Focusing of Electrons in LEEM by Patterned Surface Structures
Low energy electron microscopy (LEEM) is a surface sensitive reflection electron microscopy which allows real-time imaging of evolving structures with a spatial resolution of several nm. We have developed our own LEEM instrument at LPS, one of only a small number operating in the world, to study and control the topography of semiconductor surfaces at the nm scale during epitaxial growth, sublimation, gas-phase etching, ion bombardment, and other technologically important processes. In LEEM, surface sensitivity relies on low energy incidence, typically only a few eV. To use such low energies, and still form acceptably resolved images, a much higher electron energy is used for most of the optical path, and the electrons are decelerated in the region immediately in front of the sample. The sample thus sits within a strong electrostatic field, and thus becomes one element (the cathode) of an immersion objective lens. For flat surfaces, contrast in the images comes from variations in local atomic arrangement or composition. However, strongly varying topography alters the accelerating field locally and is expected to produce focusing effects, complicating analysis of the images. Surprisingly, to date there has been no systematic attempt to study these effects.
In recent work , we have used our LEEM to investigate these effects, imaging samples with strongly varying topography, Si(001) substrates lithographically patterned with arrays of cylindrical pits. Similarly patterned surfaces will be used in future studies of self assembly on the nm scale during regrowth of Si. Atomic force microscopy (AFM) shows the sidewalls of each pit to be abrupt, and the bottom of each pit to be flat, as is the surrounding surface.
Fig. 1. AFM map of topography of patterned Si(001) substrate.
Fig. 2. LEEM images of Si pit array. Incident energy (top to bottom) = -1 eV (mirror mode), 0.1 eV, 1 eV.
LEEM images of this array consist of a series of bright “dots”, whose diameters at optimum focus is approximately a factor of three smaller than that measured by AFM, indicating that the field associated with each pit focuses the initially collimated incident electron
Fig. 3. Calculated trajectories for a single Si pit of 0.8 micron diameter and 0.1 micron depth. Incident energy is 0.1 eV.
Fig. 4. Calculated variation of focal point with impact parameter and with incident energy for a single Si pit.
beam. The contrast in the image, as well as the apparent width of the bright spots varies strongly with incident energy. Our electron-optical trajectory calculations show an energy-dependent focusing which is in good semiquantitative agreement with that seen in the LEEM images, and indicate that each submicron-sized pit acts as an aberrated electron lens. Both our images and our calculations demonstrate that this effect is pronounced only at very low incident energies, approximately 1 eV or below. Imaging at higher energies than this should allow a straightforward interpretation of cellular patterns of steps which are expected to evolve around pits or protrusions during epitaxial growth, and which in turn will serve as a substrate for fabrication of quantum dot arrays.
 H. C. Kan and R. J. Phaneuf, J. Vac. Sci. and Technol., 19, 523 (2001).