In structures with GaAs, which are the structures most used, because of their physical and electronic proprieties, nevertheless seems a compromise between the increase of doping and reduced mobility. The use of quantum hetero structures can overcome this limitation by creating a 2D carrier gas. Using the COMSOL software this work present three models: the first model computes the electronic states for the heterojunction AlGaAs/GaAs in 1D dimension, the second model computes the electronic states for the heterojunction AlGaAs/GaAs but in 2D dimension (nanowire) and the third model we permitted the study of this hetero junction (steep) wich inevitably involves the resolution of the system of equations Schrödinger-Poisson due to quantum effects that occur at the interface. The validity of this model can be effectuated with a comparison of our results with the result of different models developed in the literature of the related work, from this point of view the validity of our model is confirmed.

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The composing semiconductors became the support privileged of information and the communication, in particular grace to the faster development of Internet, for the systems of telecommunications to high debit, some components are necessary. It is for this reason that of the alternative structures have been proposed: the IV-IV heterostructures or III-V. The most effective components in this domain are the field effect transistors (High Electron Mobility Transistor: HEMT) on IIIV substratum. The present work is dedicated to the contribution to the development of a numeric physical model which based on the influence of the different parameters (physical and geometric) on the parameters characterizing the potential at the interface of a heterostructure in GaAsAl/GaAs. The present work also has aim to characterize dynamics carriers in a HEMT heterostructure which we will consider later a dynamic study of quantum well solar cells in a rigorous and complete manner.

The present work is dedicated to the numeric physical modelisation of the potential to the interface of a heterostructure in GaAsAl/GaAs. Calculs, using some projective methods, permitting the integration of Hamiltonian, with Green functions in the equation of Schrödinger, for a rigorous resolution with the equation of Poisson are elaborated. A study of convergence of globally no linear system is done and it confirmed for ten bases functions and a very determined electric wall position. The different parameter influence on performances of the GaAsAl/GaAs heterostructure is put in evidence; what will permit us subsequently to consider the dynamic of the carriers in a HEMT heterostructure by rigorous and complete manner.