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This paper is devoted to the numerical study, using the deterministic particle method, of the parallel transport of a bidimensional electron gas confined in a potential well near a heterojunction interface. The geometry makes it possible to solve independently the transport under the electric field and the well shape. We simulate the electronic transport with a kinetic model and use the deterministic particle method. As for the description of the potential well, we use different models and compare their influence on the thermodynamic equilibrium and on the transport properties of the electron gas.

The progress of semiconductor fabrication technology, particularly the heteroepitaxial technology (MOCVD, MBE, etc.) has permitted the fabrication of structures and devices whose behaviour is dominated by ballistic and/or quantum‐interference effects through heterojunctions.

Presents a simplified mathematical model of electron transport in a one‐dimensional semiconductor device of N+ ‐ N ‐ N + type. The model is based on a singular perturbation approach of the kinetic equation which describes the transport processes. This so‐called Child‐Langmuir asymptotics is obtained by assuming that the injected electrons at the N + ‐ N junction on the source side have a very weak energy compared with what they are able to gain under the influence of the electric field. Formally establishes the limit model when a realistic collision model for electron‐phonon interaction is considered. Compares the results with both experiments and particle simulations.