1063-7397/04/3306- © 2004 MAIK “Nauka /Interperiodica”
Russian Microelectronics, Vol. 33, No. 6, 2004, pp. 362–372. Translated from Mikroelektronika, Vol. 33, No. 6, 2004, pp. 445–458.
Original Russian Text Copyright © 2004 by Zhukov, Bagraev, Titov, Zhurkin.
Recent years have seen numerous attempts to
achieve implantation delta-doping of monocrystalline
semiconductors in both vertical and lateral directions
. One reason for these efforts is that heavily doped
delta-barriers could be used to make silicon nanostruc-
tures of different crystallographic orientation: quantum
wells, wires, and dots . The newly discovered ferro-
electric behavior of the barriers allows one to obtain
high carrier mobility in quantum-well structures by cre-
ating short-range scattering potential barriers .
Our molecular-dynamics computations for the low-
energy surface scattering of Al and Sb ions (energy
100–150 eV) have shown that ultranarrow vertical
(Figs. 1a, 1b) and lateral (Figs. 2a, 2b) doping proﬁles
can indeed be formed in monocrystalline silicon.
The ultimate goal of the above attempts is to pro-
duce integrated circuits with up to
devices per chip . According to our estimation, this
implies doping proﬁles whose full width at half maxi-
mum (FWHM) is within 35 nm in a lateral direction
and within 3 nm in the vertical direction. Ideally, doped
regions for quantum wires should be the cuboids of
Fig. 3a. In practice, Al- or Sb-doped regions might
appear as Fig. 3b, with doping concentrations approxi-
mately represented by gray levels; the parts of highest
, are marked in black.
At the present time, experiments on implantation
delta-doping almost invariably employ focused ion
beams (FIBs) with a spot size of over 1
m on the tar-
get. The implanters use a gas-discharge source of non-
metal ions (B, P, or Si) or a liquid-metal source (Ga or
Zn) of ion energy 300–1000 eV .
The main purpose of this study is to investigate the
potential of FIB resistless lithography for Al and Sb
implantation delta-doping with the aim of producing up
qubits per chip with a gate size of about 20 nm.
This level of integration would make it possible to build
a prototype solid-state quantum computer that could
outperform conventional computers in, e.g., factoriza-
tion . Another purpose is to derive a formalism for
the evaluation of ion projection lithography (IPL) as a
potential method of implantation delta-doping.
2. FORMULATION OF THE PROBLEM
2.1 Conditions on the Chip and Feature Sizes
Imagine a nanoscale planar solid-state qubit with a
probability of failure per state transition less than 1
Assume that the qubit is based on a quantum dot or
quantum wires. Let us take the mean gate size as 20 nm
and the mean area as
. If a quantum
computer is to compete with conventional ones in fac-
torization, it should use a register chip containing 10
such qubits, which would occupy about 0.2
. This implies a subﬁeld size of 0.2 mm.
2.2 Conditions on the Ion Optics
On the basis of Section 2.1, let us identify condi-
tions on the ion optics to be used for Al or Sb delta-dop-
ing by FIB implantation.
Delta-Doping of Monocrystalline Semiconductors by Al and Sb
Implantation Using FIB Resistless Lithography
V. A. Zhukov*, N. T. Bagraev**, A. I. Titov***, and E. E. Zhurkin***
* St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences, St. Petersburg, Russia
** Ioffe Physicotechnical Institute, Russian Academy of Sciences, St. Petersburg, Russia
*** St. Petersburg State Technical University, St. Petersburg, Russia
Received April 14, 2004
—The potential is investigated of FIB lithography for implantation delta-doping in order to produce
desired arrangements of quantum wires and dots. Both raster and vector scanning are considered. The results
are brieﬂy reported of molecular-dynamics and Monte Carlo (SRIM'2003) computations concerned with the
scattering of low-energy Al and Sb ions from a monocrystalline-semiconductor surface. It is concluded that the
ion energy should be taken within the range 100–300 eV if implantation depths of 1–5 nm are required. A for-
malism is derived for evaluating the ultimate resolution and the processing time of FIB implanters that use a
Gaussian or a vector-scanned variable shaped beam. It is noted that the formalism can be modiﬁed to apply to
IPL implanters. It is shown that an FIB implanter with an electrostatic objective can provide a lateral resolution
better than 20 nm. It is also demonstrated that using a vector-scanned variable shaped beam enables one to cre-
ate an experimental quantum register containing up to 10