STRUCTURE OF ATOM
Sub atomic Particles
Atomic Models
Atomic spectrum of hydrogen atom:
Photoelectric effect
Planck’s quantum theory
Heisenberg’s uncertainty principle
Quantum Numbers
Rules for filling of electrons in various orbitals
This document provides an overview of the development of atomic models over time, including:
- Thomson's model which depicted the atom as a uniform sphere of positive charge with electrons embedded within it.
- Rutherford's model based on his gold foil experiment, which determined that the positive charge and nearly all of the mass of the atom are concentrated in a very small, dense nucleus at the center.
- Bohr's model built on Rutherford's by proposing that electrons orbit the nucleus in fixed, quantized energy levels. It helped explain atomic emission spectra but had limitations.
- Later developments including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle
1. Bohr's model of the atom describes electrons orbiting the nucleus in fixed, quantized energy levels.
2. Light is emitted when an electron moves from a higher to lower energy level, with frequency determined by Planck's equation.
3. Hydrogen emits a line spectrum due to its quantized energy levels. The Rydberg equation calculates wavelengths from transitions between levels in Lyman, Balmer, Paschen, Brackett, and Pfund series.
The document discusses band theory of solids, which explains the electrical, thermal, and magnetic properties of solids. It begins by covering classical and quantum free electron theories, before introducing band theory. Band theory states that the motion of free electrons in solids is characterized by allowed energy bands separated by forbidden bands. The width of bands and size of gaps depends on factors like the periodic potential of the lattice and strength of scattering. Semiconductors have a small forbidden band gap, allowing electrical conductivity to be controlled by doping with impurities.
- The atom consists of a small, dense nucleus surrounded by an electron cloud.
- Electrons can only exist in certain discrete energy levels around the nucleus. Their wavelengths are determined by the principal quantum number.
- The Bohr model improved on earlier models by introducing energy levels and quantization, but had limitations. The quantum mechanical model treats electrons as waves and uses Schrodinger's equation.
1) The document provides information about a physical chemistry course on bonding taught by Professor Naresh Patwari, including recommended textbooks, websites with course materials, and what topics will be covered in the course like quantum mechanics, atomic structure, and chemical bonding.
2) Key concepts from quantum mechanics that will be discussed include the particle-wave duality of light and matter demonstrated by experiments, Planck's hypothesis and the photoelectric effect, the de Broglie hypothesis and diffraction of electrons, and the Heisenberg uncertainty principle.
3) Historical models of the atom will also be examined, like the Rutherford model, Bohr's model, and how Schrodinger's wave equation improved our understanding of
This document discusses electromagnetic radiation and atomic structure. It begins by explaining the wave characteristics of electromagnetic radiation like wavelength, frequency, and speed. It then discusses Planck's discovery that energy is quantized and Einstein's proposal that electromagnetic radiation consists of photons. The photoelectric effect is explained, providing evidence that light behaves as particles. The development of quantum mechanics and concepts like wave-particle duality, the Heisenberg uncertainty principle, and quantum numbers are summarized. The shapes and energies of atomic orbitals are described, along with how the periodic table developed based on patterns in elements' properties.
Semiconductor theory describes how small amounts of impurities can be added to intrinsic semiconductors to create n-type and p-type materials. N-type semiconductors are created by adding elements with extra electrons, while p-type are created by adding elements with electron deficiencies. The junction between a p-type and n-type material allows current to flow in only one direction, forming the basis for important semiconductor devices such as diodes, transistors, and solar cells.
STRUCTURE OF ATOM
Sub atomic Particles
Atomic Models
Atomic spectrum of hydrogen atom:
Photoelectric effect
Planck’s quantum theory
Heisenberg’s uncertainty principle
Quantum Numbers
Rules for filling of electrons in various orbitals
This document provides an overview of the development of atomic models over time, including:
- Thomson's model which depicted the atom as a uniform sphere of positive charge with electrons embedded within it.
- Rutherford's model based on his gold foil experiment, which determined that the positive charge and nearly all of the mass of the atom are concentrated in a very small, dense nucleus at the center.
- Bohr's model built on Rutherford's by proposing that electrons orbit the nucleus in fixed, quantized energy levels. It helped explain atomic emission spectra but had limitations.
- Later developments including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle
1. Bohr's model of the atom describes electrons orbiting the nucleus in fixed, quantized energy levels.
2. Light is emitted when an electron moves from a higher to lower energy level, with frequency determined by Planck's equation.
3. Hydrogen emits a line spectrum due to its quantized energy levels. The Rydberg equation calculates wavelengths from transitions between levels in Lyman, Balmer, Paschen, Brackett, and Pfund series.
The document discusses band theory of solids, which explains the electrical, thermal, and magnetic properties of solids. It begins by covering classical and quantum free electron theories, before introducing band theory. Band theory states that the motion of free electrons in solids is characterized by allowed energy bands separated by forbidden bands. The width of bands and size of gaps depends on factors like the periodic potential of the lattice and strength of scattering. Semiconductors have a small forbidden band gap, allowing electrical conductivity to be controlled by doping with impurities.
- The atom consists of a small, dense nucleus surrounded by an electron cloud.
- Electrons can only exist in certain discrete energy levels around the nucleus. Their wavelengths are determined by the principal quantum number.
- The Bohr model improved on earlier models by introducing energy levels and quantization, but had limitations. The quantum mechanical model treats electrons as waves and uses Schrodinger's equation.
1) The document provides information about a physical chemistry course on bonding taught by Professor Naresh Patwari, including recommended textbooks, websites with course materials, and what topics will be covered in the course like quantum mechanics, atomic structure, and chemical bonding.
2) Key concepts from quantum mechanics that will be discussed include the particle-wave duality of light and matter demonstrated by experiments, Planck's hypothesis and the photoelectric effect, the de Broglie hypothesis and diffraction of electrons, and the Heisenberg uncertainty principle.
3) Historical models of the atom will also be examined, like the Rutherford model, Bohr's model, and how Schrodinger's wave equation improved our understanding of
This document discusses electromagnetic radiation and atomic structure. It begins by explaining the wave characteristics of electromagnetic radiation like wavelength, frequency, and speed. It then discusses Planck's discovery that energy is quantized and Einstein's proposal that electromagnetic radiation consists of photons. The photoelectric effect is explained, providing evidence that light behaves as particles. The development of quantum mechanics and concepts like wave-particle duality, the Heisenberg uncertainty principle, and quantum numbers are summarized. The shapes and energies of atomic orbitals are described, along with how the periodic table developed based on patterns in elements' properties.
Semiconductor theory describes how small amounts of impurities can be added to intrinsic semiconductors to create n-type and p-type materials. N-type semiconductors are created by adding elements with extra electrons, while p-type are created by adding elements with electron deficiencies. The junction between a p-type and n-type material allows current to flow in only one direction, forming the basis for important semiconductor devices such as diodes, transistors, and solar cells.
This document discusses atomic structure and periodicity. It begins by explaining electromagnetic radiation and its wave characteristics. It then discusses Planck's discovery that energy is quantized and Einstein's proposal that light can be viewed as particles called photons. Next, it explains the photoelectric effect and how it provided evidence that light behaves as particles. It discusses the Bohr model of the hydrogen atom and how it correctly predicted the atom's quantized energy levels but was fundamentally incorrect. Finally, it summarizes the development of the modern quantum mechanical model of the atom and periodic trends in atomic properties such as ionization energy and atomic radius.
1. The document discusses optical properties of semiconductors when exposed to electromagnetic radiation like light.
2. It explains concepts like absorption, reflection, transmission and emission spectra that can be obtained from materials and how they provide information about electronic band structures.
3. Key optical phenomena discussed include photon absorption promoting electrons from the valence to conduction band if the photon energy exceeds the semiconductor bandgap, and the interaction of light with materials leading to processes like reflection, refraction, scattering and dispersion.
The document summarizes key concepts in atomic structure:
- John Dalton proposed atoms as the smallest indivisible particles containing electrons, protons and neutrons.
- Rutherford's nuclear model presented atoms as mostly empty space with a dense positively charged nucleus.
- Bohr's model improved on this by proposing electrons orbit in fixed shells with discrete energies, explaining atomic spectra.
- Planck and Einstein established the particle-like nature of electromagnetic radiation as photons.
Chemistry- JIB Topic 3 Electron ConfigurationsSam Richard
The document discusses Bohr's model of the hydrogen atom and how it led to the concept of electron configurations and quantized energy levels in atoms. It introduces quantum numbers like principal quantum number n, azimuthal quantum number l, magnetic quantum number ml, and spin quantum number ms that describe the possible electron configurations. Rules for filling orbitals like the Aufbau principle and Hund's rule are explained.
This document provides an overview of quantum dots. It discusses how quantum dots confine electrons in nanometer-sized volumes, behaving like artificial atoms. Transport in quantum dots exhibits Coulomb blockade, where conduction only occurs when the energy needed to add an electron to the dot is balanced by the gate potential. This leads to peaks in the conductance that are spaced by either the charging energy or level spacing of the dot. The spacing of these peaks can provide information about interactions between electrons in the quantum dot.
This document outlines topics related to semiconductor physics and optoelectronics physics, including:
1. Free electron theory of metals, Bloch's theorem, energy band diagrams, direct and indirect bandgaps, density of states, and the types of electronic materials including metals, semiconductors and insulators.
2. Lasers, which use stimulated emission of radiation to produce an intense, coherent beam of light. Key concepts covered include spontaneous emission, stimulated absorption, population inversion, and semiconductor lasers.
3. Photodetectors and noise sources, with reference made to the Fermi Golden Rule. The document provides an overview of key concepts that will be covered in more depth within these physics courses.
This document summarizes key concepts from a chapter on atomic structure:
1. Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate as waves. Light is a type of electromagnetic radiation detectable by the human eye.
2. Atoms can only absorb or emit electromagnetic radiation at specific quantized energy levels. This explains the emission spectrum of hydrogen, which shows only certain discrete wavelengths.
3. Niels Bohr's early model of the hydrogen atom proposed that electrons orbit the nucleus at fixed distances corresponding to discrete energy levels. Later, the quantum mechanical model described electron behavior as wave-like standing waves.
4. Werner Heisenberg's uncertainty principle states that the more precisely the position
The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
This Presentation "Energy band theory of solids" will help you to Clarify your doubts and Enrich your Knowledge. Kindly use this presentation as a Reference and utilize this presentation
Chapter3 introduction to the quantum theory of solidsK. M.
The document provides an introduction to the quantum theory of solids, including:
1. How allowed and forbidden energy bands form in solids due to the interaction of atomic electron wave functions when atoms are brought close together in a crystal lattice.
2. Electrical conduction in solids is explained using the concept of electron effective mass and holes, within the framework of the energy band model.
3. The Kronig-Penney model is used to quantitatively relate the energy, wave number, and periodic potential within a solid, resulting in allowed and forbidden energy bands.
The document discusses atomic structure and provides details about atomic number, mass number, isotopes, and other atomic terms. It describes Rutherford's model of the atom including the discovery of the electron, proton, and neutron as fundamental atomic particles. Bohr's model of the hydrogen atom is explained along with concepts like energy levels, ionization energy, and spectral lines. Other quantum mechanical models like de Broglie's hypothesis, Heisenberg's uncertainty principle, and Schrodinger's wave equation are introduced. Atomic orbitals and the four quantum numbers - principal, azimuthal, magnetic, and spin - are defined.
1. The document summarizes the structure and components of an atom according to John Dalton's atomic theory from 1808. Atoms are the smallest indivisible particles of matter and contain subatomic particles like electrons, protons, and neutrons.
2. It describes the properties of these subatomic particles, including their relative masses and electric charges. Electrons were discovered through cathode ray experiments, protons through anode ray experiments, and neutrons by James Chadwick in 1932.
3. The document also summarizes the historical progression of atomic models from Thomson's plum pudding model to Rutherford's nuclear model to Bohr's model of electron orbits to the modern quantum mechanical model developed by Schrodinger and He
This document discusses the development of atomic structure models from the early 20th century to the present. It describes experiments that showed light and matter have both wave-like and particle-like properties. This led to the development of quantum mechanics and quantum numbers to describe electron orbitals. The Bohr model of the hydrogen atom was an early success but did not apply to other atoms. Modern quantum mechanics uses probability distributions and accounts for electron spin and the Pauli exclusion principle.
The Hall effect occurs when a current-carrying conductor is placed in a magnetic field. This causes charge carriers to experience a Lorentz force and build up on one side of the conductor, creating a voltage (the Hall voltage) perpendicular to both the current and the magnetic field. Measuring the Hall voltage allows determining properties of the charge carriers such as their type (electrons or holes) and density. The classical Drude model describes the Hall effect by considering electrons as particles scattering between collisions. It relates the Hall coefficient to the carrier density, providing a way to experimentally measure carrier density via the Hall effect.
The document discusses various length scales that are important in physics, chemistry, and biology. It provides examples of fundamental length scales in quantum physics where quantum effects become prominent below 7 nanometers. In electric phenomena, the charging energy of a single electron becomes comparable to thermal energy below 9 nanometers. For magnetic structures, the energy barrier for flipping the spin of a magnetic particle must be larger than thermal energy, which requires a size above 3 nanometers. The document also discusses important length scales for polymers, electrolytes, and self-organization driven by competing short-range attraction and long-range repulsion forces between different blocks or particles.
The document discusses the band structure of electrons in solids. It explains that when electrons are placed in a periodic potential, as in metals and semiconductors, the allowed energy levels split and form bands separated by band gaps. The nearly-free electron model is introduced to account for this band structure by treating electrons as interacting with a periodic lattice potential rather than being completely free. The key outcomes are that the energy-momentum relationship becomes a series of bands rather than continuous, and band gaps open up where electron states are forbidden. This distinguishes conductors, semiconductors and insulators.
This document provides an introduction to lasers and their applications. It begins with recommended textbooks on the subject, then provides a chart showing the laser spectrum and examples of different laser types and their wavelengths. The remainder of the document discusses the basic components and functioning of lasers, including the gain medium that provides stimulated emission, the pump source to create population inversion, and the optical cavity formed by mirrors. It also provides brief histories of the development of masers and the first ruby laser.
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This document discusses atomic structure and periodicity. It begins by explaining electromagnetic radiation and its wave characteristics. It then discusses Planck's discovery that energy is quantized and Einstein's proposal that light can be viewed as particles called photons. Next, it explains the photoelectric effect and how it provided evidence that light behaves as particles. It discusses the Bohr model of the hydrogen atom and how it correctly predicted the atom's quantized energy levels but was fundamentally incorrect. Finally, it summarizes the development of the modern quantum mechanical model of the atom and periodic trends in atomic properties such as ionization energy and atomic radius.
1. The document discusses optical properties of semiconductors when exposed to electromagnetic radiation like light.
2. It explains concepts like absorption, reflection, transmission and emission spectra that can be obtained from materials and how they provide information about electronic band structures.
3. Key optical phenomena discussed include photon absorption promoting electrons from the valence to conduction band if the photon energy exceeds the semiconductor bandgap, and the interaction of light with materials leading to processes like reflection, refraction, scattering and dispersion.
The document summarizes key concepts in atomic structure:
- John Dalton proposed atoms as the smallest indivisible particles containing electrons, protons and neutrons.
- Rutherford's nuclear model presented atoms as mostly empty space with a dense positively charged nucleus.
- Bohr's model improved on this by proposing electrons orbit in fixed shells with discrete energies, explaining atomic spectra.
- Planck and Einstein established the particle-like nature of electromagnetic radiation as photons.
Chemistry- JIB Topic 3 Electron ConfigurationsSam Richard
The document discusses Bohr's model of the hydrogen atom and how it led to the concept of electron configurations and quantized energy levels in atoms. It introduces quantum numbers like principal quantum number n, azimuthal quantum number l, magnetic quantum number ml, and spin quantum number ms that describe the possible electron configurations. Rules for filling orbitals like the Aufbau principle and Hund's rule are explained.
This document provides an overview of quantum dots. It discusses how quantum dots confine electrons in nanometer-sized volumes, behaving like artificial atoms. Transport in quantum dots exhibits Coulomb blockade, where conduction only occurs when the energy needed to add an electron to the dot is balanced by the gate potential. This leads to peaks in the conductance that are spaced by either the charging energy or level spacing of the dot. The spacing of these peaks can provide information about interactions between electrons in the quantum dot.
This document outlines topics related to semiconductor physics and optoelectronics physics, including:
1. Free electron theory of metals, Bloch's theorem, energy band diagrams, direct and indirect bandgaps, density of states, and the types of electronic materials including metals, semiconductors and insulators.
2. Lasers, which use stimulated emission of radiation to produce an intense, coherent beam of light. Key concepts covered include spontaneous emission, stimulated absorption, population inversion, and semiconductor lasers.
3. Photodetectors and noise sources, with reference made to the Fermi Golden Rule. The document provides an overview of key concepts that will be covered in more depth within these physics courses.
This document summarizes key concepts from a chapter on atomic structure:
1. Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate as waves. Light is a type of electromagnetic radiation detectable by the human eye.
2. Atoms can only absorb or emit electromagnetic radiation at specific quantized energy levels. This explains the emission spectrum of hydrogen, which shows only certain discrete wavelengths.
3. Niels Bohr's early model of the hydrogen atom proposed that electrons orbit the nucleus at fixed distances corresponding to discrete energy levels. Later, the quantum mechanical model described electron behavior as wave-like standing waves.
4. Werner Heisenberg's uncertainty principle states that the more precisely the position
The document discusses the effective mass approximation in quantum mechanics. It begins by defining the effective mass as inversely proportional to the curvature of energy bands. Having a effective mass allows electrons in crystals to be treated similarly to classical particles, with the crystal forces and quantum properties accounted for in the mass. The effective mass can be a tensor and depends on the crystal direction. It then discusses measuring the effective mass using cyclotron resonance and how it varies by crystallographic direction. In general, the effective mass incorporates the quantum mechanical behavior of electrons in crystals to allow a classical particle treatment.
This Presentation "Energy band theory of solids" will help you to Clarify your doubts and Enrich your Knowledge. Kindly use this presentation as a Reference and utilize this presentation
Chapter3 introduction to the quantum theory of solidsK. M.
The document provides an introduction to the quantum theory of solids, including:
1. How allowed and forbidden energy bands form in solids due to the interaction of atomic electron wave functions when atoms are brought close together in a crystal lattice.
2. Electrical conduction in solids is explained using the concept of electron effective mass and holes, within the framework of the energy band model.
3. The Kronig-Penney model is used to quantitatively relate the energy, wave number, and periodic potential within a solid, resulting in allowed and forbidden energy bands.
The document discusses atomic structure and provides details about atomic number, mass number, isotopes, and other atomic terms. It describes Rutherford's model of the atom including the discovery of the electron, proton, and neutron as fundamental atomic particles. Bohr's model of the hydrogen atom is explained along with concepts like energy levels, ionization energy, and spectral lines. Other quantum mechanical models like de Broglie's hypothesis, Heisenberg's uncertainty principle, and Schrodinger's wave equation are introduced. Atomic orbitals and the four quantum numbers - principal, azimuthal, magnetic, and spin - are defined.
1. The document summarizes the structure and components of an atom according to John Dalton's atomic theory from 1808. Atoms are the smallest indivisible particles of matter and contain subatomic particles like electrons, protons, and neutrons.
2. It describes the properties of these subatomic particles, including their relative masses and electric charges. Electrons were discovered through cathode ray experiments, protons through anode ray experiments, and neutrons by James Chadwick in 1932.
3. The document also summarizes the historical progression of atomic models from Thomson's plum pudding model to Rutherford's nuclear model to Bohr's model of electron orbits to the modern quantum mechanical model developed by Schrodinger and He
This document discusses the development of atomic structure models from the early 20th century to the present. It describes experiments that showed light and matter have both wave-like and particle-like properties. This led to the development of quantum mechanics and quantum numbers to describe electron orbitals. The Bohr model of the hydrogen atom was an early success but did not apply to other atoms. Modern quantum mechanics uses probability distributions and accounts for electron spin and the Pauli exclusion principle.
The Hall effect occurs when a current-carrying conductor is placed in a magnetic field. This causes charge carriers to experience a Lorentz force and build up on one side of the conductor, creating a voltage (the Hall voltage) perpendicular to both the current and the magnetic field. Measuring the Hall voltage allows determining properties of the charge carriers such as their type (electrons or holes) and density. The classical Drude model describes the Hall effect by considering electrons as particles scattering between collisions. It relates the Hall coefficient to the carrier density, providing a way to experimentally measure carrier density via the Hall effect.
The document discusses various length scales that are important in physics, chemistry, and biology. It provides examples of fundamental length scales in quantum physics where quantum effects become prominent below 7 nanometers. In electric phenomena, the charging energy of a single electron becomes comparable to thermal energy below 9 nanometers. For magnetic structures, the energy barrier for flipping the spin of a magnetic particle must be larger than thermal energy, which requires a size above 3 nanometers. The document also discusses important length scales for polymers, electrolytes, and self-organization driven by competing short-range attraction and long-range repulsion forces between different blocks or particles.
The document discusses the band structure of electrons in solids. It explains that when electrons are placed in a periodic potential, as in metals and semiconductors, the allowed energy levels split and form bands separated by band gaps. The nearly-free electron model is introduced to account for this band structure by treating electrons as interacting with a periodic lattice potential rather than being completely free. The key outcomes are that the energy-momentum relationship becomes a series of bands rather than continuous, and band gaps open up where electron states are forbidden. This distinguishes conductors, semiconductors and insulators.
This document provides an introduction to lasers and their applications. It begins with recommended textbooks on the subject, then provides a chart showing the laser spectrum and examples of different laser types and their wavelengths. The remainder of the document discusses the basic components and functioning of lasers, including the gain medium that provides stimulated emission, the pump source to create population inversion, and the optical cavity formed by mirrors. It also provides brief histories of the development of masers and the first ruby laser.
Similar to ECE692_3_1008.pptdfdfdfdfdfdfdffdfdfdfddf (20)
1. Review of Semiconductor Physics
Energy bands
• Bonding types – classroom discussion
• The bond picture vs. the band picture
Bonding and antibonding
Conduction band and valence band
2. • The band picture – Bloch’s Theorem
Notice it’s a theorem, not a law. Mathematically derived.
The theorem:
Physical picture
The eigenstates (r) of the one-electron Hamiltonian
where V(r + R) = V(r) for all R in a Bravais lattice, can be chosen to have
the form of a plane wave times a function with the periodicity of the
Bravais lattice:
)
(
)
( ,
, r
r k
r
k
k n
i
n u
e
where un,k(r + R) = un,k(r) .
Equivalently,
)
(
)
( ,
, r
R
r k
R
k
k n
i
n e
- Wave function
)
(
2
ˆ 2
2
r
V
m
H
5. Limitations of the band theory
Static lattice: Will introduce phonons
Perfect lattice: Will introduce defects
One-electron Shrödinger Eq: We in this class will live with this
Justification: the effect of other electrons can be regarded as a kind of
background.
6. Semi-classic theory
Free electron Block electron
ħk is the momentum. ħk is the crystal momentum, which is not
a momentum, but is treated as momentum
in the semiclassical theory.
n is the band index.
m
k
E
2
)
(
2
2
k *
2
0
2
2
|
|
)
(
m
E
k
k
k
En(k) = En(k+K)
1D
dk
dE
m
k
v
1
)
(
1
k
k
v k E
m
3D
dk
dE
m
k
k
v n
n
1
)
(
*
0
)
(
1
|
|
)
( *
0
k
k
k
k
v k n
n E
m
1D
3D
r
k
k r
i
e
)
(
)
(
)
( ,
, r
r k
r
k
k n
i
n u
e
un,k(r + R) = un,k(r)
7. The Bloch (i.e. semiclassic) electron behaves as a particle following Newton’s laws.
(We are back in the familiar territory.)
• With a mass m*
• Emerging from the other side of the first Brillouin zone upon hitting a boundary
Newton’s 1st law: the Bloch electron moves forever – No resistance?
Oscillation in dc field. So far not observed yet.
Newton’s 2nd law:
F = dp/dt = ħdk/dt
8. Real crystals are not perfect. Defects scatter electrons.
On average, the electron is scattered once every time period . Upon scattering,
the electron forgets its previous velocity, and is “thermalized.”
E
E
*
*
m
q
m
F
vd *
m
q
E
E
qn
qnv
J d
*
2
m
n
q
qn
Mobility
9. Values of k
k = 2n/L, n = 1, 2, 3, …, N
Run the extra mile:
Show the above by using the “periodic boundary” condition.
Holes
A vacancy in a band, i.e. a k-state missing the electron, behaves like a particle with
charge +q.
Run the extra mile:
Show the above.
Discrete but quasi-continuous
L = Na
10. Review of Semiconductor Physics
Carrier Statistics
• Fermi-Dirac distribution
Nature prefers low energy.
Lower energy states (levels) are filled first.
Imaging filling a container w/ sands, or rice, or balls, or whatever
- Each particle is still T = 0 K
- Each has some energy, keeping bouncing around T > 0 K
• Density of States
How many states are there in the energy interval dE at E?
D(E)dE
1D case derived in class.
The take-home message: D(E) E1/2
11. 2D case
Run the extra mile
Derive D(E) in 2D.
Hint: count number of k’s in 2D.
The answer: 2
*
2
2
)
(
m
L
E
D
Or, for unit area 2
*
2
1
)
(
m
E
D
The take-home message: D(E) = constant
3D case
Run the extra mile
Derive D(E) in 3D.
Hint: count number of k’s in 2D.
For unit area, E
m
E
D 3
2
/
3
*
2
)
(
2
2
)
(
The take-home message: D(E) E1/2
12. Things we have ignored so far: degeneracies
Spin degeneracy: 2
Valley degeneracy: Mc
Mc = 6 for Si
E
m
M
E
D c 3
2
/
3
*
2
)
(
2
2
2
)
(
13. Total number of carriers per volume (carrier density, carrier concentration)
Run the extra mile
Derive the electron density n.
Hint: Fermi-Dirac distribution approximated by Boltzmann distribution.
Results for n and p are given.
Doping
One way to manipulate carrier density is doping.
Doping shifts the Fermi level.
np = ni
2
p is the total number of states NOT occupied.
14. One small thing to keep in mind:
Subtle difference in jargons used by EEs and physicists
We use the EE terminology, of course.
EF = EF(T)
Physicists:
Chemical potential (T)
Fermi level
Fermi energy EF = (0)
Same concept
We already used for mobility.
15. Before we talk about device, what are semiconductors anyway?
Why can we modulate their properties by orders of magnitude?
Classroom discussion
Classroom discussion
16. Real crystals are not perfect. Defects scatter electrons.
On average, the electron is scattered once every time period . Upon scattering,
the electron forgets its previous velocity, and is “thermalized.”
E
E
*
*
m
q
m
F
vd *
m
q
E
E
qn
qnv
J d
*
2
m
n
q
qn
Mobility
We have mentioned defect scattering:
Any deviation from perfect periodicity is a defect. A perfect surface is a defect.
17. Phonons
Static lattice approximation
Atoms vibrate
Harmonic approximation
Vibration quantized
Each quantum is a phonon.
Similar to the photon: E = ħ, p = ħk
Phonons scatter carriers, too.
The higher the temperature, the worse phonon scattering.
You can use the temperature dependence of conductivity or mobility to determine
the contributions of various scattering mechanisms.
18. Phonons
Sound wave in continuous media = vk
Microscopically, the solid is discrete.
Phonon dispersion
Wave vector folding, first Brillouin zone.
Watch video at http://en.wikipedia.org/wiki/File:Phonon_k_3k.gif
Recall that
Crystal structure = Bravais lattice + basis
If there are more than 1 atom in the basis, optical phonons
19. Phonons in the 3D world -- Si
In 3D, there are transverse
and longitudinal waves.
E = h = ħ
15 THz 62 meV
When electron energy is low, the electron
only interacts with acoustic phonons,
20. Optical phonons and transport
At low fields, th
d v
v
E
T
k
v
m B
th
2
3
2
1 2
*
For Si, vth = 2.3 × 107 cm/s
= 38 meV
At high fields, vd comparable to vth
Electrons get energy from the field, hotter than the lattice – hot electrons
E
vd
vsat
When the energy of hot electrons becomes comparable to that of optical phonons,
energy is transferred to the lattice via optical phonons.
Velocity saturation
For Si, vsat ~ 107 cm/s
22. Topics
• Review of Semiconductor physics
- Crystal structure, band structures, band structure modification by alloys,
heterostructurs, and strain
- Carrier statistics
- Scattering, defects, phonons, mobility, transport in heterostructures
• Device concepts
- MOSFETs, MESFETs, MODFETs, TFTs
- Heterojunction bipolar transistors (HBT)
- Semiconductor processing
- Photodiodes, LEDs, semiconductor lasers
- (optional) resonant tunneling devices, quantum interference devices,
single electron transistors, quantum dot computing, ...
- Introduction to nanoelectronics
We will discuss heterostructures in the context of devices.
More discussions on semiconductor physics will be embedded in the device
context.