Quantum-mechanical analysis of the elastic propagation of electrons in the Au/Si system: Application to ballistic-electron-emission microscopy

Abstract

We present a Green's function approach based on a LCAO scheme to compute the elastic propagation of electrons injected from a STM tip into a metallic film. The obtained 2D current distributions in real and reciprocal space furnish a good representation of the elastic component of Ballistic Electron Emission Microscopy (BEEM) currents. Since this component accurately approximates the total current in the near threshold region, this procedure allows -in contrast to prior analyses -to take into account effects of the metal band structure in the modeling of these experiments. The Au band structure, and in particular its gaps appearing in the [111] and [100] directions, provides a good explanation for the previously irreconcilable results of nanometric resolution and similarity of BEEM spectra on both Au/Si(111) and Au/Si(100).

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

“…Above 384 layers, the 6-fold symmetry is lost, and the results converge to the ones reported in Ref. [21]. The red curve has been obtained by making η negative; establishing that by exchanging the retarded and the advanced Green's functions the symmetry is recovered.…”

“…(5). Finally, the current at layer n + 1 can be written as an integral over a window of energies from Schottky's barrier φ SB to the applied voltage, eV [21]:…”

“…The study of the Au(111)/Si(111) and Au(111)/Si(001) interfaces was instrumental to demonstrating the critical role of the electronic band structure in BEEM propagation, as opposed to the initial use of a free-electron dispersion [11,21]. In this section, we (111) made with 10 layers only.…”

“…This concept can be illustrated in the simplest approximation; we follow the procedure in Ref [21], and we compare these currents with the available density of states in the projected 2D Brillouin zones for Si(001) and Si(111) respectively. The result is shown in figure 4.…”

Theory of real space imaging of Fermi surface parts

“…We see from the last equation [Eq. (22)] that the denominator is a crucial factor. If the denominator is very small meaning that the constant energy surface has a flat region, big values of the charge density are obtained from this k region, leading to a strong focusing of intensity in space region as determined by the group velocity v j .…”