ISSN 1063-7397, Russian Microelectronics, 2007, Vol. 36, No. 3, pp. 203–207. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © A.I. Aleksandrov, S.N. Dobryakov, V.V. Privezentsev, 2007, published in Mikroelektronika, 2007, Vol. 36, No. 3, pp. 236–240.
Isolated defects and complexes in solids have
recently come into focus owing to their potential use in
electron-spin quantum computers. In particular,
C complexes in diamond have been
proposed as a two-qubit quantum register. A CNOT
quantum logic gate has thus been implemented, operat-
ing at close to room temperature .
In silicon, Zn–P complexes were detected by electron-
spin resonance (ESR) by Dobryakov et al. . They can be
formed in the course of the pulling growth of n-type sili-
con doped with phosphorus and zinc. An alternative tech-
nique is phosphorus doping of monocrystalline silicon fol-
lowed by zinc diffusion compensation and annealing. The
Zn–P complex results from the interaction between one of
the two valence electrons of a Zn atom and a positively
charged P ion. It was identiﬁed by Dobryakov and
Privezentsev  as a two-spin system undergoing a sin-
glet-to-triplet transition (to
= 1) in the temperature range
from 300 down to 250 K, the conduction-electron density
in the silicon decreasing. The Zn–P interatomic distance
was estimated at 10 Å, or twice the Si lattice spacing.
Below, we present the results of an ab-initio calcu-
lation of the structure and the spatial electron-spin-den-
sity distribution for the Zn–P complex in a silicon host.
It is our hope that they will contribute to the implemen-
tation of an electron-spin qubit register based on this
complex. We also report a computer simulation of ESR
spectra for the Zn–P complex on the basis of previous
experimental results . Spectroscopic characteristics
of the two paramagnetic centers are thus evaluated.
2. AB-INITIO CALCULATION
In a Si lattice, we considered a cluster described by
the empirical formula ZnPSi
. It is formed from a
collection of Si atoms two of which are replaced by a
Zn and a P atom subject to the condition
the dangling Si bonds satisﬁed by H atoms . Cova-
lent bonding thus arises in the lattice. The structure of
the cluster is depicted by Fig. 1.
The structural relaxation of the cluster and the
distribution of the electron-spin density
atoms were determined by ab-initio calculation fol-
lowing the BLYP density-functional method [5, 6].
In doing so, we employed the Kohn–Sham theory [7,
8] and a basis set of Dunning–Hay double-exponent
atomic functions for heavy elements . The cluster
structure was fully optimized with the GAUSSIAN
98 software .
The quantities to be calculated were (i) the dis-
tances from the Zn and P atoms to their respective
neighboring Si atoms; (ii) the Si interatomic dis-
tances; and (iii) the electron-spin densities at the Zn,
P, and all the Si atoms.
Figure 2 is a bar chart representing the spin-density
distribution thus obtained. Notice that there are only
seven atoms having a nonzero spin density:
Zn–P Complex in Si: An Ab-Initio Calculation
of the Structure and Electron-Spin Properties
A. I. Aleksandrov
, S. N. Dobryakov
and V. V. Privezentsev
Institute of Synthetic Polymeric Materials, Russian Academy of Sciences, Moscow, Russia
N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia
Institute of Physics and Technology, Russian Academy of Sciences, Moscow, Russia
Received August 9, 2006
—An ab-initio calculation of the structure and electron-spin properties is performed for the Zn–P
complex in Si, which is considered to be a part of the ZnPSi
cluster. The distribution of electron-spin den-
sity is calculated over the Zn, P, and Si atoms of the cluster. Comparatively high spin densities are found to occur
at 1Zn, 2Si, and 13Si. The interatomic distances in the cluster are determined. ESR spectroscopic characteristics
of the Zn–P complex are evaluated by computer simulation on the basis of previous experimental results. The
ESR data obtained indicate a complicated nature of the spin exchange between the two paramagnetic centers.
PACS numbers: 72.25.Rb