Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{ö}dinger-Poisson system and a reduced nonlinear model

Virginie Bonnaillie-Noël (1) , Ali Faraj (2) , Francis Nier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 MIP - Mathématiques pour l'Industrie et la Physique

Two different models are compared for the simulation of the transverse electronic transport through an heterostructure: a $1D$ self-consistent Schr{ö}dinger-Poisson model with a numerically heavy treatment of resonant states and a reduced model derived from an accurate asymptotic nonlinear analysis. After checking the agreement at the qualitative and quantitative level on quite well understood bifurcation diagrams, the reduced model is used to tune double well configurations for which nonlinearly interacting resonant states actually occur in the complete self-consistent model.

Mots clés: resonant tunneling diode; Schrödinger-Poisson system

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Virginie Bonnaillie-Noël, Ali Faraj, Francis Nier. Simulation of resonant tunneling heterostructures: numerical comparison of a complete Schr{ö}dinger-Poisson system and a reduced nonlinear model. 2008. ⟨hal-00267725⟩