Caustic imaging of gallium droplets using mirror electron microscopy

Flat electron mirror

Electron beams can be reflected by an electrode that is at a more negative potential than the cathode from which the beam is emitted. We want to design a mirror with a flat mirror electrode where the electrons are reflected at a plane very close to the electrode. The wave front of an electron can then be shaped when the mirror contains a surface topography or modulated potential. However, electron beams reflected by flat electron mirrors are usually characterized by high coefficients of chromatic and spherical aberration. When the mirror is combined with an electrostatic lens to form a tetrode mirror system, the situation deteriorates even further. This places a restrictive limit on the maximum aperture angle of the beam, and consequently also limits the attainable resolution at the image plane. We have numerically studied the dependence of these aberrations as a function of design parameters of the tetrode mirror consisting of a ground, lens, cap, and mirror electrode, and limited ourselves to only using flat electrodes with round apertures, at fixed electrode spacing. It turns out that the third order spherical aberration can be made negative. The negative third order aberration is then used to partially compensate the positive fifth order aberration. This way, a system configuration is obtained that, at 2 keV beam energy, provides a diffraction limited resolution of 7.6 nm at an image plane 25 mm from the mirror at beam semi-angles of 2.3 mrad, enabling an illumination radius of 40 μm at the mirror. The presented tetrode mirror design could spark innovative use of patterned electron mirrors as phase plates for electron microscopy in general, and for use as coherent beam splitters in Quantum Electron Microscopy in particular. An appendix presents a method to calculate the spot size of a focused beam in the presence of both third and fifth order spherical aberration coefficients, which is also applicable to Scanning (Transmission) Electron Microscopes with aberration correctors.

Droplet Epitaxy Image Contrast in Mirror Electron Microscopy

Image simulation methods are applied to interpret mirror electron microscopy (MEM) images obtained from a movie of GaAs droplet epitaxy. Cylindrical symmetry of structures grown by droplet epitaxy is assumed in the simulations which reproduce the main features of the experimental MEM image contrast, demonstrating that droplet epitaxy can be studied in real-time. It is therefore confirmed that an inner ring forms at the droplet contact line and an outer ring (or skirt) occurs outside the droplet periphery. We believe that MEM combined with image simulations will be increasingly used to study the formation and growth of quantum structures.

Reliable synthesis of self-running Ga droplets on GaAs (001) in MBE using RHEED patterns

Self-running Ga droplets on GaAs (001) surfaces are repeatedly and reliably formed in a molecular beam epitaxial (MBE) chamber despite the lack of real-time imaging capability of a low-energy electron microscope (LEEM) which has so far dominated the syntheses and studies of the running droplets phenomenon. Key to repeatability is the observation and registration of an appropriate reference point upon which subsequent sublimation conditions are based. The reference point is established using reflection high-energy electron diffraction (RHEED), not the noncongruent temperature used in LEEM where temperature discrepancies up to 25°C against MBE is measured. Our approach removes instrumental barriers to the observation and control of this complex dynamical system and may extend the usefulness of many droplet-related processes.

Self-running Ga droplets on GaAs (111)A and (111)B surfaces

Thermal decomposition of GaAs (111)A and (111)B surfaces in ultrahigh vacuum results in self-running Ga droplets. Although Ga droplets on the (111)B surface run in one main direction, those on the (111)A surface run in multiple directions, frequently taking sharp turns and swerving around pyramidal etch pits, leaving behind mixed smooth-triangular trails as a result of simultaneous in-plane driving and out-of-plane crystallographic etching. The droplet motion is partially guided by dislocation strain fields. The results hint at the possibilities of using subsurface dislocation network and prepatterned, etched surfaces to control metallic droplet motion on single-crystal semiconductor surfaces.

Origin of quantum ring formation during droplet epitaxy

Droplet epitaxy of GaAs is studied in real time using in situ surface electron microscopy. The resulting movies motivate a theoretical model for quantum ring formation which can explain the origin of nanoscale features such as double rings observed under a variety of experimental conditions. Inner rings correspond to GaAs deposition at the droplet edge, while outer rings result from the reaction of Ga and As atoms diffusing along the surface. The observed variety of morphologies primarily reflects relative changes in the outer rings with temperature and As flux.

Characterizing the geometry of InAs nanowires using mirror electron microscopy

Mirror electron microscopy (MEM) imaging of InAs nanowires is a non-destructive electron microscopy technique where the electrons are reflected via an applied electric field before they reach the specimen surface. However strong caustic features are observed that can be non-intuitive and difficult to relate to nanowire geometry and composition. Utilizing caustic imaging theory we can understand and interpret MEM image contrast, relating caustic image features to the properties and parameters of the nanowire. This is applied to obtain quantitative information, including the nanowire width via a through-focus series of MEM images.

Addendum. Laplacian image contrast in mirror electron microscopy

We extend the theory of Laplacian image contrast in mirror electron microscopy (MEM) to the case where the sample is illuminated by a parallel, collimated beam. This popular imaging geometry corresponds to a modern low energy electron microscope equipped with a magnetic objective lens. We show that within the constraints of the relevant approximations; the results for parallel illumination differ only negligibly from diverging MEM specimen illumination conditions.