Theory of ballistic electron emission microscopy

The present status of theories for interpreting experimental ballistic elec tron emission microscopy (BEEM) data is reviewed. Current formalisms may be divided into two broad classes: one-electron theories, where carriers do n ot exchange energy with other excitations in the solid, and scattering appr oaches, where such losses are considered. While the former theories have be en formulated with the help of Green's functions (GFs), the latter have rel ied more on simulation by Monte-Carlo techniques. For the one-electron appr oach, we discuss why the originally suggested free propagation of carriers (e.g., ballistic electrons) does not offer a consistent interpretation of t he experimental database and should be replaced instead by considering the coherent propagation of electrons interacting with the periodic potential i n the metal base. Bridging towards the scattering formalisms, it is shown h ow GFs incorporating a complex self-energy are still a feasible approach, w hen only a single inelastic source of scattering (e.g., electron-electron ( e-e) interaction) is operative. Within this one-electron scheme, the import ance of an accurately computed transmission coefficient at the metal-semico nductor interface is stressed, when aiming to obtain absolute BEEM currents . Analyzing results from scattering techniques, it is argued that this coef ficient should be modified to take into account the back-injection of elect rons from the semiconductor into the metal. A general expression for BEEM c urrents is given that can be used to simulate results in real-space, recipr ocal-space or energy-space (spectroscopy with BEEM). Some experimental resu lts are discussed in relation to the theories presented. (C) 2001 Elsevier Science Ltd. All rights reserved.