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Title: Homogenization limit for a multiband effective mass model in heterostructures

We study the homogenization limit of a multiband model that describes the quantum mechanical motion of an electron in a quasi-periodic crystal. In this approach, the distance among the atoms that constitute the material (lattice parameter) is considered a small quantity. Our model include the description of materials with variable chemical composition, intergrowth compounds, and heterostructures. We derive the effective multiband evolution system in the framework of the kp approach. We study the well posedness of the mathematical problem. We compare the effective mass model with the standard kp models for uniform and non-uniforms crystals. We show that in the limit of vanishing lattice parameter, the particle density obtained by the effective mass model, converges to the exact probability density of the particle.
Authors:
 [1]
  1. Institut de Physique et Chimie des Matériaux de Strasbourg, 23 rue du Loess, F-67034 Strasbourg (France)
Publication Date:
OSTI Identifier:
22306208
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CRYSTALS; DENSITY; EFFECTIVE MASS; ELECTRONS; LATTICE PARAMETERS; QUANTUM MECHANICS