Diffraction | EPFL Graph Search

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic bending pattern is most pronounced when a wave from a coherent source (such as a laser) encounters a slit/aperture that is comparable in size to its wavelength, as shown in the inserted image. This is due to the addition, or interference, of different points on the wavefront (or, equivalently, each wavelet) that travel by paths of different lengths to the re

Simulations d'une structure cristalline incommensurable à caractère désordonné

Eric Germaneau

Incommensurate crystal structures do not display three-dimensional periodicity. Discovered in the 1960's, a mathematical model has been established in 1974 only. Incommensurate structures belong to the big family of aperiodic structures. The modulation of incommensurate structures manifests itself as satellite reflections around the main peaks on X-rays diffractograms. Short range order correlations in crystals lead to diffuse scattering between Bragg peaks in the diffraction pattern. The computing power available today allows for very time consuming simulations of the incommensurate or disordered crystal structures. Simulations based on Monte-Carlo and the molecular dynamic techniques have been performed. The former is based on stochastic algorithms, whereas the latter is deterministic. This PhD thesis strove to combine these two methods, using a four-isomermodel, in order to study the incommensurate, disordered polymorph of p-azoxydiphenetol (PAP), which crystallises below 356 K. One of the main features of the PAP molecule is its dative bond. A Monte-Carlo program, using true empirical potentials, has been developed in order to explain the behaviour of PAP. This code (6000 lines), written in C, uses the GSL and OpenMP libraries. Using numerical and experimental tools, this thesis provides explanations for the origin, from an atomic point of view, of the incommensurate and disordered behaviour of PAP. Calculations have been performed on the clusters of École Polytechnique Fédérale de Lausanne. Simulated diffraction patterns have been compared to experimental data, collected before and during this study. Moreover, a set of differential scanning calorimetry (DSC) measurements has been carried out during this work, the results of which have been analysed based on Arrhenius's law. For a better understanding of the role played by the dative bond, and the relation between the complexity of the molecule and the structure, DFT and ab initio calculations have been performed. This work has successfully woven the results from different experimental and numerical techniques into a comprehensive model for this very complex system indeed.

EPFL2008

Accurate, Stable and Efficient Modal Calculations of Photoelectrically Useful Absorption in Lamellar Metallic and Semiconductor Diffraction Gratings

David Isaak Gablinger

Solar energy has seen tremendous advances in the past years. For thin film photovoltaics, which use less of the expensive semiconductor materials, insufficient light absorption can be a limiting factor. It is hoped that by using diffractive optics to improve the light absorption, the cost per Watt could sink. Correspondingly, the optics of such structures need to compensate for the low absorption by high (structural) resonance, which is challenging to calculate. To estimate optimal structures, a numerical method should be able to assess feasible structures with widely varying geometries quickly. Modal methods allow for an efficient analysis of structures with varying height through the separation of eigenvalue and boundary value problem. First, the thesis aspires to further develop the modal methods for the calculation of optical properties of layered structures containing weakly absorbing metals and semiconductors. Second, the thesis aims to calculate absorption enhancements in idealized, prototypical structures by applying the newly developed methods. The calculations should only depend on material parameters and not contain additional assumptions. These absorption enhancements are not tied to a priori assumptions such as mode couplings, but they solely follow the physics of the structure investigated. The first part of the thesis is concerned with the methodical improvements. A first emphasis is put on studying peculiar properties of the eigenvalue problem, and on new developments of methods to solve it within a layer. Furthermore, it shows several variants for the numerical implementation of the eigenvalue problem. This part includes a new method to calculate the eigenvalues that can be adapted to two dimensional grating problems of arbitrary shape. The new method integrates the eigenvalue problem by making use of a two point trapezoidal formula, and satisfies the boundary condition between different materials exactly. It is energy conserving and the rate of convergence depends on the approximation order. The eigenvalues show a monotonic convergence that allows for extrapolation. The second methodical emphasis is placed on variants of the implementation of the boundary value problem that connects the grating to the incoming and outgoing plane waves. This algorithm describes the propagation of the incident energy to the semiconductor layer and the substrate by solving a non-recursive and numerically stable system of linear equations. A novel variant reduces the bandwidth of the corresponding matrix by a third. The third part of the thesis concerns calculations using the improved methods. First, the improved calculations are verified by showing that the energy conservation of the modal method, as well as the well-behavedness of the condition number of the calculation. Next, numerical results for the new methods are compared to results from the literature for analytic modal methods, and a comparison with existing software is made. Thereafter, the interface plasmons occuring for H polarization are investigated. In the last part of the thesis, calculations are made for the material specific absorption of light in metallic gratings covered by semiconductors, with a special interest in the absorption in the semiconductor. Here, the spectra for rectangular, sinusoidal gratings, and asymmetric gratings are calculated, and the absorption improvement is investigated through an analysis of the involved modes.

EPFL2016

Interface Investigations on Titanium Nitride Bilayer Systems

Dominik Anwar Jaeger

Nanocomposite coatings composed of two phases with atomically sharp phase boundaries, show interesting mechanical properties. These properties are often originating from their high interface to volume ratio. Composites of nanocrystalline titanium nitride (TiN) grains surrounded by a one to two monolayer thick interlayer of silicon nitride (Si3N4) show an enhanced nanohardness. The central theme of this thesis is concernedwith the interfacial properties of two-dimensional bilayer systems, which are used as model systems to describe the interfaces occurring in nanocomposite coatings. The systems under investigation are TiN interfaces in contact with silicon (Si), silicon nitride (Si3N4) and aluminum nitride (AlN). The primary tool used to analyze the interfaces of bilayer systems is X-ray Photoelectron Spectroscopy (XPS) with emphasis put on the shake-up feature of the Ti 2p photoelectron line. Shake-ups in TiN are observed as an additional peak on the lower binding energy side of the energy lines of the Ti 2p orbitals. Shake-ups are strongly influenced by valence electrons and electron density distributions. This makes them a powerful tool to probe the chemical and electronic structure of TiN interfaces. The aim of this study is to utilize the shake-up energy and its intensity to gain insight into interfacial structures and correlate their changes to interfacial polarization and macroscopic mechanical properties. Single crystalline (sc-) and oxygen-free TiN as well as oxygen-free bilayer systems were deposited by unbalanced magnetron sputtering and analyzed by Angle Resolved (AR-)XPS. Bilayer samples were deposited and their quality was controlled using X-ray diffraction (crystallinity), Rutherford back scattering (elemental composition), and atomic force microscopy (roughness). All XPS samples were fabricated, transfered and analyzed whilst maintaining ultra high vacuum. A precise and self-consistent XPS data processing method was developed to evaluate Ti 2p spectra. This method accounts for the correct photoelectron line shape, background subtraction and photoelectron peak area intensity. Binding energy, shake-up energy and intensity ratios of shake-ups taken frompristine TiN surfaces are precisely determined, and the influence of oxygen on the information content in peak positions and intensities was investigated. The shake-up energy and intensity of bulk sc-TiN and its origin of the shake-up are discussed. An analytical description for the XPS signal ratio of bilayer systems is derived to separate the interfacial signals from the bulk information. The results obtained by this analytical description are strongly influenced by the interface thickness that has been found to be proportional to the overlayer thickness. The revealed interface properties show a correlation between the shake-up intensity and the interface morphology, oxygen content, overlayer material and overlayer thickness. AR-XPS and X-ray Photoelectron Diffraction (XPD) results were used to interpret the crystalline structure of the different TiN/AlN and TiN/Si3N4 bilayer systems. AlN shows XPD patterns indicating a crystalline growth of AlN on sc-TiN. The electrically insulating AlN overlayer creates a charge accumulation at the TiN interface, which results in an enhanced shake-up intensity. XPD patterns of Si3N4 systems revealed a crystalline growth of Si3N4 in the first 0.6nm. The intensity of the diffraction patterns reduces with increasing Si3N4 overlayer thickness due to a change in the growth behavior from crystalline to amorphous structures. Si3N4 films show, in comparison to AlN, reduced interface charging and hence a lower shakeup intensity. The crystalline growth of Si3N4 in the initial stages is hindered in systems where a bias voltage is applied to the substrate during the deposition process. In contrast to the unbiased systems, which have crystalline interfacial structures, the biased systems no longer show XPD patterns due to a loss of crystallinity. Additionally the shake-up intensity of biased systems is thickness-independent, which is in contrast to unbiased systems. The difference in the shake-up intensity of biased and unbiased Si3N4 is explained by a different band gap of the Si3N4 structure in the first two monolayers. This thesis shows that the increase in the shake-up intensity is correlated to intrinsic and extrinsic interface charging. The obtained results, in combination with theoretical structure models from literature, show that in one to two monolayer thick interlayers a build-up of interface polarization is unlikely. The observed nanohardness enhancement in TiN/Si3N4 systems is explained with already known hardness effects.

EPFL2012