Control of the valley degree of freedom of donor electrons near a Si/SiO2 interface
A. Baena,1 A.L. Saraiva,2 Belita Koiller,2 and M.J. Calderon1
1Instituto de Ciencia deMateriales de Madrid, ICMM-CSIC, Cantoblanco, E-28049 Madrid, Spain
2Instituto de Fisica, Universidade Federal do Rio de Janeiro,
Caixa Postal 68528, 21941-972 Rio de Janeiro, Brazil(Dated: March 29, 2012)
We analyze the valley composition of one electron bound to a shallow donor close to a Si/barrier
interface as a function of an applied electric eld. A fullsix-valley eective mass model Hamiltonian
is adopted. For low elds, the electron ground state is essentially conned at the donor. At high
elds the ground state is such thatthe electron is drawn to the interface, leaving the donor practically
ionized. Valley splitting at the interface occurs due to the valley-orbit coupling, V I
vo = jV I
vojei. Atintermediate electric elds, close to a characteristic shuttling eld, the electron states may constitute
hybridized states with valley compositions dierent from the donor andthe interface ground states.
The full spectrum of energy levels shows crossings and anti-crossings as the eld varies. The degree of
level repulsion, thus the width of theanti-crossing gap, depends on the relative valley compositions,
which vary with jV I
voj, and the interface-donor distance. We focus on the valley congurations of
the states involvedin the donor-interface tunneling process, given by the anti-crossing of the three
lowest eigenstates. A sequence of two anti-crossings takes place and the complex phase aectsthe symmetries of the eigenstates and level anti-crossing gaps. We discuss the implications of our
results on the practical manipulation of donor electrons in Si nanostructure.
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