Theory of ballistic electron emission microscopy

The present status of theories for interpreting experimental ballistic electron emission microscopy (BEEM) data is reviewed. Current formalisms may be divided into two broad classes: one-electron theories, where carriers do not exchange energy with other excitations in the solid, and scattering approaches, where such losses are considered. While the former theories have been formulated with the help of Green's functions (GFs), the latter have relied more on simulation by Monte-Carlo techniques. For the one-electron approach, we discuss why the originally suggested free propagation of carriers (e.g., ballistic electrons) does not offer a consistent interpretation of the experimental database and should be replaced instead by considering the coherent propagation of electrons interacting with the periodic potential in the metal base. Bridging towards the scattering formalisms, it is shown how GFs incorporating a complex self-energy are still a feasible approach, when only a single inelastic source of scattering (e.g., electron–electron (e–e) interaction) is operative. Within this one-electron scheme, the importance of an accurately computed transmission coefficient at the metal-semiconductor interface is stressed, when aiming to obtain absolute BEEM currents. Analyzing results from scattering techniques, it is argued that this coefficient should be modified to take into account the back-injection of electrons from the semiconductor into the metal. A general expression for BEEM currents is given that can be used to simulate results in real-space, reciprocal-space or energy-space (spectroscopy with BEEM). Some experimental results are discussed in relation to the theories presented.