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The Electron Transport of Boron Nitride
Nanoribbons with Defects.
MD HASANUR RAHMAN, Yan-Dong Guo
School of Electronics and Information Engineering, Nanjing University of Posts and
Telecommunications, Nanjing, China.
ABSTRACT
Boron nitride nanoribbons (BNNRs) are a relatively novel class of materials that have attracted
considerable interest in the field of nanoelectronics owing to their exceptional electronic properties.
In particular, BNNRs have a large bandgap and exhibit semiconducting behavior, making them
promising candidates for use in a variety of electronic devices. Nevertheless, the presence of
defects in BNNRs can have a significant effect on their electronic transport properties, which has
become an important research topic in recent years. Using the Atomistix Toolkit (ATK) software,
we investigate the effect of defects on the electronic transport properties of BNNRs in this thesis.
To model the behavior of BNNRs with different classes of defects, we employ two simulation
techniques: density functional theory (DFT) and non-equilibrium Green's function (NEGF)
formalism.Using DFT permits us to accurately model the electronic structure and transport
properties of BNNRs with defects, whereas the NEGF formalism provides a potent instrument for
simulating the transport of electrons through nanoscale systems. Our method enables us to
investigate in great detail the effect of defects on the electronic transport properties of BNNRs,
thereby shedding light on the fundamental physics of these materials.
We provide an introduction to the realm of BNNRs, including their synthesis and properties,
in the first chapter of our article. We also discuss the significance of these materials' flaws and the
effect that they can have on their electronic transport properties. We provide a concise history of
BNNRs, focusing on the most significant developments in their discovery and study over the past
decade.
In the second chapter, we describe in greater detail the two simulation methods used in our
investigation. We discuss the theoretical foundations of these methods and detail how they are
implemented in the ATK software suite. We also discuss the benefits and drawbacks of these
methods, emphasizing the significance of employing multiple simulation techniques in order to
gain a comprehensive comprehension of the behavior of BNNRs with defects.
In the third chapter, the results of our simulations and analysis of the electronic transport
properties of BNNRs with defects are presented. We analyze the effect of various categories of
defects, such as vacancies, substitutional dopants, and Stone-Wales defects, on the electronic
transport behavior of BNNRs. Our findings indicate that the presence of defects can substantially
modify the electronic transport properties of BNNRs, including conductivity, electron mobility,
and transmission coefficient. We also investigate how temperature and strain affect the transport
behavior of BNNRs with defects.
By providing a comprehensive comprehension of the effect of defects on their electronic
transport properties, our study makes a significant contribution to the field of BNNR research.
Utilizing ATK software and advanced simulation techniques represents a substantial advancement
in the development of BNNRs for nanoelectronics applications. In addition, our findings
demonstrate the significance of considering the effects of defects when designing and optimizing
electronic devices based on these materials.
Keywords: Boron nitride nanoribbons, Electronic transport, Defects, Density functional theory
(DFT), Non-equilibrium Green's function (NEGF) formalism, Nanoscale systems.
Chapter I: Introduction
1.1 Nanotechnology
Nanotechnology, which is often shortened to "nanotech," is the economic use of matter at the
atomic, molecular, and supramolecular scales. When nanotechnology was first talked about, it was
usually in terms of the goal of controlling atoms and molecules in a precise way to make large-
scale goods. This is now called molecular nanotechnology. The National Nanotechnology
Initiative later came up with a more general definition of nanotechnology. It said that
nanotechnology is the manipulation of matter with at least one measurement that is between 1 and
100 nm. This definition is appropriate for this scale because it takes into account the significance
of quantum mechanical effects. Because of this, the definition changed from a specific
technological goal to a research category that includes everything from academic studies to
cutting-edge technology that focus on matter's peculiar characteristics that happen below the given
size threshold. Because of this, "nanotechnologies" and "nanoscale technologies" are both popular
ways to talk about a wide range of studies and applications that have one thing in common: size.
Fig. 1.1: Nano-particles
Nanotechnology is a broad field because it is based on size. It includes areas of science as different
such as nanotechnology, microfabrication, molecular engineering, energy storage, and physics of
semiconductors. The related research and uses are just as varied, ranging from extending
traditional device physics to totally new methods based on molecular self-assembly, from making
materials having nanoscale dimensions to directly controlling matter on the atomic scale.
Scientists argue about what nanotechnology will mean in the future. Nanotechnology might be
able to make a lot of new materials and gadgets that can be used in many different ways, such as
in nanomedicine, nanoelectronics, biomaterials, energy production, and market goods. On the
other hand, nanotechnology brings many of the same concerns as any new technology. These
include worries about nanomaterials' toxicity and impact on the environment, as well as their
possible effects on the global economy and rumors about different doomsday scenarios. Because
of these worries, interest groups and countries have talked about whether nanotechnology needs
special rules.
Origins
In 1959, the famous physicist Richard Feynman gave a talk called "There's Plenty of Room at the
Bottom," in which he talked about the chance of synthesis through direct manipulation of atoms.
This talk was the start of nanotechnology.
Fig. 1.2: Nano-scale
Norio Taniguchi used the word "nanotechnology" for the first time in 1974, but not many people
knew what it meant. K. Eric Drexler used the term "nanotechnology" in his 1986 book Engines of
Creation: The Coming Era of Nanotechnology. This book proposed the idea of a nanoscale
"assembler" that could build copies of itself and other things of any complexity with atomic control.
In 1986, Also Drexler helped start the Foresight Institute, which he is no longer a part of, to help
people learn more about nanotechnology and understand what it means.
In the 1980s, nanotechnology became a field because of the public and theoretical contributions
of Drexler, who invented and popularized a theoretical framework for nanotechnology, and high-
profile experimental advances, which brought more attention to the idea of atomic control of matter.
In the 1980s, there were two big breakthroughs that helped nanotechnology grow into what it is
today.
First, the scanning tunneling microscope was invented in 1981. It made it possible to see individual
atoms and links in a way that had never been done before. In 1989, it was used to successfully
move individual atoms. Gerd Binnig and Heinrich Rohrer at the IBM Zurich Research Laboratory
made the microscope. In 1986, they won the Nobel Prize in physics. In the same year, Binnig,
Quate, and Gerber also came up with a similar atomic force microscope.
Fig. 1.3: Buckminsterfullerene
Second, Harry Kroto, Richard Smalley, and Robert Curl, who shared the 1996 Nobel Prize in
Chemistry, found fullerenes in 1985. Nanotechnology wasn't used to describe C60 at first. This
phrase was coined to describe later work with similar carbon nanotubes that showed possible uses
for electronics devices on the nanoscale. Carbon nano-tubes were mostly found by Sumio lijima
of NEC in 1991. For his work, in 2008 lijima won the first Kavli Prize in Nanoscience.
At the beginning of the 2000s, the field attracted more interest from scientists, politicians, and
businesses. This led to both controversy and progress. As shown by the Royal Society's study on
nanotechnology, there were disagreements about how to define nanotechnologies and what effects
they might have. There were questions about whether the applications that supporters of molecular
nanotechnology thought were possible were possible. This led to a public argument between
Drexler and Smalley in 2001 and 2003.
At the same time, goods based on advances in nanoscale technologies started to become available
for sale. These goods only use nanomaterials in large quantities and have nothing to do with
controlling matter at the atomic level. Some examples are the Silver Nano platform, which uses
silver nanoparticles as an antibiotic agent, nanoparticle-based clear sunscreens, silica nanoparticles
to strengthen carbon fibre, and carbon nanotubes to make clothes that don't stain.
The government took steps to support and fund nanotechnology research. The National
Nanotechnology Initiative in the United States established a definition of nanotechnology based
on scale and set up funding for nanoscale research. In Europe, this was also accomplished via the
European Union's research and development funding programs.
By the middle of the 2000s, there was a lot of new and serious scientific interest. Nanotechnology
roadmaps are being made, and they focus on controlling matter at the atomic level. They talk about
current and future goals, powers, and applications.
Fundamental Concepts
Nanotechnology is the process of making things that do molecular-level work. This goes over both
ongoing work and more advanced ideas. The original meaning of the word "nanotechnology" was
the idea that it would be possible to build things employing techniques and apparatus from the
ground up that are being made right now to make complete, high-performance items.
One nanometer (nm), or 10−9 of a meter, is equal to one billionth of a meter. Carbon-carbon bond
lengths, or how far apart these atoms are in a molecule, are usually between 0.12 and 0.15 nm, and
the width of a DNA double-helix is about 2 nm. On the other hand, bacteria in the genus
Mycoplasma, which are the smallest biological life forms, are about 200 nm long. The National
Nanotechnology Initiative in the US uses the scale range of 1 to 100 nm as the standard meaning
of nanotechnology. Since nanotechnology uses atoms and molecules to make its gadgets, the size
of atoms sets the lower limit. Hydrogen has the smallest atoms, which are about a quarter of a nm
in diameter. The upper limit is more or less made up, but it is around the size where things start to
happen that aren't seen in bigger structures and can be used in a Nano device. Because of these
new things, nanotechnology is different from devices that are just smaller versions of similar
macroscopic devices. These devices are on a wider scale and are called micro technology.
To compare this scale to something else, a nanometer is about the same size as a pebble compared
to the size of the earth. Or, to put it another way, a nanometer is how much a man's beard grows
in the time it takes him to reach for the razor.
In nanotechnology, there are two main ways to do things. In the "bottom-up" method, materials
and devices are made from molecular parts that put themselves together chemically based on
molecular recognition principles. In the "top-down" method, Nano-objects are made from bigger
things without control at the atomic level.
In the last few decades, fields of physics like nanoelectronics, Nano mechanics, Nano photonics,
and nanoionics have grown to provide a theoretical base for nanotechnology.
Nanotechnology will let us:
• Get the highest level of accuracy: almost every atom in the right place.
• Make shapes that are complicated at the molecular level as easily and cheaply as simple ones.
• Keep the cost of making the product close to the cost of the raw materials and energy it needs.
Applications of Nanotechnology
As of the 21st of August 2008, the Initiative on Emerging Nanotechnologies says that over 800
nanotech products made by different companies are offered to the public, and that 3–4 new ones
come out every week. All of the goods are listed in a public online database that is part of the
project. Most uses are limited to "first-generation" passive nanomaterials, such as titanium dioxide
in sunscreen, cosmetics, surface coatings, and some food products; carbon allotropes used to make
gecko tape; silver in food packaging, clothing, disinfectants, and home appliances; zinc oxide in
sunscreens and cosmetics, surface coatings, paints, and outdoor furniture varnishes; and cerium
oxide as a fuel catalyst.
Bowling balls, golf balls, and tennis balls can all benefit from the material's hardness and durability.
Nanotechnology has been added to trousers and socks to make them last longer and keep people
cooler in the summer. Bandages are being made with tiny pieces of silver to help cuts heal faster.
Thanks to nanotechnology, video game systems and computers may become cheaper, faster, and
have more memory. Also, construct optical architectures for on-chip computing, information
transfer in picoseconds and on-chip optical quantum computing are two examples.
Nanotechnology might be able to make it cheaper and easier to use medical tools in places like
doctors' offices and people's homes. Nanomaterials are being used to make cars in a way that
means car parts will need less metal to make and less petrol to run in the future.
Scientists are now using nanotechnology to try to make gasoline engines that give off less pollution.
At the moment, the diesel engine catalyst in these engines is made of platinum. The catalyst is
what gets rid of the particles in the gas. First, a reduction catalyst is used to take the nitrogen atoms
out of the NOx molecules so that the oxygen can be freed. The hydrocarbons and carbon monoxide
are then broken down by the oxidation catalyst into carbon dioxide and water. [Needs citation]
Both the reduction and oxidation catalysts use platinum. But using platinum is wasteful because it
is expensive and can't be kept up for long. The Danish company Innovations Fonder put up DKK
15 million to use nanotechnology to find new catalyst replacements. The goal of the project, which
began in the autumn of 2014, is to use as little material as possible while getting as much surface
area as possible. Objects tend to have the least amount of surface energy possible. For example,
two drops of water will join to make one drop, which reduces the surface area. If as much of the
catalyst as possible is exposed to the exhaust fumes, the catalyst will work as well as possible. The
goal of the team working on this project is to make nanoparticles that don't stick together. Material
is saved every time the surface is made as good as it can be. So, making these nanoparticles will
make the diesel engine catalyst work well, which will lead to cleaner pollution fumes and save
money. If the team is successful, they hope to cut the use of platinum by 25%.
Nanotechnology is also a big part of Tissue Engineering, which is an area that is growing quickly.
Researchers try to make scaffolds that look like the nanoscale features of a cell's surroundings so
that the cell's differentiation goes in the right direction. For example, experts may make scaffolds
that look like osteoclast resorption pits to help bones grow.
Researchers have been able to target drug delivery in cockroaches by making nanobots out of DNA
origami that can carry out logic functions. It is said that these nanobots can be made to have as
much computing power as a Commodore 64.
The Future and Risks of Nanotechnology
In the last few years, nanotechnology has been at the center of many new ideas. Both academia
and business saw right away that this new technology had a huge amount of promise. Being able
to change so many parts of modern life can actually be a way to change the way things are done.
Many people say that nanotechnology could pose a lot of risks and dangers in the future. This
could be caused by bad uses of the new technology, like making more powerful weapons or spying
systems that invade everyone's privacy, which raises social, ethical, and safety concerns. Since it's
already a part of our lives, it's pretty safe to say that it will change how we live.
1.2 Boron nitride
Boron nitride is a refractory substance made of boron and nitrogen. It is resistant to heat and
chemicals and has the chemical formula BN. It comes in different crystalline forms that have the
same electronic structure as a carbon grid. The hexagonal form corresponding to graphite is the
most stable and soft among BN polymorphs and is therefore used as a lubricant and an additive to
cosmetic goods. The diamond-like structure of zincblende, also known as sphalerite, is called c-
BN. It is softer than diamond, but it is more stable in both heat and chemicals. The rare BN form
of wurtzite is like lonsdaleite, but it is a little softer than the cubic form.
Boron nitride ceramics are used in high-temperature tools and metal casting because they are stable
in both heat and chemicals. In nanotechnology, boron nitride could be used.
Fig. 1.4: Boron nitride bonding
1.2.1 Definition of Boron Nitride
Boron nitride's (BN) empirical formula is not what it seems to be. BN is not at all like carbon
monoxide (CO) or hydrogen chloride (HCl), which are also made up of two atoms. Instead, it has
a lot in common with carbon, which is also misrepresented as a single atom (the C). BN, like
carbon, can take on different shapes. hBN is the most stable structure of BN. It shares the same
hexagonal shape as graphite and has the same softness and lubricant qualities. hBN can also be
made in sheets that look like graphene and can be rolled into nanotubes. On the other hand, cubic
BN (cBN) has the same electrons as diamond. It's not quite as hard, but it's more stable when it
comes to heat and chemicals. Also, it is much simpler to make. At high temperatures, it doesn't
dissolve in metals like diamond does. This makes it useful as an abrasive as well as an oxidation-
resistant metal layer. There is also a type that looks like amorphous carbon, which is called
amorphous BN (see below). BN is mostly made in a lab, but there has been a mention of it being
found in nature. Since the beginning of the 20th century, people have tried to make pure BN, but
the first kinds that can be sold have only been made in the last 70 years. In a 1958 patent issued
by the Carborundum Company in Lewiston, NY, Kenneth M. Taylor made BN shapes by heating
boric acid (H3BO3) via a metal salt of an oxyacid like phosphate with the aid of ammonia to make
a "mix" of BN, which was then pressed into shape. Methods that start with boric trioxide (B2O3)
or H3BO3 along with ammonia or urea as a nitrogen source are still used today. All ways of making
a BN make a BN that isn't completely pure. Heating aBN at higher temperatures than those used
in the synthesis cleans it up and turns it into hBN. With high pressure and temperature, hBN is
changed into cBN, which is similar to how manmade diamonds are made.
Fig. 1.5: Wurtzite Boron nitride (3D from)
1.2.2 Characteristics of Boron Nitride
Boron nitride is a type of chemical that is made up of atoms of both boron and nitrogen. It is
possible to find it in a number of different configurations, such as hexagonal boron nitride (h-BN)
& cubic boron nitride (c-BN). The structure and appearance of hexagonal boron nitride are similar
to those of graphite. The material is composed of stacked layers of hexagonal sheets that are held
together by weak van der Waals forces. It is a good electrical insulator, is white in color, and has
a slick and slippery texture. Cubic boron nitride, on the other hand, is a man-made material that
has a crystal structure that is comparable to that of diamond. As a result, it is exceptionally hard
and is frequently utilized as an abrasive in cutting tools. Because of their excellent thermal
conductivity, chemical stability, and tolerance to high temperatures, both forms of boron nitride
are extremely useful in a variety of industries, including ceramics, electronics, lubricants, and
coatings, among others.
1.2.2.1 Structure
Boron nitride comes in different forms that differ in how the boron and nitrogen atoms are arranged.
This makes the material have different bulk qualities.
Amorphous form (a-BN)
Boron nitride in its amorphous (a-BN) form is not solid because its atoms are not arranged in a
way that is the same over long distances. It is like amorphous carbon in that way.
Boron nitride comes in solid forms in all other cases.
Hexagonal form (h-BN)
The hexagonal solid form, also called h-BN, α-BN, g-BN, and graphitic boron nitride, is the most
stable. Hexagonal boron nitride has the same layering as graphite (point group = D6h, space group
= P63/mmc). Boron and nitrogen atoms are held together by strong covalent bonds inside each
layer, while weak van der Waals forces hold the layers together. But these sheets' "registry"
between layers is different from the pattern seen in graphite because the atoms are obscured, with
boron atoms on top of nitrogen atoms. This list shows the local polarity of the B-N bonds and the
features of the N-donor/B-acceptor pairs between layers. In the same way, there are many
metastable forms that are made up of polytypes built in different ways. So, h-BN and graphite are
very close neighbors, and the material can take carbon as a substituent element to make BNCs.
Scientists have made BC6N mixtures in which carbon takes the place of some of the B and N atoms.
Fig. 1.6: Hexagonal form (h-BN)
Cubic form (c-BN)
The crystal structure of cubic boron nitride is the same as that of diamond. Like how diamond is
less stable than graphite, the cubic form is less stable than the hexagonal form, but the rate of
change between the two is negligible at room temperature, just like it is for diamond. The cubic
form has the same structure as diamond (ordered B and N atoms) and is also called β-BN or c-BN.
It has the same crystal structure as sphalerite (space group = F43m), which is the same as that of a
diamond.
Fig. 1.7: Cubic form (c-BN)
Wurtzite form (w-BN)
Boron nitride in its wurtzite form (w-BN; point group = C6v; space group = P63mc) has the same
structure as lonsdaleite, a rare hexagonal version of carbon. The boron and nitrogen atoms are
grouped into tetrahedra, just like they were in cubic form. The boron and nitrogen atoms in wurtzite
are grouped into six-membered rings. In the cubic form, all of the rings are in a chair shape, but in
the w-BN form, the rings between the "layers" are in a boat shape. Earlier, optimistic reports said
that the wurtzite form would be very strong. A simulation suggested that it could be 18% stronger
than diamond. Since the element is only found in small amounts in nature, this has not been proven
yet. Its hardness is 46 GPa, which is slightly harder than commercial borides but softer than the
cubic form of boron nitride.
Fig. 1.8: Wurtzite form (w-BN)
1.2.2.2 Properties
Physical
Properties of amorphous and crystalline BN, graphite and diamond.
Some properties of h-BN and graphite differ within the basal planes (∥) and perpendicular to them (⟂)
Table no. 1.1
The partially ionic structure of the BN layers in h-BN decreases the covalency and conductivity of
electricity while increasing the interaction between layers. This makes h-BN harder than graphite.
Hexagonal-BN has no color and a big band gap, which are both signs that its electrons are not
spread out as much as they could be. Most of the features of h-BN have a high level of anisotropy
because the bonds between the boron and nitrogen atoms are strong within the basal planes but
weak between them.
For instance, the hardness, electrical conductivity, and temperature conductivity are all much
higher along the lines than they are across them. On the other hand, c-BN and w-BN have more
uniform and consistent qualities.
These materials are very hard, with bulk c-BN being slightly less hard than diamond and bulk w-
BN being even harder than diamond. People have also said that polycrystalline c-BN with grain
sizes on the order of 10 nm is as hard as or harder than diamond. Because c-BN is much more
stable around heat and transition metals than diamond, it is better for mechanical tasks like cutting
steel. BN has one of the best thermal conductivities of all the things that don't let electricity through
(see table).
Boron nitride can be made p-type by adding beryllium, and it can be made n-type by adding boron,
sulfur, silicon, or both carbon and nitrogen. Both hexagonal and cubic BN are wide-gap
Material
Boron nitride (BN)
Graphite
Diamond
a-
h-
c-
w-
Density (g/cm3)
2.28
~2.1
3.45
~3.49
~2.1
3.515
Knoop hardness (GPa)
10
45
34
100
Bulk modulus (GPa)
100
36.5
400
400
34
440
Thermal conductivity
(W/m·K)
3
600 ∥,
30 ⟂
740
200-2000 ∥,
2-800 ⟂
600-2000
Thermal expansion (10−6/K)
-2.7 ∥,
38 ⟂
1.2
2.7
-1.5 ∥,
25 ⟂
0.8
Band gap (eV)
5.05
5.9-6.4
6.4
4.5-5.5
0
5.5
Refractive index
1.7
1.8
2.1
2.05
2.4
Magnetic susceptibility
(µemu/g)
-0.48 ∥,
-17.3 ⟂
-0.2 - -2.7 ∥,
-20 - -28 ⟂
-1.6
semiconductors with a band gap energy that corresponds to the UV region. When h-BN or c-BN
is given a voltage, it gives off UV light in the range of 215–250 nm. This means they could be
used as light-emitting diodes (LEDs) or lasers.
Little is known about how boron nitride behaves when it melts. At normal pressure, it sublimates
at 2973 °C, giving off nitrogen gas and boron. At high pressure, however, it melts.
Mechanical Properties
Boron nitride, which is only a few atoms thick, is one of the best electrically insulating elements.
Monolayer boron nitride has an average Young's modulus of 0.865TPa and a fracture strength of
70.5GPa. Unlike graphene, whose strength drops dramatically with increasing thickness, few-layer
boron nitride sheets have the same strength as monolayer boron nitride.
Thermal Stability
Chemically and thermally, hexagonal and cubic BN (and probably w-BN) are very stable. For
example, h-BN doesn't break down until it reaches 1000 °C in air, 1400 °C in a vacuum, and
2800 °C in an atmosphere with no oxygen or nitrogen. Both h-BN and c-BN have a similar level
of reactivity. The results for c-BN are shown in the table below.
Reactivity of c-BN with solids
Solid
Ambient
Action
Threshold
temperature (°C)
Mo
10−2 Pa vacuum
Reaction
1360
Ni
10−2 Pa vacuum
Wetting
1360
Fe, Ni, Co
Argon
React
1400-1500
Al
10−2 Pa vacuum
Wetting and reaction
1050
Si
10−3 Pa vacuum
Wetting
1500
Cu, Ag, Au, Ga, In, Ge, Sn
10−3 Pa vacuum
No wetting
1100
B
No wetting
2200
Al2O3 + B2O3
10−2 Pa vacuum
No reaction
1360
Table no.: 1.2
To sum up c-BN's thermal stability, we can say the following:
In air or oxygen, a protective layer of B2O3 stops further oxidation up to about ~1300°C.
At 1400°C, there is no change to a hexagonal shape.
There is some change to h-BN in nitrogen after 12 hours at 1525 °C.
In a vacuum (1 0−5 Pa), the change to h-BN happens between 1550-1600 °C.
Chemical Stability
Boron nitride is insoluble in the usual acids, but is soluble in alkaline molten salts and nitrides,
such as LiOH, KOH, NaOH-Na2CO3, NaNO3, Li3N, Mg3N2, Sr3N2, Ba3N2 or Li3BN2, which are
therefore used to etch BN.
Thermal Conductivity
The theoretical temperature conductivity of hexagonal boron nitride nanoribbons (BNNRs) can be
close to 1700–2000 W/(mK). This is on the same order of magnitude as the experimentally
measured value for graphene and can be compared to the theoretical predictions for graphene
nanoribbons. Also, there are differences in how heat moves through the BNNRs. At room
temperature, the thermal conductivity of BNNRs with zigzag edges is about 20% greater than that
of BNNRs with armchair edges.
1.2.2.3 Synthesis
Preparation and Reactivity of Hexagonal BN
Boron nitride is made in a laboratory. Boron trioxide (B2O3) or boric acid (H3BO3) reacts with
ammonia (NH3) or urea (CO(NH2)2) in a nitrogen-filled room to make hexagonal boron nitride.
B2O3 + 2 NH3 → 2 BN + 3 H2O (T = 900 °C)
B(OH)3 + NH3 → BN + 3 H2O (T = 900 °C)
B2O3 + CO(NH2)2 → 2 BN + CO2 + 2 H2O (T > 1000 °C)
B2O3 + 3 CaB6 + 10 N2 → 20 BN + 3 CaO (T > 1500 °C)
The resulting disordered (amorphous) boron nitride is made up of 92–95% BN and 5–8% B2O3.
In a second step, the leftover B2O3 can be evaporated at temperatures above >1500 °C to get a BN
concentration of more than >98%. BN also gets crystallised in this way, and the size of the
crystallites grows as the temperature of the heating process goes up.
Parts made of h-BN can be made cheaply by hot pressing and then cutting. Boron nitride powder
is used to make the parts, and boron oxide is added to make them easier to crush. Chemical vapour
deposition can be used to make thin films of boron nitride from boron trichloride and nitrogen.
When boron powder is burned in a nitrogen plasma at 5500 °C, tiny boron nitride is made, which
is used in lubricants and toners.
At -30 °C, boron nitride mixes with iodine fluoride in trichlorofluoromethane to make NI3, a low-
yield explosive that is very sensitive to touch. Nitrides of lithium, alkaline earth metals, and
lanthanides combine with boron nitride to make nitridoborate compounds. For example:
Li3N + BN → Li3BN2
Intercalation of Hexagonal BN
Similar to graphite, different molecules, like NH3 or alkali metals, can be put between the layers
of hexagonal boron nitride. Experiments and theories show that BN is much harder to intercalate
than graphite.
Fig. 1.9: Structure of hexagonal
Preparation of Cubic BN
c-BN is made in the same way that diamond is: by putting hexagonal boron nitride through high
pressure and temperature. This is similar to how man-made diamonds are made from graphite. At
pressures between 5 and 18 GPa and temperatures between 1730 and 3230 °C, a straight change
from hexagonal to cubic boron nitride has been seen. These conditions are the same as for the
direct change from graphite to diamond. By adding a small amount of boron oxide, the needed
pressure can be lowered to 4–7 GPa and the temperature can be lowered to 1500 °C. As in the
process of making diamonds, a catalyst like lithium, potassium, or magnesium, their nitrides, their
fluoronitrides, water with ammonium compounds, or hydrazine is added to lower the pressures
and temperatures even more. Using a temperature gradient or an explosive shock wave to grow
crystals is another way to do things in the business world. This idea comes from how diamonds
grow. The shock wave method is used to make heterodiamond, which is made of boron, carbon,
and nitrogen and is very hard.
Thin films of cubic boron nitride can be put down under low pressure. As with the growth of
diamonds, the biggest problem is stopping the growth of hexagonal stages (h-BN or graphite,
depending on the material). For diamond growing, this is done by adding hydrogen gas. For c-BN,
this is done by adding boron trifluoride. Physical vapour deposition is also done with ion beam
deposition, plasma-enhanced chemical vapour deposition, pulsed laser deposition, reactive
sputtering, and other means.
Preparation of Wurtzite BN
Methods involving either static high pressure or dynamic shock can be used to produce wurtzite
BN. There is a lack of clarity regarding the boundaries of its stability. Compressing h-BN results
in the synthesis of both c-BN and w-BN, however the formation of w-BN takes place at
temperatures far lower than 1700°C.
Production Statistics
The production and use numbers for boric acid and boron trioxide, which are used to make boron
nitride, are well known (see boron). However, the same numbers for boron nitride are not included
in statistical records. About 300 to 350 metric tonnes are thought to have been made around the
world in 1999. The United States, Japan, China, and Germany are the main places that make and
use BN. In 2000, prices for normal industrial-grade h-BN ranged from $75 to $120/kg and went
up to $200 to $400/kg for high-purity BN grades.
1.2.2.4 Applications
Hexagonal BN
Most of the time, hexagonal BN (h-BN) is used. It works well as a lube at both low and high
temperatures (up to 900 °C, even in an oxidising atmosphere). h-BN grease is especially useful
when the electrical conductivity or chemical reactivity of graphite (another lubricant) would be a
problem. h-BN, which is more stable at high temperatures, can be added to engine oils. This is
because graphite can be oxidised and turn into carbon sludge in internal combustion engines.
Brownian-motion settlement is a problem for all nanoparticle solutions. Settlement can clog oil
filters, so solid lubricants can only be used in a combustion engine for racing cars, where engines
are often rebuilt. Because carbon dissolves easily in some alloys (like steel), which can cause the
properties to change, BN is often a better choice for high temperature and/or high pressure uses.
h-BN is also better than graphite because it doesn't need water or gas molecules stuck between its
layers to make it slick. So, h-BN lubricants can be used in places where there is no air, like in
space. Fine-grained h-BN is used in cosmetics, paints, tooth cements, and pencil leads because it
makes things smooth.
Fig. 1.10: Ceramic BN crucible
Around 1940, in Japan, hexagonal BN was first used in makeup. Because h-BN was too expensive
for this use, it was not used. Its use was brought back to life in the late 1990s when h-BN production
methods were improved. Today, almost all of the top cosmetics companies use h-BN in
foundations, makeup, eye shadows, blushers, kohl pencils, lipsticks, and other skin care products.
Boron nitride ceramics have been used for a long time in high-temperature equipment because
they are very stable in both heat and chemicals. h-BN can be used to give self-lubricating qualities
to ceramics, alloys, resins, plastics, rubbers, and other materials. These kinds of products can be
used to make things like bearings and steel. Plastics that have BN in them don't expand as much
when heated, and they also conduct heat and electricity better. Due to its good dielectric and
thermal properties, BN is used in electronics as a base for semiconductors, a window that lets
microwaves through, a filler in thermal pastes that conducts heat but doesn't carry electricity, and
as a structural material for seals. As a base material, multilayer h-BN is used in a lot of quantum
devices. It can also be used in resistive random access memories as a lubricant.
Hexagonal BN is used as the charge-leaking barrier layer of the photo drum in xerography and
laser printers. In the auto business, h-BN mixed with a binder (boron oxide) is used to seal oxygen
sensors, which provide feedback for adjusting fuel flow. The binder takes advantage of how stable
h-BN is at different temperatures and how well it insulates.
Four industrial grades of h-BN can be hot-pressed to make parts. HBN is held together by boron
oxide. It can be used up to 550–850 °C in an oxidising atmosphere and up to 1600 °C in a vacuum,
but it is sensitive to water because of the boron oxide. Grade HBR is held together with calcium
borate and can be used at 1600 °C. Grades HBC and HBT don't have binders and can be used up
to 3000 °C.
Boron nitride nanosheets (h-BN) can be made by catalytically breaking down borazine at about
~1100 °C in a chemical vapour deposition setup and spreading them out over an area of about 10
cm2. They are used as bases for graphene-based products because their atomic structure is
hexagonal, their lattice mismatch with graphene is small (~2%), and they are very uniform. BN
nanosheets are also very good at carrying protons. With their high electrical resistance and high
rate of proton transport, they could be used in fuel cells and water electrolysis.
Since the middle of the 2000s, h-BN has been used as a bullet and bore lubricant in precise target
rifles instead of molybdenum disulfide coating, which is often called "moly." It is said to make the
barrel last longer, make it so you don't have to clean the bore as often, and make the difference
between the point of impact of the first shot with a clean bore and future shots smaller.
Cubic BN
Cubic boron nitride, also known as CBN or c-BN, is often used as a grinding tool. Its value comes
from the fact that it doesn't dissolve in iron, nickel, and similar alloys at high temperatures, while
diamond does. So, polycrystalline c-BN (PCBN) abrasives are used to machine steel, while
aluminium alloys, ceramics, and stone are better machined with diamond abrasives. BN forms a
layer of boron oxide when it comes into contact with oxygen at high temperatures. Boron nitride
sticks well to metals because layers of metal borides or nitrides form between the layers of boron
nitride. Cutting tool bits are often made of materials with cubic boron nitride crystals. Softer media
like resin, porous ceramics, and soft metals are used for grinding. You can also use ceramic
connectors. Products sold to the public are called "Borazon" by Hyperion Materials &
Technologies and "Elbor" or "Cubonite" by Russian sellers.
In contrast to diamond, it is easy to make large c-BN pellets by annealing c-BN powders in a flow
of nitrogen at temperatures just below the BN decomposition point. This is called "sintering."
Because c-BN and h-BN powders can melt together, it is cheap to make big BN parts.
Like diamond, c-BN is great for heat spreaders because it has the best thermal conductivity and
the lowest electrical resistivity.
Cubic boron nitride is a popular material for X-ray membranes because it is made of light atoms
and is strong both chemically and mechanically. Its low mass means that it doesn't absorb many
X-rays, and its good mechanical qualities let it be made into thin membranes, which further reduces
the amount of X-rays it absorbs.
Amorphous BN
Some semiconductor devices, like MOSFETs, use layers of amorphous boron nitride (a-BN). They
can be made by using caesium in order to break up trichloroborazine chemically or by using
thermal chemical vapour deposition. Thermal CVD can also be used to put down layers of h-BN
or c-BN at high temperatures.
1.3 Defects in Boron nitride
Boron nitride can have flaws on a variety of length scales, ranging from atomic vacancies and
impurities to more significant structural irregularities. These flaws can be classified as defects.
Atomic vacancies cause the crystal lattice to become disorganized, which in turn has an effect on
the crystal's electrical, mechanical, and thermal characteristics. The electrical structure, thermal
conductivity, and chemical reactivity of a material are all susceptible to change as a result of
impurities, regardless of whether they were accidentally or purposefully introduced. Lattice
deviations can cause structural defects such as dislocations, stacking faults, and grain boundaries,
all of which have an impact on the mechanical strength and thermal behavior of the material. Boron
nitride nanostructures can have their electrical and mechanical properties altered by nanoscale
defects such as vacancies and edge dislocations. In order to fully exploit the potential of boron
nitride in a variety of sectors, including electronics, optoelectronics, catalysis, and energy storage,
among others, researchers are working to minimize and manage the effects of defects by
employing accurate synthesis, post-synthesis treatments, and hybrid structures.
1.3.1 Types of Defects in Boron Nitride
Boron nitride, which is made up of atoms of both boron and nitrogen, is well-known for its unique
qualities and wide range of uses in many fields. But, like any other material, boron nitride can have
flaws that change its qualities and how well it works. Boron nitride can have flaws on many
different length scales, from missing atoms and impurities to bigger structural flaws.
Atomic vacancies are one of the most common types of flaws in boron nitride. This is when a
boron or nitrogen atom is missing from its usual place in the crystal structure. These vacancies can
have a big effect on the material's electrical, mechanical, and thermal properties because they
change the way the atoms are arranged and form areas where the bonds are different.
Boron nitride can also have impurities, which are another type of flaw. During the synthesis
process, these impurities can be added accidentally or on purpose to change certain properties.
Boron nitride can be affected in different ways by impurities, depending on what they are and how
many there are. They can change the electronic structure, thermal conductivity, and chemical
reaction of a material, making it less or more suitable for certain uses.
Boron nitride can have structural flaws if there are changes in the crystal lattice, like dislocations,
stacking faults, or grain boundaries. Dislocations happen when there is a difference in how the
atoms are arranged along a line defect. This can cause localized strain and lower the tensile strength
of the material. Stacking faults, on the other hand, are caused by the misalignment of atomic layers
within the crystal structure, which makes the hexagonal pattern look different than it should. Grain
boundaries are the points where different crystal grains meet, and they can change the mechanical
and thermal qualities of a material.
Boron nitride can also have flaws that show up at the nanoscale level. Nanotubes and nanosheets
of boron nitride, for example, can have flaws like vacancies, edge dislocations, and grain borders
because it is hard to make perfect nanostructures. The electronic and mechanical properties of
boron nitride crystals can be changed by these tiny flaws, which makes it important for
nanotechnology to be able to characterize and control them.
Researchers are looking for ways to reduce and control defects in boron nitride in order to improve
its qualities and find new uses for it. Some ways to deal with the effects of defects are to use precise
synthesis methods, treatments after synthesis, and hybrid structures. Scientists hope to use boron
nitride's full potential to make improvements in many fields, such as electronics, optoelectronics,
catalysis, energy storage, and many others, if they can figure out and fix its flaws.
1.3.2 Intrinsic Defect in Boron Nitride
Intrinsic faults in boron nitride are flaws that come from the material itself and are not caused by
adding impurities on purpose. These flaws can happen during the synthesis or growth of boron
nitride because of how the boron and nitrogen atoms move and interact with each other.
Atomic gaps are a common problem in boron nitride that can't be fixed. Atomic gaps happen when
a boron or nitrogen atom is not where it should be in the crystal lattice. These empty spots change
how the atoms are normally arranged and lead to places where the bonds are different. Boron
nitride's electrical, mechanical, and thermal qualities can be changed by vacancies because they
change the structure and behavior of the material as a whole.
Boron nitride also has point defects, such as substitutional defects and interstitial defects, which
are part of the material itself. When an atom of boron or nitrogen is swapped out for an atom of a
different element, this is called a substitutional flaw. In the crystal structure, for example, a carbon
atom can stand in for a boron or nitrogen atom. This change adds a different type of atom to the
structure of boron nitride, which changes the way the material works.
On the other hand, interstitial flaws happen when an atom moves into a space between the crystal
lattice. Interstitial defects can happen in boron nitride when atoms like boron or nitrogen move
into places between the normal lattice sites. These flaws can change the density and order of the
atoms, which changes the properties of the material.
Boron nitride's inherent flaws can also show up as line flaws, like dislocations. When atoms along
a line flaw aren't lined up right or are arranged in an odd way, this is called a dislocation. These
flaws can have a big effect on the mechanical strength of the material and on its structural stability
as a whole.
To predict and control the traits and behavior of boron nitride, it is important to understand and
describe its inherent defects. Researchers use different methods, such as experimental
characterization and theoretical models, to study how intrinsic defects form, what effects they have,
and how they can be controlled. Scientists want to improve the performance of boron nitride and
find new ways to use it in areas like electronics, optoelectronics, catalysis, and energy storage by
learning more about its defects.
1.4 Boron Nitride Nanomesh
Boron nitride nanomesh is a two-dimensional material that has a nanostructure. It is made up of a
single layer of BN, which self-assembles into a very regular mesh when a clean rhodium or
ruthenium surface is exposed to borazine at a high temperature and under very high pressure. The
nanomesh looks like a group of hexagonal holes put together. The space between two pores is 3.2
nm, and the width of a pore is about ~2 nm. This material is also called white graphene or
boronitrene.
The boron nitride nanomesh doesn't break down in a vacuum, in air, or in some liquids. It's also
stable up to 800 °C. It also has the amazing ability to catch molecules and metal clusters that are
the same size as the nanomesh pores and form a well-ordered array. Because of these features, the
nanomesh could be used in interesting ways in areas like catalysis, surface functionalization,
spintronics, quantum computing, and data storage media like hard drives.
Fig. 1.11: BN nanomesh observed with a scanning tunneling microscope. The center of each ring
corresponds to the center of the pores.
1.5 Boron Nitride Nanotubes
Boron nitride tubules were initially created by Shore and Dolan in 1989. This work was initially
published in 1989 in Dolan's thesis and then again in 1993 in Science. It was patented in 1989.
Additionally, the production of amorphous BN using B-trichloroborazine and cesium metal was
accomplished for the first time in the 1989 work.
Boron nitride nanotubes were first discovered experimentally in 1995, although they had been
anticipated in 1994. One could see them as a sheet of hBN that has been folded up. Its structure is
quite similar to that of the carbon nanotube, which is characterized by a long cylinder with a
diameter of several to one hundred nanometers and a length of many micrometers. However,
instead of carbon atoms, it has alternately nitrogen and boron atoms as its building blocks.
However, the properties of BN nanotubes are quite dissimilar to those of carbon nanotubes.
Whereas carbon nanotubes can either be metallic or semiconducting depending on the rolling
direction and radius, a BN nanotube is an electrical insulator with a bandgap of ~5.5 eV and is
essentially unaffected by the chirality of the tube or its shape. Additionally, in comparison to a
graphitic carbon structure, the layered BN structure exhibits a significantly higher level of thermal
and chemical stability.
Fig. 1.12: BN nanotubes are flame resistant
1.6 Boron Nitride Aerogel
Boron nitride aerogel is an aerogel made of BN that has a lot of tiny holes in it. Usually, it is made
up of a mix of bent BN nanotubes and nanosheets. It can have a density as low as 0.6 mg/c m3 and
a specific surface area as high as 1050 m2/g. Because of this, it could be used as an absorber, a
support for a catalyst, or a place to store gas. Aerogels made from BN are very resistant to water
and can soak up 160 times their weight in oil. They don't break down in the air at temperatures up
to 1200 °C, so they can be used again after the oil they soaked up is burned off. Borazine can be
used as the feed gas for chemical vapor deposition with a template to make BN aerogels.
1.7 Composites Containing BN
The thermal shock resistance of the material that is produced is improved when boron nitride is
added to ceramics that are made from silicon nitride. Ceramics composed of silicon nitride-
alumina and titanium nitride-alumina can also have BN included in their composition for the same
reason. Other materials, including alumina and zirconia, borosilicate glasses, glass ceramics,
enamels, and composite ceramics with compositions like titanium boride-boron nitride, titanium
boride-aluminum nitride-boron nitride, and silicon carbide-boron nitride, are also being reinforced
with boron nitride.
Chapter II: Simulation Method
This is the major part of this thesis that looks into how hydrogenated boron nitride transfers
electrons. The Quantum ATK programme is the system I will use for this thesis. Python is the
language used by this programme to run these simulations. This programme lets me compare a lot
of different situations. For every chemical on the periodic table, and in this experiment, the atoms
of boron nitride bonded with hydrogen. In the first part of the simulation, the simulation will be
run on pure boron nitride to see how electrons move through it. This first simulation will be the
control response, which will let us see how the other simulations compare. In the next parts of the
simulations, many simulations will be run with different amounts of hydrogenation on the boron
nitride. From 10%, 30%, 50%, and 100% hydrogenation, you can see what happens. I will be able
to finish this thesis based on these facts.
The amount of Femi's energy is one of the most important key performance parameters. The Fermi
level is the name for the highest energy level that an electron can be at at absolute zero. The Fermi
level is between the valence band and the conduction band because all of the electrons are in their
lowest energy state at absolute zero temperature. This idea comes from the data of Fermi and Dirac.
Since electrons are fermions, the Pauli Exclusion Principle says that they can't be in the same
energy state at the same time. So, at absolute zero, the electrons crowd into the lowest energy states
and form a "fermi sea" of energy states. At absolute zero, the Fermi level is the surface of that sea,
where no electrons have enough energy to rise above the surface. Fermi energy is a very important
idea to understand if you want to know about the electrical and thermal qualities of solids. The
energy of a small part of an electron volt is used in both everyday electrical and thermal processes.
Metals, on the other hand, have Fermi energies on the order of electron volts. This means that the
vast majority of electrons can't get energy from those processes because there are no energy states
within a fraction of an electron volt of their current energy where they could go.
2.1 Introduction of ATK
Except that the molecular device's ability to move electricity can be affected by the molecule itself,
In fact, many other things, like the size of the electrode chosen, the temperature, the quantum
interference effect, the how far away the molecule is from the wire, etc. But it's too bad that people
can't control all of these things, which makes it hard to control how electrical current moves
through molecular devices. For instance, in the real operation of the experiment, and it's hard to
measure and control the distance between the left and right electrodes. It's also hard to play with
the electrical transport properties of molecular devices by changing the bias and the distance
between the electrodes. Polytomy is also a problem because molecules and sensors can only touch
each other with a single atom. This problem happens because molecules and electrodes will
interact when the molecules are connected to the left and right electrodes. The orientation of the
molecules will affect the number of molecules and electrode contacts, which will cause the carbon-
based small molecules to rotate.
People often run into problems in different experiments. This is because you can't see the real
geometry of a molecular device at the atomic level, so the performance of molecular devices varies
from experiment to experiment. Research on molecular devices is very hard. Small molecules
made of boron nitride can have their transport qualities changed in many ways, such as by changing
the way the devices are set up or by adjusting the field effect gate. People have used gate voltage
control because it has a high working rate, uses little energy, etc. As a result, a lot of molecular
devices have been made with this method. In short, the electrical transport properties of molecular
devices are affected by a number of things, such as how the devices are set up, how the world
affects the devices, and so on. In this graduation project, we use ATK simulation and Origin to
draw. By putting an electrode in contact with a specific boron nitride-based molecule, we can study
how well it transmits electricity. The type of molecule made of boron nitride will be used to
carefully choose the electrode material. Expect electronic transport to have special qualities, and
we will look into the physics behind them.
We can use the following software to model the behavior of a nanosystem or any other kind of
material: As we've already talked about, we'll focus on simulating how electrons move through
our nanosystem, which is made of boron nitride nanotubes.
We can use this program to figure out the I-V characteristic curve and the transmission spectrum,
which show the steps that will be used to simulate our experiment below:
ATK Interface
1. Build and Optimize Geometry
After installing the programme, the first step will be to open the part. This will let us start building
our design. For this thesis, boron nitride atoms are the main thing we're looking at. You press the
plus button and then choose nanoribbons from the list of plugins. One thing to remember about
this thesis is that the nanoribbons must be the same size to make sure that the results are going to
be correct.
Fig. 2.1: Interface of Quantum ATK
Fig. 2.2: Builder
From the builder, one can select the size of the nanoribbon and also the layers of the other atoms
that we would want to use like the hydrogen atoms. After all, is done there is a small arrow that is
on the bottom of the builder this will move you to the next section of the simulation which is the
script generator.
2. Script Generator
This is also a crucial piece for the simulation we're doing. In order to compute the outcomes, the
script generator is equipped with the proper software. The new calculator is the initial addition
and can only be used in the ATK-SE enhanced Huckel. The analytical tool is another crucial
resource and from this, one must choose the transmission spectrum that will aid us in our
electron transfer calculations and IV-plot graphs.
Fig. 2.3: Script generator
Under this part, it's important to save your work the right way so that the results won't be too
confusing. After all, the job planner is the next step, which is also where the simulation is done.
The process takes some time, so you need to be patient.
Fig. 2.4: New calculator configuration interface.
Fig. 2.5: Transmission spectrum configuration interface.
Fig. 2.6: IV curve configuration interface.
When we click the job manager, a new window opens where we can see that the programme is
starting. It will first make a Python file, which we can name and save in a separate window that
opens when we click the job manager. When all of these steps are done, our software will make a
total of three files and save them at the PC location we found earlier. Check to see that all three of
these files in the project file menu have the Python, Log, and HdF5 formats. After that, we can
find an I-V plot and Transmission Analyzer tab on our software window and click on them.
Fig. 2.7: Calculation and analysis interface.
As soon as we click, the analysis of the results will be shown, which will be shown in this article
later. A transmission band and an I-V curve are the best ways to show how electrons move through
nanotubes. You can use them to compare and analysis how materials behave electrically or
electronically, which would be taken into account along with other factors when making an
electronic component.
2.2 Atomic Configuration
Atomic modelling has many different options that can be used for analysis and calculations. We
will talk about the following key functions and theories:
1. Density Function Theory
2. Electronic transport Theory
3. Equilibrium Green’s function
4. Landauer Theory
The bulk configuration of a gadget is by far the most important thing to think about when setting
it up. In atomistic modeling or molecular simulation, a bulk configuration is the simplest kind of
molecule configuration. It explains a system made up of a group of atoms and their positions. For
systems like crystals that are inherently periodic and need a different treatment, a bulk
configuration can work because it contains the central cell and repeats it periodically in all
directions during simulations. A simulation cell can be a unit cell, like that of a crystal, or it can
be used as a supercell to include systems that don't have a strong periodic character, like amorphous,
liquid, or interface systems, as well as slab geometries. Atomic modeling software (ATK) has more
than just bulk and molecule configurations. It also has so-called device (two-probe) configurations,
which have a center area and a left and right electrode. A configuration of a gadget is periodic in
two directions, but the third dimension is limited by two electrodes that go on forever. The parts
of the central region and the electrodes are each defined as bulk configurations. For a description
to be valid, the left and right parts of the central region must be the same as the parts of the adjacent
electrodes. With the non-equilibrium Green's functions (NEGF) method, these arrangements can
be used to model how electrons or phonons move. Lastly, ATK offers surface (one-probe)
configurations, which are device configurations with only one electrode and correctly describe a
semi-infinite surface geometry beyond the common slab supercell approximation. These
configurations can be used to study surface chemistry.
2.2.1 Density Function Theory
Density-functional theory (DFT) is a computer-based quantum mechanical modelling method used
in physics, chemistry, and materials science to study the electronic structure (or nuclear structure)
(mainly the ground state) of many-body systems. Certain atoms, molecules, and stages that have
become more compact. Using this theory, you can figure out the features of a system with many
electrons by using functional, which are functions of functions. In the case of DFT, these are the
functions of the electron concentrations that depend on where they are. DFT is one of the most
famous and useful methods in condensed-matter physics, computational physics, and
computational chemistry.
Since the 1970s, DFT has been used a lot in solid-state physics to do calculations. But until the
1990s, when the approximations used in the theory were greatly improved to better model the
exchange and correlation interactions, DFT was not thought to be accurate enough for calculations
in quantum chemistry. Compared to traditional methods, the cost of computing isn't that high.
Since then, DFT has become an important tool for nuclear spectroscopy techniques like Mossbauer
spectroscopy or perturbed angular correlation, which are used to figure out why certain electric
field variations happen in crystals. Even though there have been improvements, density functional
theory still has trouble describing intermolecular interactions, especially van der Waals forces
(dispersion), charge transfer excitations, transition states, global potential energy surfaces, dopant
interactions, and some strongly correlated systems, as well as the band gap and electromagnetism
in semiconductors.
As usual in many-body electronic structure studies, the nuclei of the molecules or clusters being
looked at are thought to be fixed (the Born–Oppenheimer approximation). This makes an external
potential V that stays the same, in which the electrons move. A fixed point Then, the electronic
state is described by a wave function Ψ (r1,..., rN) that fits the many-electron time-independent
Schrodinger equation
Equation no.2.1
where, for the N-electron system, Ĥ is the Hamiltonian, E is the total energy, T
is the kinetic energy,
V
is the potential energy from the external field due to positively charged nuclei, and Û is the
electron–electron interaction energy. The operators T
and Û are called universal operators, as they
are the same for any N-electron system, while V
is system-dependent. This complicated many-
particle equation is not separable into simpler single-particle equations because of the interaction
term Û.
Here DFT provides an appealing alternative, being much more versatile, as it provides a way to
systematically map the many-body problem, with Û, onto a single-body problem without Û. In
DFT the key variable is the electron density n(r), which for a normalized Ψ is given by
Equation no.2.2
This relation can be reversed, i.e., for a given ground-state density n0(r) it is possible, in principle,
to calculate the corresponding ground-state wave-function Ψ0(r1,…, rN). In other words, Ψ is a
unique functional of n0:
Equation no.2.3
And consequently the ground-state expectation value of an observable Ô is also a functional of n0:
Equation no.2.4
In particular, the ground-state energy is a functional of n0:
Equation no.2.5
,
ˆˆˆ oooo nUVTnnEE
.
ˆooo nonnO
,
oo n
.,...,,,...,,*... 22
3
2
3NNN rrrrrrrdrdNrn
ErrUrV
m
h
UVTH N
ji ji
N
i
N
iii
i
,
2
ˆˆˆˆ 2
2
Where the contribution of the external potential energy can be written explicitly in terms of the
ground-state density:
Equation no.2.6
More generally, the contribution of the external potential can be written explicitly in terms of the
density:
Equation no.2.7
The functional T[n] and U[n] are called universal functional, while V[n] is called a non-universal
functional, as it depends on the system under study. Having specified a system, i.e., having
specified V
, one then has to minimize the functional
Equation no.2.8
With respect to n(r), assuming one has reliable expressions for T[n] and U[n]. A successful
minimization of the energy functional will yield the ground-state density n0 and thus all other
ground-state observables.
The variational problems of minimizing the energy functional E[n] can be solved by applying
the Lagrangian method of undetermined multipliers. First, one considers an energy functional
that does not explicitly have an electron–electron interaction energy term,
Equation no.2.9
Where T
denotes the kinetic-energy operator, and V
s is an external effective potential in which the
particles are moving, so that ns(r) ≝ n(r).
Thus, one can solve the so-called Kohn–Sham equations of this auxiliary non interacting system,
Equation no.2.10
.
3rdrnrVnV oo
.
3rdrnrVnV
rdrnrVnUnTnE 3
,
ˆˆ nVTnnE sssS
,
2
2
2rrrV
m
h
iiis
Which yields the orbitals φi that reproduce the density n(r) of the original many-body system
Equation no.2.11
The effective single-particle potential can be written in more detail as
Equation no.2.12
Where the second term denotes the so-called Hartree term describing the electron–
electron Coulomb repulsion, while the last term VXC is called the exchange–correlation potential.
Here, VXC includes all the many-particle interactions. Since the Hartree term and VXC depend
on n(r), which depends on the φi, which in turn depend on Vs, the problem of solving the Kohn–
Sham equation has to be done in a self-consistent (i.e., iterative) way. Usually one starts with an
initial guess for n(r), then calculates the corresponding Vs and solves the Kohn–Sham equations
for the φi. From these one calculates a new density and starts again. This procedure is then repeated
until convergence is reached. A non-iterative approximate formulation called Harris
functional DFT is an alternative approach to this.
Density functional theory (DFT) proposed local density approximation (LDA), Hohenberg-Kohn
theorem, Kohn-Sham equation.
In LDA, from we can see,
Equation no.2.13
The electron density at this position determines the exchange density functional. Its associated
potential is,
The total energy of the system is,
Equation no.2.14
N
iis
def rrnrn .
2
,)(
)(
)()( 3
2
rnVrd
rr
rne
rVrV sxc
s
S
drrE xcxcLDA )()(
nEnUnTnE xct
The charge density can be expressed as follows,
Equation no.2.15
According to the conservation of the number of particles, after the variational tr
These three equations above are the Kohn-Sham equation.
2.2.2 Electronic Transport Theory
Due to the potential for device size reduction provided by control over specific physical features
at the atomic level, the topic of nanoscale electronics has attracted a great deal of scientific
attention in the last ten years. Quantum mechanical properties are becoming increasingly
significant as devices get closer to the nanometer scale. There is a lot of interest in understanding
the fundamentals of quantum transport at the nanoscale because of the impact of the wave-particle
nature (duality) associated with quantum mechanics. In order to comprehend some of the
fundamental characteristics of electron and energy transport phenomena, which are connected to
a detailed electronic structure description of these building blocks, many body theories and first
principle calculations within the framework of density functional theory in scattering approaches
have been applied. These theories are applicable to a wide range of device characteristics in nano-
junctions operating with a gated field in a three-terminal design and a finite source-drain bias.
Additionally, temperature effects must be included for both nuclei and electrons (non-Born-
Oppenheimer method) and electrons (quantum electronics dynamics), while we also draw attention
to the fact that relativistic effects have also been overlooked. The methods begin by splitting the
full Hamiltonian of the system into H = H0 + V, where H0 is the Hamiltonian resulting from the
N
iirrn
1
2
)()(
iiiKS ErV
)(
2
12
Equation no.2.16.1
N
ii
M
PP
P
xcKS
rr
r
Z
rVdr
r
r
rV
1
2
11
12
12
2
1
)()(
)(
)(
Equation no.2.16.2 and 16.2 respectively
bare electrodes, which are modelled as being separated by a distance and made of electron jellium,
and V is the scattering potential of the nano-structured object that connects the electrodes with a
planar surface in the illustration. In our case, the scattering potential of the nano-junction (molecule)
is the sum of three terms: the first term, which represents the electron-ion interaction; the second
term, which describes interference effects using the exchange-correlation potential in the local;
and the third term, which is the Coulomb interaction between electrons.
Fig. 2.8: Insight of a semiconductor.
Typical atomistic junction schematics the entire system (b) (H = H0 + V) is made up of the bare
electrode (a) (H0), which is located along the scattering region (V). Here in (c), Vps depicts how
ions and core electrons interact. For electrons that are near and far from the ion, respectively, it is
the sum of two terms: an attracting and a repulsive one. Since it is straightforward and incorporates
the underlying physics, the particular Vxc is chosen, whereas Vh can be viewed as an on-site
potential generated by the electrons. V. Density Approximation (LDA): full details In the LDA, it
is assumed that the electron density within the molecule is distributed uniformly. We can model
the entire system as a tunnelling junction because the electrode is considerably larger than the
molecule or nanostructure that bridges the bimetallic junction. The unperturbed Hamiltonian is the
metal-vacuum-metal (M-V-M), which is represented by electron jellium. More specifically,
jellium is a straightforward model for explaining electron interactions in which valence electrons
are rigorously addressed and core electrons and ions are equally distributed to produce a positive
background.
2.2.3 Equilibrium Green Function
Lack of balance Current and charge densities in nanoscale (including molecule and semiconductor)
conductors under bias are frequently calculated using Green's function techniques. Although it can
be expanded to account for inelastic scattering, this approach is mostly employed for ballistic
conduction. Equilibrium-like Green functions and Non-Equilibrium Green functions are the two
types of equilibrium Green functions. The non-equilibrium Green function, abbreviated as NEGF,
offers a potent conceptual and computational framework for dealing with the quantum transport
of nano-devices, which is the main distinction between these two functions. Multi-body theory is
the foundation of NEGF. While the non-equilibrium Green's function becomes the virtual time
integral and can be changed by analytical extension, the equilibrium Green's function realizes the
scattering matrix in real time. So that the answer to the first problem can be applied to the second
one. The equation of motion is unquestionably the most effective way to solve the equilibrium
Green's function. The Dyson equation and the Keldysh equation are connected, and there are sub-
level approaches.
Equation of motion
Equation no.2.17
Dyson equation
Equation no.2.18
Keldysh equation
Equation no.2.19
2.2.4 Landauer Theory
The Landauer formula is a relationship between a quantum conductor's electrical resistance and its
scattering characteristics. It is named after Rolf Landauer, who proposed its prototype in 1957.
The formula reads as follows in the simplest scenario where there are only two terminals in the
system and the conductor's scattering matrix is independent of energy.
Equation no.2.20
jiji
r
ji aHaaaaai ,,)( 0
C C ttgttttGdtdtttgttG )',(),(),()',()',( 21121
aaa GGGGGGGG 0000
),()( 0
nn
TGG
Where is the electrical conductance, is the
conductance quantum, are the transmission eigenvalues of the channels, and the sum runs over all
transport channels in the conductor. This equation is both physically logical and relatively easy to
use: The sum of all the transmission options that an electron has when travelling with an energy
equal to the chemical potential determines the conductance of a nanoscale conductor,
A generalization of the Landauer formula for multiple probes is the Landauer–Büttiker formula,
proposed by Landauer and Markus Büttiker [de]. If probe has voltage (that is, its chemical
potential is), and is the sum of transmission probabilities from probe to probe (note that may
or may not equal), the net current leaving probe is,
Equation no.2.21
152
01075.7)/( heG
.
E
j
i
i
)(
2,,
2
ijij
jiji VTVT
h
e
I
Chapter III: Simulation and Analysis Result
3.1 Simulation and Analysis of the Result
This work will do everything possible to accurately portray the characteristics of the electrical
transport properties of monolayer boron nitride nanoribbons in this important chapter. To choose
the appropriate chiral and reasonable width of the structure of boron nitride nanobelts, take into
account the superior physical and chemical properties of monolayer boron nitride, its unique
structure, etc. Because the impact of monolithic boron nitride structure and its properties is
dependent on many factors, the analysis is very complex, as are the primary research methods. To
study how the structure of boron nitride affects the two parameters, current-voltage and
transmission spectra, by analyzing changes in the IV curve and transmission curve analysis data,
the data of the changes in the law and characteristics of the data analysis is to control the variable
method, that is, other parameters set unchanged, by setting a specified parameter change brought
about by the change in the characteristics of the use of control variables. And so on, to be implanted,
a device is developed with a certain set of functional properties, which, in accordance with the
design specifications, may complete the current in the 1V bias up to 10nA. Although this work is
based on computer simulation experiments rather than actual experiments, it should be highlighted
that the accuracy of these simulation trials has been very good, and they have received unanimous
approval, giving them a high level of credibility.
3.2 Selection of Research Objects
Study Object
As was already said, this study is about how electrons move through boron nitride nanoribbons
that have flaws. This chapter will talk about how boron nitride is made and what its physical
features are. In the last two chapters, we talked about the idea of crystal structure and the
Schrodinger quantum physics wave function. This part will show how to use these important skills.
There are two reasons why it is important for the structure of boron nitride to have an electric band
structure. One reason is that it is the place to start learning about the physical properties of solid
boron nitride and analyzing those qualities in depth. Second, boron nitride nanoribbons are the
starting point of the structure because they are easy to understand and figure out. We can start with
the way boron is made and then move on to boron nitride, including its band structure and other
things.
Boron, a metalloid element with the symbol B and the atomic number 5, makes for an extremely
interesting area of research. Because of its unique physical and chemical features, including its
lightweight nature, high melting temperature, and ability to form covalent bonds, it is a vital
element in a wide variety of sectors, including ceramics and electronic manufacturing. In addition,
the examination of boron's role as a micronutrient in plant growth, as well as its prospective
applications in medicinal practices and its impact on the environment, adds depth to the
understanding of this multipurpose element.
And Boron nitride nanoribbons (BNNRs) are one-dimensional nanostructures made of boron and
nitrogen atoms grouped in a honeycomb lattice structure, similar to graphene. These unique
nanoribbons are very stable in both heat and chemicals, which makes them very appealing for a
wide range of uses in technology. Unlike graphene, BNNRs can survive high temperatures without
oxidizing or losing their shape. This makes them great choices for use in high-temperature
environments. Their excellent thermal conductivity and mechanical strength make them perfect
for use as thermal contact materials and nanoscale heat sinks in heat management systems. BNNRs
are also good at insulating electricity, which makes them good candidates for use in electronic
devices, especially in places where electrical separation is important. BNNRs also have good
optical qualities and a wide bandgap, which means they can be used in optoelectronics and
photonics. Because of these qualities, BNNRs are useful for making nanoscale electronics like
transistors, sensors, and systems that store energy. BNNRs are also chemically inert and
biocompatible, which makes them good options for biomedical uses like drug delivery systems
and scaffolds for tissue engineering. As research on BNNRs moves forward, more exploration and
characterization of their unique properties will surely lead to the discovery of new possibilities and
uses. This will help science and technology make progress in many areas.
3.3 Selection of Reference and Experimental Groups
Two experiments were set up for this paper. The length and angle of the boron nitride nanoribbons
were different from those of the boron nitride chains, which was the difference between the two
groups. We first divided the system into two categories in order to evaluate the impact of changing
the length of the boron nitride chain and the angle of the boron nitride thin on the entire system.
The first variable control factor was to investigate the regulation of the boron nitride chain. The
second wide category's control variable differs from the first in that it has an impact on the
nanoribbons structure. It investigates how the current-voltage and transmission spectra are affected
by the length or inclination of the nanoribbons.
3.3.1 Experiment 1
Fig. 3.1: Defect of Boron Nitride.
Boron nitride is used in a lot of different ways all over the world. Boron nitride is used so often
that it is standard for some of it to have flaws. Taking steps to avoid failure in application systems
is a must for better understanding and more accurate calculations in applications. Here is the
structure of a boron nitride nanoribbon with random defects so that it can be reproduced and used
in the real world.
Fig. 3.1.1: The transmission spectrum of the configuration in Fig. 3.1 under zero bias
Fig. 3.1.2: The transmission coefficients of the configuration in Fig. 3.1 under zero bias
The reason of showing the transmission spectra at 0.0V bias is a curve is seen at this point. The
transmission spectrum will give us a wider picture of that curve, at the y coordinate (0,0) it is
considered to be the fermi level, if the transmission at this point is greater than zero than the system
is a conductor, if it is less than zero it is an insulator, so we can see at point y(0,0) that is actually
zero electron volts the transmission is 7.30674.
Fig. 3.1.3: The I-V curve of the configuration in Fig. 3.1.1
The simulation of the boron nitride nanoribbon with random defects may be seen in Fig. 3.1. It
was carried out by VNL and ATK Software. A voltage is supplied by the input source, and the
amplitude of the current flowing through the circuit is observed. The IV curve can be used to tell
the difference between boron nitride that has been randomly found and boron nitride that has been
produced in a laboratory. Due to the presence of defection in the boron nitride, the initial
relationship between the current and voltage amplitudes is proportional. The initial increase in
voltage results in an increase in the current's amplitude. After reaching a certain point, however,
at which the amplitude of the current is at its maximum possible point, the amplitude of the current
suddenly drops considerably, and it eventually returns to a value that is practically identical to its
starting point. After that point, the curve oscillates within a rather narrow range.
Fig. 3.1.4: The transmission spectrum of the configuration in Fig. 3.1.1 under the bias of 1.1V.
Fig. 3.1.5: The transmission spectrum of the configuration in Fig. 3.1.1 under the bias of 1.4V.
Overall. There, the difference between the two resistances is zero. This is called "negative
differential resistance," or "NDR," and it is very useful for making Nano-electronic devices. We
take two biases from the I-V curve, 1.1V and 1.4V, and plot the transmission bands under these
biases to figure out where the NDR comes from. Figure 3.1.4 shows the spectrum of transmission
with a tilt of 1.1V. The chance of an electron having a certain amount of energy in the bias range
of [1.1, 1.4] V, it is interesting to note that as the bias goes up, the current goes down. This is
shown by the transmission coefficient, which is the value of the curve. In the picture, the bias
window is shown by the two dashed lines. According to the DFT+NEGF theory, the current of the
system is proportional to the area under the transmission curve within the bias window. Here, S1.1
stands for the area of integration with a tilt of 1.1V. Next, we draw the spectrum of transmission
under 1.4V. As the amount of bias goes up, the bias area gets bigger. Compared to 1.1V, though,
the transmission range as a whole shrinks. Since the integrating area gets smaller as the bias
window gets bigger, S1.4 is smaller than S1.1. So, the current under 1.4V (16648.3 nA) is less
than the current under 1.1V (23184.9 nA). The NDR comes into being.
3.3.2 Experiment 2
Fig. 3.2: Defect of Boron Nitride.
In Fig. 3.2, I created a defect by deleting two atoms from the top and bottom of the boron nitride
thin. So, I believe that is a nice flaw, and we will now present the simulation and calculation of
Fig 3.2.
Fig. 3.2.1: the transmission spectrum of the configuration in Fig. 3.2 under zero bias
Fig. 3.2.2: the transmission coefficients of the configuration in Fig. 3.2 under zero bias
The chance of an electron transmitting from the left electrode to the right electrode is defined as
transmission. So, for a large number of electrons, it is a ratio of successfully transported electrons
to failed electrons. The transmission coefficients for electrons with different energy are shown in
Fig. 3.2.1. The transmission coefficient is finite at the Fermi level. In other words, it is none zero.
As a result, it is metallic.
Fig. 3.2.3: The I-V curve of the configuration in Fig. 3.2.1
The boron nitride nanoribbon with random defects is mimicked by VNL-ATK, as seen in Fig. 3.2.
Voltage is applied from the input source, and current amplitude is tracked. The I-V curve can be
used to distinguish between a pure boron nitride and one that has random defects. Initial current
amplitude is proportional to voltage amplitude when boron nitride has defection. Initial voltage
rises are accompanied by an increase in current amplitude. The current amplitude, however,
abruptly drops considerably and returns to practically its initial value after reaching a specific point
when it is at its highest possible level. Following that, the curve experiences brief fluctuations.
Figure 3.2 shows two x and y axes, with the x axis measuring voltage and the y axis measuring
current amplitude. I start at (0,0), after which the current amplitude increases, and when the bias
reaches 1.1V, the current amplitude then begins to drop. Voltage rises at the same moment. Current
amplitude again increases at point 1.5V. After 1.6V decreases once more.
Fig. 3.2.4: The transmission spectrum of the configuration in Fig. 3.2.3 under the bias of 1.1V.
Fig. 3.2.5: The transmission spectrum of the configuration in Fig. 3.2.3 under the bias of 1.5V.
Overall. There is a negative differential resistance there. This phenomenon is known as negative
differential resistance (NDR), and it is extremely beneficial in the creation of nano-electronic
devices. We pick two biases in the I-V curve, 1.1V and 1.5V, and plot the transmission spectra
under these biases to get insight into the cause of the NDR. Figure 3.2.4 depicts the transmission
spectrum with a bias of 1.1V. The possibility of a particular energy electron surprisingly, in the
bias range of [1.1, 2.0] V, the current reduces as the bias increases, as reflected by the transmission
coefficient, i.e., the value of the curve. The bias window is shown in the illustration by the two
dashed lines. The integrating area under the transmission curve within the bias window is
proportional to the system current, according to the DFT+NEGF theory. In this case, S1.1 denotes
the integrating area with a bias of 1.1V.
The transmission spectrum is then plotted under 1.5V. The bias window expands as the bias grows.
However, as compared to 1.1V, the transmission spectrum reduces overall. As a result, while the
bias window grows bigger, the integrating area shrinks, i.e. S1.1 is greater than S1.5. As a result, the
current at 1.5V (14351.6 nA) is lower than at 1.1V (24640.2 nA). As a result, the NDR arises.
When we compare Fig. (3.1.3) and (3.2.3), we can see the current and voltage (I-V curve). Figure
(3.1.3) has a pick point of 1.1V and a minimum amplitude of 1.4V. In addition, the pick point for
Fig (3.2.3) is 1.1V and the lowest amplitude is 1.5V. As a result, the two IV curves (Figs. 3.1.3
and 3.2.3) are nearly identical.
3.3.3 Experiment 3
Fig. 3.3: Defect of Boron Nitride.
Fig. 3.3.1: the transmission spectrum of the configuration in Fig. 3.3 under zero bias
Fig. 3.3.2: the transmission coefficients of the configuration in Fig. 3.3 under zero bias
Fig. 3.3.3: The I-V curve of the configuration in Fig. 3.3.1
The random defects in the boron nitride nanoribbon are replicated by VNL and ATK. The input
source (0, 0) sends a voltage, and the amount of the current is watched. The IV curve can tell the
difference between pure boron nitride and boron nitride with random flaws. Boron nitride has a
flaw, so at first the size of the current is proportional to the size of the voltage. As the voltage goes
up at first, the current's peak goes up at 1.0V. But after a certain point (1.1) V, when the amplitude
of the current is as high as it can get, the amplitude of the current suddenly drops at (1.1) V and
goes back to almost its original value. Then, at 1.2V, it jumps to a high pick and moves along the
curve. After that, the curve moves in a fairly small area.
We use the I-V curve to find two biases, 1.0V and 1.3V, and then plot the transmission spectra
under these biases. Figure 3.3.3 shows the spectrum of gearbox with a bias of 1.2V. The chance
of an electron having a certain amount of energy in the bias range of [1.2, 2.0] V, it's interesting
that as the bias goes up, the current goes down. This is shown by the transmission coefficient,
which is the value of the curve. In the picture, the bias window is shown by the two dashed lines.
According to the DFT+NEGF theory, the current of the system is proportional to the area under
the transmission curve within the bias window. Here, S1.0 stands for the area of integration when
the bias is 1.0V.
Fig. 3.3.4: The transmission spectrum of the configuration in Fig. 3.3.3 under the bias of 1.0V.
Fig. 3.3.5: The transmission spectrum of the configuration in Fig. 3.3.3 under the bias of 1.3V.
Next, we draw the spectrum of gearbox under 1.3V. As the amount of bias goes up, the bias area
gets bigger. But compared to 1.0V, the transmission range as a whole gets smaller. So, as the bias
window gets bigger, the integrating area gets smaller. This is shown by the I-V curve.
S1.3 isn't as big as S1.0. So, the current under 1.0 V (13324.2 nA) is greater than the current under
1.3 V (9668.78 nA). The NDR comes into being.
Before experiment 1 and experiment 2, (Fig. 3.1.3 and 3.2.3), this IV slope looked nothing like it
does now. The magnitude of the current was very similar between these two IV curves, but not in
my experiment 3 (fig. 3.3.2). The point where the current and voltage start is (0, 0), (x, y). This IV
curve usually goes up from 1.0V to 1.1V, then goes down. Then keep going up until you reach
1.2V. After all, it's supposed to go up and down. From 1.7 to 1.9, get back to the pick-up point. So,
the magnitude of this IV curve is very different.
3.3.4 Experiment 4
Fig. 3.4: Defect of Boron Nitride.
Fig. 3.4.1: the transmission spectrum of the configuration in Fig. 3.4 under zero bias
Fig. 3.4.2: the transmission coefficients of the configuration in Fig. 3.4 under zero bias
Fig. 3.4.3: The I-V curve of the configuration in Fig. 3.4.1
As shown in Fig3.4.3, the boron nitride nanoribbon with random defects is simulated by simulation
software. Voltage is applied from input source and the amplitude of current is monitored. The
difference between a pure boron nitride and randomly detected boron nitride can be distinguished
by the IV curve. The boron nitride having detection, initially the current amplitude is proportional
to voltage amplitude. Current amplitude increases as the voltage increases initially. But after
reaching a certain point when the current amplitude is the highest as it can be the and then suddenly
the amplitude of current falls dramatically and it reaches to the almost initial value. After then the
curve fluctuates within a short range.
Fig. 3.4.4: The transmission spectrum of the configuration in Fig. 3.4.3 under the bias of 1.2V.
Fig. 3.4.5: The transmission spectrum of the configuration in Fig. 3.3.3 under the bias of 1.8V.
We select two biases in the I-V curve, 1.2V and 1.8V, and plot the transmission spectra for these
biases. Figure 3.4.4 depicts the transmission spectrum with a bias of 1.2 V. The possibility of a
particular energy electron surprisingly, in the bias range of [1.2, 2.0] V, the current reduces as the
bias increases, as reflected by the transmission coefficient, i.e., the value of the curve. The bias
window is shown in the illustration by the two dashed lines. The integrating area under the
transmission curve within the bias window is proportional to the system current, according to the
DFT+NEGF theory. In this case, S1.2denotes the integrating area with a bias of 1.2V.
The transmission spectrum is then plotted under 1.8V. The bias window expands as the bias grows.
However, when compared to 1.2 V, the transmission spectrum reduces overall. As a result, while
the bias window grows broader, the integrating area shrinks.
S1.8 is smaller than S1.2. As a result, the current under 1.8V (8662.29 nA) is smaller than that of
1.2V (11744.2 nA). So, the NDR emerges
Chapter IV: Conclusion and outlook
4.1 Conclusion
In brief, the study of how electrons move through boron nitride nanoribbons (BNNRs) with defects
has given us a deep understanding of their basic features and how they might be used in advanced
technologies. The in-depth study of BNNRs with structure flaws has shown that these flaws have
a big effect on how their electronics work. This has led to the discovery of interesting phenomena
with important implications for technological progress.
Through careful experimentation and theory, it has been shown beyond a doubt that defects are
the most important factor in changing the electronic features of BNNRs. These flaws, which
include vacancies, substitutional impurities, and adatoms, create localised electronic states within
the bandgap, which changes the way BNNRs move a lot. When there are defects, scattering
processes appear that have a big effect on how electrons move, how well they conduct electricity,
and how they move in general.
Also, research into electron transport has shown that defects in BNNRs behave in different ways
depending on their type, quantity, and location. By manipulating and controlling these defects with
engineering methods, it is now possible to change the electronic properties of BNNRs in ways that
have never been done before. Having a deep understanding of how defects affect how electrons
move makes it possible to build and optimise nanoscale devices with better functionality and
performance.
The results of this graduation thesis will have a big impact on the way nanoelectronic systems are
made in the future. The ability to control defects in BNNRs is a huge step forward. It makes it
possible to build new electronic parts, like transistors, diodes, and sensors that are more efficient
and reliable. Also, studying how defects change the electronic properties of BNNRs helps advance
cutting-edge fields like quantum computing and spintronics, where exact control over how
electrons move is essential.
Also, looking into how electrons move in BNNRs with flaws has given us important clues about
how basic physical things work. This has opened up new ways to study these things. Future studies
may focus on getting a better understanding of the physics of defects, figuring out what role edge
structures play, and figuring out how defects interact with things like strain or magnetic fields.
Also, looking into how defect engineering and the optical and thermal properties of BNNRs are
related could lead to a lot of new uses in optoelectronics and thermal management.
In conclusion, the thorough study of electron transport in boron nitride nanoribbons with defects
has laid a strong basis for taking advantage of their unique electronic properties. This will open up
new frontiers in nanoelectronics, quantum computing, and other related fields that span many
different disciplines. The information learned from this study will definitely speed up the creation
of next-generation nanoscale devices and materials that work better and do more. This, in turn,
creates exciting opportunities for technological advances that will change the world in the near
future.
4.2 Outlook
One exciting thing about studying how electrons move through boron nitride nanoribbons (BNNRs)
with defects is that these defects can be fully characterized and engineered. This has the potential
to help us learn more about and change their electronic properties. To figure out what's wrong with
BNNRs, you have to do a lot of different things and use a wide range of advanced experimental
methods. Scanning tunneling microscopy and spectroscopy allow for high-resolution imaging and
spectroscopic analysis, which lets atomic-scale flaws be found and seen. Transmission electron
microscopy is a different method that gives information about the structure and location of flaws
in BNNRs in three dimensions. In addition to these experiments, computer models and theoretical
calculations can be used to learn more about how defects form and how they affect how electrons
move through a material. Researchers can figure out how different types of defects (such as
vacancies, impurities, and grain boundaries) affect the mobility, band structure, and conductance
of BNNRs by using both experimental and theoretical methods. Also, introducing flaws on purpose,
such as through controlled defect doping or defect manipulation, opens up interesting ways to
change the electronic properties of BNNRs. Researchers can change the bandgap, carrier
concentration, and charge transport properties of BNNRs by selectively adding certain defects or
changing their density. This lets them make BNNRs with the functions they need for different uses.
The fact that defect-induced electrical properties in BNNRs can be changed opens up new
possibilities in areas like nanoelectronics, nanophotonics, energy storage, and quantum computing.
Also, studying how defects affect things like spin polarization, magnetism, and quantum transport
adds another layer of complexity and interest to this area of research. Overall, the complete
characterization and engineering of defects in BNNRs offer a promising way to advance basic
knowledge and make it possible to create new materials with tailored electronic properties for
next-generation electronic devices.
Acknowledgments
The completion of my undergraduate graduation design thesis has been a journey filled with
challenges and growth, and I am deeply grateful for the invaluable support and guidance I have
received along the way. I would like to express my heartfelt appreciation to my esteemed instructor,
Yan-Dong Guo, whose unwavering commitment to my academic development has been truly
inspiring. His patient guidance, extensive knowledge, and willingness to address my questions
have been instrumental in shaping the outcome of this thesis. I am also indebted to the postgraduate
assistant students who have generously shared their expertise and provided valuable insights.
Furthermore, I would like to express my gratitude to the authors of the references whose work has
served as a cornerstone for my research, providing a solid foundation and enriching my
understanding of the subject matter.
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Authors
MD HASANUR RAHMAN
School of Electronics and Information Engineering,
Nanjing University of Posts and Telecommunications,
Nanjing, China.
Mail: f19010107@njupt.edu.cn
WeChat: MHR07-Jr
Yandong Guo
Associate Professor
College of Electronic Science and Engineering,
Nanjing University of Posts and Telecommunications
Mail: yandongguo@njupt.edu.cn
