Electron transport in ultra-thin films and ballistic electron emission microscopy

Abstract

We have developed a calculation scheme for the elastic electron current in ultra-thin epitaxial heterostructures. Our model uses a Keldysh’s non-equilibrium Green’s function formalism and a layer-by-layer construction of the epitaxial film. Such an approach is appropriate to describe the current in a ballistic electron emission microscope (BEEM) where the metal base layer is ultra-thin and generalizes a previous one based on a decimation technique appropriated for thick slabs. This formalism allows a full quantum mechanical description of the transmission across the epitaxial heterostructure interface, including multiple scattering via the Dyson equation, which is deemed a crucial ingredient to describe interfaces of ultra-thin layers properly in the future.We introduce a theoretical formulation needed for ultra-thin layers and we compare with results obtained for thick Au(1 1 1) metal layers. An interesting effect takes place for a width of about ten layers: a BEEM current can propagate via the center of the reciprocal space () along the Au(1 1 1) direction. We associate this current to a coherent interference finite-width effect that cannot be found using a decimation technique. Finally, we have tested the validity of the handy semiclassical formalism to describe the BEEM current.