S. M. Kennedy

Caustic imaging of gallium droplets using mirror electron microscopy

We discuss a new interpretation of mirror electron microscopy (MEM) images, whereby electric field distortions caused by surface topography and/or potential variations are sufficiently large to create caustics in the image contrast. Using a ray-based trajectory method, we consider how a family of rays overlaps to create caustics in the vicinity of the imaging plane of the magnetic objective lens. Such image caustics contain useful information on the surface topography and/or potential, and can be directly related to surface features. Specifically we show how a through-focus series of MEM images can be used to extract the contact angle of a Ga droplet on a GaAs (001) surface.

Laplacian image contrast in mirror electron microscopy

We discuss an intuitive approach to interpreting mirror electron microscopy (MEM) images, whereby image contrast is primarily caused by the Laplacian of small height or potential variations across a sample surface. This variation is blurred slightly to account for the interaction of the electrons with the electrical potential away from the surface. The method is derived from the established geometrical theory of MEM contrast, and whilst it loses quantitative accuracy outside its domain of validity, it retains a simplicity that enables rapid interpretation of MEM images. A strong parallel exists between this method and out of focus contrast in transmission electron microscopy (TEM), which allows a number of extensions to be made, such as including the effects of spherical and chromatic aberration.

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.

WAVE OPTICAL TREATMENT OF SURFACE STEP CONTRAST IN LOW-ENERGY ELECTRON MICROSCOPY

A wave optical treatment of surface step contrast in a low-energy electron microscopy (LEEM) is presented. The aberrations of an idealised LEEM imaging system are directly incorporated into a transfer function (TF) and image simulations of surface steps are evaluated in one and two dimensions. Under the special circumstances of a weak phase object, the simplified form of the contrast transfer function (CTF) is used to discuss LEEM image contrast and optimum defocus conditions.

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.

Laplacian and caustic imaging theories of MEM work-function contrast

We apply geometrical, Laplacian, and caustic imaging theories to simulate the mirror electron microscope (MEM) contrast arising from a surface phase boundary associated with a discontinuity in work function. The key approximations inherent in the theories are highlighted and investigated within strong and weak scattering regimes from the work-function test object. For strongly varying potentials, the approximation that the electron classical turning distance is unchanged fails, invalidating the quantitative accuracy of the geometrical and Laplacian approaches. For sufficiently small defocus and surface height or potential variations, the Laplacian approach facilitates an intuitive interpretation of MEM contrast.

Phase retrieval low energy electron microscopy

We consider the utility of phase-retrieval methods in low energy electron microscopy (LEEM). Computer simulations are presented, demonstrating recovery of the terraced height profile of atomic steps. This recovery uses phase retrieval to decode a single LEEM image, incorporating the effects of defocus, spherical aberration and chromatic aberration. The ability of the method, to obtain temporal sequences of evolving step profiles from a single LEEM movie, is discussed.

Transition between short and long wavelength limits in quantum mechanical reflection from a linear potential

The phase changes experienced by a wave reflected from an interface are a familiar fixture in introductory physics courses. Examples include the ±π phase shift acquired upon reflection from a hard mirror (for example, in thin film interference patterns and Newton’s rings) and the −π∕2 phase shift studied in soft mirror reflections (for example, in mirage ray paths and the WKB connection formulas). We focus on the transition between these two limits, where the phase change upon reflection evolves continuously between the limiting cases of −π and −π∕2. We study a simple quantum system that exhibits this transition: a one-dimensional free electron reflected from a linear potential.

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.

Electron caustic lithography

A maskless method of electron beam lithography is described which uses the reflection of an electron beam from an electrostatic mirror to produce caustics in the demagnified image projected onto a resist–coated wafer. By varying the electron optics, e.g. via objective lens defocus, both the morphology and dimensions of the caustic features may be controlled, producing a range of bright and tightly focused projected features. The method is illustrated for line and fold caustics and is complementary to other methods of reflective electron beam lithography.