Nano Electronics -PE-EC505A- Module1 ( MAKAUT-Syllabus)

 

Today, Our Communication Elements Are: - Introduction to nanotechnology, Meso Structures, Basic about Quantum Mechanics, Schrodinger's equation, DOS sealing of conditions (DOS), Particle in a box - concepts, Degeneracy, Band principle, Kronig–Penney Model, Brillouin zone.

 

Introduction to nanotechnology: -

Nanotechnology is a branch of science and engineering that belongs to the study, design, and manipulation of materials on the nanoscale (1 to 100 nanometres). A nanometre (NM) is a billionth of a metre, which is about 100,000 times less than the diameter of a human hair. In this small scale, the material shows unique physical, chemical, and biological properties that vary from their wholesale form.

Concept of nanotechnology: -

The word "nano" comes from the Greek word meaning "dwarf". Nanotechnology focuses on understanding how the drug behaves when nanoscale dimensions are reduced. At this stage, atoms and molecules can be arranged properly, which can enable the growth of new materials with increased strength, light weight, high reaction, and better electrical or optical performance.

For example, carbon is soft graphite in its normal form, but when it is arranged as a carbon nanotube on a nanoscale, it becomes 100 times stronger than steel, and still, the light is incredible.

Application of Nanotechnology

Nanotechnology has a wide range of applications in many fields:

• Medication – Nanoparticles are used to detect targeted drug distribution, imaging, and early illness.
• Electronics – Nano transistors and pieces enable small and more energy-efficient devices.
• Energy – Nanomaterials improve solar cells, fuel cells, and energy storage batteries.
• Environment – Nanotechnology helps with water purification, pollution control, and efficient waste treatment.
• Clothes and consumer products – nano-coatings make clothes coloured and provide durability to everyday products.

Advantages of Nanotechnology

• Miniature of equipment
• Better performance and durability
• Better medical treatment
• Continuous energy solution

Nanotechnology challenges

While nanotechnology is promising, there are also challenges such as high production costs, unknown health risks in nanopathy, and moral concerns about abuse. Research continues to ensure safe and durable applications.

conclusion

Nanotechnology is considered one of the most revolutionary scientific advances of the 21st century. By using the unique properties of materials at the nanoscale it provides success in therapy, electronics, energy, and environmental protection. With continuous research, nanotechnology has the ability to change industries and significantly improve human life.

Meso Structures: -

Introduction

In material science, mesostructures refer to the intermediate levels of the structural organisation located between the micro (atom/molecular) scale and the macroscopic (bulk material) scale. The word "meso" comes from the Greek word meaning "middle", which indicates their position between subtle and macro structures. These structures are usually present in a 10-nanometre size range for multiple microns.

Meso structures play an important role in determining the mechanical, electrical, thermal, and optical properties of the material. By designing and controlling them carefully, researchers can develop advanced materials with better performance.

Characteristics of Meso Structures

• Middle scale: larger than atoms, but less than visual structures.
• Asymmetrical nature: grains, holes, fibre, or layers can be included.
• Property control: The strength, cruelty, conductivity, and stability of materials greatly affect.
• Versatility: Found in metals, ceramics, polymers, composites, and biological materials.

Examples of mesostructures

• Limits for grain in metals: The grain system at the meso level affects hardness and flexibility.
• Porous material: mesoporous silica and carbon structures are used in catalysis, sensors, and drug delivery.
• Fibre-reinforced composite: A matrix form improves built-in fibre, strength, and flexibility in meso-scale enhancement.
• Biological system: Bone and shells show mesostructures that give them unique power and light properties.

Application of mesostructures

• Nanotechnology and electronics-eso-composed materials increase the conductivity of semi-circulators and improve battery performance.
• Medication – Cleaning Meso structures are used for controlled drug release and tissue technology.
• Construction and aerospace – Total Messo structures increase the strength by reducing the weight of aircraft and buildings.
• Catalysis and filtration – mesoporous catalysts increase the surface and efficiency of chemical reactions.

Advantage

• Extended relationship between power and waste
• Greater shelf life and reliability
• Better energy efficiency
• High surface area for reactions and storage

conclusion

Meso structures form an important bridge between the subtle and macroparameters of the materials. They play an important role in controlling the overall properties of substances and have applications in various fields such as medicine, engineering science, electronics and environmental science. By mastering meso-structural design, researchers can create new materials that contribute to technical and scientific progress.

Basic about Quantum Mechanics: -

Introduction

Quantum mechanics is a basic branch of physics that explains the behaviour of matter and energy on the smallest scales, such as atoms and subatomic particles. Unlike classical physics, which describes macroscopic objects, quantum mechanics belongs to particles that follow potential laws instead of determining people. It is necessary to understand modern techniques such as semiconductors, lasers, quantum computers and nanotechnology.

Main concepts in quantum mechanics

• Wave-dual duality – According to quantum theory, both electrons and photons show both wave-like and particle properties. For example, light can act as a wave (intervention pattern) and particles (photons).
• Quantisation of Energy – Energy is not constant but is present in small, discrete packages called quanta. For example, electrons occupy certain energy levels in an atom instead of randomly moving forward.
• Heisenberg’s Uncertainty Principle – It is impossible to measure both the exact location and the speed of a particle at the same time. This theory illuminates the limits of precision in quantum measurement.
• Superposition Principle – Quantum particles may be present in several states at the same time until they are measured. For example, one electron can occur in two separate energy levels at the same time.
• Quantum Entanglement – When two particles interact and are wrapped, their properties remain connected, even if they differ from a great distance. One affects the other immediately.

Applications of Quantum Mechanics

• Electronics: Transistors and integrated circuits are based on quantum principles.
• Medical imaging: MRI machines depend on the quantum spinning conditions of atoms.
• Laser: Quantum infection produces communication, surgery and regular lights used in industries.
• Quantum Computing: Uses superposition and complication to create a faster complex calculation compared to classical computers.

conclusion

Quantum mechanics provides a powerful structure to understand the invisible world of atoms and sub-quantum particles. Although the principles may seem justifiable, they have revolutionised modern science and technology. From electronics to medicine and from communication to calculation, quantum mechanics forms the future.

Shrouding's equation: -

Introduction

The 'shoding' equality proposed by Austrian physicist Erwin Schrödinger in 1925 is one of the most important foundations for quantum mechanics. This describes how the quantum position of a system develops over time. Just like Newton's laws control classical mechanics, the Schrödinger equation controls the speed of microparticles such as electrons, protons and atoms.

The Wave Function (ψ)

The wave function (ψ) lies at the heart of the Schrödinger equation. It represents the dimension of finding a specific position, speed or the ability to find a particle in the state. Wave function Square | ψ |2 Oction | The ability to detect the particle provides density.

Forms of the Schrodinger Equation

1. Time-Dependent Schrodinger Equation

• Describes how the wave function changes with time.
• Used for dynamic systems (e.g., particles in motion, evolving quantum states).

2. Time-Independent Schrodinger Equation   

H^ψ=Eψ

• Applies when the system has constant energy.
• Used to calculate allowed energy levels of particles in potential fields, such as electrons in an atom.

Importance of the Schrodinger equation

• Nuclear structure explains why electrons live at the incomparable energy level.
• The quantity forms the basis for chemistry to predict molecular bonds and reactions.
• Chips and nanodevices are used in semiconductor physics to design.
• Atoms and particles help in physics to understand basic powers.

Application

• Explains the hydrogen atom spectrum.
• Design quantum dots and nanomaterials.
• The basis for quantum calculation.
• To predict the tuning effects in diodes and transistors.

conclusion

The Shroudinger equation is the backbone of quantum mechanics. This provides a mathematical structure to understand the wave-like behaviour of particles and explains why atoms and molecules behave as they do. Without it, modern physics, chemistry and technology would not be present in their current form.

DOS sealing of conditions (DOS): -

Introduction

In solid physics, the density (DOS) in the States describes the number of available quantum conditions that electrons (or other particles) can occupy a given energy level. This is an important concept for understanding the electronic, optical and thermal properties of the material.

The DOS function, usually written as G (s), provides the number of conditions per energy area per unit. Simply put, it tells us how many electron states are available at a specific energy for particles.

concept

There are electrons in solids in the energy tape instead of discomfort levels. Dos helps decide:

• How many states exist for each energy.
• How do electrons fill these conditions at different temperatures.

Electron distribution in these conditions follows the Fermi-Dirac data, which is important in semiconductors and metals.

Density of conditions in different systems

1D System (Nanowires)
The DOS is proportional to $\frac{1}{\sqrt{E}}$, It shows sharp peaks, known as van Hove ecosystems.

2D System (thin movies, Quantum Wales)

Dos is stable in terms of energy, acts as a step.

3D System (Bulk Materials)

Dos grows with the square root of energy:

This is used on metals, semiconductors and insulators in bulk form.

The importance of DOS

• Metal: High DOS at the Fermi level allows simple electron movement and explains good conductivity.
• Semiconductor: DOS helps calculate the carrier concentration in the drive and valence band.
• Nanomaterials: DOS changes explain the effect of quantum size in nanostructures such as quantum dots and nanoviruses.
• Optics: DOS absorption and content emissions affect spectra.

conclusion

The density of the state is fundamental to guessing how electrons behave in different materials. By analysing DOS, researchers and engineers can design better semiconductors, nanomaterials and electronic devices. It draws on quantum mechanics with practical applications in modern.

Particle in a box - concepts: -

Introduction

In a box, a particle (also called an endless capacity) is a basic model in quantum mechanics. It describes a particle (for example, an electron) in a space area where it can move freely inside the box, but cannot survive due to infinitely high possible obstacles on the boundaries.

This simple model helps go to the shallow energy level and explain the concept of the wave nature of particles. It is widely used as an early point to understand electrons in atoms, molecules and nanostructures.

Model assumptions

• The particle is free to enter the box only (between x = 0 and x = l).
• Outside the box, the capacity is endless, so the particles may not be present there.
• The particulate behaves like a steep wave of nodes on the walls of the box.

Mathematical Concept

The time-independent Schrödinger equation is solved for a 1D box of length $L$. The allowed wave functions are:

Central concepts

• Prevention: The energy level is discrete, not continuous.
• Wave behaviour: The particle is present as a permanent wave, not a point.
• Size power: Small box size L leads to high energy vacancy, which is important in nanokines.

Application

• It is explained why electron atoms live at the discrete level.
• Basis for understanding quantum dots, nanovir and molecular orbitals.
• Useful for explaining absorption and emission spectra in molecules.

Conclusion

A particle in a boxing model is a simple but powerful tool in quantum mechanics. It shows the idea of ​​volume-bound energy levels and wave functions, which are important for modern physics, chemistry and nanotechnology.

Degeneracy: -

Introduction

In quantum mechanics and solid-state physics, degeneracy refers to the condition where two or more different quantum conditions have the same energy level. Although the states are different (different wave functions or quantum numbers), they correspond to the same energy value.

Digenarically is an important concept, as it helps to explain the structure of atoms, molecules and materials, especially when it comes to their spectra, stability and symmetry.

Original concept

An energy level degeneration (G) is the number of independent states sharing the same energy. For example:

• In a hydrogen atom, the energy depends only on the most important quantity n. For a given n, separate orbital quantity numbers l and magnetic quantum number ml can produce many conditions with the same energy → impure conditions.
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• In a box, some of the energy levels calculated from a 3D particle (NX, new, NZ) can provide the same total energy, even if the quantity is different.

Mathematical Expression

For a hydrogen atom, the degeneracy of the $n^{th}$ energy level is:  g=n2

This means:

• For $n = 1$, degeneracy = 1 (only 1 state).

• For $n = 2$, degeneracy = 4 (four different states with the same energy).

• For $n = 3$, degeneracy = 9 (nine states).

Lifting of Degeneracy

When an external influence works on the system, degeneration can be removed or shared:

• Magnetic field → Zemen effect (energy level divided).
• Electric field → Stark power.
• Crystal Field Division in solid-state materials.

Application

• Explains the spectral lines in atoms and molecular physics.
• Important in semiconductor physics, where the ribbon affects degenerate conductivity.
• Quantity helps with chemistry, where degeneration affects binding and molecular stability.
• Important in statistical mechanics, since degeneration affects entropy and probability distribution.

Conclusion

Degeneracies are an important feature of the quantum system, and show that many states can share the same energy. It highlights the role of symmetry in physics and is necessary to explain events such as nuclear spectra, magnetism and solid properties.

Band principle: -

Introduction

The band theory of solids is a basic concept in the physics of the solid state that explains the electrical properties of materials such as conductors, semiconductors and insulators. It is based on quantum mechanics and ideas such as electrons in a solid occupied energy bands instead of discrete energy levels, as seen in insulated atoms.

Energy tape formation

When atoms come together to make a solid, they overlap their outer electron shells. Due to the Pauli exclusion theory, two electrons may not have the same quantum condition. This leads to dividing the levels of unspoiled nuclear power into close levels, which form constant boundaries called energy strips.

The most important bands are:

• Valence Band: The highest energy band filled with electrons at Absolute Zero.
• Challan Band: High-Energy Bands where electrons are free to transfer and generate power.
• Band GAP (eg): The prohibited energy gap separates the valence band and the conduction band.

Type of material

Leader (metal):

• Valence bands and wire strips overlap.
• Electrons run independently → high conductivity.

Semiconductor:

• Small Band Gap (≈ 1 eV).
• Electrons can jump into the wiring tape with thermal or light energy.
• Example: Silicon, Germanium.

Insulator:

• Large band gap (> 5 EV).
• Electrons cannot run lightly → very poor conductivity.

Application of band theory

• Electrical conductivity in solids is explained.
• Basic for semiconductor units such as diodes, transistors and solar cells.
• Helps the design of LEDs, lasers and microscopes.
• The optical properties of the material (absorption and emissions of light) are explained.

conclusion

The band theory of solids provides a clear understanding of why some materials operate as conductors while others do not. It forms the basis for modern electronics and semiconductor technology, one of the most important principles of physics and engineering.

Kronig–Penney Model: -

Introduction

The chronic Penny model is a simplified quantum mechanical model used to interpret the formation of energy bands in solids. It was proposed in 1931 by Ralph Croning and William Penny that permission for periodic arrangements of atoms in a crystal and prohibited energy areas (ribbon and band interval).

Model concept

• In a solid, electrons are arranged in a periodic capacity created by positively charged ions systematically charged in a crystal lattice.
• Instead of solving an accurate complex capacity, the chronic-pennic model considers a dimensional periodic capacity with high (obstacles) and alternative areas with low (wells) capacity.
• By solving the shoding equation for this capacity, it achieves a condition that determines which electron energy is allowed.

Key Results

Energy Bands and Gaps

• Electrons can only capture some energy cleaners (allowed ties).
• Prohibited areas (tape intervals) between these ties are where no electron states exist.

Baloch's theorem

• The model supports Baloch's theorem and says that the electron wave functions form 

ψ(x)=uk​(x)eikx

Where

The UK (X) has a periodicity similar to the grid.

Dependence on Potential

• The width of the energy tape and the interval depend on the strength and periodicity of potential obstacles.
• Strong periodic capacity → Wide tape interval.

Application

• It is explained why the material can be a conductor, a semiconductor or an insulator.
• The ribbon with solid materials forms the theoretical basis for the principle.
• The semiconductor device helps to understand physics.
• Electron provides insight into transport in crystals.

Conclusion

The Croning Penny model is not an accurate depiction of real solids, but it provides a simple and mathematical way to understand how the skilled capacity makes energy tape and tape interval. It forms a bridge between quantum mechanics and solid-state physics, which lays the foundation for modern electronics.

Brillouin zone: -

Introduction

In the physics of the solid state, the Brillouin zone is a basic concept used to describe the behavior of electrons in periodic crystals. They are defined in a mutual place (space) instead of the actual place. A Brillson's representation represents a primitive cell with mutual grids, which is produced using the winner -sitz method.

Brillouin zone electronic ribbons help to understand wave spread in structures, telephones, and solids.

Brillouin Construct

1. Start with a mutual grid, which is the furthest conversion of the actual grid in the crystal.
2. Draw nearest neighbors from a mutual grid.
3. The boundaries of the bilateral are perpendicular to these vectors.
4. The area enclosed by a grid point is the first Brillouin zone.

• First Brillouin Zone: Minimum, Middle Region, which includes unique wave vectors.
• High Brlyoin Zone: First, the outskirts around one, important for high-energy storms.

Importance in physics

• Wave Vector Representation: Bryoin zones define possible values ​​of electron wave vectors (K) in a periodic grid.
• Energy band: Public and prohibited electron energy can be understood by checking how the ties are folded into the Brillouin zone.
• Synamicity: The symmetry of the brillosonness reflects the symmetry of the crystal grid.
• Theorem of Baloch: Electron states in a crystal are periodic and can be limited to the first Brillouin zone.
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Application

• Electronic tape structure: Explains the cord in metals, semiconductors, and insulators.
• Phone: Used to study vibration mode for grids.
• Optical properties: Important for understanding absorption and emissions in crystals.
• Nanomaterials: Brillouin zone analysis helps explain quantum size effects in 2D materials like graphene.

Conclusion

Brillouin zones provide a clear way to study electrons and waves with periodic forged. By mapping electron states to mutual space, they act as a powerful tool to explain many basic properties of solids, especially electrical conductivity and tape structure.

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