  After the discovery of GMR by Fert and Gr\"unberg, electronics had a
breakthrough with the birth of a new branch called spintronics. This
discipline, while still young, exploits the spin of electrons. Most quantum
devices exploiting this property of electrons consists of alternating magnetic
and nonmagnetic thin layers on a semiconductor substrate. One of the best tools
used for characterizing these structures is the so-called Ballistic Electron
Emission Microscope (BEEM). Originally, it was dedicated to the imaging of
buried objects and to the study of the potential barrier formed at the
interface of a metal and a semiconductor. With the development of spintronics,
the BEEM became an essential spectroscopy technique but still fundamentally
misunderstood. The first realistic model, based on the non-equilibrium Keldysh
formalism, was proposed to describe the transport of electrons during BEEM
experiments. However, despite its success, its use was limited to the study of
semi-infinite structures through a calculation method called decimation of
Green functions. In this context, we have extended this model to the case of
thin films and hetero-structures like spinvalves: starting from the same
postulate that electrons follow the band structure of materials in which they
propagate, we have established an iterative formula allowing calculation of the
Green functions of the finite system by tight-binding method and encoded it in
a F90 code. In parallel, we have developed a simpler method which allows to
avoid passing through the non-equilibrium Keldysh formalism. Despite its
simplicity, we have shown that this intuitive approach gives some physical
interpretation qualitatively similar to the non-equilibrium approach. However,
for a more detailed study, the use of "non-equilibrium approach" is inevitable,
especially for the detection of thickness effects linked to layer interfaces.
