Knut Müller

Measurement of specimen thickness and composition in Al(x)Ga(1-x)N/GaN using high-angle annular dark field images.

In scanning transmission electron microscopy using a high-angle annular dark field detector, image intensity strongly depends on specimen thickness and composition. In this paper we show that measurement of image intensities relative to the intensity of the incoming electron beam allows direct comparison with simulated image intensities, and thus quantitative measurement of specimen thickness and composition. Simulations were carried out with the frozen lattice and absorptive potential multislice methods. The radial inhomogeneity of the detector was measured and taken into account. Using a focused ion beam (FIB) prepared specimen we first demonstrate that specimen thicknesses obtained in this way are in very good agreement with a direct measurement of the thickness of the lamella by scanning electron microscopy in the FIB. In the second step we apply this method to evaluate the composition of Al(x)Ga(1-x)N/GaN layers. We measured ratios of image intensities obtained in regions with unknown and with known Al-concentration x, respectively. We show that estimation of the specimen thickness combined with evaluation of intensity ratios allows quantitative measurement of the composition x. In high-resolution images we find that the image intensity is well described by simulation if the simulated image is convoluted with a Gaussian with a half-width at half-maximum of 0.07 nm.

Composition mapping in InGaN by scanning transmission electron microscopy

We suggest a method for chemical mapping that is based on scanning transmission electron microscopy (STEM) imaging with a high-angle annular dark field (HAADF) detector. The analysis method uses a comparison of intensity normalized with respect to the incident electron beam with intensity calculated employing the frozen lattice approximation. This procedure is validated with an In(0.07)Ga(0.93)N layer with homogeneous In concentration, where the STEM results were compared with energy filtered imaging, strain state analysis and energy dispersive X-ray analysis. Good agreement was obtained, if the frozen lattice simulations took into account static atomic displacements, caused by the different covalent radii of In and Ga atoms. Using a sample with higher In concentration and series of 32 images taken within 42 min scan time, we did not find any indication for formation of In rich regions due to electron beam irradiation, which is reported in literature to occur for the parallel illumination mode. Image simulation of an In(0.15)Ga(0.85)N layer that was elastically relaxed with empirical Stillinger-Weber potentials did not reveal significant impact of lattice plane bending on STEM images as well as on the evaluated In concentration profiles for specimen thicknesses of 5, 15 and 50 nm. Image simulation of an abrupt interface between GaN and In(0.15)Ga(0.85)N for specimen thicknesses up to 200 nm showed that artificial blurring of interfaces is significantly smaller than expected from a simple geometrical model that is based on the beam convergence only. As an application of the method, we give evidence for the existence of In rich regions in an InGaN layer which shows signatures of quantum dot emission in microphotoluminescence spectroscopy experiments.

Atomic electric fields revealed by a quantum mechanical approach to electron picodiffraction.

By focusing electrons on probes with a diameter of 50 pm, aberration-corrected scanning transmission electron microscopy (STEM) is currently crossing the border to probing subatomic details. A major challenge is the measurement of atomic electric fields using differential phase contrast (DPC) microscopy, traditionally exploiting the concept of a field-induced shift of diffraction patterns. Here we present a simplified quantum theoretical interpretation of DPC. This enables us to calculate the momentum transferred to the STEM probe from diffracted intensities recorded on a pixel array instead of conventional segmented bright-field detectors. The methodical development yielding atomic electric field, charge and electron density is performed using simulations for binary GaN as an ideal model system. We then present a detailed experimental study of SrTiO3 yielding atomic electric fields, validated by comprehensive simulations. With this interpretation and upgraded instrumentation, STEM is capable of quantifying atomic electric fields and high-contrast imaging of light atoms.

Determination of the chemical composition of GaNAs using STEM HAADF imaging and STEM strain state analysis.

The nitrogen concentration of GaN(0.01≤x≤0.05)As(1-x) quantum wells was determined from high resolution scanning transmission electron microscopy (HRSTEM) images taken with a high-angle annular dark field (HAADF) detector. This was done by applying two independent methods: evaluation of the scattering intensity and strain state analysis. The HAADF scattering intensity was computed by multislice simulations taking into account the effect of static atomic displacements and thermal diffuse scattering. A comparison of the mean intensity per atom column on the experimental images with these simulations enabled us to generate composition maps with atomic scale resolution. STEM simulations of large supercells proved that local drops of the HAADF intensity observed close to embedded quantum wells are caused by surface strain relaxation. The same STEM images were evaluated by strain state analysis. We suggest a real space method which is not affected by fly-back errors in HRSTEM images. The results of both evaluation methods are in accordance with data obtained from X-ray diffraction measurements.

Strain measurement in semiconductor heterostructures by scanning transmission electron microscopy.

This article deals with the measurement of strain in semiconductor heterostructures from convergent beam electron diffraction patterns. In particular, three different algorithms in the field of (circular) pattern recognition are presented that are able to detect diffracted disc positions accurately, from which the strain in growth direction is calculated. Although the three approaches are very different as one is based on edge detection, one on rotational averages, and one on cross correlation with masks, it is found that identical strain profiles result for an In x Ga1-x N y As1-y /GaAs heterostructure consisting of five compressively and tensile strained layers. We achieve a precision of strain measurements of 7-9·10-4 and a spatial resolution of 0.5-0.7 nm over the whole width of the layer stack which was 350 nm. Being already very applicable to strain measurements in contemporary nanostructures, we additionally suggest future hardware and software designs optimized for fast and direct acquisition of strain distributions, motivated by the present studies.

Scanning transmission electron microscopy strain measurement from millisecond frames of a direct electron charge coupled device

A high-speed direct electron detection system is introduced to the field of transmission electron microscopy and applied to strain measurements in semiconductor nanostructures. In particular, a focused electron probe with a diameter of 0.5 nm was scanned over a fourfold quantum layer stack with alternating compressive and tensile strain and diffracted discs have been recorded on a scintillator-free direct electron detector with a frame time of 1 ms. We show that the applied algorithms can accurately detect Bragg beam positions despite a significant point spread each 300 kV electron causes during detection on the scintillator-free camera. For millisecond exposures, we find that strain can be measured with a precision of 1.3  × 10−3, enabling, e.g., strain mapping in a 100×100 nm2 region with 0.5 nm resolution in 40 s.

Wrinkling of atomic planes in ultrathin Au nanowires.

A detailed understanding of structure and stability of nanowires is critical for applications. Atomic resolution imaging of ultrathin single crystalline Au nanowires using aberration-corrected microscopy reveals an intriguing relaxation whereby the atoms in the close-packed atomic planes normal to the growth direction are displaced in the axial direction leading to wrinkling of the (111) atomic plane normal to the wire axis. First-principles calculations of the structure of such nanowires confirm this wrinkling phenomenon, whereby the close-packed planes relax to form saddle-like surfaces. Molecular dynamics studies of wires with varying diameters and different bounding surfaces point to the key role of surface stress on the relaxation process. Using continuum mechanics arguments, we show that the wrinkling arises due to anisotropy in the surface stresses and in the elastic response, along with the divergence of surface-induced bulk stress near the edges of a faceted structure. The observations provide new understanding on the equilibrium structure of nanoscale systems and could have important implications for applications in sensing and actuation.

Quantitative chemical evaluation of dilute GaNAs using ADF STEM: avoiding surface strain induced artifacts.

The high angle annular dark field intensity (HAADF) in scanning transmission electron microscopy (STEM) can be used for a quantitative evaluation of the chemical composition in dilute GaNAs quantum wells by comparison with simulated intensities. As the scattered intensity is highly sensitive to surface strain fields originating from the quantum wells embedded in GaAs, the HAADF intensity is difficult to evaluate in a quantitative way as long as strain contrast cannot be distinguished from chemical contrast. We present a method to achieve full 2D HAADF STEM compositional mapping of GaNAs/GaAs quantum well systems by making use of information from two different camera lengths.

Coherently Embedded Ag Nanostructures in Si: 3D Imaging and their application to SERS

Surface enhanced Raman spectroscopy (SERS) has been established as a powerful tool to detect very low-concentration bio-molecules. One of the challenging problems is to have reliable and robust SERS substrate. Here, we report on a simple method to grow coherently embedded (endotaxial) silver nanostructures in silicon substrates, analyze their three-dimensional shape by scanning transmission electron microscopy tomography and demonstrate their use as a highly reproducible and stable substrate for SERS measurements. Bi-layers consisting of Ag and GeOx thin films were grown on native oxide covered silicon substrate using a physical vapor deposition method. Followed by annealing at 800°C under ambient conditions, this resulted in the formation of endotaxial Ag nanostructures of specific shape depending upon the substrate orientation. These structures are utilized for detection of Crystal Violet molecules of 5 × 10−10 M concentrations. These are expected to be one of the highly robust, reusable and novel substrates for single molecule detection.

Simultaneous quantification of indium and nitrogen concentration in InGaNAs using HAADF-STEM.

To unambiguously evaluate the indium and nitrogen concentrations in In(x)Ga(1-x)N(y)As(1-y), two independent sources of information must be obtained experimentally. Based on high-resolution scanning transmission electron microscopy (STEM) images taken with a high-angle annular dark-field (HAADF) detector the strain state of the InGaNAs quantum well is determined as well as its characteristic HAADF-scattering intensity. The strain state is evaluated by applying elasticity theory and the HAADF intensity is used for a comparison with multislice simulations. The combination of both allows for determination of the chemical composition where the results are in accordance with X-ray diffraction measurements, three-dimensional atom probe tomography, and further transmission electron microscopy analysis. The HAADF-STEM evaluation was used to investigate the influence of As-stabilized annealing on the InGaNAs/GaAs sample. Photoluminescence measurements show an annealing-induced blue shift of the emission wavelength. The chemical analysis precludes an elemental diffusion as origin of the energy shift--instead the results are in agreement with a model based on an annealing-induced redistribution of the atomic next-neighbor configuration.