ISSN 1063-7397, Russian Microelectronics, 2009, Vol. 38, No. 3, pp. 186–198. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © A.N. Voron’ko, 2009, published in Mikroelektronika, 2009, Vol. 38, No.3, pp. 204–216.
Due to its unique properties, silicon incessantly
attracts considerable interest as one of the most impor-
tant materials of the entire semiconductor industry. An
especially topical area of research is the studies of
doped silicon. The basic feature of the impurities is
their capability for radically modifying the properties
of semiconductors: impurities induce localized states in
the energy spectra, mostly in the band gap of semicon-
ductors. Depending on the occupancy of impurity states
by electrons, impurities are divided into donors and
acceptors, and depending on the energy of the corre-
sponding localized state, impurities can be shallow and
deep. For each type of impurity, there exist proper
approaches providing an adequate description of partic-
ular impurities .
In microelectronics, shallow impurities are used
most extensively: when admixed to a semiconductor,
such dopants substantially change the conductivity of
the semiconductor. For silicon, one such dopant is
phosphorus. In this context, a problem arises to study
phosphorus complexes, e.g., embedded in silicon
Si). As the concentration of the dopants is
increased, the number of such complex defects
increases, and in this case, just these defects control the
hopping conductivity in silicon.
The experimental achievements in developing elec-
tronic devices with atomic-length-scale dimensions and
in observing and probing solitary electron spins and
elementary charges also stimulate interest in structures
Si. In future, these achievements will make it
possible to control the coherent evolution of electrons
localized in the vicinity of individual donors, speciﬁ-
cally, in order to develop a quantum computer [2, 3].
Therefore, it is extremely important to be able to pre-
dict the possible behavior of such devices.
In this study, I analyze the properties of the
system with the purpose of determining its characteris-
tics important not only for the experimental detection
of such complexes, but also for the use of the
structure as a carrier of quantum information.
The paper is arranged in the manner brieﬂy
described below. In Section 2, I describe the method of
calculations. In Section 3, I present the results of calcu-
lations of the dipole matrix elements of individual
phosphorus atoms in silicon and in the
In Section 4, I discuss and brieﬂy summarize the
2. THE METHOD OF CALCULATING
THE ENERGY SPECTRUM AND WAVE
FUNCTIONS OF THE INDIVIDUAL
PHOSPHORUS DONOR AND THE DIMER
It is known that the conduction band of the silicon
crystal involves six equivalent ellipsoidal minima along
the  directions in the reciprocal space of the crys-
tal lattice. The corresponding ellipsoidal valleys are
described by the longitudinal and transverse electron
is the free electron mass). As shown in
, the total wave function of an electron in the vicinity
Analysis of the Dipole Matrix Elements of Electronic Optical
Transitions in the
A. N. Voron’ko
Moscow Engineering Physics Institute (State University), Moscow, 115409 Russia
Received August 17, 2008
—This study is concerned with a singly ionized pair of phosphorus donors in the silicon crystal lattice.
The results of numerical calculations of the energy spectrum and dipole matrix elements in such a system are
reported. The conditions, in which the
Si system can be used in the implementation of quantum operations
with resonance laser pulses, are determined. Estimation of the time of such operations yields ~10 ps.
PACS: 73.22.-f, 78.67.-n, 71.55.-i, 85.35.-p
MODELING AND SIMULATION