Relation between lattice order and energy-resolved momentum densities in carbon films

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Abstract
The (e,2e) technique is well known to be able to measure the momentum profiles of the electron orbitals in molecules. In crystalline solids energy levels are replaced by bands, and the momentum profiles simplify to energy-dependent δ functions. In this paper the development from a molecular to a crystalline picture of the electronic structure is illustrated using a simple model of a linear chain of atoms of increasing length. From this model we try to get some insight into the (e,2e) momentum profiles expected for disordered solids. These results are compared to the experimental data for carbon films with 6 different degrees of order, i.e., amorphous carbon films, annealed amorphous carbon films, and highly oriented pyrolitic graphite (HOPG) films. The intensity of the π-electron contribution is suppressed in HOPG, due to the orientation chosen. In the annealed evaporated samples, the planes of graphite atoms have random orientation and the π electrons are clearly seen. With increasing order the momentum profiles show increasingly well defined peaks.