Semiconductor nanodevices

SEMICONDUCTOR NANOSTRUCTURES
BY: ATIF SYED

Atif Syed
Semiconductor Nanostructures
1
1. Introduction and Short History about Semiconductors:
Semiconductors are one of the widely used and building blocks of the modern day
electronics. Its ability to change its properties by adding impurities (known as
doping) has led to toggle its properties from being a conductor or insulator since the
conductivity ranges in between103
− 10−8
𝑠𝑖𝑒𝑚𝑒𝑛𝑠/𝑐𝑚.
The introduction of Semiconductors in Nanotechnology leads to a new division of
Semiconductors known as Semiconductors Nanostructures. Ever since the first
transistor was invented in Bell Labs by Shockley, Bardeen, and Brattain, the
miniaturization process of the transistors was already started and it was in 1949
when the first pnp transistor was invented by Shockley which is similar to the
present day bipolar transistors. By 1970, the transistors were scaled down to as low
as 10 µm. This introduces the concept of Moore’s law where he predicted that the
size of transistors will decrease exponentially. If we assume that is true, then within
5-10 years the structure sizes will reach of the order of the electron’s wavelength
(lhn, 2010, p. 4). Figure 1 shows a general form of the applications of Semiconductor
Nanostructures. When we look into nanostructures, quantum effects take place.
This will discussed further in the report.
Semiconductor
Nanodevices
Quantum
Computing
Optical
Sciences
Material
Sciences
Quantum
Mechanics
Low
Temperature
Physics
Electronics Medicine Nano-Robots
Figure 1: A general overview of Semiconductor Nanostructures applications

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2. Basic Physics in Semiconductor Nanostructures:
Before the physical properties of the semiconductor nanostructures are discussed, the
initial background behind this lies in the De-Broglie’s Wavelength equation given by
𝝀 =
𝒉
𝒑
2. 1
This leads to the introduction of the state function which is simply a form of a wave
which is in absence of any electromagnetic potential. Thus an electron in a vacuum at a
position s can be described as:
𝝍 = 𝒆𝒊( 𝒌.𝒔−𝝎𝒕)
2. 2
Where 𝜔 is the angular frequency and 𝑡 is the time and 𝒌 is given by:
𝒌 = | 𝒌| =
𝟐𝝅
𝝀
2. 3
The momentum described here is a quantum mechanical momentum which is given by:
−𝒊ħ𝛁𝝍 = 𝒑𝝍 2. 4
Where ∇ is given by:
𝝏𝒊̂
𝝏𝒙
+
𝝏𝒋̂
𝝏𝒚
+
𝝏𝒌�
𝝏𝒛
2. 5
This leads to the time dependant 𝑆𝑐ℎ𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′
𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 which is also associated with the
De-Broglie’s Wave-particle duality and is given by:
𝒊ħ
𝝏𝝍
𝝏𝒕
= 𝑬𝝍 2. 6
Where E is the total energy which is equal to the Kinetic Energy (K.E) of an electron in a
vacuum which is given by:
𝑬 =
ħ 𝟐 𝒌 𝟐
𝟐𝒎
2. 7
Where m is the mass of electron
Figure 2 gives an approximate by using the equations of energy and the wave vector.

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2.1 Quantum Wells:
The idea behind quantum wells is that it is a potential/quantum confinement well
with finite/discrete energy values which is comparable to the electrons and holes
which in turn exhibit the so called 2-Dimensional Properties in quasi nature. The
fabrication of quantum wells are done by using GaAs sandwiched with AlAs. The
fabrication of quantum wells is discussed in the later sections of the report. To
explain the working of quantum well, the concept of Heterostructures and
Heterojunctions is important.
2.1.1 Concept of Heterostructures, Heterojunctions and
Effective Mass Approximation:
If we consider that the crystal potential of any nanostructure can be derived through a
constant value, then the 𝑆𝑐ℎ𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′
𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 will be valid and the equation 2.6
becomes, where 𝑚∗
is the effective mass approximation:
ħ 𝟐
𝟐𝒎∗ 𝛁 𝟐
𝝍 = 𝑬𝝍 2. 8
Using the idea behind equation 2.8, Heterojunctions are nothing but 2 different
semiconductors placed adjacent to each other and Heterostructures are formed by 2 or
more Heterojunctions
E
k
Figure 2: Energy of an electron in vacuum versus wave vector curve

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2.2 Quantum Wires and Quantum Dots:
A quantum wire is just like any other electrically conducting wire which exhibits 1-
Dimensional properties in quasi nature and the quantum effects are affecting the
transport of current. The difference is that the resistivity is not calculated using the
classical formula but instead it is calculated through the transverse energies of the
confinement of electrons. A point to note is that the dimensions are simply an indication
to the degree of freedom of electron momentum therefore in quantum wires the
electron is confined in 2 directions as compared to only 1 in quantum wells. A quantum
dot on the other hand is a semiconductor whose degree of freedom is confined in 3
directions hence leaving 0 Dimensions. Therefore the degrees of freedom can be
expressed by the equation given below:
𝑭 𝒇 + 𝑭 𝒄 = 𝟑 2. 9
Where 𝐹𝑓 and 𝐹𝑐 stand for degrees of freedom and direction of confinement
respectively.
The following table describes equation 2.9 for different dimensional systems:
System 𝑭 𝒇 𝑭 𝒄
Bulk Material 0 3
Quantum Well 1 2
Quantum Wire 2 1
Quantum Dot 3 0
Table 1: Equation 2.9 compared by different systems
Figure 3: Quantum Wire showing the single degree of
freedom (Harrison, 2005, p. 245)

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2.3 Comparing the Density of States of Nanostructures:
The density of states is nothing but the ratio of the number of states per energy of
real space. It is given by the equation below:
𝑺( 𝑬) =
𝒅𝑵
𝒅𝑬
2. 10
Where 𝑁 is defined as:
𝑵 = 𝟐
𝟒𝝅𝒌 𝟑
𝟑( 𝟐𝝅) 𝟑 2. 11
If we combine equations 2.10, 2.11 and 2.8 we will get:
𝑺( 𝑬) =
𝟏
𝟐𝝅 𝟐 �
𝟐𝒎∗
ħ 𝟐 �
𝟑
𝟐
√ 𝑬 2. 12
Similarly the density of states equation for 2D, 1D and 0D can be obtained:
𝑺 𝟐𝑫( 𝑬) =
∑𝒎∗
𝝅ħ 𝟐 𝑯(𝑬 − 𝑬 𝒏) 2. 13
𝑺 𝟏𝑫( 𝑬) =
∑𝒎∗
𝝅ħ
�
𝒎∗
𝟐( 𝑬−𝑬 𝒏)
2. 14
𝑺 𝟎𝑫( 𝑬) = 𝟐(𝑬 − 𝑬 𝒏) 2. 15
Where 𝐸 𝑛 is the nth energy level and 𝐻 is the Heaviside function.
Figure 4: Quantum Dot showing the zero degree of
freedom (Harrison, 2005, p. 246)

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The density of states can be drawn as follows:
y
x
z
Figure 5: 3D Density State
x
y
Figure 6: 2D Density State

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The major differences between the nanostructures and the 3D structures (bulk) can be
explained through the table and the graph below:
𝑭 𝒇
Density of States Formula
3 (3D)
𝑆( 𝐸) =
1
2𝜋2
�
2𝑚∗
ħ2
�
3
2
√𝐸
2 (2D)
𝑆2𝐷( 𝐸) =
∑𝑚∗
𝜋ħ2
𝐻(𝐸 − 𝐸 𝑛)
1 (1D)
𝑆1𝐷( 𝐸) =
∑𝑚∗
𝜋ħ
�
𝑚∗
2( 𝐸 − 𝐸 𝑛)
0 (0D)
𝑆0𝐷( 𝐸) = 2(𝐸 − 𝐸 𝑛)
xFigure 7: 1D Density State
Table 2: Comparison of Density of States of 3D, 2D, 1D and 0D
Figure 11: 3D Figure 8: 0DFigure 9: 1DFigure 10: 2D
S(E) S(E) S(E) S(E)
E E E E

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2.4 Fermi-Dirac Distribution Function and the Concept of
Fermi Energy/Level:
The Fermi-Dirac probability function describes the electron occupation states. This in
detail can be explained occupation of electron states at some finite temperature and
is given by:
𝒇( 𝑬) =
𝟏
𝟏+𝒆
𝑬−𝑬 𝒇
𝒌𝑻
2. 16
Where 𝑘 is the Boltzmann’s constant and 𝑇 is the temperature in Kelvin.
𝐸𝑓 is the Fermi Energy or Fermi Level. It is determined when the temperature is 0 and
equation 2.16 yields ½. The electron probability for 150K, 300K, 600K and 0K is given
below assuming that the energy is 8eV and we are supposed to find the electron
probability at 8.1eV.
𝒇( 𝟖. 𝟏𝒆𝑽, 𝟏𝟓𝟎𝑲) =
𝟏
𝒆
�
(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗
𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟏𝟓𝟎
�
+𝟏
≈ 𝟎. 𝟏 2. 17
𝒇( 𝟖. 𝟏𝒆𝑽, 𝟑𝟎𝟎𝑲) =
𝟏
𝒆
�
(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗
𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟑𝟎𝟎
�
+𝟏
≈ 𝟎. 𝟐 2. 18
𝒇( 𝟖. 𝟏𝒆𝑽, 𝟔𝟎𝟎𝑲) =
𝟏
𝒆
�
(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗
𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟔𝟎𝟎
�
+𝟏
≈ 𝟎. 𝟏𝟒 2. 19
𝒇( 𝟖. 𝟏𝒆𝑽, 𝟎𝑲) =
𝟏
𝒆
�
(𝟖.𝟏−𝟖.𝟎)𝑿𝟏.𝟔𝑿𝟏𝟎−𝟏𝟗
𝟏.𝟑𝟖𝑿𝟏𝟎−𝟐𝟑 𝑿𝟎
�
+𝟏
= 𝟎. 𝟓 2. 20

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3. Fabrication of Quantum Wells, Wires and Dots:
Before the concept of fabrication is discussed, it is important to know how Silicon (Si) is
extracted.
3.1 Silicon Extraction:
The earth’s crust contains around 28% of Silicon on its crust and in production; Silicon is
made from Silica by burning it around 2000 𝑜
𝐶 and reducing it from Carbon which
follows the following chemical reaction:
𝑺𝒊𝑶 𝟐 + 𝟐𝑪 → 𝑺𝒊 + 𝟐𝑪𝑶 Chemical Reaction 3. 1
The above equation is the most common form of extracting Silicon. There are many
other methods of extracting Silicon. This brings us to the concept of Layer by Layer
growth and one of these methods is known as Molecular Beam Epitaxy (MBE) Growth.
3.2 Molecular Beam Epitaxy (MBE):
If we have a Silicon Wafer present, one could grow crystals with the MBE growth
method. So as to explain the method in detail and to give a broader point of view,
one would say that it is a refined evaporation technique which requires a pressure
of 10−10
− 10−11
𝑚𝑏𝑎𝑟. The solid particle is placed in the evaporation chamber in
such a way that the distribution of atoms can take place. The particle is constantly
rotated so that the distribution of atoms can be even which in turn improves the
growth pattern. An Ultra High Vacuum (UHV) chamber is used in MBE. The further
part of the process deals with the concept of the Crystal Lattices. The atomic beam
hits the heated substrate and the atoms stick to the substrate. They will diffuse on
the surface only after gaining an acceptable place in the Crystal Lattice1
. Normally
the growth procedure takes place at 500 𝑜
𝐶 − 600 𝑜
𝐶 and the growth rate is
about 1𝜇𝑚/ℎ𝑟. At UHV, the In-situ analysis of crystal growth takes place. This calls
the method known as RHEED (Reflected High Energy Electron Diffraction). This
method is carried out by scattering the electron beam and observing the pattern on
a fluorescent screen2
. In MBE growth, the intensity of RHEED is rotated periodically.
1
Lattices are infinite set of points which are given by the Bravais Lattice Equation𝑹 = 𝑛1 𝑎1 + 𝑛2 𝑎2 +
𝑛3 𝑎3. In Crystal Structure, the atoms are arranged in a particular way which shows some kind of
symmetry and the patterns are then seen and explained through the lattices. This is collectively known as
Crystal Lattices.
2
A fluorescent screen is a sheet coated with a fluorescent material which emits visible light when it is hit
by radiating beams such as X-ray or E-Beam.

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3.2.1 Advantages and Disadvantages of MBE:
MBE’s main advantage is the ability to control the layer thickness on a very minute
scale. The growth is homogeneous in nature and the homogeneity is maintained by
the process of rotation of the substrate. An interesting point to note is that since the
substrate are grown, for example, a quantum dot grown in MBE is known as Self
Assembled Quantum Dots (SAQD) and they have their own interesting properties
discussed later in the report.
MBE’s main disadvantage is the cost and maintenance of the machine. MBE’s can be
very complex at times and due to its strict vacuum procedures and requirements, it
can be a bit expensive and time consuming.
3.3 Optical and Electron Beam Lithography and their limits:
Ever since the miniaturization trend started three decades ago, semiconductors
today are produced with 60-65 nm dense features. Optical Lithography has enabled
this process to be seen more clearly at the sub-atomic level. Today most Integrated
As
Cracker Cell
Shutter
MBE Chamber
Sample
To Pumps
RHEED
Effusion Cell
Figure 12: Schematic diagram of MBE and important labeling.
Ga

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Circuits (IC) have been patterned using this technique. The pattern is transferred to
what is known as “mask” which is then placed on a thin layer of Photoresist3
.
Optical Integrator4
Photomask5
Projection Lens
∅
Wafer
3
A Photoresist (DiazoNaphtoQuinon-(DNQ) Sulfonate) is a photosensitive material which reacts to light
and Inden Carboxylic Acid.
4
An Optical Integrator is used to evenly distribute a light source un-diverted and un-disrupted.
5
A Photomask is an opaque plate with holes or transparencies that allow light to shine through in a
defined pattern. They are commonly used in photolithography (Photomask: Wikipedia, 2011)
Laser
Condenser Lens
Figure 13: Schematic Diagram of Optical
Lithography. The Optical Integrator and
Condenser Lens are collectively known as the
Illuminator

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In Figure 13, the laser light is directed towards the optical integrator which then diverts
the light into the condenser lens. The Optical Integrator and the Condenser are
collectively known as the Illuminator. This process expands the beam which is passed
through the Photomask. The Photomask patterns the image to be imaged onto the
wafer substrate. The Photoresist is present on the wafer. The Projection Lens is present
there to reduce the projection pattern by 2-5 factor which finally is directed to the
wafer. The following diagram summarizes the optical lithography process.
On the other hand, Electron Beam Lithography is done through the scattering of
electrons through a beam on the resist (similar to the optical beam lithography). E-Beam
Lithography is also used to create nanostructures which are then transferred into the
wafer (substrate) by the etching method.
Due to the fact that the e-beam lithography’s beam can be controlled and directed in
only one direction, it is preferred usually in many research facilities all over the globe. It
can be written down up to 30-40 nm structures. Similar to the Optical Lithography,
resists are used. In EBL, one of the most common resist which is used is PMMA
(Polymethyl Methacrylate) and the common name for this is acrylic. This brings to the
concept of different types of resists:
- Positive Resists are dissolved in the open areas during the development.
- Negative Resists are dissolved in the closed areas during the development.
Cleaning of the
Wafer
Spinning of
Photoresist
Exposure to
UV
Resist
Development
Etching of the
Semiconductor
Figure 14: Process of Optical Lithography

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One interesting thing to note is that e-beam lithography is done by using Scanning
Electron Microscope (SEM) and Scanning Tunneling Electron Microscope (STEM).
Since SEM had a resolution of about 10nm, the need for more powerful resolution
led to the introduction of Scanning Tunneling Electron Microscope (STEM) which has
a resolution of about 100nm with very less scattering of high energy electrons and
smaller electron probe diameter. The reduction of exposure has lead to higher
resolution images.
Just like in Photolithography6
, positive and negative resists are used in e-beam
lithography. In e-beam lithography, electrons are used instead of photos on the
resist. EBL has more resolution because the wavelength of electrons is smaller than
photons. Another difference from optical lithography is that electrons can be more
focused on the substrate (e.g. Si wafer) and only the areas which we are interested
in can be exposed. This in turn eliminates the need of mask in EBL. The electron
scattering on the other hand is done in two ways described below:
- Forward Scattering: In this, the electron path is deflected by the Coulomb’s
Potential7
which forces the trajectory to be in a cone like shape.
- Backward Scattering: In this, the electron path is deflected at an angle greater
than 90 𝑜
which forces the electrons to go back and focus a much wider area.
The SEM has relatively low beam energy roughly about 10keV but can go up to
30keV. This creates a new problem called back scattering in EBL’s. For example, the
backscatter will expose the entire area between them hence the accuracy is lost in
the process. Hence the need of STEM is more preferable despite the fact that many
EBL’s do not currently have STEM technology.
6
Optical Lithography is also known as Photolithography
7
Coulomb’s Potential is a scalar point which is equal to work per unit charge and is represented by the
equation
1
4𝜋𝜀 𝑜
𝑞1 𝑞2
𝑟
where 𝑞1 𝑎𝑛𝑑 𝑞2 the electric charge are by 2 ions and r is the distance between them.
Resist Electrons
Lens
Figure 16: Backscattering of ElectronsFigure 15: Front Scattering of Electrons

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The following table shows the basic limits and differences of Optical and E-Beam
Lithography.
Electron Beam Lithography Optical Lithography
Best used for hard and complex shapes
and patterns
Best used for huge and large shapes and
patterns
The ability to expose it to the point where
we are interested and to be able to get
high resolution
The ability to expose parallel and to be
able to get high resolution
Slow Speed Fast Speed
Resolution 10nm by SEM or 100nm by
STEM
Resolution 50nm-100nm
Not limited to Diffraction Limited to Diffraction
Electron Gun
Lens
Substrate
Aperture (typically includes 3
apertures and 1 deflector)
Figure 17: Basic Schematic Diagram of Electron Beam Lithography
Table 3: Limits and differences of Optical and Electron Beam Lithography

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4. Characterization of Semiconductor Nanostructures:
Semiconductor Nanostructures have unique and very useful characteristics. One of the
main characterizations and important Physical property is the Electron Transport. The
electron transport is better achieved by using III-V elements in the periodic table and
more preferably Si. Of all the things discussed in the report, the spin of electron has
been neglected. With the introduction of band structures playing a major role in the
characterizations, the Bloch Theorem and the Band Structure equation will be discussed.
4.1 Bloch Theorem and the Band Structure Equation:
The band structure has the property of the 𝑆𝑐𝑟𝑜̈ 𝑑 𝑖𝑛𝑔𝑒𝑟′
𝑠 𝐸𝑞𝑢𝑎𝑡𝑖𝑜𝑛 which is given by:
�−
ħ 𝟐
𝟐𝒎
∆ + 𝑽( 𝒈)� 𝝍( 𝒈) = 𝑬𝝍( 𝒈) 4. 1
Where 𝑉( 𝑔) is given by:
𝑽( 𝒈) = 𝑽(𝒈 + 𝑮) 4. 2
And G is an arbitrary vector that moves the lattice by itself. If we apply Fourier
transform to equation 4.2, the final band structure equation is given by:
�−
ħ 𝟐
𝟐𝒎
∆ + ∑𝑽 𝒓 𝒆𝒊𝑮𝒓
� 𝝍( 𝒈) = 𝑬𝝍( 𝒈) 4. 3
One important approximation in the band structures is the Tight-Binding Approximation.
4.2 Tight-Binding Approximation:
It regards the atoms in the lattice as weakly interacting, such that the atomic orbital
remain (almost) intact. The wave function for electrons in a particular band is a
linear combination of degenerate wave functions that are not too different from
atomic wave functions. The linear combination is chosen such that the wave
function fulfills Bloch’s theorem (lhn, 2010) (Ashcroft, Neil W, Mermin, David N,
1976). One of the most important and useful approximation led to the calculation of
Graphene structures. Graphene is a 2-D plane of carbon atoms that are arranged in
the shape of a honeycomb. Graphene shows an excellent quantum Hall Effect
(Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva,
I.V., Dubonos, S.V., and Firsov, A.A., 2005) which will be discussed later in this
section.

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4.3 Characterization Techniques:
There are many techniques and the most frequently used are discussed below:
4.3.1 Optical Spectroscopy:
As discussed in section 3 where we discussed about the Optical Lithography and its
limits and advantages, we can see that optical techniques are very useful in solid due
to their speed and that it can be easily manipulated hence the examination of the
topography, different parts of a structure can be easily determined. This method
creates 2-D map properties which in turn mean that the layer thickness or the
impurity distribution can be seen with finest details. 3-D mapping is also possible in
this technique if the light propagates perpendicular to its surface and the
penetration depends solely on the wavelength of the light.
4.3.2 Raman Spectroscopy:
Raman Signals are usually weak as compared to the excitation intensity. In Figure 18,
the laser light enters the system and the light is passed through the lens A which
converges the beam into about 10𝜇𝑚 pinhole. The lens C present in the figure makes
the laser light so as to spot the laser width and that the laser light since the lens C is
Laser
Pinhole
CCD
dectector
Beam Splitter
D
B
G
AC
F
E
Figure 18: Schematic of Raman Spectroscopy Microscope

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movable. The mirrors reflect the beam into the optical path of the microscope. The
sample can then be observed through the eyepieces which has a focus on the sample.
After the light has been passed through the CCD, the Rayleigh light is completely
removed due to the total backscattering of the light (laser) which makes the Raman light
the only visible light through the eyepiece. The CCD (Charged Coupled Device) camera
converts each pixel falling inside the camera into a charge. After the exposure of CCD to
the beam, it emits Photoelectrons. All of the data results can be seen on the computer
where the measurements and the data can be stored for further use. The conversion of
pixels into charge is done due to the fact that the CCD has rectangular 2-D Arrays.
4.3.3 Photoluminescence:
PL is one of the most useful optical methods for analyzing the intrinsic and extrinsic
properties of the semiconductors. This process absorbs photon which results in high
electronic energy states. While returning back to the low energy state it again emits
a photon. This process helps in identifying the impurities in the semiconductors
which affects the material’s properties and performance.
4.3.4 Tunneling Electron Microscopy (TEM):
By the use of TEM’s one could get the information about the topography such as
size, shape, composition, crystal structures etc. The working of TEM is fairly simple;
the laser beam in the TEM is emitted through the electron gun and is manipulated
using a magnetic lens. After this the images of the sample can be formed by the
excitation of electrons which follows a similar concept of E-Beam Lithography but
contrary to optical methods, this method uses a magnetic lens.
4.3.5 Electron Transport in Quantum Dots:
Electrons act like a wave in Quantum Dot which in turn plays the role of partial
waves of light. The electron transport in quantum dots is seen in the following two
ways/scenarios:
- Two Quantum Dots connected in Parallel
- Two Quantum Dots connected in Series
4.3.5.1 Two Quantum Dots connected in Parallel:
The main idea behind this is that the quantum dots are connected in parallel so that
they eventually allow current to flow either or both QD’s with resonance which in
turn creates electrochemical potential. Another experiment with this includes two

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quantum dots were connected in parallel with finite tunneling coupling between
them were performed (Hofmann, F., Heinzel, T., Wharam, D.A., Kotthaus, J.P., Bohm,
G.,Klein, W., Trankle, G., and Weimann, G., 1995). Quantum dots connected in
parallel with mutual tunneling coupling can also be realized by vertical stacking (lhn,
2010).
4.3.5.2 Two Quantum Dots connected in Series:
Quantum Dots are connected in series is entirely different from the parallel
connection. Series connections are more often found in today’s electronic devices. If
we are to achieve the electron flow at low source-drain bias, it is only possible by
using triple points of charge stability.
In Figure 19, the Coupled Quantum Dots are arranged in such a way that the 2 dots
are perfectly aligned with each other with the electrochemical potential in between
the leads. The transfer of electrons in this configuration is done elastically. In
Figures 20 and 21, the alignment is done only in one Quantum Dots. In this type
arrangement, the electron transfer from source to the drain is done due to the weak
tunneling coupling between the leads and the dots. The coupling between the
quantum dots and the leads can lead to different characteristics. Stronger coupling
can be achieved by increasing the gate voltage8
. For weaker coupling, the transport
happens only at the triple points. If we try to increase the coupling even further, the
phenomenon known as quantum dot regime is observed.
8
Gate Voltage is the voltage applied to the gate of the electrode in a Field Effect Transistors (FET’s). Gate
Source voltage on the other hand is the direct current voltage between the gate and the source
electrodes.
Dot 1 Dot 2
Dot 1 Dot 2 Dot 1 Dot 2
Figure 20: Last QD’s alignedFigure 21: 2 QD’s aligned Figure 19: First QD aligned

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19
5. Applications of Semiconductor Nanostructures:
Semiconductor Nanostructures are used in many applications. Since the field is quite
vast, this report will be brief and will cover some interesting applications.
5.1 Quantum Information Processing:
Information processing in general is based on physical systems and processes. Ever since
the exchange of information has started, this field has seen enormous amount of
achievement and merits. But as time passes by and with the introduction of
nanotechnology, the shrinking and miniaturization process of everything has started,
the biggest question arises, does the laws of Quantum Physics change the way we see
the information processing now? If yes, then how is it possible? More questions like, can
we transmit radio signals, electron by electron and photon by photon? Can we use the
electron spin and do much more complicated calculations much better than what we
are able to today? Many more questions like this can be answered and we will try to
understand the concept behind all this and how this can be achieved.
5.1.1 The Classical Bit:
The information processing is an entirely probabilistic entity. Keeping this in mind and
getting inspired from (lhn, 2010) and (Timpson, 2004) the following example can be
given to better explain this concept. If we assume that there are X number of possible
outcomes that can occur with a probability of 𝑝 =
1
𝑥
and we give the outcomes before
and after the uncertainty has occurred as 𝑄 𝑏𝑒𝑓𝑜𝑟𝑒 𝑎𝑛𝑑 𝑄 𝑎𝑓𝑡𝑒𝑟 respectively then the
following equation is valid:
∆𝑮 = 𝑸 𝒃𝒆𝒇𝒐𝒓𝒆 − 𝑸 𝒂𝒇𝒕𝒆𝒓 5. 1
With this concept in mind9
, the Shannon Entropy is given by the equation:
𝑯({ 𝒑𝒊}) ≡
𝑸
𝑵
= −∑𝒑𝒊 𝒍𝒐𝒈 𝟐 𝒑𝒊 𝒃𝒊𝒕 5. 2
9
For simplicity and compactness sake, the derivation is not given in this report but can be found in many
Quantum Computers/Information Processing textbooks.

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20
Where N is the total number of outcomes and 𝑝𝑖 is the different possible probabilities.
With this, the unit of measurement for Shannon Entropy is the bit as mentioned in
equation 5.2.
The classical bit can now be defined in terms of quantum physics and by using the Dirac
Notation10
. If we want to use the Dirac Notation on the binary bit 00102 it will be
written as|0010 >. Classical bits can be represented, copied and transferred n number
of times. But with the introduction of Qbits, the evolution process has already started.
Quantum Computer promises much advancement like better memory management,
more information stored on minute sizes and this information can be stored without the
need of actually destroying them ever.
5.1.2 Quantum Bits (Qbits):
The smallest Hilbert space suitable for information storage is spanned by two
orthogonal quantum states (lhn, 2010). A qbit is represented by the superposition of
two bits. In other words, the classical bit 0 and 1 can be used twice or together by the
superposition and this is achieved by the theory of Spin Theory and Azimuthal Quantum
Numbers. The Qbits can be represented by using the Dirac Notations, one general form
of this given below:
| 𝝍 > = 𝜶 𝟎| 𝟎 > +𝜶 𝟏|𝟏 > 5. 3
With reference to equation 5.3, a feature called normalization feature occurs which is
nothing but the sum of the squares of the 2 state bits is always equal to 1:
𝜶 𝟎
𝟐
+ 𝜶 𝟏
𝟐
= 𝟏 5. 4
If the wave functions of the two bits cannot be written as the product of two single bits,
then it is called as entanglement or entangled bits which are given by the following
example:
|𝝍 > =
𝟏
√ 𝟐
(|𝟎𝟎 > ±|11 >) 5. 5
A qbit can be represented by using a spherical diagram known as the Bloch sphere
representation. To explain that in a better way, density matrix of a single quantum bit
can be written as:
10
A Dirac Notation is a representation of two quantum states where one is represented by bra <|x and
the ket y|>.

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21
𝝆� =
𝟏
𝟐
�
𝟏 + 𝑷 𝒛 𝑷 𝒙 − 𝒊𝑷 𝒚
𝑷 𝒙 + 𝒊𝑷 𝒚 𝟏 − 𝑷 𝒛
� 5. 6
Where,
𝑃𝑥 = sin 𝜃 cos 𝛿
𝑃𝑦 = sin 𝜃 sin 𝛿
𝑃𝑧 = cos 𝜃
|𝜓 >
𝜃
𝛿
|0>
|0>-|1>
|0> - i|1>
|1>
|0>
|0> + |1>
Figure 22: Quantum Bit represented as a sphere following the Bloch Spherical Representation

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22
Figure 23: Prototype of a Quantum Computer (lhn, 2010) (Bucktard, G., Engel, H.-A., and Loss, D., 2000)
As far as the uses of quantum computers are concerned, it is pretty much told by the
amount of possibilities quantum computers can bring about in the computer industry.
With Quantum Computers, every computer can be a super computer because trillions of
calculations can be done with very few quantum bits, for example 9 qbits represent 512
values and 10 represents 1024 and so on, doubling the number of values in each
increase of quantum bit. With this in mind, calculating a trillion worth of values will only
take probably around 40 qbits which is 100,000 times less bits used as compared to
today’s classical bits. "A supercomputer's going to take trillions of steps, and this
algorithm will take a few hundred," says mechanical engineering professor Seth Lloyd,
who along with Avinatan Hassidim, a postdoc in the Research Lab of Electronics, and the
University of Bristol's Aram Harrow '01, PhD '05, came up with the new algorithm
(Quantum computing may actually be useful, 2009). With qubits, however, "you can
make any measurement you like," Lloyd says, "You can figure out, for instance, their
average value. You can say, okay, what fraction of them is bigger than 433?" Such
measurements take little time but may still provide useful information. They could,
Lloyd says, answer questions like, "In this very complicated ecosystem with, like, 10 to
the 12th different species, one of which is humans, in the steady state for this particular
model, do humans exist? That's the kind of question where a classical algorithm can't
even provide anything." (Quantum computing may actually be useful, 2009). To yield
accurate results, a weather prediction model might require data from millions of
sensors transmitted continuously over high-speed optical fibers for hours. Such
quantities of data would have to be loaded into quantum memory, since they would
overwhelm all the conventional storage in the world. Once all the data are in, however,
the resulting forecast needs to be calculated immediately to be of any use. (Quantum
computing may actually be useful, 2009).

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23
5.2 Nanorobotics:
Nanorobots are another important and very interesting application in the field of
nanotechnology. There are many applications of Nanorobots and this report will
focus on some of them. Just like its counterpart, macro robots, Nanorobots also
follow some of the same concepts.
5.2.1 Working of Nanorobots and its applications:
The main idea behind Nanorobots is the construction and fabrication of robots at
nano scale. The challenges hidden behind this are:
- Construction of robots at nano scale
- Programming the robots
- Manipulation and Self-Assembly of Nanorobots
The dimensions of Nanorobots are comparable to that of cells and organelles and
hence the biggest useful application of Nanorobots is in the field on medicine known
as bio Nanorobots. Just imagine that (Nanorobots) patrol the blood circulatory
system and destroy any harmful pathogens without them causing any harm to the
human body or may be able to repair the damaged cells.
5.2.2 Design, Control and Programming of Nanorobots:
In this section we will focus briefly on the working on Nanorobots step by step.
Sensors:
Just like a normal robots, Nanorobots will also use sensors. A true nanoscale sensor
doesn’t exist but according to Kong who says, “A device that exploits the change in
conductivity of a carbon nanotube when it is exposed to a specific gas is perhaps the
closest to a true nanosensor” Many things like bacteria or chemical sensors can be
used for the Nanorobots sensors but it is still under research.
Actuators:
- Artificial Molecular Machines:
There is a good progress in this part of the research. These machines are either
single molecules or supramolecular systems of interlocked molecules. In either case,
they are atomically precise, that is, each atom is in a known and precisely
established location with respect to the others (Nanorobots, NEMS and

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24
Nanoassembly, 2002). The two molecular machines synthesized are: a linear shuttle
(A. M. Brower, C. Frochot, F. C. Gatti, D. A. Leigh, L. Mottier, F. Paolucci, S. Roffia and
G. W. H. Wurpel, 2001, pp. 2124-2128) and a rotary motor (Feringa, 2001, pp. 504-
513)
- Biomotors:
Biomotors tend to be on the range of 10s of nm, and are typically larger than the
synthetic molecular machines discussed above, which have overall sizes of only a
few nm. Noji and his team were the first to directly image the motion of a Biomotors
( H. Noji, R. Yasuda, M. Yoshida and K. Kinosita, Jr., 1997, pp. 299-302)
Communication:
Communication among Nanorobots by means of waves is they are acoustic,
electrical or optical, is likely to be difficult because of the small antenna sizes. The
communication in Nanorobots can be better understood if we look at nature. Bees
communicate by dancing, ants communicate by chemical signals which vary with
respect to the environment and bacteria releases chemicals as well and one of the
chemical signals released by bacteria is more commonly known as quorum sensing
which assess similar bacteria near them. (Nanorobots, NEMS and Nanoassembly,
2002)
Programming:
One of the main things that are needed in Nanorobots programming is the fact that
better co-ordination is needed. Yet again, bacteria or organelles play an important
role in it. Bacteria show very limited coordination behavior; ants use elaborate
algorithms (E. Bonabeau, M. Dorigo and G. Theraulaz, 1999); and the human
immune system has an extremely complex coordination and (chemical) signaling
scheme, which is still far from being completely understood (L. A. Segel and I. R.
Cohen, 2001).

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25
Figure 24: Bio Nanorobots: An Overview (Ummat A., Dubey A., Sharma G., Mavroidis C)
Figure 25: The working of Nanorobots in the field of medicine. (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)
Figure 26: Nanorobot Molecule Delivery (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)

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26
Figure 27: Nanorobots with sensors and obstacle detectors. (Adriano Cavalcanti, Robert A. Freitas Jr., 2005)
Figure 28: Nanorobots using chemical sensors to avoid and detects objects. (Adriano Cavalcanti, Lior Rosen, Luiz C.
Kretly, Moshe Rosenfeld, Shmuel Einav, 2004)
Figure 29: Vein inside view without the red blood cells. The target plaque is represented by the pink
spheres surrounding the vessel wall. The Nanorobots swim in a near-wall region searching for the
atherosclerotic lesion. (Adriano Cavalcanti, Lior Rosen, Luiz C. Kretly, Moshe Rosenfeld, Shmuel Einav,
2004)

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27
5.3 Will Nanotechnology solve the Solar Cells problem?
Figure 30: Working of a Solar Cell. (How Solar Cells Work, 2005)
The solar power/cells we have currently have little effect on the large power grid
systems in place and it’s impossible to replace everything with solar power with the
current technology in solar cells. Scott Aldous, an engineer for the North Carolina Solar
Center explains that, “These two effects alone account for the loss of around 70 percent
of the radiation energy incident on the cell” (How Solar Cells Work, 2005). The biggest
question now arises is that, does the current system in place is efficient enough? The
maximum efficiency achieved today is only around 25 percent (An unexpected discovery
could yield a full spectrum solar cell., 2002). Some chemists at UC, Berkeley has
managed to produce cheap plastic solar cells which can adapt any surface whatsoever.
The plastic solar cells utilize small nanorods which are then dispersed in a polymer.
Nanorods behave similar to Quantum Wires because they can absorb light and emit
electrons. These electrons keep on flowing until they reach Aluminum electrode and
conduct electricity. (Sanders, 2002)
Figure 31: Working of a Nano-Solar Cell (Sanders, 2002)
Konarka, a company specializing in making solar nano cells says they have “built fully
functional solar cells that have achieved efficiencies of around 8%” Currently, the

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28
researchers have been successful in tuning the nanorods such that they absorb certain
wavelengths of light so as to exploit a wider range of color spectrum. If solar cells have
been integrated into large scale, the environment will be protected and the utilization of
renewable energy will be at its epitome. Nano Solar Cells will also eradicate the problem
of electricity in rural and poorer countries where generating a large amount of
electricity could be a costly affair. Although it might be a bit skeptical to use nano solar
cells on a large scale but the opportunities on a medium or small scale is enormous. The
question is still open for discussion and debate while a lot of researchers and companies
are getting involved in making this a reality.
References
H. Noji, R. Yasuda, M. Yoshida and K. Kinosita, Jr. (1997). Direct observation of the rotation of
F1-ATPase. Nature .
A. M. Brower, C. Frochot, F. C. Gatti, D. A. Leigh, L. Mottier, F. Paolucci, S. Roffia and G. W. H.
Wurpel. (2001). Photoinduction of fast, reversible translational motion in a hydrogen-bonded
molecular. 2124-2128.
Adriano Cavalcanti, Lior Rosen, Luiz C. Kretly, Moshe Rosenfeld, Shmuel Einav. (2004).
NANOROBOTIC CHALLENGES IN BIOMEDICAL APPLICATIONS, DESIGN AND CONTROL. IEEE ICECS
Int’l Conf. on Electronics, Circuits and Systems .
Adriano Cavalcanti, Robert A. Freitas Jr. (2005). Nanorobotics Control Design: A Collective
Behavior Approach for Medicine . IEEE TRANSACTIONS ON NANOBIOSCIENCE , 133-140.
An unexpected discovery could yield a full spectrum solar cell. (2002, 11 18). Retrieved 04 01,
2011, from Berkeley Lab: http://www.lbl.gov/Science-Articles/Archive/MSD-full-spectrum-solar-
cell.html
Ashcroft, Neil W, Mermin, David N. (1976). Solid State Physics.
Bucktard, G., Engel, H.-A., and Loss, D. (2000). Fortschr. Phys.
E. Bonabeau, M. Dorigo and G. Theraulaz. (1999). Swarm Intelligence: From Natural to Artificial
Systems. Oxford: Oxford University Press.
Feringa, B. L. (2001). In control of motion: from molecular switches to molecular motors.
Accounts of Chemical Research , 504-513.
Harrison, P. (2005). Quantum Wells, Wires and Dots. Leeds: Wiley.

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Hofmann, F., Heinzel, T., Wharam, D.A., Kotthaus, J.P., Bohm, G.,Klein, W., Trankle, G., and
Weimann, G. (1995). Phys. Rev.
How Solar Cells Work. (2005, 05 22). Retrieved 01 04, 2011, from How Stuff Works:
http://science.howstuffworks.com/environmental/energy/solar-cell1.htm
L. A. Segel and I. R. Cohen. (2001). Design Principle for the Immune System and Other Distributed
Autonomous Systems. Oxford: Oxford University Press.
lhn, T. (2010). Semiconductor Nanostructors. Oxford Publishing.
Nanorobots, NEMS and Nanoassembly. (2002). Retrieved 04 01, 2011, from USC:
http://ilab.usc.edu/classes/2002cs597f/RequichaProc9-5.pdf
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos,
S.V., and Firsov, A.A. (2005). Nature.
Photomask: Wikipedia. (2011, 03 30). Retrieved 03 30, 2011, from Wikipedia:
http://en.wikipedia.org/wiki/Photomask
Quantum computing may actually be useful. (2009, 10 09). Retrieved 04 01, 2011, from MIT:
http://web.mit.edu/newsoffice/2009/quantum-algorithm.html
Sanders, B. (2002, 03 28). Cheap, Plastic Solar Cells May Be On The Horizon. Retrieved 04 01,
2011, from UC Berkeley Campus News:
http://www.berkeley.edu/news/media/releases/2002/03/28_solar.html
Timpson, C. G. (2004). Quantum Information Theory.
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