I will present some results on double barrier structures in a semi-conductor. The resonances of the Hamiltonian of the system are well described when the plank constant h tends to zero by the eigenvalues of a perturbed Hamiltonian. In dimension 1, accounting that the density involved in the Schrodinger-Poisson system charges principally the resonant energies, it is possible to perform fast computation and to write a simplified model.

In dimension 2 and 3, similar asymptotic is obtained rigorously in the case of a bounded domain.