Christoph Mahr

Theoretical study of precision and accuracy of strain analysis by nano-beam electron diffraction.

Measurement of lattice strain is important to characterize semiconductor nanostructures. As strain has large influence on the electronic band structure, methods for the measurement of strain with high precision, accuracy and spatial resolution in a large field of view are mandatory. In this paper we present a theoretical study of precision and accuracy of measurement of strain by convergent nano-beam electron diffraction. It is found that the accuracy of the evaluation suffers from halos in the diffraction pattern caused by a variation of strain within the area covered by the focussed electron beam. This effect, which is expected to be strong at sharp interfaces between materials with different lattice plane distances, will be discussed for convergent-beam electron diffraction patterns using a conventional probe and for patterns formed by a precessing electron beam. Furthermore, we discuss approaches to optimize the accuracy of strain measured at interfaces. The study is based on the evaluation of diffraction patterns simulated for different realistic structures that have been investigated experimentally in former publications. These simulations account for thermal diffuse scattering using the frozen-lattice approach and the modulation-transfer function of the image-recording system. The influence of Poisson noise is also investigated.

A versatile sol–gel coating for mixed oxides on nanoporous gold and their application in the water gas shift reaction

Based on a sol–gel coating method, a series of nanoporous gold (npAu) catalysts functionalized with titania–ceria mixed oxides were prepared. Metal-oxides with different composition were formed inside the mesoporous material (ligaments and pores ∼45 nm) after thermal treatment at over 200 °C for 2 h. The water-gas shift (WGS) reaction (H2O + CO → H2 + CO2) was studied in a continuous flow reactor at ambient pressure using these Ce–TiOx/npAu catalytic materials. Formation of CO2 was observed at temperatures between 200 °C and 450 °C. The addition of CeO2 to TiO2 resulted in an strongly increased activity; the sample (with the molar ratio of Ce : Ti = 1 : 2 abbreviated as Ce1Ti2Ox/npAu) shows the highest activity which was nearly twice as high as the activity of all other samples at 300 °C. The loss of activity after 2 catalytic runs was only about 10% at 450 °C for the Ce1Ti2Ox/npAu sample and no coarsening was observed. Raman spectroscopic characterization of the materials indicates a dynamic correlation between the crystallization (oxygen storage) of the metal-oxides under oxidizing and reducing conditions.

Optimization of NBED simulations for disc-detection measurements

Nano-beam electron diffraction (NBED) is a method which can be applied to measure lattice strain and polarisation fields in strained layer heterostructures and transistors. To investigate precision, accuracy and spatial resolution of such measurements in dependence of properties of the specimen as well as electron optical parameters, simulations of NBED patterns are required which allow to predict the result of common disc-detection algorithms. In this paper we demonstrate by focusing on the detection of the central disc in crystalline silicon that such simulations require to take several experimental characteristics into account in order to obtain results which are comparable to those from experimental NBED patterns. These experimental characteristics are the background intensity, the presence of Poisson noise caused by electron statistics and blurring caused by inelastic scattering and by the transfer quality of the microscope camera. By means of these optimized simulations, different effects of specimen properties on disc detection - such as strain, surface morphology and compositional changes on the nanometer scale - are investigated and discussed in the context of misinterpretation in experimental NBED evaluations. It is shown that changes in surface morphology and chemical composition lead to measured shifts of the central disc in the NBED pattern of tens to hundreds of µrad. These shifts are of the same order of magnitude or even larger than shifts that could be caused by an electric polarisation field in the range of MV/cm.

Measurement of local crystal lattice strain variations in dealloyed nanoporous gold

ABSTRACT Reversible macroscopic length changes in nanoporous structures can be achieved by applying electric potentials or by exposing them to different gases or liquids. Thus, these materials are interesting candidates for applications as sensors or actuators. Macroscopic length changes originate from microscopic changes of crystal lattice parameters. In this report, we show spatially resolved measurements of crystal lattice strain in dealloyed nanoporous gold. The results confirm theory by indicating a compression of the lattice along the axis of cylindrically shaped ligaments and an expansion in radial direction. Furthermore, we show that curved npAu surfaces show inward relaxation of the surface layer. GRAPHICAL ABSTRACT IMPACT STATEMENT We show spatially resolved measurements of strain in nanoporous gold confirming theory: Crystal lattice is compressed along the axis of cylindrical ligaments and expanded in radial direction, surfaces relax inward.

Influence of distortions of recorded diffraction patterns on strain analysis by nano-beam electron diffraction

Images acquired in transmission electron microscopes can be distorted for various reasons such as e.g. aberrations of the lenses of the imaging system or inaccuracies of the image recording system. This results in inaccuracies of measures obtained from the distorted images. Here we report on measurement and correction of elliptical distortions of diffraction patterns. The effect of this correction on the measurement of crystal lattice strain is investigated. We show that the effect of the distortions is smaller than the precision of the measurement in cases where the strain is obtained from shifts of diffracted discs with respect to their positions in images acquired in an unstrained reference area of the sample. This can be explained by the fact that diffraction patterns acquired in the strain free reference area of the sample are distorted in the same manner as the diffraction patterns acquired in the strained region of interest. In contrast, for samples without a strain free reference region such as nanoparticles or nanoporous structures, where we evaluate ratios of lattice plane distances along different directions, the distortions are usually not negligible. Furthermore, two techniques for the detection of diffraction disc positions are compared showing that for samples in which the crystal orientation changes over the investigated area it is more precise to detect the positions of many diffraction discs simultaneously instead of detecting each disc position independently.

Strain analysis from nano-beam electron diffraction: influence of specimen tilt and beam convergence

Strain analyses from experimental series of nano-beam electron diffraction (NBED) patterns in scanning transmission electron microscopy are performed for different specimen tilts. Simulations of NBED series are presented for which strain analysis gives results that are in accordance with experiment. This consequently allows to study the relation between measured strain and actual underlying strain. A two-tilt method which can be seen as lowest-order electron beam precession is suggested and experimentally implemented. Strain determination from NBED series with increasing beam convergence is performed in combination with the experimental realization of a probe-forming aperture with a cross inside. It is shown that using standard evaluation techniques, the influence of beam convergence on spatial resolution is lower than the influence of sharp rings around the diffraction disc which occur at interfaces and which are caused by the tails of the intensity distribution of the electron probe.

Measurement of strain in nanoporous gold using nano-beam electron diffraction

Nanoporous gold (npAu) has attracted a lot of attention during the last decade as it has interesting applications particularly in the field of catalysis [1]. It is prepared by corrosion of a suitable gold master alloy, e.g. gold/silver. The remaining material forms a sponge-like structure built of ligaments and pores still preserving a crystalline structure over several tens of nanometres. A high surface to volume ratio, open porosity making it permeable for gases and liquids and a strongly curved ligament surface providing surface atoms of different coordination are only some properties which qualify npAu as catalytic material with well adjustable and reproducible structure. One important structural property that is expected to have strong influence on the catalytic activity is lattice strain, because strain affects the electronic states [2]. Here we present measurements of strain in npAu. A measurement of lattice strain by means of high-resolution TEM for example by the analysis of lattice plane distances is possible only in a very small field of view for npAu. As the positions of intensity maxima in the images depend on several experimental parameters, such as defocus, orientation, composition, lens aberrations and especially specimen thickness, maxima detection in TEM micrographs succeeds only in small parts of the sample, because thickness is varying strongly. This can be seen in Fig. 1. Close to the surface intensity maxima can be detected and thus strain can be measured, in this case tensile strain up to 5% has been found. But as the ligament gets thicker and defects become visible, contrast changes and strain analysis fails. A method that overcomes these problems is strain analysis using nano-beam electron diffraction (NBED) [3]. Here a focussed electron probe is scanned across the sample and at each position of the scanning beam the corresponding diffraction pattern is recorded. As distances between the non-overlapping diffraction discs depend basically on the local lattice parameter according to Braggs law, strain can be measured by comparing distances between diffraction discs at different positions of the scanning beam. By an analysis of distances between diffraction discs in two linearly independent directions strain as well as shear-strain and rotation can be measured. A further advantage of strain analysis by NBED is its large field of view, because at first sight it is limited only by the size of the scanned part of the sample. Hence strain and rotation of neighbouring ligaments in npAu can be measured. On the other hand a large field of view requires the acquisition of a large number of diffraction patterns in a short time to avoid effects of sample drift, beam induced sample damage and contamination. Here we present strain and rotation maps of npAu measured using a delay-line detector for the acquisition of the diffraction patterns. With this detector strain maps at a scanning raster of e.g. 100x100 pixels can be recorded, allowing measurements in a field of view of several hundreds of nanometers (Fig. 2) still preserving a sampling limited spatial resolution of about 1.6 nm [4]. Furthermore we show by evaluation of simulations that two important aspects concerning the precision of the measurement have to be taken into account. As the precision of the measurement suffers from noise in the diffraction pattern, the precision degrades for shorter image integration times. On the other hand the precision can be increased using a precessing [5, 6] electron beam, as the diffraction discs are illuminated more homogeneously and hence their positions can be detected more precisely. In this way a compromise between precision and speed / size of the measurement has to be found. Keywords: nanoporous gold; strain measurement; NBED; precision