Orbital Stark effect and quantum confinement transition of donors in silicon

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Rajib Rahman,¹ G. P. Lansbergen,² Seung H. Park,¹ J. Verduijn,² Gerhard Klimeck,^1,3 S. Rogge,² and Lloyd C. L. Hollenberg⁴
¹Network for Computational Nanotechnology, Purdue University, West Lafayette, Indiana 47907, USA
²Kavli Institute of Nanoscience, Delft University of Technology, Delft, Lorentzweg 1, 2628 CJ Delft, The Netherlands
³Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109, USA
⁴Center for Quantum Computer Technology, School of Physics, University of Melbourne, Victoria 3010, Australia

Received 28 April 2009; revised 21 July 2009; published 9 October 2009

Adiabaticshuttling of single impurity bound electrons to gate-induced surface statesin semiconductors has attracted much attention in recent times, mostlyin the context of solid-state quantum computer architecture. A recenttransport spectroscopy experiment for the first time was able toprobe the Stark shifted spectrum of a single donor insilicon buried close to a gate. Here, we present thefull theoretical model involving large-scale quantum mechanical simulations that wasused to compute the Stark shifted donor states in orderto interpret the experimental data. Use of atomistic tight-binding techniqueon a domain of over a million atoms helped notonly to incorporate the full band structure of the host,but also to treat realistic device geometries and donor models,and to use a large enough basis set to captureany number of donor states. The method yields a quantitativedescription of the symmetry transition that the donor electron undergoesfrom a three-dimensional Coulomb confined state to a two-dimensional (2D)surface state as the electric field is ramped up adiabatically.In the intermediate field regime, the electron resides in asuperposition between the atomic donor states and the 2D surfacestates. In addition to determining the effect of field anddonor depth on the electronic structure, the model also providesa basis to distinguish between a phosphorus and an arsenicdonor based on their Stark signature. The method also capturesvalley-orbit splitting in both the donor well and the interfacewell, a quantity critical to silicon qubits. The work concludeswith a detailed analysis of the effects of screening onthe donor spectrum.

URL:	http://link.aps.org/doi/10.1103/PhysRevB.80.165314
DOI:	10.1103/PhysRevB.80.165314
PACS:	71.70.Ej; 03.67.Lx; 71.55.Cn 71.70.Ej Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect (condensed matter) 03.67.Lx Quantum computation architectures and implementations 71.55.Cn Impurity and defect levels in elemental semiconductors YEAR: 2009
KEYWORDS:	arsenic, band structure, elemental semiconductors, impurity states, phosphorus, quantum computing, silicon, Stark effect, surface states, tight-binding calculations

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