K.
First, using spin-resolved measurements, we confirm that electronic states are spin-split at the G point via a magnetic proximity effect. Second, combining spin-resolved measurements and DFT computations for MoS2 monolayer in the K point region, we demonstrate the appearance of a small in-plane spin polarisation in the valence band top and predict a full in-plane spin polarisation for the conduction band bottom.
We move forward discussing how these findings are related to the MoS2 monolayer optical properties, in particular the possibility of dark exciton observation. Additionally, we speculate on the control of the MoS2 valley energy via magnetic proximity from cobalt.
As graphene is spatially buffering the MoS2 monolayer from the Co thin film, we speculate on the role of graphene in the magnetic proximity transfer by replacing graphene with vacuum and other 2D materials in our computations.
We finish our discussion by investigating the K-doped MoS2/graphene/Co system and the influence of this doping on the electronic and spin structure as well as on the magnetic proximity effect.
In summary, using a scalable MBE approach we synthesised
MoS2/Au(111) and MoS2/graphene/Co systems. We found a Rashba effect taking place in MoS2/Au(111) which proves that the MoS2 monolayer in-plane spin structure can be modified. In MoS2/graphene/Co the in-plane magnetic proximity effect indeed takes place which rises the possibility of fine tuning the MoS2 optical properties via manipulation of the the substrate magnetisation.
Unveiling the Local Universe
(2023)
The near-Earth space environment is a highly complex system comprised of several regions and particle populations hazardous to satellite operations. The trapped particles in the radiation belts and ring current can cause significant damage to satellites during space weather events, due to deep dielectric and surface charging. Closer to Earth is another important region, the ionosphere, which delays the propagation of radio signals and can adversely affect navigation and positioning. In response to fluctuations in solar and geomagnetic activity, both the inner-magnetospheric and ionospheric populations can undergo drastic and sudden changes within minutes to hours, which creates a challenge for predicting their behavior. Given the increasing reliance of our society on satellite technology, improving our understanding and modeling of these populations is a matter of paramount importance.
In recent years, numerous spacecraft have been launched to study the dynamics of particle populations in the near-Earth space, transforming it into a data-rich environment. To extract valuable insights from the abundance of available observations, it is crucial to employ advanced modeling techniques, and machine learning methods are among the most powerful approaches available. This dissertation employs long-term satellite observations to analyze the processes that drive particle dynamics, and builds interdisciplinary links between space physics and machine learning by developing new state-of-the-art models of the inner-magnetospheric and ionospheric particle dynamics.
The first aim of this thesis is to investigate the behavior of electrons in Earth's radiation belts and ring current. Using ~18 years of electron flux observations from the Global Positioning System (GPS), we developed the first machine learning model of hundreds-of-keV electron flux at Medium Earth Orbit (MEO) that is driven solely by solar wind and geomagnetic indices and does not require auxiliary flux measurements as inputs. We then proceeded to analyze the directional distributions of electrons, and for the first time, used Fourier sine series to fit electron pitch angle distributions (PADs) in Earth's inner magnetosphere. We performed a superposed epoch analysis of 129 geomagnetic storms during the Van Allen Probes era and demonstrated that electron PADs have a strong energy-dependent response to geomagnetic activity. Additionally, we showed that the solar wind dynamic pressure could be used as a good predictor of the PAD dynamics. Using the observed dependencies, we created the first PAD model with a continuous dependence on L, magnetic local time (MLT) and activity, and developed two techniques to reconstruct near-equatorial electron flux observations from low-PA data using this model.
The second objective of this thesis is to develop a novel model of the topside ionosphere. To achieve this goal, we collected observations from five of the most widely used ionospheric missions and intercalibrated these data sets. This allowed us to use these data jointly for model development, validation, and comparison with other existing empirical models. We demonstrated, for the first time, that ion density observations by Swarm Langmuir Probes exhibit overestimation (up to ~40-50%) at low and mid-latitudes on the night side, and suggested that the influence of light ions could be a potential cause of this overestimation. To develop the topside model, we used 19 years of radio occultation (RO) electron density profiles, which were fitted with a Chapman function with a linear dependence of scale height on altitude. This approximation yields 4 parameters, namely the peak density and height of the F2-layer and the slope and intercept of the linear scale height trend, which were modeled using feedforward neural networks (NNs). The model was extensively validated against both RO and in-situ observations and was found to outperform the International Reference Ionosphere (IRI) model by up to an order of magnitude. Our analysis showed that the most substantial deviations of the IRI model from the data occur at altitudes of 100-200 km above the F2-layer peak. The developed NN-based ionospheric model reproduces the effects of various physical mechanisms observed in the topside ionosphere and provides highly accurate electron density predictions.
This dissertation provides an extensive study of geospace dynamics, and the main results of this work contribute to the improvement of models of plasma populations in the near-Earth space environment.
This dissertation focuses on the understanding of the optical manipulation of microgels dispersed in aqueous solution of azobenzene containing surfactant. The work consists of three parts where each part is a systematic investigation of the (1) photo-isomerization kinetics of the surfactant in complex with the microgel polymer matrix, (2) light driven diffusiosmosis (LDDO) in microgels and (3) photo-responsivity of microgel on complexation with spiropyran.
The first part comprises three publications where the first one [P1] investigates the photo-isomerization kinetics and corresponding isomer composition at a photo-stationary state of the photo-sensitive surfactant conjugated with charged polymers or micro sized polymer networks to understand the structural response of such photo-sensitive complexes. We report that the photo-isomerization of the azobenzene-containing cationic surfactant is slower in a polymer complex compared to being purely dissolved in an aqueous solution. The surfactant aggregates near the polyelectrolyte chains at concentrations much lower than the bulk critical micelle concentration. This, along with the inhibition of the photo-isomerization kinetics due to steric hindrance within the densely packed aggregates, pushes the isomer-ratio to a higher trans-isomer concentration for all irradiation wavelengths.
The second publication [P2] combines experimental results and non-adiabatic dynamic simulations for the same surfactant molecules embedded in the micelles with absorption spectroscopy measurements of micellar solutions to uncover the reasons responsible for the slowdown in photo induced trans → cis azobenzene isomerization at concentrations higher than the critical micelle concentration (CMC). The simulations reveal a decrease of isomerization quantum yields for molecules inside the micelles and observes a reduction of extinction coefficients upon micellization. These findings explain the deceleration of the trans → cis switching in micelles of the azobenzene-containing surfactants.
Finally, the third publication [P3] focusses on the kinetics of adsorption and desorption of the same surfactant within anionic microgels in the dark and under continuous irradiation. Experimental data demonstrate, that microgels can serve as a selective absorber of the trans isomers. The interaction of the isomers with the gel matrix induces a remotely controllable collapse or swelling on appropriate irradiation wavelengths. Measuring the kinetics of the microgel size response and knowing the exact isomer composition under light exposure, we calculate the adsorption rate of the trans-isomers.
The second part comprises two publications. The first publication [P4] reports on the phenomenon of light-driven diffusioosmotic (DO) long-range attractive and repulsive interactions between micro-sized objects, whose range extends several times the size of microparticles and can be adjusted to point towards or away from the particle by varying irradiation parameters such as intensity or wavelength of light. The phenomenon is fueled by the aforementioned photosensitive surfactant. The complex interaction of dynamic exchange of isomers and photo-isomerization rate yields to relative concentrations gradients of the isomers in the vicinity of micro-sized object inducing a local diffusioosmotic (DO) flow thereby making a surface act as a micropump.
The second publication [P5] exclusively aims the visualization and investigation of the DO flows generated from microgels by using small tracer particles. Similar to micro sized objects, the flow is able to push adjacent tracers over distances several times larger than microgel size. Here we report that the direction and the strength of the l-LDDO depends on the intensity, irradiation wavelength and the amount of surfactant adsorbed by the microgel. For example, the flow pattern around a microgel is directed radially outward and can be maintained quasi-indefinitely under exposure at 455 nm when the trans:cis ratio is 2:1, whereas irradiation at 365 nm, generates a radially transient flow pattern, which inverts at lower intensities.
Lastly, the third part consists of one publication [P6] which, unlike the previous works, reports on the study of the kinetics of photo- and thermo-switching of a new surfactant namely, spiropyran, upon exposure with light of different wavelengths and its interaction with p(NIPAM-AA) microgels. The surfactant being an amphiphile, switches between its ring closed spiropyran (SP) form and ring open merocyanine (MC) form which results in a change in the hydrophilic–hydrophobic balance of the surfactant as MC being a zwitterionic form along with the charged head group, generates three charges on the molecule. Therefore, the MC form of the surfactant is more hydrophilic than in the case of the neutral SP state. Here, we investigate the initial shrinkage of the gel particles via charge compensation on first exposure to SP molecules which results from the complex formation of the molecules with the gel matrix, triggering them to become photo responsive. The size and VPTT of the microgels during irradiation is shown to be a combination of heating up of the solution during light absorption by the surfactant (more pronounced in the case of UV irradiation) and the change in the hydrophobicity of the surfactant.
My thesis chiefly aims to shed light on the favourable properties of LHP semiconductors from the point of view of their electronic structure.
Currently, various hypotheses are circulating to explain the exceptionally favourable transport properties of LHPs. Seeking an explanation for the low non-radiative recombination rates and long carrier lifetimes is particularly interesting to the halide perovskites research community.
The first part of this work investigates the two main hypotheses that are believed to play a significant role: the existence of a giant Rashba effect and large polarons. The experimental method of ARPES is mainly applied to verify their credibility.
The first hypothesis presumes that a giant Rashba effect restricts the recombination losses of the charge carriers by making the band gap slightly indirect. The Rashba effect is based on a strong SOC that could appear in LHPs thanks to incorporating the heavy element Pb in their structure. Earlier experimental work had pointed out this effect at the VBM of a hybrid LHP as a viable explanation for the long lifetimes of the charge carriers.
My systematic ARPES studies on hybrid MAPbBr3 and spin-resolved ARPES studies on the inorganic CsPbBr3 disprove the presence of any Rashba effect in the VBM of the reported order of magnitude. Therefore, neither the spin texture nor an indirect band gap character at the VBM in the bulk or at the surface can explain the high efficiency of LHP. In case of existence, this effect is in terms of the Rashba parameter at least a factor of a hundred smaller than previously assumed.
The second hypothesis proposes large polaron formation in the electronic structure of LHPs and attributes it to their high defect tolerance and low non-radiative recombination rate. Because the perovskite structure consists of negative and positive ions, polarons of this kind can be expected due to the Coulomb interaction between carriers and the polar lattice at intermediate electron-phonon coupling strength. Their existence is proposed to screen the carriers and defects to avoid recombination and trapping, thus leading to long carrier lifetimes. ARPES results by one group supported this assumption, reporting a 50% effective mass enhancement over the theoretical effective mass for CsPbBr3 in the orthorhombic structure.
The current thesis examines this hypothesis experimentally by photon-energy-dependent ARPES spectra and theoretically by GW band calculations of CsPbBr3 perovskites. The investigation is based on the fact that a polaron contribution in charge transport can become evident by an increase of the effective mass as measured by ARPES over the calculated one without polaron effects. However, my experiments on crystalline CsPbBr3 did not imply a larger effective mass for which one could postulate large polarons. In fact, the effective masses determined from ARPES agree with that of theoretical predictions.
The second part of my thesis thoroughly investigates the possibility of spontaneously magnetizing LHPs by introducing Mn2+ ions. Mn doping was reported to cause ferromagnetism in one of the most common LHPs, MAPbI3, mediated by super-exchange. The current work investigates the magnetic properties of a wide concentration range of Mn-doped MAPbI3 and triple-cation films by XAS, XMCD, and SQUID measurements. Based on the XAS line shape and a sum-rule analysis of the XMCD spectra, a pure Mn2+ configuration has been confirmed. Negative Curie temperatures are extracted from fitting the magnetization with a Curie-Weiss law. However, a remanent magnetization, which would be an indication of the absence of ferromagnetism down to 2K. As far as the double exchange is concerned, the element-specific XAS excludes a sufficient amount of Mn3+ as a prerequisite for this mechanism. All the findings show no evidence of significant double exchange or ferromagnetism in Mn-doped LHPs. The magnetic behavior is paramagnetic rather than ferromagnetic.
In the dissertation's last chapter, orthorhombic features of CsPbBr3 are revealed by ARPES, including an extra VBM at the Γ-point. The VBM of CsPbBr3 shows a temperature-dependent splitting, which decreases by 190 meV between 38K and 300K and tracks a shift of a saddle point at the cubic M-point. It is possible to reproduce the energy shift using an atomic model with a larger unit cell for room temperature, allowing local inversion symmetry breaking. This indicates the importance of electric dipoles for the inorganic LHPs, which may contribute to their high efficiency by breaking inversion symmetry and a Berry-phase effect.
International migration has been an increasing phenomenon during the past decades and has involved all the regions of the globe. Together with fertility and mortality rates, net migration rates represent the components that fully define the demographic evolution of the population in a country. Therefore, being able to capture the patterns of international migration flows and to produce projections of how they might change in the future is of relevant importance for demographic studies and for designing policies informed on the potential scenarios. Existing forecasting methods do not account explicitly for the main drivers and processes shaping international migration flows: existing migrant communities at the destination country, termed diasporas, would reduce the costs of migration and facilitate the settling for new migrants, ultimately producing a positive feedback; accounting for the heterogeneity in the type of migration flows, e.g. return and transit Ćows, becomes critical in some specific bilateral migration channels; in low- to middle- income countries economic development could relax poverty constraint and result in an increase of emigration rates.
Economic conditions at both origin and destination are identified as major drivers of international migration. At the same time, climate change impacts have already appeared on natural and human-made systems such as the economic productivity. These economic impacts might have already produced a measurable effect on international migration flows. Studies that provide a quantification of the number of migration moves that might have been affected by climate change are usually specific to small regions, do not provide a mechanistic understanding of the pathway leading from climate change to migration and restrict their focus to the effective induced flows, disregarding the impact that climate change might have had in inhibiting other flows.
Global climate change is likely to produce impacts on the economic development of the countries during the next decades too. Understanding how these impacts might alter future global migration patterns is relevant for preparing future societies and understanding whether the response in migration flows would reduce or increase population's exposure to climate change impacts.
This doctoral research aims at investigating these questions and fill the research gaps outlined above. First, I have built a global bilateral international migration model which accounts explicitly for the diaspora feedback, distinguishes between transit and return flows, and accounts for the observed non-linear effects that link emigration rates to income levels in the country of origin. I have used this migration model within a population dynamic model where I account also for fertility and mortality rates, producing hindcasts and future projections of international migration flows, covering more than 170 countries. Results show that the model reproduces past patterns and trends well. Future projections highlight the fact that,depending on the assumptions regarding future evolution of income levels and between-country inequality, migration at the end of the century might approach net zero or be still high in many countries. The model, parsimonious in the explanatory variables that includes, represents a versatile tool for assessing the impacts of different socioeconomic scenarios on international migration.
I consider then a counterfactual past without climate change impacts on the economic productivity. By prescribing these counterfactual economic conditions to the migration model I produce counterfactual migration flows for the past 30 years. I compare the counterfactual migration flows to factual ones, where historical economic conditions are used to produce migration flows. This provides an estimation of the recent international migration flows attributed to climate change impacts. Results show that a counterfactual world without climate change would have seen less migration globally. This effect becomes larger if I consider separately the increase and decrease in migration moves: a Ągure of net change in the migration flows is not representative of the effective magnitude of the climate change impact on migration. Indeed, in my results climate change produces a divergent effect on richer and poorer countries: by slowing down the economic development, climate change might have reduced international mobility from and to countries of the Global South, and increased it from and to richer countries in the Global North.
I apply the same methodology to a scenario of future 3℃ global warming above pre-industrial conditions. I Ąnd that climate change impacts, acting by reorganizing the relative economic attractiveness of destination countries or by affecting the economic growth in the origin, might produce a substantial effect in international migration flows, inhibiting some moves and inducing others.
Overall my results suggest that climate change might have had and might have in the future a significant effect on global patterns of international migration. It also emerges clearly that, for a comprehensive understanding of the effects of climate change on international migration, we need to go beyond net effects and consider separately induced and inhibited flows.
Es wird ein Überblick über verschiedene spektroskopische Techniken, mit denen dünne organische Schichten, wie sie in der Fotovoltaik, bei Leuchtdioden oder organischen Halbleitern Anwendung finden, gegeben. Mit einfachen Zusatzgeräten lassen sich Schichtdicke, Schichtaufbau und Zusammensetzung untersuchen. Die Schichtdicke kann monomolekular sein. Unter bestimmten Voraussetzungen sind einzelne Moleküle in einer Schicht charakterisierbar.