Valley Splitting in V-Shaped Quantum Wells

Timothy B. Boykin, University of Alabama - Huntsville
Gerhard Klimeck, Network for Computational Nanotechnology, Purdue University
Paul von Allmen, JPL, Cal Tech
Seungwon Lee, JPL, Cal Tech
Fabiano Oyafuso, JPL, Cal Tech

Date of this Version



Journal of Applied Physics 97, 113702 (2005).


We especially acknowledge interesting discussions with S. N. Coppersmith; we also thank M. Friesen, R. Joynt, and M. A. Eriksson for useful conversations. Work at JPL and UAH sponsored in major proportion by the U.S. Army Research Office through the ARDA program and directly through ARDA. The work at Purdue was supported by the National Science Foundation, Grant No. EEC-0228390. part of the work described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology under a contract with the National Aeronautics and Space Administration. Funding was provided at JPL under grants from ARDA, ONR, and JPL.


The valley splitting 􏰀energy difference between the states of the lowest doublet􏰁 in strained silicon quantum wells with a V-shaped potential is calculated variationally using a two-band tight-binding model. The approximation is valid for a moderately long 􏰀approximately 5.5 – 13.5 nm􏰁 quantum well with a V-shaped potential which can be produced by a realistic delta-doping on the order of nd 􏰈 1012 cm−2. The splitting versus applied field 􏰀steepness of the V-shaped potential􏰁 curves show interesting behavior: a single minimum and for some doublets, a parity reversal as the field is increased. These characteristics are explained through an analysis of the variational wave function and energy functional.