ABSTRACT
Several solid-state quantum information processor proposals are
based on silicon [16-18, 20, 52], including the original architecture
conceived by Kane in 1998 [22], in which the quantum information
was stored in the spin states of 31P donors. The interest raised
by silicon in the field of quantum information is twofold. On the
one hand, it represents the main semiconductor used for large-
scale fabrication. On the other hand, it owns interesting physical
properties suitable for preserving andmanipulating quantum states,
such as long coherence times and relatively low disturbance of
nuclear spins, which are further enhanced by employing purified 28Si. The employment of individual donors in silicon covers all
the aspects of quantum information encoding and processing, like
quantumbit (qubit) storage, implementation of quantum logic gates,
coherent transfer of quantum states, and readout schemes. This
chapter is devoted to the physics of few dopants in nanometric
silicon devices and their applications to quantum information
processing purposes. In the first part, an overview of the physics of
themost common donors and acceptors in silicon is presented. Next,
the quantum information key concepts and their implementation
in donor-based architectures are discussed. Finally, decoherence
effects and the concept of measurement of quantum states are
presented for the case of electron states bound to donors in silicon.
Between the sixties and the early eighties of the twentieth century,
all the theoretical and experimental aspects related to the doping
of bulk silicon have been investigated and explained. A silicon
crystal consists of a diamond lattice constituted by two interleaved
cubic lattices (face-centered cubic, FCC), the second of which has
the origin in the center of the tetrahedron given by the origin
(0,0,0) and the centers of the faces 100. Each Si atom has four
valence electrons, which create a covalent bond with the shared
electrons of four other Si atoms. The substitution of silicon atoms
with atoms of a group V element (indicated as donors, typically P, As,
and Sb in silicon) generates an n-doped silicon crystal (n-Si). Each donor introduces an eccess electron in the crystal, and it provides
new energy levels in the band gap, close to the conduction band
edge. Similarly, substituting silicon atoms with atoms of a group
III element (an acceptor, typically B in silicon) generates a p-doped silicon crystal (p-Si). Each acceptor introduces an electron hole in the crystal, and it provides new energy levels in the band gap, close
to the valence band. The diffusion of impurities in semiconductors
alters the conduction properties from an insulating to a metallic
regime. Depending on the different doping concentration, the
wavefunction of the electron (hole) states introduced by each
donor (acceptor) may overlap negligibly or substantially with those
of neighboring sites. Such a transition from low doping to high
doping as a function of the average distance between neighboring
sites is described in terms of an Anderson-Mott transition and
produces additional impurity bands (Hubbard bands) below the
conduction band edge at sufficiently high concentration [1, 34]. The
transport is governed by mechanisms based on localized states at
low density, while it is based on delocalized states at high density.
Four conventional regimes of impurity concentration are defined
[50]. The dilute concentration of impurities holds for n < 1 · 1016 cm−3. There, the problem of the donor is that of a hydrogen atom with a scaled Rydberg and radius. Between the densities n of 1 ·1016 cm−3 and 2 · 1017 cm−3 (rNN = 11.9 nm), respectively, the regime is called semidilute, and it is characterized by formation of pairs. Above
2 · 1017 cm−3 and below the metallic behavior, which occurs at 3.7 · 1018 cm−3, the regime is called intermediate, and the formation of random clusters leads to effects generally accounted by the Hubbard
band formation. Above n > 3.7 · 1018 cm−3, silicon is treated as a metal. In this section the physics of the first three regimes of donor
concentration and the Anderson-Mott transition are described. The
Anderson-Mott transition has been observed down to microscopic
scale by employing arrays of few deterministically implanted As
ions (see chapter 5) in Si transistors [39]. Analogous arguments and
treatment can be given to acceptor concentration regimes.
