A theoretical analysis of ballistic electron emission microscopy: k-space distributions and spectroscopy

We present a theoretical framework well suited to analyze ballistic electron emission microscopy (BEEM) experiments. At low temperatures and low voltages, near the threshold value of the Schottky barrier, the BEEM current is dominated by the elastic component. Using a Keldysh Greenʹs functions method, we analyze the injected distribution of electrons and the subsequent propagation through the metal. Elastic scattering by the lattice results in the formation of focused beams and narrow lines in real space. To obtain the current injected in the semiconductor, we compute the current distribution in reciprocal space and, assuming energy and k∼ conservation, we match states to the projected conduction band minima of the semiconductor. Our results show an important focalization of the injected electron beam and explain the similarity between BEEM currents for Au/Si(111) and Au/Si(100).