The Use of Synchrotron Radiation to study Overgrowth Phenomena in InAs/GaAs Nanostructures

This work focuses on the investigation of overgrowth phenomena in InAs/GaAs nanostructures using synchrotron radiation. Surface-sensitive grazing incidence small angle x-ray scattering (GISAXS) and grazing incidence diffraction (GID) are applied to study shape, strain, and interdiffusion in self-organised grown nanostructures. The technique of anomalous x-ray diffraction at the weak (200) superstructure reflection enhances the chemical sensitivity of the measurements. For the investigation of (partially) buried nanostructures finite-element simulations (FEM) have been performed. The following sample systems were investigated: ((1)) Free-standing and buried InGaAs quantum dots: Free-standing In(x)Ga(1-x)As islands grown on GaAs (001) by molecular beam epitaxy (MBE) with a nominal concentration of x=0.5 have been investigated. Contrast variation close to the K edge of As by anomalous GID at the (200) superstructure reflection is used for a direct determination of the InAs concentration as a function of the lateral strain in the quantum dots (QDs). The evaluation of intensity mappings recorded in reciprocal space close to the (200) reflection together with atomic force micrographs (AFM) allows to attribute the strain and the InAs concentration to a certain height in the quantum dots. Thereby, a three-dimensional model of the strain and interdiffusion profile of the InGaAs QDs can be reconstructed. A discussion of measurements taken on buried InGaAs QDs and free-standing islands grown on the strain modulated surface of a buried QD layer shows the limits of this technique. ((2)) InGaAs quantum rings: The formation of nanoscopic InGaAs ring structures on a GaAs (001) substrate takes place when InAs quantum dots, grown by Stranski-Krastanov self-organisation, are covered by a thin layer of GaAs. The shape transformation into rings is governed by strain, diffusion and surface tension, quantities which are of importance to understand magneto-optical and electronic applications of the rings. GISAXS and GID is applied to characterise morphology and structural properties such as strain and chemical composition of the rings in three dimensions. From GISAXS the shape is found to be of circular symmetry with an outer radius of 26nm, a height of 1.5nm, and a hole in the middle, in good agreement with AFM measurements. The most surprising results are obtained from intensity mappings in reciprocal space close to the (220) and (2-20) reflection done in surface sensitive GID geometry. From a comparison of the intensity maps with FEM model calculations the InGaAs interdiffusion profile in the ring is determined. It strongly depends on the crystallographic orientation. In the ring a maximum InAs concentration of more than 80% along [1-10] is found while along [110] it is below 20%. This is explained by the preferred diffusion of In along [1-10]. ((3)) Quantum wires formed by cleaved edge overgrowth: Quantum wires (QWRs) fabricated by the cleaved edge overgrowth (CEO) technique use tensile strain to confine the charge carriers to one dimension. The cleaved edge of a pseudomorphically strained In0.1Al0.9As/Al0.33Ga0.67As superlattice (SL) is overgrown by a GaAs layer of 10nm thickness. The lateral charge carrier localisation in the overgrown layer is induced by the periodic strain modulation of the SL. Using GID this strain state of the system is determined. The strain modulation due to the overgrown superlattice occurs only within 3micron of the total wafer thickness of 150micron. The GID technique allows for a clear separation of the strain modulation in the cap layer and the superlattice underneath. It can be proved that the strain modulation in the GaAs cap layer is not of compositional origin but purely elastic with an average lattice parameter change of (0.8+-0.1)% with respect to relaxed GaAs. The strain profile obtained is confirmed by FEM model calculations.Die vorliegende Arbeit befasst sich mit methodischen Entwicklungen zur Untersuchung von Strukturänderungen beim Überwachsen von InAs/GaAs Nanostrukturen mittels Synchrotronstrahlung. Die oberflächenempfindlichen Methoden der Röntgen-Kleinwinkelstreuung (GISAXS) und der Röntgenbeugung unter streifendem Einfall (GID) ermöglichen es, Form, Verspannung und Interdiffusion in selbst-organisierten Nanostrukturen zu studieren. Die Methode der anomalen Röntgenbeugung am schwachen (200) Überstrukturreflex erhöht die chemische Empfindlichkeit der Messungen. Zur Untersuchung von (teilweise) vergrabenen Nanostrukturen wurden Finite-Elemente-Simulationsrechnungen (FEM) durchgeführt. Im Einzelnen wurden folgende Probensysteme untersucht: ((1)) Freistehende und vergrabene InGaAs Quantenpunkte: Anomale Röntgenbeugung am (200) Überstrukturreflex wurde zur Charakterisierung von freistehenden In0.5Ga0.5As Inseln, hergestellt mittels Molekularstrahlepitaxie (MBE), verwendet. Durch die Kontrastvariationsmessungen nahe der K Absorptionskante von As kann die InAs Konzentration direkt als Funktion des lateralen Gitterparameters der Quantenpunkte bestimmt werden. Die Auswertung von 2D-Kartierungen des reziproken Raumes nahe des (200) Reflexes zusammen mit Rasterkraftmikroskopie ermöglichen es, den lateralen Gitterparameter sowie die InAs Konzentration einer bestimmten Höhe im Quantenpunkt zuzuordnen. Daraus lässt sich ein 3D-Modell des Verspannungs- und Interdiffusionsprofiles der InGaAs Inseln rekonstruieren. Bei der Untersuchung von vergrabenen InGaAs Quantenpunkten und von freistehenden Inseln, die auf der verspannten Oberfläche einer vergrabenen Schicht von Quantenpunkten gewachsen wurden, stößt diese Methode jedoch an ihre Grenzen. ((2)) InGaAs Quantenringe: Die Bildung von nanoskopischen InGaAs Ringen auf einer GaAs (001) Oberfläche wird beobachtet, wenn InAs Inseln, hergestellt mittels Stranski-Krastanov-Selbstorganisation, mit einer dünnen Schicht GaAs überwachsen werden. Die Oberflächenmorphologie und strukturelle Eigenschaften, wie Verspannung und chemische Zusammensetzung, dieser Strukturen wurde mittels GISAXS und GID analysiert. Gemäss der GISAXS-Auswertung, die gut mit den AFM Untersuchungen übereinstimmt, besitzen die Ringe eine kreisförmige Symmetrie mit einem äußeren Radius von 26nm und einer Höhe von 1.5nm. Das überraschendste Ergebnis liefert die Analyse von Kartierungen des reziproken Raums in der Nähe des (220) and (2-20) Reflexes in GID-Geometrie. Die chemische Zusammensetzung des Rings, die durch den Vergleich der Messungen mit Modellrechnungen basierend auf FEM-Simulationen bestimmt wurde, hängt sehr stark von der kristallographischen Orientierung ab. In [1-10] Richtung wird eine maximale InAs Konzentration von über 80% beobachtet, während in [110] Richtung diese unter 20% liegt. Die erhöhte Diffusion von In in [1-10] Richtung erklärt diese Beobachtung. ((3)) Quantendräte hergestellt auf überwachsenen Spaltflächen: Die (110) Spaltfläche eines pseudomorph verspannten In0.1Al0.9As/Al0.33Ga0.67As Übergitters wurde mit einer 10nm dicken Schicht GaAs überwachsen. In diesem Fall wird die Beweglichkeit der Ladungsträger in der überwachsenen Schicht lateral durch die periodische, tensile Verspannung des Übergitters auf eine Dimension beschränkt (Quantendraht). Mittels GID lässt sich die Verspannungsmodulation, die nur innerhalb von 3micron der Gesamtdicke des Wafers von 150micron auftritt, quantisieren [im Mittel (0.8+-0.1)%]. Hierbei erlaubt GID eine klare Trennung der Verspannungsmodulation in der überwachsenen Schicht vom darunterliegenden Übergitter. Es kann gezeigt werden, dass die Verspannungsmodulation in der überwachsenen GaAs Schicht rein elastischer Natur ist und keine Interdiffusion stattfindet. Das Verspannungsprofil lässt sich durch FEM-Modellrechnungen bestätigen

A phase separation in diluted Laponite suspensions: evidence of empty liquid and equilibrium gel states

The relevance of anisotropic interactions in colloidal systems has recently emerged in the context of rational design of novel soft materials. Theoretical studies have predicted the possibility of a gas-liquid phase separation confined at low densities and the formation of empty liquids and equilibrium gels in low-valence systems. Here we provide experimental evidence of this scenario in Laponite, a complex colloidal clay with discotic shape and anisotropic interactions. We also report simulations of a patchy model for Laponite platelets, able to reproduce the observed experimental phase diagram and structural properties, confirming the crucial role of the reduced valence

Competing interactions in arrested states of colloidal clays

Using experiments, theory and simulations, we show that the arrested state observed in a colloidal clay at intermediate concentrations is stabilized by the screened Coulomb repulsion (Wigner glass). Dilution experiments allow us to distinguish this high-concentration disconnected state, which melts upon addition of water, from a low-concentration gel state, which does not melt. Theoretical modelling and simulations reproduce the measured Small Angle X-Ray Scattering static structure factors and confirm the long-range electrostatic nature of the arrested structure. These findings are attributed to the different timescales controlling the competing attractive and repulsive interactions.Comment: Accepted for publication in Physical Review Letter

Two-Photon Spectroscopy Between States of Opposite Parities

Magnetic- and electric-dipole two-photon absorption (MED-TPA), recently introduced as a new spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. A new approximation, referred to as {\it weak quasi-closure approximation}, is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric-dipole two-photon absorption (ED-TPA).Comment: 7 pages, Revtex File, to be published in Physical Review

Rheo-acoustic gels: Tuning mechanical and flow properties of colloidal gels with ultrasonic vibrations

Colloidal gels, where nanoscale particles aggregate into an elastic yet fragile network, are at the heart of materials that combine specific optical, electrical and mechanical properties. Tailoring the viscoelastic features of colloidal gels in real-time thanks to an external stimulus currently appears as a major challenge in the design of "smart" soft materials. Here we introduce "rheo-acoustic" gels, a class of materials that are sensitive to ultrasonic vibrations. By using a combination of rheological and structural characterization, we evidence and quantify a strong softening in three widely different colloidal gels submitted to ultrasonic vibrations (with submicron amplitude and frequency 20-500 kHz). This softening is attributed to micron-sized cracks within the gel network that may or may not fully heal once vibrations are turned off depending on the acoustic intensity. Ultrasonic vibrations are further shown to dramatically decrease the gel yield stress and accelerate shear-induced fluidization. Ultrasound-assisted fluidization dynamics appear to be governed by an effective temperature that depends on the acoustic intensity. Our work opens the way to a full control of elastic and flow properties by ultrasonic vibrations as well as to future theoretical and numerical modeling of such rheo-acoustic gels.Comment: 21 pages, 14 figure

Concentration dependent pathways in spontaneous self-assembly of unilamellar vesicles

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We report on the structural dynamics underlying the formation of unilamellar vesicles upon mixing dilute solutions of anionic and zwitterionic surfactant solutions. The spontaneous self-assembly was initiated by rapid mixing of the surfactant solutions using a stopped-flow device and the transient intermediate structures were probed by time-resolved small-angle X-ray scattering. The initial surfactant solutions comprised of anionic lithium perfluorooctanoate and zwitterionic tetradecyldimethylamine oxide, where the mixtures form unilamellar vesicles over a wide range of concentrations and mixing ratios. We found that disk-like transient intermediate structures are formed at higher concentrations while more elongated forms such as cylinder-like and torus-like micelles are involved at lower concentrations. These differences are attributed to monomer addition mechanism dominating the self-assembly process when the initial concentration is well below the critical micellar concentration of the anionic surfactant, while at higher concentrations the process is governed by fusion of disk-like mixed micelles. This means that the pathway of vesicle formation is determined by the proximity to the critical micellar concentration of the more soluble component

Drying dip-coated colloidal films

We present the results from a small-angle X-ray scattering (SAXS) study of lateral drying in thin films. The films, initially 10 μm thick, are cast by dip-coating a mica sheet in an aqueous silica dispersion (particle radius 8 nm, volume fraction ϕs = 0.14). During evaporation, a drying front sweeps across the film. An X-ray beam is focused on a selected spot of the film, and SAXS patterns are recorded at regular time intervals. As the film evaporates, SAXS spectra measure the ordering of particles, their volume fraction, the film thickness, and the water content, and a video camera images the solid regions of the film, recognized through their scattering of light. We find that the colloidal dispersion is first concentrated to ϕs = 0.3, where the silica particles begin to jam under the effect of their repulsive interactions. Then the particles aggregate until they form a cohesive wet solid at ϕs = 0.68 ± 0.02. Further evaporation from the wet solid leads to evacuation of water from pores of the film but leaves a residual water fraction ϕw = 0.16. The whole drying process is completed within 3 min. An important finding is that, in any spot (away from boundaries), the number of particles is conserved throughout this drying process, leading to the formation of a homogeneous deposit. This implies that no flow of particles occurs in our films during drying, a behavior distinct to that encountered in the iconic coffee-stain drying. It is argued that this type of evolution is associated with the formation of a transition region that propagates ahead of the drying front. In this region the gradient of osmotic pressure balances the drag force exerted on the particles by capillary flow toward the liquid–solid front

Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry

Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models.Comment: 16 pages, Tex fil

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB2, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up