On the theory of the lateral resolution of BEEM

We study the origin of the nanometric resolution seen in BEEM experiments. The problem is separated in three steps: (1) tunnelling from the STM tip to the metal, (2) elastic propagation in the metallic layer, and (3) overcoming the Schottky barrier in the metal-semiconductor interface. For the first step we apply an LCAO model and a Green's functions formalism due to Keldysh. The second step is investigated extending our formulation for step 1. To compute the necessary Green's functions we use an asymptotic approximation for thick layers where metallic band structure effects are included, and a decimation technique for thin layers. The third step is analyzed by looking at the matching of the incoming electrons and the available states in the semiconductor. For thick metallic layers (approximate to 100 - 150 Angstrom), the elastic interaction between propagating electrons and the metallic periodic lattice results in a few focalized beams of nanometric size, providing a simple explanation for the observed resolution For thin metallic layers (approximate to 20 - 50 Angstrom), we study the propagation layer by layer and we analyze the distribution of current as a function of the depth in the metal.