| A new theory of Ballistic Electron Emission Microscopy (BEEM) is presented that incorporates both constant tunnel current feedback and the transmission coefficient for the entire BEEM apparatus without recourse to fitting parameters. Feedback is accomplished via an iterative root finding technique. The inclusion herein of a fully, self-consistent calculated feedback process—as exists in experiments—is the first known instance of such a mechanism in a BEEM model. The transmission coefficient of the entire BEEM apparatus is determined by considering all the key physical features of BEEM simultaneously, and coupling all these features together via boundary condition (BC) matching, as opposed to the piecemeal approach employed in the earlier BEEM models. Included in the full transmission coefficient are all the key physical components typical of BEEM, namely, the scanning tunneling microscope (STM) tip, the tip/metal overlayer interface, metal overlayer, the metal overlayer/semiconductor interface (Schottky barrier) and the semiconductor/metal electrical collector contact. In addition, two more key items incorporated into the model are detailed treatments of the Γ, L and X-point semiconductor conduction channels and the 3-dimensional k-space current injection dependency. The Γ, L and X-point analyses take into account the full symmetries of these points. A direct result of including symmetry is that now multiple current channels, i.e., several propagating and evanescent bands of various symmetries, can be included simultaneously in the analysis and these bands can all interact with one another. To motivate the development of this theory a review of earlier BEEM theories is presented. Thereafter, this new theory is presented and I-V predictions based upon it are made for experimentally controllable quantities (e.g., doping, temperature, metal overlayer thickness, tip size, tunnel current bias dependencies, etc.), after which a comparison of these predictions with available experimental data is presented. And lastly, comments are made as to possible future efforts that this model could be used to investigate. |
