Understanding the role of van der Waals forces in solids from first principles

The study of cohesion in solids is among the most fundamental research subjects in condensed-matter physics. The search for a deeper understanding of cohesion has lead to a steady progress in electronic-structure methods, enabling us to better understand structural, electronic, and mechanical properties of solids. The quantitative description of cohesion in solids requires solving the many-body Schr¨odinger equation and such exact treatment remains an unsolved problem. In this context, the correct treatment of cohesive properties (lattice constants, cohesive energies, and bulk moduli) requires an accurate description of the long-range electron correlation. In particular, van der Waals (vdW) interactions, being ubiquitous and arising from correlations between electrons, have been proposed to affect the cohesion in solids since a long time. This leads to two unsolved questions: (1) How to properly and effectively model vdW interactions in solids?, and (2) What is the quantitative role of vdW interactions in the cohesive properties of different types of solids? In this thesis, we address both questions by developing novel methods for vdW interactions in solids and assessing the role of the long-range vdW energy for a wide variety of non-metallic solids in the context of density-functional theory (DFT). Among first-principles approaches to the many-body Schr¨odinger equation, DFT has become the method of choice for obtaining ground-state properties of molecules and materials. A great advantage of DFT is that it is in principle an exact theory and the complexity of the full many-body problem is replaced by the electronic exchange-correlation (XC) functional. However, this functional is only known approximately and all widely employed (semi-)local and hybrid functionals suffer from the so-called self-interaction errors and lack the longrange vdW energy tail, often yielding noticeable deviations from experimental data. This issue will be illustrated in my thesis by assembling a large database of 64 solids and employing the LDA, PBE, and M06-L functionals to study their cohesive properties. This assessment shows that none of these functionals is sufficient to describe the cohesion for a broad range of solids, leading us to propose that the missing long-range vdW interaction accounts for part of the deviations found in approximate XC functionals. To assess the role of vdW interactions in solids, we develop the so-called DFT+vdWTS+SCS method that accurately models the electrodynamic response effects in the polarizability and vdW coefficients. This method is essentially free of adjustable parameters; the only necessary ingredients are the electron density and reference polarizabilities for free (isolated) atoms in the gas phase. Together with a benchmark study based upon experimental and time-dependent DFT optical spectra, I show that the concept of atoms-in-solids can be successfully utilized to define polarizabilities for finite-gap materials. Remarkably, my analysis demonstrates the validity of the Clausius-Mossotti relation for linking the macroscopic dielectric function to the microscopic response in covalentlybonded semiconductors – a matter of long debate in the literature. Upon the inclusion of long-range vdW interactions on top of the nonempirical PBE functional, a factor-of-two improvement is found in the cohesive properties with respect to the standard PBE values. I conclude that the vdW energy plays a crucial role in the cohesion of semiconductors and ionic solids. The proposed DFT+vdWTS+SCS approach represents a promising way towards extending the applicability of standard density functionals, and thus will be useful for a wide variety of applications in molecules and materialsDie Bindungskräfte in Festkörpern sind von grundlegendem Interesse in der Physik kondensierter Materie. Eine quantitative Beschreibung von Kohäsion in Festkörpern bedarf der Lösung der Vielteilchen-Schrödinger-Gleichung, die allerdings meist nicht exakt lösbar ist. Für die Kohäsions-Eigenschaften ist eine genaue Beschreibung der langreichweitigen Korrelation der Elektronen maßgeblich. Insbesondere können van der Waals (vdW) Wechselwirkungen, die durch Korrelationen zwischen Elektronen auftreten, die Kohäsion in Festkörpern beeinflussen. Es stellen sich zwei Fragen: (1) Wie können vdW-Wechselwirkungen in Festkörpern präzise und effektiv modelliert werden?, und (2) Welche quantitative Rolle spielen sie? In dieser Arbeit werden beide Fragen behandelt, indem neue Methoden zur Beschreibung von vdW-Wechselwirkungen in Festkörpern entwickelt werden und die Rolle der langreichweitigen vdW-Energie für eine Vielzahl von nicht-metallischen Festkörpern im Kontext der Dichtefunktionaltheorie (DFT) untersucht wird. Unter den ab initio Ansätzen zur Lösung der Schrödinger-Gleichung hat sich die DFT zur Methode der Wahl entwickelt, um die Grundzustands-Eigenschaften von Molekülen und Materialien zu bestimmen. Ein bedeutender Vorteil der DFT liegt darin, dass es sich im Prinzip um eine exakte Theorie handelt, wobei die Komplexität des vollen Vielteilchen-Problems durch das elektronische Austausch-Korrelations- Funktional ersetzt wird. Allerdings ist dieses Funktional nur näherungsweise bekannt und alle (semi-)lokalen und Hybrid-Funktionale, die breite Anwendung finden, sind mit sogenannten Selbstwechselwirkungsfehlern behaftet und berücksichtigen außerdem nicht die langreichweitigen vdW-Energiebeiträge, was oft zu merklichen Abweichungen im Vergleich zu experimentellen Messwerten führt. Diese Problematik wird in meiner Arbeit erläutert, indem die Bindungseigenschaften von 64 Feststoffen unter Verwendung von LDA, PBE und M06-L Funktionalen untersucht werden. Es wird gezeigt, dass keines der Funktionale ausreichend ist, um Kohäsion in Festkörpern für einen weiten Bereich von Materialien zu beschreiben. Wir folgern, dass dies zum Teil auf das Fehlen der vdW-Wechselwirkung zurückzuführen ist. Zur Untersuchung der vdW-Wechselwirkungen in Festkörpern entwickeln wir die sogenannte DFT+vdWTS+SCS Methode für eine genaue Modellierung der elektrodynamischen response-Effekte in der Polarisierbarkeit und den vdW-Koeffizienten. Diese Methode ist im Wesentlichen frei von anzupassenden Parametern; einzig die Elektronendichte und Referenz-Polarisierbarkeiten für freie Atome in der Gasphase werden benötigt. Zusammen mit einer Benchmark-Studie, die auf experimentellen und mit zeitabhängiger DFT bestimmten, optischen Spektren basiert, zeigen wir, dass das Konzept atoms-in-solids (Atome im Festkörper) erfolgreich verwendet werden kann, um Polarisierbarkeiten für Materialien mit endlicher Bandlücke zu definieren. Besonders bemerkenswert ist, dass meine Analyse die Gültigkeit der Clausius-Mossotti Relation für die Verknüpfung der makroskopischen dielektrischen Funktion mit der mikroskopischen Antwort in kovalent gebundenen Halbleitern zeigt – dies war Gegenstand langer Diskussionen in der Literatur. Durch die Einbeziehung von langreichweitigen vdW-Wechselwirkungen wird eine Verbesserung um einen Faktor zwei in der Beschreibung der Bindungs-Eigenschaften mit Bezug auf die entsprechenden Standard-PBE-Ergebnisse erreicht. Wir schließen daraus, dass die vdW-Energie eine entscheidende Rolle für die Kohäsion in Halbleitern und ionischen Festkörpern spielt. Die vorgestellte DFT+vdWTS+SCS Methode zeigt einen vielversprechenden Weg auf, um die Anwendbarkeit von Standard-Dichtefunktionalen zu erweitern, und wird folglich für eine Vielzahl von Anwendungen in Molekülen und Materialien nutzbar sein

A non-destructive analytic tool for nanostructured materials : Raman and photoluminescence spectroscopy

Modern materials science requires efficient processing and characterization techniques for low dimensional systems. Raman spectroscopy is an important non-destructive tool, which provides enormous information on these materials. This understanding is not only interesting in its own right from a physicist's point of view, but can also be of considerable importance in optoelectronics and device applications of these materials in nanotechnology. The commercial Raman spectrometers are quite expensive. In this article, we have presented a relatively less expensive set-up with home-built collection optics attachment. The details of the instrumentation have been described. Studies on four classes of nanostructures - Ge nanoparticles, porous silicon (nanowire), carbon nanotubes and 2D InGaAs quantum layers, demonstrate that this unit can be of use in teaching and research on nanomaterials.Comment: 32 pages, 13 figure

Epitaxial metal nanocrystal-semiconductor quantum dot hybrid structures for plasmonics

Many mathematical objects are closely related to each other. While studying certain aspects of a mathematical object, one tries to find a way to "view" the object in a way that is most suitable for a specific problem. Or, in other words, one tries to find the best way to model the problem. Many related fields of mathematics have evolved from one another this way. In practice, it is very useful to be able to transform a problem into other terminology: it gives a lot more available knowledge and that can be helpful to solve a problem. This thesis deals with various closely related fields in discrete mathematics, starting from linear error-correcting codes and their weight enumerator. We can generalize the weight enumerator in two ways, to the extended and generalized weight enumerators. The set of generalized weight enumerators is equivalent to the extended weight enumerator. Summarizing and extending known theory, we define the two-variable zeta polynomial of a code and its generalized zeta polynomial. These polynomials are equivalent to the extended and generalized weight enumerator of a code. We can determine the extended and generalized weight enumerator using projective systems. This calculation is explicitly done for codes coming from finite projective and affine spaces: these are the simplex code and the first order Reed-Muller code. As a result we do not only get the weight enumerator of these codes, but it also gives us information on their geometric structure. This is useful information in determining the dimension of geometric designs. To every linear code we can associate a matroid that is representable over a finite field. A famous and well-studied polynomial associated tomatroids is the Tutte polynomial, or rank generating function. It is equivalent to the extended weight enumerator. This leads to a short proof of the MacWilliams relations for the extended weight enumerator. For every matroid, its flats form a geometric lattice. On the other hand, every geometric lattice induces a simple matroid. The Tutte polynomial of a matroid determines the coboundary polynomial of the associated geometric lattice. In the case of simple matroids, this becomes a two-way equivalence. Another polynomial associated to a geometric lattice (or, more general, to a poset) is the Möbius polynomial. It is not determined by the coboundary polynomial, neither the other way around. However, we can give conditions under which the Möbius polynomial of a simple matroid together with the Möbius polynomial of its dual matroid defines the coboundary polynomial. The proof of these relations involves the two-variable zeta polynomial, that can be generalized from codes to matroids. Both matroids and geometric lattices can be truncated to get an object of lower rank. The truncated matroid of a representable matroid is again representable. Truncation formulas exist for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the known truncation formula of the Tutte polynomial of a matroid. Several examples and counterexamples are given for all the theory. To conclude, we give an overview of all polynomial relations

Cluster-surface and cluster-cluster interactions: Ab initio calculations and modeling of van der Waals forces

We present fully ab-initio calculations of van der Waals coefficients for two different situations: i) the interaction between hydrogenated silicon clusters; and ii) the interactions between these nanostructures and a non metallic surface (a silicon or a silicon carbide surface). The methods used are very efficient, and allow the calculation of systems containing hundreds of atoms. The results obtained are further analyzed and understood with the help of simple models. These models can be of interest for molecular dynamics simulations of silicon nanostructures on surfaces, where they can give a very fast yet sufficiently accurate determination of the van der Waals interaction at large separations.Comment: Phys. Rev.

Improving Performance of InGaN/GaN Light-Emitting Diodes and GaAs Solar Cells Using Luminescent Gold Nanoclusters

We studied the optoelectronic properties of the InGaN/GaN multiple-quantum-well light emitting diodes (LEDs) and single-junction GaAs solar cells by introducing the luminescent Au nanoclusters. The electroluminescence intensity for InGaN/GaN LEDs increases after incorporation of the luminescent Au nanoclusters. An increase of 15.4% in energy conversion efficiency is obtained for the GaAs solar cells in which the luminescent Au nanoclusters have been incorporated. We suggest that the increased light coupling due to radiative scattering from nanoclusters is responsible for improving the performance of the LEDs and solar cells

Infrared nanospectroscopy at cryogenic temperatures and on semiconductor nanowires

Die vorliegende Dissertation befasst sich mit der streuenden, infraroten Rasternahfeldmikroskopie (engl. s-SNIM) in Kombination mit dem Freie-Elektronen Laser (FEL) am Helmholtz-Zentrum Dresden-Rossendorf. Der FEL ist eine intensive,schmalbandige Strahlungsquelle, welche vom mittleren bis ferninfraroten Spektralbereich durchstimmbar ist (5 meV bis 250 meV). Die s-SNIM Technik ermöglicht Infrarotmikroskopie- und spektroskopie mit einer wellenlängenunabhängigen räumlichen Auflösung von etwa 10nm. Der erste Ergebnisteil demonstriert die Erweiterung eines FEL-basierten s- SNIM hinsichtlich der Möglichkeit, bei tiefen Temperaturen bis 5K messen zu können. So verdeutlichen wir die Funktionalität unseres Tieftemperatur-s-SNIM anhand verschiedener Proben wie Au, strukturiertem Si/SiO2 sowie Gallium-Vanadium-Sulfid (GaV4S8). Das letztgenannte Material erregt momentan ein hohes wissenschaftliches Interesse, da es sogenannte Skyrmionen des Néel-Typs – periodische angeordnete Spinwirbel – enthält. GaV4S8 hat einen strukturellen Phasenübergang bei T = 42K und beinhaltet bei niedrigeren Temperaturen ferroelektrische Domänen, die wir unter anderem mittels s-SNIM abbilden können. Hierbei beobachten wir einen beträchtlichen Einfluss der Infrarotstrahlung auf die Domänenstruktur. Dies nutzen wir, um den lokalen Hitzeeintrag der Infrarotstrahlung lokal unter der s-SNIM Sonde zu quantifizieren. Der zweite Teil der Ergebnisse beinhaltet s-SNIM Messungen an hochwertigen Halbleiter-Nanodrähten (ND), welche mittels Molekularstrahlepitaxie gewachsen wurden. Derartige ND sind, unter anderem aufgrund ihrer hohen Ladungsträgermobilität, vielversprechende Komponenten für schnelle optoelektronische Nanoelemente der Zukunft. So untersuchen wir beispielsweise hochdotierte GaAs/InGaAs Kern/Schale ND, bei denen wir – unter Verwendung eines Dauerstrich CO2 Lasers – eine spektral scharfe plasmonische Resonanz bei etwa 125 meV beobachten. Betrachten wir selbige ND mittels intensiver, gepulster FEL-Strahlung, ist eine signifikante Rotverschiebung zu Energien kleiner als 100 meV sowie eine Verbreiterung der Resonanz festzustellen. Dieses nichtlineare Verhalten wird zurückgeführt auf eine starke Erhitzung des Elektronengases unter dem Einfluss der intensiven FEL-Pulse. Unsere Erkenntnisse zeigen dahingehend die Möglichkeiten auf, Nichtgleichgewichtszustände im s-SNIM gezielt zu induzieren und zu beinflussen. Abgesehen von den Messungen der Nichtlinearität ist die Herstellung und Charakterisierung von ND-Querschnitten – sowohl der genannten homogen dotierten, als auch modulationsdotierten– Gegenstand des zweiten Ergebniskapitels.:Abstract iii Zusammenfassung v 1 Introduction 1 2 Fundamentals 3 2.1 Scanning probe techniques 3 2.1.1 Atomic force microscopy 4 2.1.2 Piezoresponse force microscopy 8 2.1.3 Kelvin-probe force microscopy 9 2.2 Infrared nanospectroscopy 10 2.2.1 The diffraction limit 10 2.2.2 Scattering scanning near-field infrared microscopy 11 2.2.3 Point-dipole model 12 2.2.4 Signal detection 17 2.2.5 Higher harmonic demodulation and contrast 19 2.2.6 Advantages and limitations of s-SNIM 22 2.3 Infrared light sources 24 2.3.1 Carbon dioxide laser 24 2.3.2 Free-electron laser 26 3 Infrared nanospectroscopy at cryogenic temperatures 31 3.1 Introduction 31 3.2 Samples 33 3.3 Experimental details 36 3.3.1 Low-temperature atomic force microscopy 36 3.3.2 Optical setup 38 3.3.3 Low-temperature scattering scanning near-field infrared microscopy 39 3.3.4 Measurement modes and data acquisition 42 3.4 Results and discussion 44 3.4.1 Performance and IR heating calibration 44 3.4.2 s-SNIM study of gallium vanadium sulfide 49 3.5 Conclusion 51 4 Infrared nanospectroscopy on semiconductor nanowires 53 4.1 Introduction 53 4.2 Samples 55 4.2.1 GaAs/InGaAs core/shell nanowires 55 4.2.2 Modulation doped nanowires 56 4.2.3 Nanowire cross sections 57 4.2.4 Infrared response of doped nanowires 59 4.3 Experimental details 61 4.3.1 Room-temperature atomic force microscopy 61 4.3.2 Room-temperature scattering scanning near-field infrared microscopy 63 4.3.3 Properties of the free-electron laser pulses 65 4.4 Results and discussion 68 4.4.1 GaAs/InGaAs core/shell nanowires 68 4.4.2 Nanowire cross sections 75 4.5 Conclusion 79 5 Summary and outlook 81 A Citation metrics 85 B Additional nanospectroscopic studies 87 B.1 Silicon carbide nanoparticle probes 87 B.2 Individual impurities in Si 91 B.3 Surface phonon polaritons in moybdenum disulfide 96 C Derivation of the nonparabolic effective mass and density of states 99 C.1 Effective mass 99 C.2 Density of states 100 D Comparison of self-homodyne and pseudo-heterodyne detection 103 Bibliography 105 List of Abbreviations 125 List of Symbols 132 List of Publications 133 Acknowledgments 137 Versicherung 139This PhD thesis concentrates on scattering scanning near-field infrared microscopy (s-SNIM) which utilizes the radiation from the free-electron laser (FEL) at the Helmholtz-Zentrum Dresden-Rossendorf. The FEL is an intense, narrow-band radiation source, tunable from the mid- to far-infrared spectral range (5 meV to 250 meV). The s-SNIM technique enables infrared microscopy and spectroscopy with a wavelength-independent spatial resolution of about 10nm. The first part demonstrates the extension of s-SNIM at the FEL towards cryogenic temperatures as low as 5K. To this end, we show the functionality of our low-temperature s-SNIM apparatus on different samples such as Au, structured Si/SiO2, as well as the multiferroic material gallium vanadium sulfide (GaV4S8). The latter material recently attracted a lot of interest since it hosts a Néel-type skyrmion lattice – a periodic array of spin vortices. Below T = 42K, GaV4S8 undergoes a structural phase transition and then forms ferroelectric domains, which we can map out by low-tempererature s-SNIM. Notably, we found a strong impact on the ferroelectric domains upon infrared irradiation, which we further utilize to calibrate the local heat contribution of the focused infrared beam beneath the s-SNIM probe. The second part of this thesis contains comprehensive s-SNIM investigations of high-quality semiconductor nanowires (NWs) grown by molecular beam epitaxy. Such NWs are promising building blocks for fast opto-)electronic nanodevices, amongst others due to their high carrier mobility. We have examined highly doped GaAs/InGaAs core/shell NWs and observed a strong and spectrally sharp plasmonic resonance at about 125 meV, using a continuous wave CO2 laser for probing. If we probe the same NWs utilizing the intense, pulsed FEL radiation, we observe a pronounced redshift to energies less than 100 meV and a broading of the plasmonic response. This nonlinear response is most likely induced by heating of the electron gas upon irradiation by the strong FEL pulses. Our observations open up the possibility to actively induce and observe non-equilibrium states in s-SNIM directly by the mid-infrared beam. Beside the nonlinear effect, we prepared and measured cross sections of both homogeneously-doped and modulation-doped core/shell NWs.:Abstract iii Zusammenfassung v 1 Introduction 1 2 Fundamentals 3 2.1 Scanning probe techniques 3 2.1.1 Atomic force microscopy 4 2.1.2 Piezoresponse force microscopy 8 2.1.3 Kelvin-probe force microscopy 9 2.2 Infrared nanospectroscopy 10 2.2.1 The diffraction limit 10 2.2.2 Scattering scanning near-field infrared microscopy 11 2.2.3 Point-dipole model 12 2.2.4 Signal detection 17 2.2.5 Higher harmonic demodulation and contrast 19 2.2.6 Advantages and limitations of s-SNIM 22 2.3 Infrared light sources 24 2.3.1 Carbon dioxide laser 24 2.3.2 Free-electron laser 26 3 Infrared nanospectroscopy at cryogenic temperatures 31 3.1 Introduction 31 3.2 Samples 33 3.3 Experimental details 36 3.3.1 Low-temperature atomic force microscopy 36 3.3.2 Optical setup 38 3.3.3 Low-temperature scattering scanning near-field infrared microscopy 39 3.3.4 Measurement modes and data acquisition 42 3.4 Results and discussion 44 3.4.1 Performance and IR heating calibration 44 3.4.2 s-SNIM study of gallium vanadium sulfide 49 3.5 Conclusion 51 4 Infrared nanospectroscopy on semiconductor nanowires 53 4.1 Introduction 53 4.2 Samples 55 4.2.1 GaAs/InGaAs core/shell nanowires 55 4.2.2 Modulation doped nanowires 56 4.2.3 Nanowire cross sections 57 4.2.4 Infrared response of doped nanowires 59 4.3 Experimental details 61 4.3.1 Room-temperature atomic force microscopy 61 4.3.2 Room-temperature scattering scanning near-field infrared microscopy 63 4.3.3 Properties of the free-electron laser pulses 65 4.4 Results and discussion 68 4.4.1 GaAs/InGaAs core/shell nanowires 68 4.4.2 Nanowire cross sections 75 4.5 Conclusion 79 5 Summary and outlook 81 A Citation metrics 85 B Additional nanospectroscopic studies 87 B.1 Silicon carbide nanoparticle probes 87 B.2 Individual impurities in Si 91 B.3 Surface phonon polaritons in moybdenum disulfide 96 C Derivation of the nonparabolic effective mass and density of states 99 C.1 Effective mass 99 C.2 Density of states 100 D Comparison of self-homodyne and pseudo-heterodyne detection 103 Bibliography 105 List of Abbreviations 125 List of Symbols 132 List of Publications 133 Acknowledgments 137 Versicherung 13