Ian K. Robinson

GexSi1−x/Si strained‐layer superlattice grown by molecular beam epitaxy

Ge x Si1−x films are grown on Si by molecular beam epitaxy and analyzed by Nomarski optical interferencemicroscopy, Rutherford ion backscattering and channeling, x‐ray diffraction, and transmission electron microscopy. The full range of alloy compositions will grow smoothly on silicon. Ge x Si1−x films with x≤0.5 can be grown free of dislocations by means of strained‐layer epitaxy where lattice mismatch is accommodated by tetragonal strain. Critical thickness and composition values are tabulated for strained‐layer growth. Multiple strained layers are combined to form a Ge x Si1−x /Si strained‐layer superlattice.

Surface X‐Ray Diffraction

A general introduction to X-ray diffraction and its application to the study of surfaces and interfaces is presented. The application of X-ray diffraction to various problems in surface and interface science is illustrated through five different techniques: crystal truncation rod analysis; two-dimensional crystallography; three-dimensional structure analysis; the evanescent wave method; and lineshape analysis. These techniques are explained with numerous examples from experiments and with the aid of an extensive bibliography.

Three-dimensional Mapping of a Deformation Field inside a Nanocrystal

Coherent X-ray diffraction imaging is a rapidly advancing form of microscopy: diffraction patterns, measured using the latest third-generation synchrotron radiation sources, can be inverted to obtain full three-dimensional images of the interior density within nanocrystals. Diffraction from an ideal crystal lattice results in an identical copy of this continuous diffraction pattern at every Bragg peak. This symmetry is broken by the presence of strain fields, which arise from the epitaxial contact forces that are inevitable whenever nanocrystals are prepared on a substrate. When strain is present, the diffraction copies at different Bragg peaks are no longer identical and contain additional information, appearing as broken local inversion symmetry about each Bragg point. Here we show that one such pattern can nevertheless be inverted to obtain a ‘complex’ crystal density, whose phase encodes a projection of the lattice deformation. A lead nanocrystal was crystallized in ultrahigh vacuum from a droplet on a silica substrate and equilibrated close to its melting point. A three-dimensional image of the density, obtained by inversion of the coherent X-ray diffraction, shows the expected facetted morphology, but in addition reveals a real-space phase that is consistent with the three-dimensional evolution of a deformation field arising from interfacial contact forces. Quantitative three-dimensional imaging of lattice strain on the nanometre scale will have profound consequences for our fundamental understanding of grain interactions and defects in crystalline materials. Our method of measuring and inverting diffraction patterns from nanocrystals represents a vital step towards the ultimate goal of atomic resolution single-molecule imaging that is a prominent justification for development of X-ray free-electron lasers.

Beyond crystallography: Diffractive imaging using coherent x-ray light sources

X-ray crystallography has been central to the development of many fields of science over the past century. It has now matured to a point that as long as good-quality crystals are available, their atomic structure can be routinely determined in three dimensions. However, many samples in physics, chemistry, materials science, nanoscience, geology, and biology are noncrystalline, and thus their three-dimensional structures are not accessible by traditional x-ray crystallography. Overcoming this hurdle has required the development of new coherent imaging methods to harness new coherent x-ray light sources. Here we review the revolutionary advances that are transforming x-ray sources and imaging in the 21st century.

Three-dimensional imaging of strain in a single ZnO nanorod

Nanoscale structures can be highly strained because of confinement effects and the strong influence of their external boundaries. This results in dramatically different electronic, magnetic and optical material properties of considerable utility. Third-generation synchrotron-based coherent X-ray diffraction has emerged as a non-destructive tool for three-dimensional (3D) imaging of strain and defects in crystals that are smaller than the coherence volume, typically a few cubic micrometres, of the available beams that have sufficient flux to reveal the materials structure. Until now, measurements have been possible only at a single Bragg point of a given crystal because of the limited ability to maintain alignment; it has therefore been possible to determine only one component of displacement and not the full strain tensor. Here we report key advances in our fabrication and experimental techniques, which have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time. All three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.

Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals.

Distorted Nanoparticle Nanoparticles have found many applications in modern technology; however, the full characterization of individual particles is challenging. One of the most interesting mechanical properties is the particles response to lattice distortion. This property has been probed for ensembles of nanoparticles, but the required averaging may distort the results. Clark et al. (p. 56, published online 23 May; see the Perspective by Hartland and Lo) were able to image the generation and subsequent evolution of coherent acoustic phonons from an individual perturbed gold nanocrystal on the picosecond time scale. An x-ray free-electron laser is used to probe the elastic modes of a gold nanocrystal. [Also see Perspective by Hartland and Lo] Key insights into the behavior of materials can be gained by observing their structure as they undergo lattice distortion. Laser pulses on the femtosecond time scale can be used to induce disorder in a “pump-probe” experiment with the ensuing transients being probed stroboscopically with femtosecond pulses of visible light, x-rays, or electrons. Here we report three-dimensional imaging of the generation and subsequent evolution of coherent acoustic phonons on the picosecond time scale within a single gold nanocrystal by means of an x-ray free-electron laser, providing insights into the physics of this phenomenon. Our results allow comparison and confirmation of predictive models based on continuum elasticity theory and molecular dynamics simulations.

Commensurate and incommensurate structures in molecular beam epitaxially grown GexSi1−xfilms on Si(100)

The transition between commensurate and incommensurate growth of GexSi1−x alloys on Si is observed directly by means of ion channeling and x‐ray diffraction measurements. Molecular beam epitaxial films of thickness h up to 2500 A thick show commensurate epitaxy for x≲50% and h≲hc, a critical thickness dependent upon x. The observed values of hc are discussed in terms of a model invoking the maximum theoretical interfacial shear strength and a barrier to misfit dislocation formation.

Translation position determination in ptychographic coherent diffraction imaging

Accurate knowledge of translation positions is essential in ptychography to achieve a good image quality and the diffraction limited resolution. We propose a method to retrieve and correct position errors during the image reconstruction iterations. Sub-pixel position accuracy after refinement is shown to be achievable within several tens of iterations. Simulation and experimental results for both optical and X-ray wavelengths are given. The method improves both the quality of the retrieved object image and relaxes the position accuracy requirement while acquiring the diffraction patterns.

Critical thickness of GaN thin films on sapphire (0001)

Synchrotron x‐ray diffraction was employed to measure the lattice constants a and c of GaN films grown with an AlN buffer layer on sapphire (0001) over a thickness range of 50 A to 1 μm. We used multiple reflections and a least‐squares fit method for high reliability. As the thickness increased, the lattice constant a increased from 3.133 A to 3.196 A and c decreased from 5.226 A to 5.183 A. The expected trend was fitted to an equilibrium theory, allowing the critical thickness of GaN on AlN to be estimated at 29 A ± 4 A in good agreement with a theoretical prediction.

Hard X-ray dark-field imaging with incoherent sample illumination

We report on a non-interferometric technique enabling dark-field imaging by using incoherent illumination and two achromatic optical elements. The simultaneous retrieval of absorption and differential phase images in the hard X-ray regime is also provided. We show that three projection images are sufficient to separate three signals: absorption, differential phase, and scattering. The method is highly efficient, also in terms of the dose delivered to the sample, flexible, robust against environmental vibrations, and scalable. It can be easily implemented in laboratories and translated into commercial systems, lending itself to a wide range of applications.