Knut Müller

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.

We report on strain analysis by nano-beam electron diffraction with a spatial resolution of 0.5nm and a strain precision in the 4–710⁻⁴ range. Series of up to 160000 CBED patterns have been acquired in STEM mode with a semi-convergence angle of the incident probe of 2.6mrad, which enhances the spatial resolution by a factor of 5 compared to nearly parallel illumination. Firstly, we summarise 3 different algorithms to detect CBED disc positions accurately: selective edge detection and circle fitting, radial gradient maximisation and cross-correlation with masks. They yield equivalent strain profiles in growth direction for a stack of 5 In_xGa_1−xN_yAs_1−y/GaAs layers with tensile and compressive strain. Secondly, we use a direct electron read-out pnCCD detector with ultrafast readout hardware and a quantum efficiency close to 1 both to show that the same strain profiles are obtained at 200 times higher readout rates of 1kHz and to enhance strain precision to 3.510⁻⁴ by recording the weak 008 disc.

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 nm 2 region with 0.5 nm resolution in 40 s.

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_xGa_1−xN_yAs_1−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.

We report on a Transmission Electron Microscopy 3-beam technique based on the interference of 000, 200 and 220. Nonlinear imaging artefacts are eliminated by Fourier filtering, yielding 200 and 220 lattice fringe images, from which chemically sensitive contrast and strain are measured, respectively. In this way, In and N composition can be mapped at atomic scale in quaternary InGaNAs by comparison with simulated reference data. Our Bloch wave simulations are based on structure factors derived from supercells with 10⁶ atoms, which have been strain-relaxed by valence force field methods. Additionally, the influence of electron redistributions due to chemical bonding is accounted for by modified atomic scattering amplitudes derived from density functional theory. By comparing local compositions in an annealed In_0.28Ga_0.72N_0.025As_0.975 sample with its as-grown counterpart, we find homogenisation of InGaNAs layer thickness and –stoichiometry upon annealing.

A transmission electron microscopy (TEM) method for simultaneous measurement of indium and nitrogen content in InGaNAs at atomic scale is introduced, tested, and applied to investigate thermal annealing effects on structural properties. Our technique is based on the extraction of strain and chemical sensitive contrast from a single three-beam TEM lattice fringe image by subsequent decomposition into 220 and 020 two-beam fringe images, being free of nonlinear imaging artifacts. From comparison with simulated strain and 020 fringe amplitude, concentration maps and profiles are derived. For this purpose, the Bloch-wave approach is used with structure factors adapted for chemical bonding, static atomic displacements, as well as diffuse losses due to static and thermal disorder. Application to In0.28Ga0.72N0.025As0.975 before and after annealing at 670$\hskip0.3em${}\ifmmode^\circ\else\textdegree\fi{}C yields dissolution of In-rich islands and N-rich clusters and formation of a quantum well with nearly constant thickness and homogeneous elemental distributions, resulting in symmetric profiles along growth direction. To verify that these structural transitions are indeed correlated with typically observed changes of optical properties during thermal annealing, photoluminescence spectra are presented, revealing an increase in intensity by a factor of 20 and a strong blue shift of 60 meV.