Engineered Valley-Orbit Splittings in Quantum-Confined Nanostructures in Silicon

Rajib Rahman, Sandia National Laboratories
J. Verdujin, Delft University of Technology, Delft, The Netherlands
Neerav Kharche, Rensselaer Polytechnic Institute
Gabriel Lansbergen, Delft University of Technology, Delft, The Netherlands
Purdue University Gerhard Klimeck, Purdue University - Main Campus
Lloyd Hollenberg, University of Melbourne
Sven Rogge, University of New South Wales

Date of this Version



Phys. Rev B 83 195323 (2011)


This is the published version of R. Rahman, J. Verduijn, N. Kharche, G. P. Lansbergen, G. Klimeck, L. C. L. Hollenberg, and S. Rogge. (26 May 2011). Engineered valley-orbit splittings in quantum-confined nanostructures in silicon. First published in the Physical Review B and is available online at:


An important challenge in silicon quantum electronics in the few electron regime is the poten- tially small energy gap between the ground and excited orbital states in 3D quantum confined nanostructures due to the multiple valley degeneracies of the conduction band present in silicon. Understanding the “valley-orbit” (VO) gap is essential for silicon qubits, as a large VO gap prevents leakage of the qubit states into a higher dimensional Hilbert space. The VO gap varies considerably depending on quantum confinement, and can be engineered by external electric fields. In this work we investigate VO splitting experimentally and theoretically in a range of confinement regimes. We report measurements of the VO splitting in silicon quantum dot and donor devices through excited state transport spectroscopy. These results are underpinned by large-scale atomistic tight-binding calculations involving over 1 million atoms to compute VO splittings as functions of electric fields, donor depths, and surface disorder. The results provide a comprehensive picture of the range of VO splittings that can be achieved through quantum engineering.


Nanoscience and Nanotechnology