Electron-Boundary Scattering in Quantum Wires

Abstract

To reduce the dimensionality of an electronic system it must be confined within artificially imposed boundaries. In the most idealized consideration of the problem, the properties of confined electrons depend solely upon the volume containing them. In all real systems, however, the characteristics of the boundaries themselves play a significant role in the physics observed. Recent advances in epitaxial growth techniques now permit nearly ideal heterointerfaces to be created over appreciable areas. But even for these, the crystallographic (and therefore the electronic) properties at the surfaces are quite different that those of the bulk. Recent dramatic demonstrations of surface reconstructions obtained through scanning tunneling microscopy provide a particularly striking example. However the more general situation is even far from this ideal. Any real boundary, when viewed over a large enough area, always reveals randomness. In the case of the best epitaxially-grown interfaces this will be manifested as a finite domain size for the last few atomic layers, as schematically depicted in Fig. 1 (left). The edges of these domains delineate random patches of surfaces in registry with the underlying crystal. A quantum well between two such interfaces would be characterized by a thickness which varies stochastically across the growth plane.