Exploring transmission Kikuchi diffraction using a Timepix detector

Electron backscatter diffraction (EBSD) is a well-established scanning electron microscope (SEM)-based technique [1]. It allows the non-destructive mapping of the crystal structure, texture, crystal phase and strain with a spatial resolution of tens of nanometers. Conventionally this is performed by placing an electron sensitive screen, typically consisting of a phosphor screen combined with a charge coupled device (CCD) camera, in front of a specimen, usually tilted 70° to the normal of the exciting electron beam. Recently, a number of authors have shown that a significant increase in spatial resolution is achievable when Kikuchi diffraction patterns are acquired in transmission geometry; that is when diffraction patterns are generated by electrons transmitted through an electron-transparent, usually thinned, specimen. The resolution of this technique, called transmission Kikuchi diffraction (TKD), has been demonstrated to be better than 10 nm [2,3]. We have recently demonstrated the advantages of a direct electron detector, Timepix [4,5], for the acquisition of standard EBSD patterns [5]. In this article we will discuss the advantages of Timepix to perform TKD and for acquiring spot diffraction patterns and more generally for acquiring scanning transmission electron microscopy micrographs in the SEM. Particularly relevant for TKD, is its very compact size, which allows much more flexibility in the positioning of the detector in the SEM chamber. We will furthermore show recent results using Timepix as a virtual forward scatter detector, and will illustrate the information derivable on producing images through processing of data acquired from different areas of the detector. We will show results from samples ranging from gold nanoparticles to nitride semiconductor nanorods

Diffraction effects and inelastic electron transport in angle-resolved microscopic imaging applications

We analyze the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolor orientation imaging using multiple, angle-resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in-depth theoretical modeling of the energy and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channeling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocations

Diffractive triangulation of radiative point sources

We describe a general method to determine the location of a point source of waves relative to a twodimensional single-crystalline active pixel detector. Based on the inherent structural sensitivity of crystalline sensor materials, characteristic detector diffraction patterns can be used to triangulate the location of a wave emitter. The principle described here can be applied to various types of waves, provided that the detector elements are suitably structured. As a prototypical practical application of the general detection principle, a digital hybrid pixel detector is used to localize a source of electrons for Kikuchi diffraction pattern measurements in the scanning electron microscope. This approach provides a promising alternative method to calibrate Kikuchi patterns for accurate measurements of microstructural crystal orientations, strains, and phase distributions

Spatial auction markets with unique consumer price

We consider a collection of auctions representing zonal electricity markets, which are joined by transmission lines in a spatial system. At each market, generating companies (traders) and customers (buyers) submit their fixed offer/bid prices together with maximal offer/bid volumes, respectively. In addition to the usual balance and capacity constraints, we consider also the additional requirement of utilizing the minimal unique purchase price for all the zones. As a result, we obtain spatial equilibrium type problems with special parameter for finding zonal prices and offer/bid volumes. We show that the streamlined formulation can be inconsistent under rather natural assumptions and propose a relaxed formulation. This problem admits suitable solution methods. We propose a parametric method combined with a bisection type procedure to solve this problem.© 2011 by Nova Science Publishers, Inc. All rights reserved

Digital direct electron imaging of energy-filtered electron backscatter diffraction patterns

Electron backscatter diffraction is a scanning electron microscopy technique used to obtain crystallographic information on materials. It allows the nondestructive mapping of crystal structure, texture, and strain with a lateral and depth resolution on the order of tens of nanometers. Electron backscatter diffraction patterns (EBSPs) are presently acquired using a detector comprising a scintillator coupled to a digital camera, and the crystallographic information obtainable is limited by the conversion of electrons to photons and then back to electrons again. In this article we will report the direct acquisition of energy-filtered EBSPs using a digital complementary metal-oxide-semiconductor hybrid pixel detector, Timepix. We show results from a range of samples with different mass and density, namely diamond, silicon, and GaN. Direct electron detection allows the acquisition of EBSPs at lower (≤5 keV) electron beam energies. This results in a reduction in the depth and lateral extension of the volume of the specimen contributing to the pattern and will lead to a significant improvement in lateral and depth resolution. Direct electron detection together with energy filtering (electrons having energy below a specific value are excluded) also leads to an improvement in spatial resolution but in addition provides an unprecedented increase in the detail in the acquired EBSPs. An increase in contrast and higher-order diffraction features are observed. In addition, excess-deficiency effects appear to be suppressed on energy filtering. This allows the fundamental physics of pattern formation to be interrogated and will enable a change in the use of electron backscatter diffraction (EBSD) for crystal phase identification and the mapping of strain. The enhancement in the contrast in high-pass energy-filtered EBSD patterns is found to be stronger for lighter, less dense materials. The improved contrast for such materials will enable the application of the EBSD technique to be expanded to materials for which conventional EBSD analysis is not presently practicable

Diffraction effects and inelastic electron transport in angle-resolved microscopic imaging applications

We analyse the signal formation process for scanning electron microscopic imaging applications on crystalline specimens. In accordance with previous investigations, we find nontrivial effects of incident beam diffraction on the backscattered electron distribution in energy and momentum. Specifically, incident beam diffraction causes angular changes of the backscattered electron distribution which we identify as the dominant mechanism underlying pseudocolour orientation imaging using multiple, angle-resolving detectors. Consequently, diffraction effects of the incident beam and their impact on the subsequent coherent and incoherent electron transport need to be taken into account for an in-depth theoretical modelling of the energy- and momentum distribution of electrons backscattered from crystalline sample regions. Our findings have implications for the level of theoretical detail that can be necessary for the interpretation of complex imaging modalities such as electron channelling contrast imaging (ECCI) of defects in crystals. If the solid angle of detection is limited to specific regions of the backscattered electron momentum distribution, the image contrast that is observed in ECCI and similar applications can be strongly affected by incident beam diffraction and topographic effects from the sample surface. As an application, we demonstrate characteristic changes in the resulting images if different properties of the backscattered electron distribution are used for the analysis of a GaN thin film sample containing dislocationsThis work was carried out with the support of EPSRC Grant Nos. EP/J015792/1 and EP/M015181/1 and through support of a Carnegie Trust Research Incentive Grant No. 70483

Structural and luminescence imaging and characterisation of semiconductors in the scanning electron microscope

The scanning electron microscopy techniques of electron backscatter diffraction (EBSD), electron channelling contrast imaging (ECCI) and hyperspectral cathodoluminescence imaging (CL) provide complementary information on the structural and luminescence properties of materials rapidly and non-destructively, with a spatial resolution of tens of nanometres. EBSD provides crystal orientation, crystal phase and strain analysis, whilst ECCI is used to determine the planar distribution of extended defects over a large area of a given sample. CL reveals the influence of crystal structure, composition and strain on intrinsic luminescence and/or reveals defect-related luminescence. Dark features are also observed in CL images where carrier recombination at defects is non-radiative. The combination of these techniques is a powerful approach to clarifying the role of crystallography and extended defects on a materials' light emission properties. Here we describe the EBSD, ECCI and CL techniques and illustrate their use for investigating the structural and light emitting properties of UV-emitting nitride semiconductor structures. We discuss our investigations of the type, density and distribution of defects in GaN, AlN and AlGaN thin films and also discuss the determination of the polarity of GaN nanowires

Scanning electron microscope as a flexible tool for investigating the properties of UV-emitting nitride semiconductor thin films

In this paper we describe the scanning electron microscopy techniques of electron backscatter diffraction, electron channeling contrast imaging, wavelength dispersive X-ray spectroscopy, and cathodoluminescence hyperspectral imaging. We present our recent results on the use of these non-destructive techniques to obtain information on the topography, crystal misorientation, defect distributions, composition, doping, and light emission from a range of UV-emitting nitride semiconductor structures. We aim to illustrate the developing capability of each of these techniques for understanding the properties of UV-emitting nitride semiconductors, and the benefits were appropriate, in combining the techniques

Advances in electron channelling contrast imaging and electron backscatter diffraction for imaging and analysis of structural defects in the scanning electron microscope

In this article we describe the scanning electron microscopy (SEM) techniques of electron channelling contrast imaging and electron backscatter diffraction. These techniques provide information on crystal structure, crystal misorientation, grain boundaries, strain and structural defects on length scales from tens of nanometres to tens of micrometres. Here we report on the imaging and analysis of dislocations and sub-grains in nitride semiconductor thin films (GaN and AlN) and tungsten carbide-cobalt (WC-Co) hard metals. Our aim is to illustrate the capability of these techniques for investigating structural defects in the SEM and the benefits of combining these diffraction-based imaging techniques