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Nanodevices and Nanostructures – Quantum
Wires and Quantum Dots
Wan-Ching Hung
Abstract— This article describes how quantum dots and
quantum wires are integrating to semiconductor nanostructures
and the single electron effects such as quantum confinement,
tunnel effect, and Coulomb blockade. In the end, several
fabrication processes are introduced.
Index Terms—Quantum dots, Quantum wires
I. INTRODUCTION
A
quantum dot typically contains between 1 to 200 atoms
in diameter and its length, width, and high are generally
defined less than 100nm. The key point determines whether a
semiconductor nanostructure is a quantum dot or not is the
motion of electrons having 0 degree of freedom. This is
retrained by Fermi wavelength (1).
"F = 2!
kF
L=
n
!
2
(2)
Where L = the full width of the well
n = a quantum number with the value of
any positive integer.
! = de Broglie wavelength
En =
n2h2
(3)
8mL2
Where En = the totoal engergy level.
n = a quantum number with the value of
any positive integer.
h = a modified Planck’s constant
m =the mass of the electron.
When the isolation layer in transistor shrinks to nanometer
in size, the electrons could tunnel through the potential barrier.
The tunneling effect would cause transistors fail but it can also
be used to develop scanning tunneling microscope. The ability
(1)
Where ! F = the Fermi wavelength; wavelength of carriers
that dominate electrical transport.
k F = the Fermi wave vector.
The Quatum wires confine the motion of electrons or holes
to one spatial direction
Fig. 2. Tunneling effect
II. SINGLE ELECTRON EFFECTS
When nanodevices work in quantum state, there are 3
effects: quantum confinement, tunneling effect, and Coulomb
blockade that can be observed. Quantum confinement effect
occurs when one or more of the dimensions of the
nanomaterial are smaller than the Fermi wavelength, the
boundary conditions of electrons and holes are not infinite and
restricted in one or more dimensions. The equation (2), (3) and
Fig. 1. Quantum confinement
Figure 1 are the quantum confinement of electrons.
of a single electron passes through barrier is called tunneling
effect (Figure 2).
In order to let single electron tunnel through one atom to
another atom, the electron must overcome the Coulomb
blockade energy. The equation (4) defines the Coulomb
blockade energy.
(4)
Ec = e 2 / 2C!
Where Ec = the Coulomb blockade energy, which is the
repelling energy of the previous electron to the
next electron.
e = the electron charge
C! = the capacitance.
The Coulomb blockade is the increased resistance at small
bias voltage of an electronic device comprising at lease one
low-capacitance tunnel junction. The tunnel junction capacitor
is charged with one elementary charge by the tunneling
electron. If the capacitance is very small, the voltage buildup
can be large enough to prevent another electron from
tunneling. The electrical current is then suppressed at low bias
2
voltages and the resistance of the device is no longer constant.
The increase of the differential resistance around zero bias is
called the Coulomb blockade.
quantum well to create nano devices such as single electron
transistor and single electron memory. There are four
fabrication processes are currently used. The self-assembly
method and chemical colloidal method are bottom-up
approach.
III. QUANTUM DOTS AND QUANTUM WIRES APPLICATIONS
The quantum dot applications in various fields include
blue-laser diodes, single electron transistor (Figure 3),
light-emitting devices, etc. The single electron transistor
(SET) [1] which is based on Coulomb blockade and tunneling
effect is a single electron device in which the addition or
subtract of a small numbers of electrons to/from an electrode
can be controlled with one-electron precision using the charge
effect. These quantum dot applications have the advantages of
small size, low power consumption, and high speed.
A. Self-assembly method
There are two methods to accomplish the process. One of
the methods is called dip coating. It dips the material in to
solution and washes away the part that is unwanted to form a
film. The other method uses molecular-beam epitaxy or
chemical vapor deposition to effectively form the quantum dot
arrays on specific material under the theory of lattice
mismatch. It is a combination of techniques, where particle
arrangement is controlled by differences in reactivity – a
characteristic determined by exposing particles and surfaces to
an assortment of chemical treatments. Solar cell, light-emitting
diodes, and capsule in drug delivery system are using this
process to fabricate. (Figure 5)
Fig. 3. Silicon based single electron transistor
The Blue-laser diodes are a kind of quantum dot lasers
which succeeds in minimizing temperature sensitive output
fluctuations, something that not possible with previous
semiconductor lasers. The blue-lasers diodes are made of GaN
and used in optical data communications and optical networks.
The commonly seen commercial product of blue-laser diodes
is used as light source of High Definition DVD.
A quantum wire application is nanobarcodes [2] which is
used in medical field. Nanobarcodes (Figure 4) are made
different quantum wires of different metals that have different
reflectivity. Barcode readout is accomplished by bright field
reflectance imaging, typically using blue illumination to
enhance contrast between Au and Ag stripes
Fig. 5. Self-assembly method
B. Chemical colloidal method
The process is easy and can be used in mass production to
produce multilayered quantum dots. An example for chemical
colloidal method is to grow CdSe with sizes between 2~6nm.
CdSe is a material used to made quantum dot light emitting
diodes. Figure 6 is the process flow of how to cap for CdSe.
Nanobarcodes is also fabricated by this process.
Fig. 4. Nanobarcodes
IV. FABRICATION METHODS
There are 2 ways to realize nanodevices. One of them is
based on the current integrated circuits to minimize the line
width. It is called “top-down’ approach. The electronic
devices only shrink in size and the basic structure of electronic
devices do not change. The other way is called “bottom-up”
approach. It is totally different from the structure of current
integrated circuit and it uses quantum dot, quantum wire, and
Fig. 6. Synthesis of CdSe
C. Abbreviations and Acronyms
Besides photolithography which is the most commercial
form, a large number of promising of promising
nanolithography methods are including electron bream
lithography, ion beam lithography, nanoimpring lithography
[3], and dip pen nanolithography [4].
3
[6]
Fig. 7. Dip pen nanolithography
Etching is the process of using liquid acids or gas to
dissolve away or remove unwanted material such as
semiconductor material. Dry etching and wet etching are two
commonly known processes in semiconductor fabrication.
D. Split-gate approach
It uses additional voltage to create 2 dimensional
confinements to control the shape and size of the quantum
dot’s gate. It means metal gates with a sub-micron sized gap
between them are deposited
onto
a
semiconductor
substrate. (Figure 5)
Fig. 8. The concept of split-gate technique[5]
The black regions correspond to metallic gates and in the
figure 5 on the left the gates are grounded and there is no
effect on the underlying two dimensional electrons. In the
figure 5 on the right, a negative voltage is applied to the
depleting electrons underneath them and leaving a narrow
region of electrons in the gap between the gates.
The split-gate approach offers a number of advantages
compared to other techniques available for the fabrication of
nanostructures. Electrical contact to the nanostructure of
interest is easily achieved. It’s a combination of electron beam
lithography, evaporation, lift off, and contact annealing.
However, this method is suitable for research.
REFERENCES
[1]
[2]
[3]
[4]
[5]
K. K. Likharvey, “Single-Electron Devices and Their Applications”,
Proc. IEEE, vol. 87, no. 4, pp. 606-632. 1999.
http://research.chem.psu.edu/cdkgroup/sensors.htm
http://www.princeton.edu/~chouweb/newproject/page3.html
http://www.chem.northwestern.edu/~mkngrp/dpn.htm
http://www.eas.asu.edu/~bird/
Nanotechnology Knowledge Working Group, Nanotechnology
Handbook, Nikkei Business Publications, Japan, 2003.