F.H. Baumann

Quantitative chemical lattice imaging: theory and practice

Abstract We describe how the composition of materials may be quantitatively mapped with near-atomic resolution and sensitivity. The procedure combines chemical lattice imaging (which sensitively records the compositional information) with vector pattern recognition (which efficiently extracts and quantifies the local information content). We describe the theoretical underpinnings which allow the local information content to be related to the local sample composition, and the procedure by which this may be realized in practice. Single and double atom substitutions in individual atomic columns of semiconductors can thus be detected at about 60% and 90% confidence levels, respectively. Potential complications due to nonlocal effects (Fresnel fringing, dynamical scattering), geometrical sample imperfections (thickness changes, surface roughness), radiation damage, and photographic nonlinearities are shown to be negligible.

Real-space analysis of lattice images and its link to conventional theory

Abstract We show that real-space analysis of lattice images in terms of multidimensional vectors rests on a small number of physically significant dimensions, each representing the contribution of a characteristic pattern forming a basis vector. In many cases, these basis vectors can be linked to “spatial periodicities”, and expressed in terms of conventional formalisms of dynamical scattering. This provides a link between the more abstract (but convenient) real-space image analysis and the more familiar formalisms of image formation in terms of Bloch waves. Within this framework, the simplest implementations of QUANTITEM and Chemical Mapping may be viewed as limiting cases of a more general approach. This helps delineate the application domain for each. The paper is illustrated by reference to the Al x Ga 1 − x As system in the 〈1 0 0〉, 〈1 1 0〉 and 〈1 1 1〉 projections. The historically popular 〈1 1 0〉 projection is shown to be the most complex for quantitative data extraction.

Quantitative chemical mapping: Spatial resolution

Abstract We show that the spatial resolution of quantitative chemical mapping is determined by the larger of two factors: the periodicity of the chemically sensitive reflections, or the size of the unit cell adopted for pattern recognition. Under appropriate chemically sensitive imaging conditions, nonlocal effects due to dynamical scattering and Fresnel fringing are insignificant, even when artifically large discontinuities in the sample projected potential are introduced.

CHARACTERIZATION OF STACKED GATE OXIDES BY ELECTRON HOLOGRAPHY

We have used off‐axis electron holography at a resolution of 3 A to investigate amorphous bilayer gate oxides consisting of thermal and chemically deposited SiO2. The values of the mean inner potential were measured to be: thermal oxide: (10.51±0.35)V (undensified); (10.65±0.32)V (‘‘densified’’); deposited oxide: (11.19±0.38)V (undensified); (10.58±0.69)V (densified). Exploiting the chemical etch rate differences between different oxides, we have delineated stacked gate oxides consisting of closely similar layers. Our results establish that measurement of thickness differences produced by etching can be used to reveal the densification state of the oxide.

Chemical lattice imaging of a Ni-based superalloy

Abstract We demonstrate the application of quantitative chemical lattice imaging techniques to a metallic system. The first results establish that the chemical interface between γ and γ′ phases of a nickel-based superalloy can be quantitatively identified.

Quantitative Hrtem: Measuring Projected Potential, Surface Roughness and Chemical Composition

We describe how general lattice images may be used to measure the variation of the potential in crystalline solids in any projection, with no knowledge of the imaging conditions. This approach is applicable to structurally perfect samples, in which interfacial topography, or changes in composition are of interest. We present the first atomic-level topographic map of a Si/SiO 2 interface in plan-view, and the first microscopic compositional map of a Si/GeSi/Si quantum well in cross-section.