Electron scattering by a large molecule:: Application to (n,n) nanotubes

Electron point projection microscopes, such as the Fresnel projection microscope (FPM), provide a convenient tool to observe large molecules, such as carbon nanotubes, over a long period of time, without risking destroying them. In this paper, a Green's function technique is used to simulate FPM images of(n,n) carbon nanotubes, with realistic distances, incident electron energies, and molecular potential. We show that, indeed, the resolution of the three-dimensional (3D) Schrodinger equation gives similar results to the Fresnel theory of diffraction by a 2D mask. Furthermore, the criterium, given by Fresnel theory, for observing the shape of the objects in the images is well verified. Finally our study of the influence of the widths and the lengths of the nanotubes on the images shows that for long nanotubes, the central fringe appears darker as the diameter of the tube is increased, in agreement with experiment. [S1050-2947(99)09609-2].