Orbital Start effect and quantum confinement transition of donors in silicon

Rajib Rahman, Network for Computational Nanotechnology, Purdue University
G. P. Lansbergen, Kavli Institute of Nanoscience
Seung H. Park, Network for Computational Nanotechnology, Purdue University
J. Verdujin, Kavli Institute of Nanoscience
Gerhard Klimeck, Network for Computational Nanotechnology, Purdue University
S. Rogge, Kavli Institute of Nanoscience
Lloyd C. L. Hollenberg, Center for Quantum Computer Technology, University of Melbourne

Date of this Version



Physical Review B 80, 1


This work was supported by the Australian Research Council, the Australian Government, and the U.S. National Seccurity Agency (NSA) and the Army Research Office (ARO) under Contract No. W911NF-08-1-0527. Part of the development of NEMO-3D was initially performed at JPL, Caltech under a contract with NASA. NCN/nanohub.org computational resources wee used in this work. S.R. also acknowledges the support of Dutch Foundation for Fundamental Research on Matter (FOM) and the EU FP7 project AFSID.

This document has been peer-reviewed.



Adiabatic shuttling of single impurity bound electrons to gate-induced surface states in semiconductors has attracted much attention in recent times, mostly in the context of solid-state quantum computer architecture. A recent transport spectroscopy experiment for the first time was able to probe the Stark shifted spectrum of a single donor in silicon buried close to a gate. Here, we present the full theoretical model involving large-scale quantum mechanical simulations that was used to compute the Stark shifted donor states in order to interpret the experimental data. Use of atomistic tight-binding technique on a domain of over a million atoms helped not only 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 capture any number of donor states. The method yields a quantitative description of the symmetry transition that the donor electron undergoes from 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 a superposition between the atomic donor states and the 2D surface states. In addition to determining the effect of field and donor depth on the electronic structure, the model also provides a basis to distinguish between a phosphorus and an arsenic donor based on their Stark signature. The method also captures valley-orbit splitting in both the donor well and the interface well, a quantity critical to silicon qubits. The work concludes with a detailed analysis of the effects of screening on the donor spectrum.


Orbital Stark effect, quantum confinement


Nanoscience and Nanotechnology