Valley splitting in low-density quantum-confined heterostructures studied using tight-binding models

Timothy B. Boykin, Electrical and Computer Engineering, University of Alabama
Gerhard Klimeck, Jet Propulsion Laboratory, California Institute of Technology; Network for Computational Nanotechnology, Purdue University
Mark Friesen, Physics, University of Wisconsin, Madison; Material Science and Engineering, University of Wisconsin, Madison
S N. Coopersmith, Physics, University of Wisconsin, Madison
Paul von Allmen, Jet Propulsion Laboratory, California Institute of Technology
Fabiano Oyafuso, Jet Propulsion Laboratory, California Institute of Technology
Seungwon Lee, Jet Propulsion Laboratory, California Institute of Technology

Abstract

A detailed study of reduced-basis tight-binding models of electrons in semiconducting quantum wells is presented. The focus is on systems with degenerate valleys, such as silicon in silicon germanium heterostructures, in the low-density limit, relevant to proposed quantum computing architectures. Analytic results for the bound states of systems with hard-wall boundaries are presented and used to characterize the valley splitting in silicon quantum wells. The analytic solution in a no-spin-orbit model agrees well with larger tight-binding calculations that do include spin-orbit coupling. Numerical investigations of the valley splitting for finite band offsets are presented that indicate that the hard-wall results are a good guide to the behavior in real quantum wells.