A Theoretical Analysis of Ballistic Electron Emission Microscopy: Band Structure Effects and Attenuation Lengths

Using a quantum mechanical approach, we compute the ballistic electron emission microscopy current distribution in reciprocal space to compare experimental and theoretical spectroscopic I(V) curves. In the elastic limit, this formalism is a "parameter-free" representation of the problem. At low voltages, low temperatures, and for thin metallic layers, the elastic approximation is enough to explain the experiments (ballistic conditions). At low temperatures, inelastic effects can be taken into account approximately by introducing an effective electron-electron lifetime as an imaginary part in the energy. Ensemble Monte Carlo calculations were also performed to obtain ballistic electron emission microscopy currents in good agreement with the previous approach.