Focal Point "Cusp" Seen in Electron Imaging Data
Eric J. Heller
Simulations undertaken to understand the branched flow discovered experimentally in semiconductor two degree of freedom electron gases have shown that electrons flowing through them are subject to focusing by "lenses" which are accumulations of relative positive charge, to which they are attracted. Simulations based on ray tracing the electrons through such devices show focal cusps; these showed up in the experimental data as well. The images below show the theory and the experiment revealing a focal cusp on the submicron scale:
On the right we see a focal cusp as determined by ray tracing in a simulation of electron paths in a two degree of freedom electron gas. Darker regions are where more electrons have traveled. On the left is experimental data with an arrow pointing to the focus of a cusp seen in an electron imaging experiment. Quantum fringing is also seen, and a theoretical wave simulation of what that fringing should look like is given in the upper left as a yellow contour map. The match is very good, showing that an accumulation of relative positive charge must exist in the device in the right hand region of the panel, causing the electron focusing.