Spintronics is now a major challenge at the international level with the prospect of manipulating, storing and transporting the electron spin in semiconductors. This will lead to a whole new family of much faster devices, working at low power, including programmable spin transistors. It has been demonstrated that the efficiency of spin injection is strongly dependent on the structure of the interface between the layers involved, and therefore it is essential to be able to characterize the structural and electronic properties of these interfaces, and study the transport through all the layers. Ballistic Electron Emission Microscopy (BEEM) is a tool that was specifically designed for this purpose. It is based on Scanning Tunnelling Microscopy (STM) and consists in the injection of electrons from the STM tip across a tunnelling gapinto a thin metal layer that forms with a semiconductor substrate a Schottky barrier. At the metal/semiconductor interface, the Schottky barrier only allows a fraction of them to pass and be detected as the BEEM current. This enables in particular to study the spatial dependence of transport in buried interfaces. However, actual theoretical models to describe BEEM are based on band structure or k-space Green's function methods, and do not take into account the shape and size of the STM tip, although there is clear experimental evidence that these parameters strongly affect the properties on the electron current. Real Space Multiple Scattering (RS-MS) is a framework where this effect can be taken into account properly to give a true real space description of BEEM. The purpose of this proposal is to devise a completely new description of BEEM using the flexible RS-MS framework, in order to better understand the transport properties of the spin carried by electrons inheterostructures associating magnetic electrodes and semiconductors. These heterostructures are at the core of the research for spin injection.