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UNDERSTANDING QUANTUM DOTS, WIRES AND
THEIR IMPORTANCE IN THE NANOANTENNAS.
Anderson Amaral
Pre-Masters in Nanophysics
2
UNDERSTANDING QUANTUM DOTS , WIRES AND
THEIR IMPORTANCE IN THE NANOANTENNAS
Thesis presented for the degree of pre-masters in Nanophysics
To the
School of Physics
College of Science
By
Anderson Amaral
Research Supervisor : Brian Vohnsen
2015
3
4
Acknowledgment
I am indebted to Professor Brian Vohnsen and the UCD Physics School for all the help in the
development of this written booklet. This work was supported in part by the following agencies:
CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) , of the Brazilian Federal
Government and USP – University of de Sao Paulo. I am also thankful to HEA - Higher Education
Authority in Ireland and the Brazil-Ireland bilateral agreement that made it possible.
5
Preface
Nanotechnology has been a very exciting research and development topic in the past thirty years and
many pundits say that the next science revolution will come out from this area. The impact of the
nanoscience research in the last three decades not only for the fundamental science, but also the
industrial application has led to a sheer amount of new technologies which are still growing. Among
the many subareas of the nanoscience (or nanotechnology, as both terms are equivalent due to the
simultaneous development of academic and industrial techniques) the development of the
nanostructured materials is probably the one generating the strongest enthusiasm about new
discoveries. Exciting examples of new nanomaterials such as carbon nanotube, semiconductor
nanowire (which is one of the main subjects of this booklet) and colloidal nanocrystal are one of the
hottest topics. Nanoscience is one of the quickest fields in evolution and day by day is interfacing
with many different disciplines, from chemistry to physics, to engineer, biology and materials science.
The papers on related subjects have been bringing surprising new facts and is increasing each year.
In general the research in nanoscience is mostly interdisciplinary due to the fact of different
methodologies involved , as well as many varieties of physical techniques used. It is very common
for research groups in nanoscience to carry out collective efforts in order to achieve success. In spite
the fact that nanoscientists are coming from all different disciplines, surely the most important fact
about this research theme is how to make such nanostructured materials. For this reason, this written
booklets, after a brief introduction to quantum dots and quantum wires, focus mainly on the
nanoantennas , definitely one of the hottest topics in nanoscience as aforementioned , not only due to
intense research in order to discover new materials to assemble nanoantennas, but also because this
theme can be one of the ways out to the huge problems related to the world energy resources the
mankind is about to face up in the next decades, and that already have become serious issues in many
nations.
6
Part 1 – NANOWIRES AND QUANTUM DOTS
1 - Quantum dots (QD) ……………………………………………………13
1.1 History………………………………………………………………………………..13
1.2 Characteristics……………………………………………………………………….14
1.3 Applications………………………………………………………………………….14
1.4 Health and Safety concerns : some of the disadvantages………………………… 14
2.0 Quantum Wires (QW)…………………………………………………..16
2.1 Nanowires, basics………………………………………………………………..........16
2.2 Applications……………………………………………………………………………17
2.3 Materials used in the nanowires……………………………………………………...18
3. Nanowires and quantum dots: properties ……………………………..19
3.1 facts related to the quantum wires and dots…………………………………………19
3.2 Brief statement about nanowires and quantum dots…………………………….….21
4. Schrodinger’s equation in quantum wires……………………………….22
4.1 Schrodinger’s equation: basics…………………………………….................22
5. Near future of quantum wires…………………………………………....25
7
PART 2 – NANOANTENNAS
6. Nanoantennas………………………………………………...30
6.1 Introduction to Nanoantennas…………………………………………………....30
6.2 Nanoantennas: brief historic facts………………………………………………..31
6.3 Nanoantennas: How do they work…………………………………………….….31
6.4. Advantages of the nanoantennas…………………………………………..….…32
6.5 Drawbacks of the Nanoantennas………………………………………………....33
7. Future research and goals………………………………………….….35
8. References……………………………………………………................36
8
9
Related Vocabulary
Schottky diode: (named after German physicist Walter H. Schottky); also known as hot carrier diode is a semiconductor
diode with a low forward voltage drop and a very fast switching action. The cat's-whisker detectors used in the early days
of wireless and metal rectifiers used in early power applications can be considered primitive Schottky diodes.
Potential well: is the region surrounding a local minimum of potential energy. Energy captured in a potential well is
unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is
captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential
energy, as it would naturally tend to due to entropy.
Quantum well: is a potential well with only discrete energy values. Quantum wells are formed in semiconductors by
having a material, like gallium arsenide sandwiched between two layers of a material with a wider bandgap,
like aluminium arsenide. There are many other examples.
Qubit: is a quantum bit , the counterpart in quantum computing to the binary digit or bit of classical computing. Just as
a bit is the basic unit of information in a classical computer, a qubit is the basic unit of information in a quantum computer
.
Stylus: plural styli or styluses, is a writing utensil, or a small tool for some other form of marking or shaping.
10
SI Prefixes
11
Part 1 – NANOWIRES AND QUANTUM DOTS
12
NANOWIRES AND QUANTUM DOTS
Nanowires or (quantum wires-QI), by definition, are nanostructures with large aspect ratio
(length/diameter) that is small enough to have quantum behaviour. Generally, they would have a
diameters of 1-200 nm and length up to several micrometres. A quantum dot (QD), on the other hand
is generally between 2-50 nm.
Quantum dots embedded within nanowires represent one of the most promising technologies for
applications in photonics. Despite the fact that the top-down fabrication of such structures represents
sheer amount of complex issues, their bottom-up fabrication through self-assembly has been shown
to be a potentially more powerful strategy.
The purpose of this part (as the booklet was divided between part 1 - Nanowires and Quantum Dots
and part 2 – Nanoantennas) is to show the basics of quantum wires and quantum dots, their assembling
techniques as well as brief introduction to the recent history of the field.
13
1 - Quantum dots (QD)
1.1 History
The term quantum dots (QD) was coined by Mark Reed were discovered by Alexey Ekimov at first
in 1981 in a glass matrix and then in colloidal solutions by Louis E. Brus in 1985. The term "quantum
dot" was coined by North American physicist Mark Reed, professor at Yale University , but the
conventional idea of what is a quantum dot nowadays was actually discovered first by the Russian
physicist Alexey Ekimov, working at the Vavilov State Optical Institute in 1981 in a glass matrix and
then by the North American physicist Louis E. Brus in 1985 , through experiments with colloidal
solutions at the Columbia University.
1.2 Characteristics
Quantum dots are fluorescent semiconductor nanoparticles typically between 10 to 100 atoms in
diameter, which is about 1/1000th the width of a human hair.
Basically, the excitons * of the quantum dots are confined in all three spatial dimensions, and its
Electronic characteristics are closely related to its dimensionality and shape.
It is well known that the reduction in dimensionality produced by confining electrons (or holes) to
a thin semiconductor layer leads to a dramatic change in their behaviour. That is actually when the
object is small enough to exhibit quantum behaviour.
14
In fact, there is no official cut off size" where systems stop or start exhibiting "quantum
behaviour" , but there are well known double-slit interference experiments with molecules made up
of ~60 atoms, which is the case of the Buckminster Fullerene .
1.3 Applications
Among the many studied applications for quantum dots, the ones for transistors, solar cells, LEDs,
and diode lasers are by far the most promising. It has also been investigated the usage of quantum
dots as agents for medical imaging and as possible assembling of the quantum version of information
unit bit, known as qubits, in the development of quantum computing new techniques. In 2013 the
Japanese multinational conglomerate Sony released the first commercial product utilizing quantum
dots: the XBR X900A series of flat panel televisions.
1.4 Health and Safety concerns: some of the disadvantages.
Nowadays there are many experiments with quantum dots that can be carried out even by modest
 An exciton is a bound state of an electron and an electron hole which are attracted
to each other by the electrostatic Coulomb force. It is an electrically
neutral quasiparticle that exists in insulators, semiconductors and in some liquids.
The exciton is regarded as an elementary excitation of condensed matter that can
transport energy without transporting net electric charge.[1]
Liang, W Y (1970). "Excitons". Physics Education 5 (125301).
15
laboratories for undergraduate or even high school students , however, care must be taken as quantum
dots are believed to be very toxic due to the presence of Cadmium. Actually, despite persisting
concerns about their safety, most toxicology data about the quantum dots is derived from in vitro
studies and may not reflect in vivo responses. At the moment, the only known Laboratory/ company
capable of assemble Cadmium-free quantum dots in commercial scale (CFQD) is the British company
Nanoco Group PLC.
The biggest project-platform under construction in the world related Health and safety and totally
open to the is actually a partnership between the Polytechnic School at the University of Sao Paulo
(POLI-USP) from Sao Paulo State-Brazil in partnership with the Brown University from United
States , called HSENano . The HSEnano web-platform is a public and free of charge internet platform,
for educational and/or non-commercial use. It is a bilingual web platform (English and Portuguese)
about health, safety and environmental nanotechnology and it is supported by the Brazilian National
Science Foundation (CNPq), the National Institute of Science and Technology (INCT- Nanocarbon
Materials), the Brazilian Network of Nanotoxicity, the University of São Paulo (Brazil), LM2
C2
-
POLI/USP and the Laboratory for Environmental and Health Nanoscience/Brown University
(LEHN/USA).
Also, many countries are already in hurry of elaborating laws related to the aforementioned topic due
to the considerable growing of usage of quantum dots and nanotechnology in general by the industry
and universities .
16
2.0 Quantum Wires(QW)
2.1 Nanowires, basics
Analogously to the quantum dots, quantum wires or nanowires are electrically conducting wires small
enough to the in quantum effects influence the transport properties. In this case, electrons will
experience quantum confinement * in the perpendicular direction. As a result, their transverse
energy will be quantized into a series of discrete values. The most easily demonstrable fact related to
this phenomenon is that the well known formula for calculating the electrical resistance of a wire:
Eq.2.1
, (where = resistivity, =the length, and = cross-sectional area). is no longer valid for quantum
wires.
Instead, in order to calculate the resistance is necessary an exact measurement and of the
perpendicular energy of the confined electrons.
 Quantum confinement can be observed once the diameter of a material is of
the same magnitude as the de Broglie wavelength of the electron wave
function.[1]
When materials are this small, their electronic and optical
properties deviate substantially from those of bulk materials.[2]
Hartmut Haug; Stephan W. Koch (1994). Quantum Theory of the Optical and Electronic
Properties of Semiconductors
17
2.2 Applications
The nanowires could be used, in the near future, to link tiny components into extremely small circuits
in large scale. Using nanotechnology, such components could be created out of chemical compounds.
Actually, many experiments have just become viable, such as nanoantennas which will be seen the
part 2 of this booklet, are only becoming possible due to the increasingly number of discoveries
related to nanowires assembly .
Fig. 2.2
Reference: Jim Heath, California Institute of Technology
http://www.its.caltech.edu/~heathgrp/heath.html
18
2.3 Materials used in the nanowires.
Many different types of nanowires exist, including metallic (e.g., Ni, Pt, Au), semiconducting (e.g.,
Si, InP, GaN, etc.), and insulating (e.g., SiO2,TiO2) and even molecular nanowires either organic or
inorganic. In fact, there is a growing list of the current types of quantum wires :
a) Alumina quantum wire
b) Bismuth quantum wire
c) Boron quantum wire
d) Cadmium selenide quantum wire
e) Copper quantum wire
f) Gallium nitride quantum wire
g) Gallium phosphide quantum wire
h) Germanium quantum wire
i) Gold quantum wire
j) Indium phosphide quantum wire
k) Magnesium oxide quantum wire
l) Manganese oxide quantum wire
m) Nickel quantum wire
n) Palladium quantum wire
o) Platinum quantum wire
p) Silicon quantum wire
q) Silicon carbide quantum wire
r) Silicon nitride quantum wire
s) Silver quantum wire
t) Titanium dioxide quantum wire
u) Zinc oxide quantum wire
19
3.0 Nanowires and quantum dots: properties.
3.1 facts related to the quantum wires and dots
As aforementioned, the reduction in dimensionality produced by confined electrons to a thin
semiconductor layer leads to a dramatic change in their behaviour. This principle can be better
developed by reducing the dimensionality of the electron's environment from a two dimensional
quantum well * to a one-dimensional quantum wire and eventually to a zero-dimensional quantum
dot. In this context, of course, the dimensionality refers to the number of degrees of freedom in the
electron momentum; in fact, within a quantum wire, the electron is confined across two directions,
rather than just the one in a quantum well, and, so, therefore, reducing the degrees of freedom to one.
In a quantum dot, however, the electron is confined in all three-dimensions, thus reducing the degrees
of freedom to zero. If the number of degrees of freedom are labelled as "Df and the number of
directions of confinement are labelled as Dc, then clearly:
Df + Dc = 3
for all solid state systems. These values are highlighted for the four possibilities shown in Table 1.1.
Tradition has determined that the reduced-dimensionality systems are labelled by the remaining
degrees of freedom in the electron motion, i.e. Df, rather than the number of directions with
confinement Dc.
20
Table 3.1 The number of degrees of freedom Df in the electron motion, together with
the extent of the confinement Dc , for the four basic dimensionality systems:
System Dc Df
Bulk 0 3
Quantum Well 1 2
Quantum Wire 2 1
Quantum dot 3 0
Fig. 3.1
Fig. 3.1 shows an expanded view of a single quantum wire, where clearly the
electron (or hole) is free to move in only one direction, in this case along the Y-axis.
.
Another class of quantum wire can be formed by patterning the substrate before growth. This leads
to the formation of so-called V-grooved quantum wires. In fact there are many new classes of quantum
wires which lays beyond the scope of this booklet.
Quantum dots are also formed by further lithography and etching, e.g. if a quantum well sample is
etched to leave pillars rather than wires, then a charge carrier can become confined in all three
21
dimensions .
Figure 3.2 Schematic representation of the pyramidal shape of self-assembled quantum dots
in highly lattice mismatched systems.
3.2 Brief statement about nanowires and quantum dots
It is known that when two quantum wires acting as photon waveguides cross each other the juncture
acts as a quantum dot. Consequently, the next chapter is a summary of the physical properties of
quantum wires and quantum dots, which can be considered crucial part of the construction of
nanoantennas, to be seen in part two. . Nanolithography is probably the most important step when
constructing quantum wires and dots and is better explained in the nanoantennas chapters.
22
4 . Schrodinger’s equation in quantum wires
4.1 Schrodinger’s equation : basics.
The Schrodinger equation is the fundamental mathematical tool for the understanding of quantum
dots and quantum dots.
*The Schrödinger equation is a partial differential equation that describes how the quantum state of
a physical system changes with time. It was formulated in late 1925, and published in 1926, by the
Austrian physicist Erwin Schrödinger.[1]
When the Hamiltonian operator acts on a certain wave
function Ψ, and the result is proportional to the same wave function Ψ, then Ψ is a stationary state,
and the proportionality constant, E, is the energy of the state Ψ.
Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules" (PDF). Physical Review
The general three-dimensional Schrodinger equation * for constant effective mass is:
(3.1)
Where ħ is the Planck constant and is the rest mass. In a quantum wire it is possible to decouple
the motion along the length of the wire. Taking the axis of the wire along x, then the total potential
V(x, y, z) can always be written as the sum of a two-dimensional confinement potential plus the
potential along the wire .
23
(3.2)
The eigenfunction can then be written as a product of two components:
(3.3)
Substituting both equation (3.2) and equation (3.3) into equation (3.1), then:
Writing the energy as a sum of terms associated with the two components of the motion, then:
(3.4)
It is now possible to associate distinct kinetic and potential energies on the left-hand side of equation
(2.4), with the components Ex and Ey>z on the RHS, thus giving two decoupled equations, as follows:
24
(2.5)
(2.6)
In the
above Ψ(y,z) is not acted upon by any operator in the first equation, and similarly for if Ψ(x) in the
second equation, and thus they can be divided out. In addition, as mentioned above, the potential
component along the axis of the wire V(x) = 0, thus giving the final decoupled equations of motion
as follows
(2.7)
(2.8)
Clearly, the first of these equations is satisfied by a plane wave of the form “exp(ikx X)”,
thus giving the standard dispersion relationship:
(2.9)
This second of these equations of motion, equation , is merely the Schrodinger equation for the two-
dimensional confinement potential characterising a quantum wire.
The decoupling of the Schrodinger Equation will depend on the shape and type of the quantum wire
and quantum tods . A much further mathematical approach can be find in the book Quantum Well,
25
Dots and Wires where spherical quantum dots , deep rectangular quantum wires, tiny quantum dots
and may other classes are deeply reviewed.
Ps: The results of solving the Schrodinger equation to obtain the equations as above were plucked
from the Book Quantum Wells , Dots and Wires , Paul Harisson (3rd Edition) – Theoretical and
Computational Physics of Semiconductor Nanostructures.
5. Near future of quantum wires.
Slightly different from the quantum dots , quantum wires still belong to the experimental world of
laboratories. Nonetheless, they may replace or at least complement carbon nanotubes in some
applications. The newest experiments have shown that they are very likely to be the building blocks
of the next generation of computing gadgets .Microelectronics, field emission devices,
Optoelectronics , photonics, clothing fabric, and electronic device applications are some of the fields
that probably are going to take advantage of a further development of quantum dots and quantum
wires fabrication.
One of these specific fields, the Nanoantennas, is the subject of the second part of this written booklet.
Finally, is worth to say that nanolithography*, which is one of the main techniques related to the
fabrication the branch nanometre-scale structures definitely will play a fundamental role in the next
discoveries.
26
 Nanolithography is used during the fabrication of leading-edge semiconductor integrated
circuits (nanocircuitry) or nanoelectromechanical systems. There are currently several new
types of techniques being develop such as Scanning probe lithography in which a microscopic
or nanoscopic stylus is moved mechanically across a surface to form a pattern. It uses
scanning tunneling microscope (STM) to produce nanometre scale features on a sample.
Storex Disclosed Quantum Optical Lithography Technique", Press Release, Storage Newsletter.com, February 24th, 2012
27
Part 2
Nanoantennas
28
NANOANTENNAS
A nanoantennas (or nantenna) ) is a sort of rectifying antenna*, an experimental technology being
developed to convert electromagnetic waves such as natural light to electric power.
A nanoantenna is basically a very small rectenna the size of a light wave, when the quantum phe-
nomena leads the behaviour of the objects. In the next years it is hoped that arrays of nantennas
could be an efficient means of converting sunlight into electric power, producing solar power more
efficiently than conventional solar cells.
29
Scheme of the nanowire-nanoantenna system. The different colours in the NW are an illustrative representation of the
field energy distribution inside the NW during the excitation of transverse polarized light. The red colour indicates the
highest field energy density and the green the lowest.
“Polarization response of nanowires à la carte” Nature
Scientific Report 5 Article number:7651 doi:10.1038/srep07651 – Published 07 January 2015
30
6. Nanoantennas
6.1 Introduction to Nanoantennas
A nantenna is an electromagnetic collector designed to absorb wavelengths that are proportional to
the its size. Ideally, nantennas would be used to absorb light at wavelengths between 0.4 and 1.6
μm because these wavelengths have higher energy than far-infrared (longer wavelengths) and make
up about 85% of the solar radiation spectrum [4]
.
 A rectenna (or rectifying antenna) is a type of antenna that is used to transform micro-
wave energy into direct current electricity. They are used in wireless transmission systems
that transmit power by radio waves. A basic rectenna consists of a dipole antenna with a
rectifying diode connected across the dipole elements. The diode rectifies the AC (alternate
current) current induced in the antenna by the microwaves, to produce DC (direct current)
power, which powers a load connected to the diode.
"William C. Brown". Project #07-1726:Cutting the Cord. 2007-2008 Internet Science & Technology
Fair, Mainland High School. 2012. Retrieved 2012-03-30.
Nanoantennas can strongly enhance the interaction of light with nanoscale matter by their ability to
efficiently link propagating and spatially localized optical fields. This ability unlocks an enormous
potential for applications ranging from nanoscale optical microscopy and spectroscopy over solar
energy conversion. The focus on the part 2 of this booklet is entirely on nanoantennas, investigating
its features based on the background the researches from the last three decades. Finally, a brief account
of the current status of the field and the major established and emerging lines of investigation, and
the development of new techniques for this cutting-edge topic.
31
6.2 Nanoantennas: brief historic facts
1973 - a patent for an “electromagnetic wave converter” was given to Robert Bailey, along with
James C. Fletcher,”.
1984 - Alvin M. Marks received a patent for a device explicitly stating the use of sub-micron antennas
for the direct conversion of light power to electrical power.
1996 - Guang H. Lin was the first to report resonant light absorption by a fabricated nanostructure
and rectification of light with frequencies in the visible range.
2002 - ITN Energy Systems, Inc. published a report on their work on optical antennas coupled with
high frequency diodes.
2013 – A team lead by Federico Capasso at Harvard University in the US have made the first
electrically tunable plasmonic antennas containing graphene that work in the mid-infrared.
6.3 Nanoantennas : How do they work.
Antennas in general are used either to create electromagnetic waves with a well-defined radiation
pattern, which can then travel over large distances, or to receive electromagnetic waves from a remote
source in order to extract some encoded information, to measure changes in their intensity, or to
exploit the transmitted power . The importance of antennas nowadays is dominated by two of their
ability: to provide an interface between localized information processing using electrical signals and
the free-space wireless transmission. Not only because of these properties, but also due to continuous
search for new ways to improve transmission/reception involving energetic efficacy, nanoantennas
are one of the hottest topics in energetic enhancement.
32
As a means for capturing or converting the abundant energy from solar radiation, an nanoantenna
would be the ideal device because it is an efficient transducer between free space and guided waves.
In the case of conventional solar cells, solar radiation is only absorbed if the photon energy is greater
than the bandgap.
The average power per unit area is about 1500 W/m2 , with a maximum intensity at about 0.5 µm.
Solar radiation has a moderately broadband electromagnetic frequency spectrum, ranging from a
frequency of about 150 THz to about 1,000 THz, corresponding to a free-space wavelength of about
2 µm to about 0.3 µm. Over 85% of the radiation energy is contained in the frequency range from 0.4
µm to 1.6 µm. Efficient antenna/rectifiers, therefore, need to cover a frequency range on the order of
100/25 (or 4/1).
6.4 . Advantages of the nanoantennas
The most well-known advantage of nantennas, at least in theory, is their efficiency being higher than
the well-stablished Carnot efficiency. In comparison to the theoretical efficiency of single junction
solar cells (30%), nanoantennas seem to have a considerable advantage. Nonetheless, the two effi-
ciencies are calculated using different assumptions. The assumptions involved in the nantenna calcu-
lation are based on the application of the Carnot efficiency of solar collectors. The Carnot efficiency,
η, is given by
33
where Tcold is the temperature of the cooler body and Thot is the temperature of the warmer body. In
order for there to be an efficient energy conversion, the temperature difference between the two bod-
ies must be significant. R. L. Bailey, the first to received a patent related to this technology as previ-
ously stated, claims that nantennas are not limited by Carnot efficiency, whereas photovoltaics are.
However, he does not provide any argument for this claim. Moreover, when the same assumptions
used to obtain the 85% theoretical efficiency for nanoantennas are applied to single junction solar
cells, the theoretical efficiency of single junction solar cells is also greater than 85%.
In practice, the most well agreed advantage offered by nanoantennas is that they can be designed to
absorb any frequency of light. Basically, the resonant frequency of a nantenna can be selected by
varying its length. This is an advantage over semiconductor photovoltaics, due to the fact that in order
to absorb different wavelengths, it is necessary different band gaps for the semiconductor photovol-
taics.
6.5 Drawbacks of Nanoantennas
One of the biggest limitations of nanoantennas is the extremely high frequency at which they operate,
which makes the use of the typical use of Schottky diodes for normal rectennas nearly impossible
for nanoantennas . There are new technologies in diode development in order to overcome this issue,
however further research is necessary.
34
Yet another drawback is that nanoantennas are usually produced using electron beam nanolithogra-
phy (e-beam). This process is time-consuming and expensive.. In general, e-beam lithography is used
only for research purposes when extremely fine resolutions are needed for minimum feature size
(typically, on the order of nanometres). However, photolithographic techniques have advanced to
where it is possible to have minimum feature sizes on the order of tens of nanometres, making it
possible to produce nanoantennas by means of photolithography, which has a small chapter in this
written document.
35
7 . Future research and goals
Probably the most well-known enthusiast of the nanoantennas technology is Dr. Novack, from NASA
- National Aeronautics and Space Administration, who claims that nanoantennas could one day be
used to power cars, charge mobile phones, and homes. Novack expressed that in the near future
“smart” houses will work by both absorbing the infrared heat available in the room and producing
electricity which could be used to further cool the room. However, as mentioned in the previous
chapter, other scientists disagree.
Mentioning it once again, the biggest problem at moment by far is not with the antenna device, but
surely with the rectifier. As previously expressed, the current diodes are unable to efficiently rectify
at frequencies corresponding to high-infrared and visible light (390 to 700 nm). Hence, It is necessary
to design rectifiers that can properly turn the absorbed light into usable energy.
Nanophysicists currently hope to develop a rectifier which can convert around 50% of the antenna's
absorption into energy (which would end up being closer to Carnot efficiency).[
Yet another aim to be
achieved in the next years is of research will be how to properly upscale the process to mass- produc-
tion. For that to happen, the quantum dots and quantum wires researches will have to keep the pace
with the nanoantennas studies in order to allow the assembly of such devices.
In the case of the quantum dots and quantum wires, despite the presence of Cadmium, a well-known
carcinogen, in the majority of current researches , it is worth mentioning again that many researches
institutes are looking for Cadmium-free solutions and some of them have been already successful, as
the British company Nanoco , as previously mentioned .
Finally, due to the brief data presented in this book, we can conclude that nanolithographically defined
quantum wires and quantum dots are the building blocks of the nanoantennas and play a big role in
the always constant search for new energy resources.
36
8. References
Novack, Steven D., et al. “Solar Nantenna Electromagnetic Collectors.” American Society of Me-
chanical Engineers (Aug. 2008): 1–7. Idaho National Laboratory. 15 Feb. 2009
<http://www.inl.gov/pdfs/nantenna.pdf>.
Berland, B. “Photovoltaic Technologies Beyond the Horizon: Optical Rectenna Solar Cell.” National
Renewable Energy Laboratory. National Renewable Energy Laboratory. 13 Apr. 2009
<http://www.nrel.gov/docs/fy03osti/33263.pdf>.
Lin, Guang H.; Reyimjan Abdu; John O'M. Bockris (1996-07-01). "Investigation of resonance light
absorption and rectification by subnanostructures". Journal of Applied Physics 80 (1): 565–568.
Robinson, Keith. Spectroscopy: The Key to the Stars. New York: Springer, 2007. Springer Link. Uni-
versity of Illinois Urbana-Champaign. 20 Apr. 2009
<http://www.springerlink.com/content/p3878194r0p70370/?p=900b261891484572a965aca5acb7d0
79&pi=0>.
Krasnok, Alexander. "Dielectric optical nanoantennas" (1(95)). ISSN 2226-1494. Retrieved 2015.
Solarbuzz PV module pricing survey, May 2011 <http://solarbuzz.com/facts-and-figures/retail-price-
environment/module-prices>
“Nanoheating”, Talk of the Nation. National Public Radio. 22 Aug. 2008. Transcript. NPR. 15 Feb.
2009.
37
“Nano-Antennas for Solar, Lighting, and Climate Control”, Ecogeek. 7 Feb. 2008. 15 Feb. 2009.
Interview with Dr. Novack.
Moddel, Garret (2013). "Will Rectenna Solar Cells Be Practical?". In Garret Moddel; Sachit
Grover. Rectenna Solar Cells. Springer New York. pp. 3–24. ISBN
S.J. Byrnes; R. Blanchard; F. Capasso (2014). "Harvesting renewable energy from Earth’s mid-infra-
red emissions". PNAS. doi:10.1073/pnas.1402036111.
P. A. M. Dirac (1958). The Principles of Quantum Mechanics (4th ed.). Oxford University Press.
David J. Griffiths (2004). Introduction to Quantum Mechanics (2nd ed.). Benjamin Cum-
mings. ISBN 0-13-124405-1.
Brus, L.E. (2007). "Chemistry and Physics of Semiconductor Nanocrystals" (PDF). Retrieved 7
July 2009.
Norris, D.J. (1995). "Measurement and Assignment of the Size-Dependent Optical Spectrum in Cad-
mium Selenide (CdSe) Quantum Dots, PhD thesis, MIT".
Ekimov AI, Efros AL, Onushchenko AA (1985). "Quantum size effect in semiconductor microcrys-
tals". Solid State Communications 56 (11): 921–924.

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OFFICIAL Pre-Masters Anderson Amaral

  • 1. 1 UNDERSTANDING QUANTUM DOTS, WIRES AND THEIR IMPORTANCE IN THE NANOANTENNAS. Anderson Amaral Pre-Masters in Nanophysics
  • 2. 2 UNDERSTANDING QUANTUM DOTS , WIRES AND THEIR IMPORTANCE IN THE NANOANTENNAS Thesis presented for the degree of pre-masters in Nanophysics To the School of Physics College of Science By Anderson Amaral Research Supervisor : Brian Vohnsen 2015
  • 3. 3
  • 4. 4 Acknowledgment I am indebted to Professor Brian Vohnsen and the UCD Physics School for all the help in the development of this written booklet. This work was supported in part by the following agencies: CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) , of the Brazilian Federal Government and USP – University of de Sao Paulo. I am also thankful to HEA - Higher Education Authority in Ireland and the Brazil-Ireland bilateral agreement that made it possible.
  • 5. 5 Preface Nanotechnology has been a very exciting research and development topic in the past thirty years and many pundits say that the next science revolution will come out from this area. The impact of the nanoscience research in the last three decades not only for the fundamental science, but also the industrial application has led to a sheer amount of new technologies which are still growing. Among the many subareas of the nanoscience (or nanotechnology, as both terms are equivalent due to the simultaneous development of academic and industrial techniques) the development of the nanostructured materials is probably the one generating the strongest enthusiasm about new discoveries. Exciting examples of new nanomaterials such as carbon nanotube, semiconductor nanowire (which is one of the main subjects of this booklet) and colloidal nanocrystal are one of the hottest topics. Nanoscience is one of the quickest fields in evolution and day by day is interfacing with many different disciplines, from chemistry to physics, to engineer, biology and materials science. The papers on related subjects have been bringing surprising new facts and is increasing each year. In general the research in nanoscience is mostly interdisciplinary due to the fact of different methodologies involved , as well as many varieties of physical techniques used. It is very common for research groups in nanoscience to carry out collective efforts in order to achieve success. In spite the fact that nanoscientists are coming from all different disciplines, surely the most important fact about this research theme is how to make such nanostructured materials. For this reason, this written booklets, after a brief introduction to quantum dots and quantum wires, focus mainly on the nanoantennas , definitely one of the hottest topics in nanoscience as aforementioned , not only due to intense research in order to discover new materials to assemble nanoantennas, but also because this theme can be one of the ways out to the huge problems related to the world energy resources the mankind is about to face up in the next decades, and that already have become serious issues in many nations.
  • 6. 6 Part 1 – NANOWIRES AND QUANTUM DOTS 1 - Quantum dots (QD) ……………………………………………………13 1.1 History………………………………………………………………………………..13 1.2 Characteristics……………………………………………………………………….14 1.3 Applications………………………………………………………………………….14 1.4 Health and Safety concerns : some of the disadvantages………………………… 14 2.0 Quantum Wires (QW)…………………………………………………..16 2.1 Nanowires, basics………………………………………………………………..........16 2.2 Applications……………………………………………………………………………17 2.3 Materials used in the nanowires……………………………………………………...18 3. Nanowires and quantum dots: properties ……………………………..19 3.1 facts related to the quantum wires and dots…………………………………………19 3.2 Brief statement about nanowires and quantum dots…………………………….….21 4. Schrodinger’s equation in quantum wires……………………………….22 4.1 Schrodinger’s equation: basics…………………………………….................22 5. Near future of quantum wires…………………………………………....25
  • 7. 7 PART 2 – NANOANTENNAS 6. Nanoantennas………………………………………………...30 6.1 Introduction to Nanoantennas…………………………………………………....30 6.2 Nanoantennas: brief historic facts………………………………………………..31 6.3 Nanoantennas: How do they work…………………………………………….….31 6.4. Advantages of the nanoantennas…………………………………………..….…32 6.5 Drawbacks of the Nanoantennas………………………………………………....33 7. Future research and goals………………………………………….….35 8. References……………………………………………………................36
  • 8. 8
  • 9. 9 Related Vocabulary Schottky diode: (named after German physicist Walter H. Schottky); also known as hot carrier diode is a semiconductor diode with a low forward voltage drop and a very fast switching action. The cat's-whisker detectors used in the early days of wireless and metal rectifiers used in early power applications can be considered primitive Schottky diodes. Potential well: is the region surrounding a local minimum of potential energy. Energy captured in a potential well is unable to convert to another type of energy (kinetic energy in the case of a gravitational potential well) because it is captured in the local minimum of a potential well. Therefore, a body may not proceed to the global minimum of potential energy, as it would naturally tend to due to entropy. Quantum well: is a potential well with only discrete energy values. Quantum wells are formed in semiconductors by having a material, like gallium arsenide sandwiched between two layers of a material with a wider bandgap, like aluminium arsenide. There are many other examples. Qubit: is a quantum bit , the counterpart in quantum computing to the binary digit or bit of classical computing. Just as a bit is the basic unit of information in a classical computer, a qubit is the basic unit of information in a quantum computer . Stylus: plural styli or styluses, is a writing utensil, or a small tool for some other form of marking or shaping.
  • 11. 11 Part 1 – NANOWIRES AND QUANTUM DOTS
  • 12. 12 NANOWIRES AND QUANTUM DOTS Nanowires or (quantum wires-QI), by definition, are nanostructures with large aspect ratio (length/diameter) that is small enough to have quantum behaviour. Generally, they would have a diameters of 1-200 nm and length up to several micrometres. A quantum dot (QD), on the other hand is generally between 2-50 nm. Quantum dots embedded within nanowires represent one of the most promising technologies for applications in photonics. Despite the fact that the top-down fabrication of such structures represents sheer amount of complex issues, their bottom-up fabrication through self-assembly has been shown to be a potentially more powerful strategy. The purpose of this part (as the booklet was divided between part 1 - Nanowires and Quantum Dots and part 2 – Nanoantennas) is to show the basics of quantum wires and quantum dots, their assembling techniques as well as brief introduction to the recent history of the field.
  • 13. 13 1 - Quantum dots (QD) 1.1 History The term quantum dots (QD) was coined by Mark Reed were discovered by Alexey Ekimov at first in 1981 in a glass matrix and then in colloidal solutions by Louis E. Brus in 1985. The term "quantum dot" was coined by North American physicist Mark Reed, professor at Yale University , but the conventional idea of what is a quantum dot nowadays was actually discovered first by the Russian physicist Alexey Ekimov, working at the Vavilov State Optical Institute in 1981 in a glass matrix and then by the North American physicist Louis E. Brus in 1985 , through experiments with colloidal solutions at the Columbia University. 1.2 Characteristics Quantum dots are fluorescent semiconductor nanoparticles typically between 10 to 100 atoms in diameter, which is about 1/1000th the width of a human hair. Basically, the excitons * of the quantum dots are confined in all three spatial dimensions, and its Electronic characteristics are closely related to its dimensionality and shape. It is well known that the reduction in dimensionality produced by confining electrons (or holes) to a thin semiconductor layer leads to a dramatic change in their behaviour. That is actually when the object is small enough to exhibit quantum behaviour.
  • 14. 14 In fact, there is no official cut off size" where systems stop or start exhibiting "quantum behaviour" , but there are well known double-slit interference experiments with molecules made up of ~60 atoms, which is the case of the Buckminster Fullerene . 1.3 Applications Among the many studied applications for quantum dots, the ones for transistors, solar cells, LEDs, and diode lasers are by far the most promising. It has also been investigated the usage of quantum dots as agents for medical imaging and as possible assembling of the quantum version of information unit bit, known as qubits, in the development of quantum computing new techniques. In 2013 the Japanese multinational conglomerate Sony released the first commercial product utilizing quantum dots: the XBR X900A series of flat panel televisions. 1.4 Health and Safety concerns: some of the disadvantages. Nowadays there are many experiments with quantum dots that can be carried out even by modest  An exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and in some liquids. The exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge.[1] Liang, W Y (1970). "Excitons". Physics Education 5 (125301).
  • 15. 15 laboratories for undergraduate or even high school students , however, care must be taken as quantum dots are believed to be very toxic due to the presence of Cadmium. Actually, despite persisting concerns about their safety, most toxicology data about the quantum dots is derived from in vitro studies and may not reflect in vivo responses. At the moment, the only known Laboratory/ company capable of assemble Cadmium-free quantum dots in commercial scale (CFQD) is the British company Nanoco Group PLC. The biggest project-platform under construction in the world related Health and safety and totally open to the is actually a partnership between the Polytechnic School at the University of Sao Paulo (POLI-USP) from Sao Paulo State-Brazil in partnership with the Brown University from United States , called HSENano . The HSEnano web-platform is a public and free of charge internet platform, for educational and/or non-commercial use. It is a bilingual web platform (English and Portuguese) about health, safety and environmental nanotechnology and it is supported by the Brazilian National Science Foundation (CNPq), the National Institute of Science and Technology (INCT- Nanocarbon Materials), the Brazilian Network of Nanotoxicity, the University of São Paulo (Brazil), LM2 C2 - POLI/USP and the Laboratory for Environmental and Health Nanoscience/Brown University (LEHN/USA). Also, many countries are already in hurry of elaborating laws related to the aforementioned topic due to the considerable growing of usage of quantum dots and nanotechnology in general by the industry and universities .
  • 16. 16 2.0 Quantum Wires(QW) 2.1 Nanowires, basics Analogously to the quantum dots, quantum wires or nanowires are electrically conducting wires small enough to the in quantum effects influence the transport properties. In this case, electrons will experience quantum confinement * in the perpendicular direction. As a result, their transverse energy will be quantized into a series of discrete values. The most easily demonstrable fact related to this phenomenon is that the well known formula for calculating the electrical resistance of a wire: Eq.2.1 , (where = resistivity, =the length, and = cross-sectional area). is no longer valid for quantum wires. Instead, in order to calculate the resistance is necessary an exact measurement and of the perpendicular energy of the confined electrons.  Quantum confinement can be observed once the diameter of a material is of the same magnitude as the de Broglie wavelength of the electron wave function.[1] When materials are this small, their electronic and optical properties deviate substantially from those of bulk materials.[2] Hartmut Haug; Stephan W. Koch (1994). Quantum Theory of the Optical and Electronic Properties of Semiconductors
  • 17. 17 2.2 Applications The nanowires could be used, in the near future, to link tiny components into extremely small circuits in large scale. Using nanotechnology, such components could be created out of chemical compounds. Actually, many experiments have just become viable, such as nanoantennas which will be seen the part 2 of this booklet, are only becoming possible due to the increasingly number of discoveries related to nanowires assembly . Fig. 2.2 Reference: Jim Heath, California Institute of Technology http://www.its.caltech.edu/~heathgrp/heath.html
  • 18. 18 2.3 Materials used in the nanowires. Many different types of nanowires exist, including metallic (e.g., Ni, Pt, Au), semiconducting (e.g., Si, InP, GaN, etc.), and insulating (e.g., SiO2,TiO2) and even molecular nanowires either organic or inorganic. In fact, there is a growing list of the current types of quantum wires : a) Alumina quantum wire b) Bismuth quantum wire c) Boron quantum wire d) Cadmium selenide quantum wire e) Copper quantum wire f) Gallium nitride quantum wire g) Gallium phosphide quantum wire h) Germanium quantum wire i) Gold quantum wire j) Indium phosphide quantum wire k) Magnesium oxide quantum wire l) Manganese oxide quantum wire m) Nickel quantum wire n) Palladium quantum wire o) Platinum quantum wire p) Silicon quantum wire q) Silicon carbide quantum wire r) Silicon nitride quantum wire s) Silver quantum wire t) Titanium dioxide quantum wire u) Zinc oxide quantum wire
  • 19. 19 3.0 Nanowires and quantum dots: properties. 3.1 facts related to the quantum wires and dots As aforementioned, the reduction in dimensionality produced by confined electrons to a thin semiconductor layer leads to a dramatic change in their behaviour. This principle can be better developed by reducing the dimensionality of the electron's environment from a two dimensional quantum well * to a one-dimensional quantum wire and eventually to a zero-dimensional quantum dot. In this context, of course, the dimensionality refers to the number of degrees of freedom in the electron momentum; in fact, within a quantum wire, the electron is confined across two directions, rather than just the one in a quantum well, and, so, therefore, reducing the degrees of freedom to one. In a quantum dot, however, the electron is confined in all three-dimensions, thus reducing the degrees of freedom to zero. If the number of degrees of freedom are labelled as "Df and the number of directions of confinement are labelled as Dc, then clearly: Df + Dc = 3 for all solid state systems. These values are highlighted for the four possibilities shown in Table 1.1. Tradition has determined that the reduced-dimensionality systems are labelled by the remaining degrees of freedom in the electron motion, i.e. Df, rather than the number of directions with confinement Dc.
  • 20. 20 Table 3.1 The number of degrees of freedom Df in the electron motion, together with the extent of the confinement Dc , for the four basic dimensionality systems: System Dc Df Bulk 0 3 Quantum Well 1 2 Quantum Wire 2 1 Quantum dot 3 0 Fig. 3.1 Fig. 3.1 shows an expanded view of a single quantum wire, where clearly the electron (or hole) is free to move in only one direction, in this case along the Y-axis. . Another class of quantum wire can be formed by patterning the substrate before growth. This leads to the formation of so-called V-grooved quantum wires. In fact there are many new classes of quantum wires which lays beyond the scope of this booklet. Quantum dots are also formed by further lithography and etching, e.g. if a quantum well sample is etched to leave pillars rather than wires, then a charge carrier can become confined in all three
  • 21. 21 dimensions . Figure 3.2 Schematic representation of the pyramidal shape of self-assembled quantum dots in highly lattice mismatched systems. 3.2 Brief statement about nanowires and quantum dots It is known that when two quantum wires acting as photon waveguides cross each other the juncture acts as a quantum dot. Consequently, the next chapter is a summary of the physical properties of quantum wires and quantum dots, which can be considered crucial part of the construction of nanoantennas, to be seen in part two. . Nanolithography is probably the most important step when constructing quantum wires and dots and is better explained in the nanoantennas chapters.
  • 22. 22 4 . Schrodinger’s equation in quantum wires 4.1 Schrodinger’s equation : basics. The Schrodinger equation is the fundamental mathematical tool for the understanding of quantum dots and quantum dots. *The Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.[1] When the Hamiltonian operator acts on a certain wave function Ψ, and the result is proportional to the same wave function Ψ, then Ψ is a stationary state, and the proportionality constant, E, is the energy of the state Ψ. Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules" (PDF). Physical Review The general three-dimensional Schrodinger equation * for constant effective mass is: (3.1) Where ħ is the Planck constant and is the rest mass. In a quantum wire it is possible to decouple the motion along the length of the wire. Taking the axis of the wire along x, then the total potential V(x, y, z) can always be written as the sum of a two-dimensional confinement potential plus the potential along the wire .
  • 23. 23 (3.2) The eigenfunction can then be written as a product of two components: (3.3) Substituting both equation (3.2) and equation (3.3) into equation (3.1), then: Writing the energy as a sum of terms associated with the two components of the motion, then: (3.4) It is now possible to associate distinct kinetic and potential energies on the left-hand side of equation (2.4), with the components Ex and Ey>z on the RHS, thus giving two decoupled equations, as follows:
  • 24. 24 (2.5) (2.6) In the above Ψ(y,z) is not acted upon by any operator in the first equation, and similarly for if Ψ(x) in the second equation, and thus they can be divided out. In addition, as mentioned above, the potential component along the axis of the wire V(x) = 0, thus giving the final decoupled equations of motion as follows (2.7) (2.8) Clearly, the first of these equations is satisfied by a plane wave of the form “exp(ikx X)”, thus giving the standard dispersion relationship: (2.9) This second of these equations of motion, equation , is merely the Schrodinger equation for the two- dimensional confinement potential characterising a quantum wire. The decoupling of the Schrodinger Equation will depend on the shape and type of the quantum wire and quantum tods . A much further mathematical approach can be find in the book Quantum Well,
  • 25. 25 Dots and Wires where spherical quantum dots , deep rectangular quantum wires, tiny quantum dots and may other classes are deeply reviewed. Ps: The results of solving the Schrodinger equation to obtain the equations as above were plucked from the Book Quantum Wells , Dots and Wires , Paul Harisson (3rd Edition) – Theoretical and Computational Physics of Semiconductor Nanostructures. 5. Near future of quantum wires. Slightly different from the quantum dots , quantum wires still belong to the experimental world of laboratories. Nonetheless, they may replace or at least complement carbon nanotubes in some applications. The newest experiments have shown that they are very likely to be the building blocks of the next generation of computing gadgets .Microelectronics, field emission devices, Optoelectronics , photonics, clothing fabric, and electronic device applications are some of the fields that probably are going to take advantage of a further development of quantum dots and quantum wires fabrication. One of these specific fields, the Nanoantennas, is the subject of the second part of this written booklet. Finally, is worth to say that nanolithography*, which is one of the main techniques related to the fabrication the branch nanometre-scale structures definitely will play a fundamental role in the next discoveries.
  • 26. 26  Nanolithography is used during the fabrication of leading-edge semiconductor integrated circuits (nanocircuitry) or nanoelectromechanical systems. There are currently several new types of techniques being develop such as Scanning probe lithography in which a microscopic or nanoscopic stylus is moved mechanically across a surface to form a pattern. It uses scanning tunneling microscope (STM) to produce nanometre scale features on a sample. Storex Disclosed Quantum Optical Lithography Technique", Press Release, Storage Newsletter.com, February 24th, 2012
  • 28. 28 NANOANTENNAS A nanoantennas (or nantenna) ) is a sort of rectifying antenna*, an experimental technology being developed to convert electromagnetic waves such as natural light to electric power. A nanoantenna is basically a very small rectenna the size of a light wave, when the quantum phe- nomena leads the behaviour of the objects. In the next years it is hoped that arrays of nantennas could be an efficient means of converting sunlight into electric power, producing solar power more efficiently than conventional solar cells.
  • 29. 29 Scheme of the nanowire-nanoantenna system. The different colours in the NW are an illustrative representation of the field energy distribution inside the NW during the excitation of transverse polarized light. The red colour indicates the highest field energy density and the green the lowest. “Polarization response of nanowires à la carte” Nature Scientific Report 5 Article number:7651 doi:10.1038/srep07651 – Published 07 January 2015
  • 30. 30 6. Nanoantennas 6.1 Introduction to Nanoantennas A nantenna is an electromagnetic collector designed to absorb wavelengths that are proportional to the its size. Ideally, nantennas would be used to absorb light at wavelengths between 0.4 and 1.6 μm because these wavelengths have higher energy than far-infrared (longer wavelengths) and make up about 85% of the solar radiation spectrum [4] .  A rectenna (or rectifying antenna) is a type of antenna that is used to transform micro- wave energy into direct current electricity. They are used in wireless transmission systems that transmit power by radio waves. A basic rectenna consists of a dipole antenna with a rectifying diode connected across the dipole elements. The diode rectifies the AC (alternate current) current induced in the antenna by the microwaves, to produce DC (direct current) power, which powers a load connected to the diode. "William C. Brown". Project #07-1726:Cutting the Cord. 2007-2008 Internet Science & Technology Fair, Mainland High School. 2012. Retrieved 2012-03-30. Nanoantennas can strongly enhance the interaction of light with nanoscale matter by their ability to efficiently link propagating and spatially localized optical fields. This ability unlocks an enormous potential for applications ranging from nanoscale optical microscopy and spectroscopy over solar energy conversion. The focus on the part 2 of this booklet is entirely on nanoantennas, investigating its features based on the background the researches from the last three decades. Finally, a brief account of the current status of the field and the major established and emerging lines of investigation, and the development of new techniques for this cutting-edge topic.
  • 31. 31 6.2 Nanoantennas: brief historic facts 1973 - a patent for an “electromagnetic wave converter” was given to Robert Bailey, along with James C. Fletcher,”. 1984 - Alvin M. Marks received a patent for a device explicitly stating the use of sub-micron antennas for the direct conversion of light power to electrical power. 1996 - Guang H. Lin was the first to report resonant light absorption by a fabricated nanostructure and rectification of light with frequencies in the visible range. 2002 - ITN Energy Systems, Inc. published a report on their work on optical antennas coupled with high frequency diodes. 2013 – A team lead by Federico Capasso at Harvard University in the US have made the first electrically tunable plasmonic antennas containing graphene that work in the mid-infrared. 6.3 Nanoantennas : How do they work. Antennas in general are used either to create electromagnetic waves with a well-defined radiation pattern, which can then travel over large distances, or to receive electromagnetic waves from a remote source in order to extract some encoded information, to measure changes in their intensity, or to exploit the transmitted power . The importance of antennas nowadays is dominated by two of their ability: to provide an interface between localized information processing using electrical signals and the free-space wireless transmission. Not only because of these properties, but also due to continuous search for new ways to improve transmission/reception involving energetic efficacy, nanoantennas are one of the hottest topics in energetic enhancement.
  • 32. 32 As a means for capturing or converting the abundant energy from solar radiation, an nanoantenna would be the ideal device because it is an efficient transducer between free space and guided waves. In the case of conventional solar cells, solar radiation is only absorbed if the photon energy is greater than the bandgap. The average power per unit area is about 1500 W/m2 , with a maximum intensity at about 0.5 µm. Solar radiation has a moderately broadband electromagnetic frequency spectrum, ranging from a frequency of about 150 THz to about 1,000 THz, corresponding to a free-space wavelength of about 2 µm to about 0.3 µm. Over 85% of the radiation energy is contained in the frequency range from 0.4 µm to 1.6 µm. Efficient antenna/rectifiers, therefore, need to cover a frequency range on the order of 100/25 (or 4/1). 6.4 . Advantages of the nanoantennas The most well-known advantage of nantennas, at least in theory, is their efficiency being higher than the well-stablished Carnot efficiency. In comparison to the theoretical efficiency of single junction solar cells (30%), nanoantennas seem to have a considerable advantage. Nonetheless, the two effi- ciencies are calculated using different assumptions. The assumptions involved in the nantenna calcu- lation are based on the application of the Carnot efficiency of solar collectors. The Carnot efficiency, η, is given by
  • 33. 33 where Tcold is the temperature of the cooler body and Thot is the temperature of the warmer body. In order for there to be an efficient energy conversion, the temperature difference between the two bod- ies must be significant. R. L. Bailey, the first to received a patent related to this technology as previ- ously stated, claims that nantennas are not limited by Carnot efficiency, whereas photovoltaics are. However, he does not provide any argument for this claim. Moreover, when the same assumptions used to obtain the 85% theoretical efficiency for nanoantennas are applied to single junction solar cells, the theoretical efficiency of single junction solar cells is also greater than 85%. In practice, the most well agreed advantage offered by nanoantennas is that they can be designed to absorb any frequency of light. Basically, the resonant frequency of a nantenna can be selected by varying its length. This is an advantage over semiconductor photovoltaics, due to the fact that in order to absorb different wavelengths, it is necessary different band gaps for the semiconductor photovol- taics. 6.5 Drawbacks of Nanoantennas One of the biggest limitations of nanoantennas is the extremely high frequency at which they operate, which makes the use of the typical use of Schottky diodes for normal rectennas nearly impossible for nanoantennas . There are new technologies in diode development in order to overcome this issue, however further research is necessary.
  • 34. 34 Yet another drawback is that nanoantennas are usually produced using electron beam nanolithogra- phy (e-beam). This process is time-consuming and expensive.. In general, e-beam lithography is used only for research purposes when extremely fine resolutions are needed for minimum feature size (typically, on the order of nanometres). However, photolithographic techniques have advanced to where it is possible to have minimum feature sizes on the order of tens of nanometres, making it possible to produce nanoantennas by means of photolithography, which has a small chapter in this written document.
  • 35. 35 7 . Future research and goals Probably the most well-known enthusiast of the nanoantennas technology is Dr. Novack, from NASA - National Aeronautics and Space Administration, who claims that nanoantennas could one day be used to power cars, charge mobile phones, and homes. Novack expressed that in the near future “smart” houses will work by both absorbing the infrared heat available in the room and producing electricity which could be used to further cool the room. However, as mentioned in the previous chapter, other scientists disagree. Mentioning it once again, the biggest problem at moment by far is not with the antenna device, but surely with the rectifier. As previously expressed, the current diodes are unable to efficiently rectify at frequencies corresponding to high-infrared and visible light (390 to 700 nm). Hence, It is necessary to design rectifiers that can properly turn the absorbed light into usable energy. Nanophysicists currently hope to develop a rectifier which can convert around 50% of the antenna's absorption into energy (which would end up being closer to Carnot efficiency).[ Yet another aim to be achieved in the next years is of research will be how to properly upscale the process to mass- produc- tion. For that to happen, the quantum dots and quantum wires researches will have to keep the pace with the nanoantennas studies in order to allow the assembly of such devices. In the case of the quantum dots and quantum wires, despite the presence of Cadmium, a well-known carcinogen, in the majority of current researches , it is worth mentioning again that many researches institutes are looking for Cadmium-free solutions and some of them have been already successful, as the British company Nanoco , as previously mentioned . Finally, due to the brief data presented in this book, we can conclude that nanolithographically defined quantum wires and quantum dots are the building blocks of the nanoantennas and play a big role in the always constant search for new energy resources.
  • 36. 36 8. References Novack, Steven D., et al. “Solar Nantenna Electromagnetic Collectors.” American Society of Me- chanical Engineers (Aug. 2008): 1–7. Idaho National Laboratory. 15 Feb. 2009 <http://www.inl.gov/pdfs/nantenna.pdf>. Berland, B. “Photovoltaic Technologies Beyond the Horizon: Optical Rectenna Solar Cell.” National Renewable Energy Laboratory. National Renewable Energy Laboratory. 13 Apr. 2009 <http://www.nrel.gov/docs/fy03osti/33263.pdf>. Lin, Guang H.; Reyimjan Abdu; John O'M. Bockris (1996-07-01). "Investigation of resonance light absorption and rectification by subnanostructures". Journal of Applied Physics 80 (1): 565–568. Robinson, Keith. Spectroscopy: The Key to the Stars. New York: Springer, 2007. Springer Link. Uni- versity of Illinois Urbana-Champaign. 20 Apr. 2009 <http://www.springerlink.com/content/p3878194r0p70370/?p=900b261891484572a965aca5acb7d0 79&pi=0>. Krasnok, Alexander. "Dielectric optical nanoantennas" (1(95)). ISSN 2226-1494. Retrieved 2015. Solarbuzz PV module pricing survey, May 2011 <http://solarbuzz.com/facts-and-figures/retail-price- environment/module-prices> “Nanoheating”, Talk of the Nation. National Public Radio. 22 Aug. 2008. Transcript. NPR. 15 Feb. 2009.
  • 37. 37 “Nano-Antennas for Solar, Lighting, and Climate Control”, Ecogeek. 7 Feb. 2008. 15 Feb. 2009. Interview with Dr. Novack. Moddel, Garret (2013). "Will Rectenna Solar Cells Be Practical?". In Garret Moddel; Sachit Grover. Rectenna Solar Cells. Springer New York. pp. 3–24. ISBN S.J. Byrnes; R. Blanchard; F. Capasso (2014). "Harvesting renewable energy from Earth’s mid-infra- red emissions". PNAS. doi:10.1073/pnas.1402036111. P. A. M. Dirac (1958). The Principles of Quantum Mechanics (4th ed.). Oxford University Press. David J. Griffiths (2004). Introduction to Quantum Mechanics (2nd ed.). Benjamin Cum- mings. ISBN 0-13-124405-1. Brus, L.E. (2007). "Chemistry and Physics of Semiconductor Nanocrystals" (PDF). Retrieved 7 July 2009. Norris, D.J. (1995). "Measurement and Assignment of the Size-Dependent Optical Spectrum in Cad- mium Selenide (CdSe) Quantum Dots, PhD thesis, MIT". Ekimov AI, Efros AL, Onushchenko AA (1985). "Quantum size effect in semiconductor microcrys- tals". Solid State Communications 56 (11): 921–924.