In extrinsic semiconductors, the Fermi level lies close to either the conduction or valence band depending on whether there are more electrons or holes. For n-type semiconductors, donor impurities add extra electrons to the conduction band, making the Fermi level closer to the conduction band. For p-type semiconductors, acceptor impurities create more holes in the valence band, positioning the Fermi level nearer to the valence band. The Fermi level equations show its relation to factors like temperature, carrier concentration, and band properties.
This document discusses the density of states (DoS) for bulk semiconductors. It begins by defining DoS as the number of available energy states per unit energy interval per unit dimension in real space. It then derives the DoS for bulk semiconductors using the Bloch theorem and shows that the DoS is proportional to the square root of energy. Finally, it defines the effective DoS, which accounts for occupancy based on the Fermi-Dirac distribution.
This document discusses metal-semiconductor junctions, including Schottky barriers and ohmic contacts. It describes how Schottky barriers form at the junction between a metal and an n-type or p-type semiconductor due to the difference in work functions between the materials. The barrier height determines whether the junction rectifies or forms an ohmic contact. Ohmic contacts are achieved by reducing the barrier height through heavy doping or making the depletion width narrow enough for carriers to tunnel through. Surface states can also pin the Fermi level and affect the barrier height.
This document provides a summary of Lecture 2 on electrostatics. It introduces fundamental concepts such as electric charge, Coulomb's law, electric field, electric potential, and the relationship between electric field and electric potential. Continuous distributions of charge such as volume, surface, and line charges are also discussed. Key equations for calculating electric fields and potentials from these various charge distributions are presented.
Basics of semiconductor, current equation, continuity equation, injected mino...Nidhee Bhuwal
This document provides an introduction to semiconductors. It discusses topics such as the crystal structure of germanium and silicon, intrinsic and extrinsic semiconductors, carrier mobility, and diffusion currents. Equations are presented for carrier concentrations, mass action law, drift current density, and the continuity equation. Generation and recombination of charge carriers is explained. Minority carrier injection, potential variation in graded semiconductors, and the contact potential of a step graded junction are also summarized.
Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. The wavefunctions of the individual electrons, however, overlap with those of electrons confined to neighboring atoms. The Pauli exclusion principle does not allow the electron energy levels to be the same so that one obtains a set of closely spaced energy levels, forming an energy band. The energy band model is crucial to any detailed treatment of semiconductor devices. It provides the framework needed to understand the concept of an energy bandgap and that of conduction in an almost filled band as described by the empty states.
Intrinsic and extrinsic semiconductors differ in their conduction mechanisms and origin of defects. Intrinsic semiconductors have conduction between the valence and conduction bands, while extrinsic semiconductors are doped with other elements to create acceptor or donor levels near the bands leading to p-type or n-type conductivity respectively between the bands and these defect levels. The document discusses the electronic structure and defects in intrinsic and extrinsic semiconductors.
In extrinsic semiconductors, the Fermi level lies close to either the conduction or valence band depending on whether there are more electrons or holes. For n-type semiconductors, donor impurities add extra electrons to the conduction band, making the Fermi level closer to the conduction band. For p-type semiconductors, acceptor impurities create more holes in the valence band, positioning the Fermi level nearer to the valence band. The Fermi level equations show its relation to factors like temperature, carrier concentration, and band properties.
This document discusses the density of states (DoS) for bulk semiconductors. It begins by defining DoS as the number of available energy states per unit energy interval per unit dimension in real space. It then derives the DoS for bulk semiconductors using the Bloch theorem and shows that the DoS is proportional to the square root of energy. Finally, it defines the effective DoS, which accounts for occupancy based on the Fermi-Dirac distribution.
This document discusses metal-semiconductor junctions, including Schottky barriers and ohmic contacts. It describes how Schottky barriers form at the junction between a metal and an n-type or p-type semiconductor due to the difference in work functions between the materials. The barrier height determines whether the junction rectifies or forms an ohmic contact. Ohmic contacts are achieved by reducing the barrier height through heavy doping or making the depletion width narrow enough for carriers to tunnel through. Surface states can also pin the Fermi level and affect the barrier height.
This document provides a summary of Lecture 2 on electrostatics. It introduces fundamental concepts such as electric charge, Coulomb's law, electric field, electric potential, and the relationship between electric field and electric potential. Continuous distributions of charge such as volume, surface, and line charges are also discussed. Key equations for calculating electric fields and potentials from these various charge distributions are presented.
Basics of semiconductor, current equation, continuity equation, injected mino...Nidhee Bhuwal
This document provides an introduction to semiconductors. It discusses topics such as the crystal structure of germanium and silicon, intrinsic and extrinsic semiconductors, carrier mobility, and diffusion currents. Equations are presented for carrier concentrations, mass action law, drift current density, and the continuity equation. Generation and recombination of charge carriers is explained. Minority carrier injection, potential variation in graded semiconductors, and the contact potential of a step graded junction are also summarized.
Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. The wavefunctions of the individual electrons, however, overlap with those of electrons confined to neighboring atoms. The Pauli exclusion principle does not allow the electron energy levels to be the same so that one obtains a set of closely spaced energy levels, forming an energy band. The energy band model is crucial to any detailed treatment of semiconductor devices. It provides the framework needed to understand the concept of an energy bandgap and that of conduction in an almost filled band as described by the empty states.
Intrinsic and extrinsic semiconductors differ in their conduction mechanisms and origin of defects. Intrinsic semiconductors have conduction between the valence and conduction bands, while extrinsic semiconductors are doped with other elements to create acceptor or donor levels near the bands leading to p-type or n-type conductivity respectively between the bands and these defect levels. The document discusses the electronic structure and defects in intrinsic and extrinsic semiconductors.
This document summarizes a seminar on energy bands and gaps in semiconductors. It discusses the introduction of energy bands, including valence bands, conduction bands, and forbidden gaps. It describes how materials are classified as insulators, conductors, or semiconductors based on their band gap energies. Direct and indirect band gap semiconductors are also defined. Intrinsic, n-type, and p-type semiconductors are classified based on their majority charge carriers.
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
1) The photoelectric effect occurs when light shines on a metal surface and electrons are emitted. Experimental results showed that the kinetic energy of emitted electrons depended on the frequency but not the intensity of light.
2) Einstein proposed that light is quantized into discrete packets called photons. The energy of photons is related to their frequency. If a photon's energy exceeds the metal's work function, it can eject an electron.
3) Einstein's photon theory explained all experimental results, including the dependence of electron kinetic energy on frequency but not intensity and the instantaneous emission. This validated Planck's quantum hypothesis and revolutionized our understanding of the nature of light.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
This document summarizes lecture material from an Electronic Devices course taught by Arpan Deyasi at RCC Institute of Information Technology in Kolkata, India. The document discusses quasi-Fermi levels, generation and recombination of carriers, and the continuity equation as it relates to excess carriers in semiconductors. Key points include definitions of quasi-Fermi levels for n-type and p-type materials, equations describing generation and recombination rates, and the continuity equation modeling carrier transport and generation/recombination processes in non-uniformly doped semiconductors.
This document summarizes problems involving the Fermi-Dirac distribution function. It includes:
1) Calculating the velocity of electrons at the Fermi level for potassium, which is 2.1eV.
2) Computing the probability of an energy level 0.01eV below the Fermi level being unoccupied, which is 0.405.
3) Finding the probabilities of electronic states being occupied that are 0.11eV above and below the Fermi level, which are 0.0126 and 0.987 respectively.
4) Evaluating the Fermi function for an energy level kT above the Fermi energy, which is 0.269.
5) Demonstrating
1. When a P-type semiconductor is joined with an N-type semiconductor, a PN junction is formed known as a semiconductor diode.
2. Semiconductor diodes are widely used as rectifiers to convert alternating current (AC) input into direct current (DC) output.
3. In a PN junction, the diffusion of majority carriers across the junction leaves behind charged acceptor and donor ions which form an electric field called the depletion region or space charge region.
1) The document discusses carrier transport in semiconductors, including drift and diffusion currents. Carrier drift occurs due to an electric field and is characterized by carrier mobility, while diffusion is due to concentration gradients and characterized by the diffusion coefficient.
2) Mobility is affected by phonon and ionized impurity scattering. The net mobility is the sum of these scattering components. Conductivity is directly proportional to carrier concentration and mobility.
3) The Hall effect can be used to determine the type of semiconductor (n-type or p-type), carrier concentration, and carrier mobility. Measurement of the Hall voltage polarity indicates type, and its magnitude relates to concentration and mobility.
1) The document discusses the Fermi level and distribution as it relates to electrons in metals.
2) The Fermi distribution depends on the Fermi energy (EF) and describes the probability of electron occupation at different energy levels in a metal.
3) At absolute zero temperature, electrons completely fill available energy states up to the Fermi level, with the probability of occupation dropping abruptly to zero for states above EF.
The document discusses carrier and doping density in semiconductors. It provides equations for short circuit current, open circuit voltage, fill factor, and efficiency of a solar cell. It also discusses various techniques to determine carrier density, including capacitance-voltage profiling, Hall effect measurements, and optical methods like plasma resonance. The doping density can be directly measured using secondary ion mass spectrometry, photoluminescence imaging, or other techniques. The current and doping density may differ for non-uniformly doped materials.
1. Edwin Hall discovered the Hall effect in 1879 while working on his doctoral degree at Johns Hopkins University. Through his measurements of a tiny effect produced using apparatus he designed, he published findings about a new interaction between magnets and electric currents eighteen years before the electron was discovered.
2. The Hall effect is the production of a voltage difference across an electrical conductor, perpendicular to both the current in the conductor and an applied magnetic field. This effect can be used to determine various properties of the conductor such as carrier concentration and Hall coefficient.
3. Applications of the Hall effect include speed detection, current sensing, magnetic field sensing as in magnetometers, and position sensing in devices like brushless DC motors.
current ,current density , Equation of continuityMuhammad Salman
1. Electric current in metallic conductors is carried by valence electrons, or free electrons, that move under the influence of an electric field. The velocity of these electrons is called the drift velocity.
2. Drift velocity is directly proportional to the electric field intensity and mobility of the electrons in the material. Higher conductivity materials like silver, copper and aluminum have higher electron mobilities.
3. The relationship between current density J and electric field E in a metallic conductor is defined by its conductivity σ, where J = σE. Conductivity depends on the charge density and mobility of electrons in the material.
This document discusses the concept of maximum power transfer theorem (MPTT) in electrical communication circuits. It states that maximum power will be transferred from a source to a load when the source impedance equals the load impedance. The document provides steps for finding the maximum power delivered to a load using Thevenin's theorem to derive an equivalent circuit and calculate the Thevenin resistance. It also notes that applying MPTT can maximize power transfer from an audio amplifier to a loudspeaker.
The document discusses the Compton effect, which describes the scattering of photons by charged particles like electrons. It provides the mathematical description using conservation of energy and momentum. The Compton effect leads to a shift in the wavelength of scattered photons. Practical applications of the Compton effect include Compton scatter densitometry to measure electron density, Compton scatter imaging for 3D electron density mapping, and Compton profile analysis to characterize materials.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
Maxwell's equations describe the relationship between electric and magnetic fields. Gauss' law states that the divergence of the electric flux density equals the electric charge density. Gauss' magnetism law states that the divergence of the magnetic flux density is always zero. Faraday's law describes how a changing magnetic field generates an electric field. Ampere's law shows the relationship between electric current and the surrounding magnetic field. Maxwell unified electricity, magnetism, and light through his equations, which can be written in differential or integral form and describe fields in free space or harmonically varying fields.
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
This document extends the Kronig-Penney model for modeling electron interactions with atomic lattices in semiconductors to arbitrary periodic potentials using numerical matrix mechanics. It introduces the Kronig-Penney model and represents periodic potentials using matrix representations in different basis sets. Numerical solutions are obtained and band structures are compared for different periodic potentials, including the Kronig-Penney, harmonic oscillator, and inverted harmonic oscillator potentials. Effective mass is also calculated from the band structure curvature.
Semiconductor Physics
In 3 sentences:
Semiconductors have electrical properties between metals and insulators, with conductivities from 10-4 to 104 S/m. Their crystal structure leads to electrons being able to move between valence and conduction bands, making semiconductors bipolar with both electrons and holes conducting. Semiconductors are classified as intrinsic, with equal electron and hole concentrations determined by temperature, or extrinsic with additional carriers from dopant impurities making them either n-type or p-type.
1) The document discusses electronic devices and semiconductor properties. It covers topics like the importance of semiconductors, properties of semiconductors like charge carriers and transport, and interaction with electromagnetic fields.
2) It also discusses energy band theory, the differences between direct and indirect semiconductors, and how band structures vary in materials like silicon, gallium arsenide, and their alloys.
3) Quantum mechanics concepts like wave-particle duality, the uncertainty principle, and Schrodinger's wave equation are also covered in relation to understanding electron behavior in semiconductors.
1. The document discusses electron behavior in semiconductors using energy-momentum (E-K) diagrams and energy-position (E-X) diagrams.
2. It explains recombination phenomena where an electron falls from the conduction band to the valence band, requiring a change in energy and momentum. This can emit a phonon or photon depending on the momentum change.
3. Auger recombination is described where an electron directly recombines with a hole, transferring energy and momentum to another electron or hole. Conservation of energy and momentum may require an additional particle like a phonon.
4. Electron drift under an electric field is depicted, showing the electron gaining kinetic energy as potential energy decreases while
This document summarizes a seminar on energy bands and gaps in semiconductors. It discusses the introduction of energy bands, including valence bands, conduction bands, and forbidden gaps. It describes how materials are classified as insulators, conductors, or semiconductors based on their band gap energies. Direct and indirect band gap semiconductors are also defined. Intrinsic, n-type, and p-type semiconductors are classified based on their majority charge carriers.
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
1) The photoelectric effect occurs when light shines on a metal surface and electrons are emitted. Experimental results showed that the kinetic energy of emitted electrons depended on the frequency but not the intensity of light.
2) Einstein proposed that light is quantized into discrete packets called photons. The energy of photons is related to their frequency. If a photon's energy exceeds the metal's work function, it can eject an electron.
3) Einstein's photon theory explained all experimental results, including the dependence of electron kinetic energy on frequency but not intensity and the instantaneous emission. This validated Planck's quantum hypothesis and revolutionized our understanding of the nature of light.
1) Effective current in an AC circuit is 0.707 times the maximum current. Effective voltage is 0.707 times the maximum voltage.
2) Inductive reactance is directly proportional to frequency and inductance. Capacitive reactance is inversely proportional to frequency and capacitance.
3) Impedance is the total opposition to current flow in an AC circuit consisting of resistance and reactance. Power is consumed only by the resistive component of impedance and is proportional to the cosine of the phase angle.
This document summarizes lecture material from an Electronic Devices course taught by Arpan Deyasi at RCC Institute of Information Technology in Kolkata, India. The document discusses quasi-Fermi levels, generation and recombination of carriers, and the continuity equation as it relates to excess carriers in semiconductors. Key points include definitions of quasi-Fermi levels for n-type and p-type materials, equations describing generation and recombination rates, and the continuity equation modeling carrier transport and generation/recombination processes in non-uniformly doped semiconductors.
This document summarizes problems involving the Fermi-Dirac distribution function. It includes:
1) Calculating the velocity of electrons at the Fermi level for potassium, which is 2.1eV.
2) Computing the probability of an energy level 0.01eV below the Fermi level being unoccupied, which is 0.405.
3) Finding the probabilities of electronic states being occupied that are 0.11eV above and below the Fermi level, which are 0.0126 and 0.987 respectively.
4) Evaluating the Fermi function for an energy level kT above the Fermi energy, which is 0.269.
5) Demonstrating
1. When a P-type semiconductor is joined with an N-type semiconductor, a PN junction is formed known as a semiconductor diode.
2. Semiconductor diodes are widely used as rectifiers to convert alternating current (AC) input into direct current (DC) output.
3. In a PN junction, the diffusion of majority carriers across the junction leaves behind charged acceptor and donor ions which form an electric field called the depletion region or space charge region.
1) The document discusses carrier transport in semiconductors, including drift and diffusion currents. Carrier drift occurs due to an electric field and is characterized by carrier mobility, while diffusion is due to concentration gradients and characterized by the diffusion coefficient.
2) Mobility is affected by phonon and ionized impurity scattering. The net mobility is the sum of these scattering components. Conductivity is directly proportional to carrier concentration and mobility.
3) The Hall effect can be used to determine the type of semiconductor (n-type or p-type), carrier concentration, and carrier mobility. Measurement of the Hall voltage polarity indicates type, and its magnitude relates to concentration and mobility.
1) The document discusses the Fermi level and distribution as it relates to electrons in metals.
2) The Fermi distribution depends on the Fermi energy (EF) and describes the probability of electron occupation at different energy levels in a metal.
3) At absolute zero temperature, electrons completely fill available energy states up to the Fermi level, with the probability of occupation dropping abruptly to zero for states above EF.
The document discusses carrier and doping density in semiconductors. It provides equations for short circuit current, open circuit voltage, fill factor, and efficiency of a solar cell. It also discusses various techniques to determine carrier density, including capacitance-voltage profiling, Hall effect measurements, and optical methods like plasma resonance. The doping density can be directly measured using secondary ion mass spectrometry, photoluminescence imaging, or other techniques. The current and doping density may differ for non-uniformly doped materials.
1. Edwin Hall discovered the Hall effect in 1879 while working on his doctoral degree at Johns Hopkins University. Through his measurements of a tiny effect produced using apparatus he designed, he published findings about a new interaction between magnets and electric currents eighteen years before the electron was discovered.
2. The Hall effect is the production of a voltage difference across an electrical conductor, perpendicular to both the current in the conductor and an applied magnetic field. This effect can be used to determine various properties of the conductor such as carrier concentration and Hall coefficient.
3. Applications of the Hall effect include speed detection, current sensing, magnetic field sensing as in magnetometers, and position sensing in devices like brushless DC motors.
current ,current density , Equation of continuityMuhammad Salman
1. Electric current in metallic conductors is carried by valence electrons, or free electrons, that move under the influence of an electric field. The velocity of these electrons is called the drift velocity.
2. Drift velocity is directly proportional to the electric field intensity and mobility of the electrons in the material. Higher conductivity materials like silver, copper and aluminum have higher electron mobilities.
3. The relationship between current density J and electric field E in a metallic conductor is defined by its conductivity σ, where J = σE. Conductivity depends on the charge density and mobility of electrons in the material.
This document discusses the concept of maximum power transfer theorem (MPTT) in electrical communication circuits. It states that maximum power will be transferred from a source to a load when the source impedance equals the load impedance. The document provides steps for finding the maximum power delivered to a load using Thevenin's theorem to derive an equivalent circuit and calculate the Thevenin resistance. It also notes that applying MPTT can maximize power transfer from an audio amplifier to a loudspeaker.
The document discusses the Compton effect, which describes the scattering of photons by charged particles like electrons. It provides the mathematical description using conservation of energy and momentum. The Compton effect leads to a shift in the wavelength of scattered photons. Practical applications of the Compton effect include Compton scatter densitometry to measure electron density, Compton scatter imaging for 3D electron density mapping, and Compton profile analysis to characterize materials.
In this presentation we will learn Del operator, Gradient of scalar function , Directional Derivative, Divergence of vector function, Curl of a vector function and after that solved some example related to above.
Gradient in math
Directional derivative in math
Divergence in math
Curl in math
Gradient , Directional Derivative , Divergence , Curl in mathematics
Gradient , Directional Derivative , Divergence , Curl in math
Gradient , Directional Derivative , Divergence , Curl
Maxwell's equations describe the relationship between electric and magnetic fields. Gauss' law states that the divergence of the electric flux density equals the electric charge density. Gauss' magnetism law states that the divergence of the magnetic flux density is always zero. Faraday's law describes how a changing magnetic field generates an electric field. Ampere's law shows the relationship between electric current and the surrounding magnetic field. Maxwell unified electricity, magnetism, and light through his equations, which can be written in differential or integral form and describe fields in free space or harmonically varying fields.
This document discusses plane electromagnetic waves. It defines plane waves as waves whose wavefronts are infinite parallel planes of constant amplitude normal to the phase velocity vector. The electric and magnetic fields of a plane wave are perpendicular to each other and to the direction of propagation. Plane waves can be linearly, circularly, or elliptically polarized depending on the orientation and behavior of the electric field vector over time. Linear polarization occurs when the electric field is oriented along a fixed line. Circular polarization results when the electric field traces out a circle, and elliptical polarization is characterized by an elliptical trace.
This document extends the Kronig-Penney model for modeling electron interactions with atomic lattices in semiconductors to arbitrary periodic potentials using numerical matrix mechanics. It introduces the Kronig-Penney model and represents periodic potentials using matrix representations in different basis sets. Numerical solutions are obtained and band structures are compared for different periodic potentials, including the Kronig-Penney, harmonic oscillator, and inverted harmonic oscillator potentials. Effective mass is also calculated from the band structure curvature.
Semiconductor Physics
In 3 sentences:
Semiconductors have electrical properties between metals and insulators, with conductivities from 10-4 to 104 S/m. Their crystal structure leads to electrons being able to move between valence and conduction bands, making semiconductors bipolar with both electrons and holes conducting. Semiconductors are classified as intrinsic, with equal electron and hole concentrations determined by temperature, or extrinsic with additional carriers from dopant impurities making them either n-type or p-type.
1) The document discusses electronic devices and semiconductor properties. It covers topics like the importance of semiconductors, properties of semiconductors like charge carriers and transport, and interaction with electromagnetic fields.
2) It also discusses energy band theory, the differences between direct and indirect semiconductors, and how band structures vary in materials like silicon, gallium arsenide, and their alloys.
3) Quantum mechanics concepts like wave-particle duality, the uncertainty principle, and Schrodinger's wave equation are also covered in relation to understanding electron behavior in semiconductors.
1. The document discusses electron behavior in semiconductors using energy-momentum (E-K) diagrams and energy-position (E-X) diagrams.
2. It explains recombination phenomena where an electron falls from the conduction band to the valence band, requiring a change in energy and momentum. This can emit a phonon or photon depending on the momentum change.
3. Auger recombination is described where an electron directly recombines with a hole, transferring energy and momentum to another electron or hole. Conservation of energy and momentum may require an additional particle like a phonon.
4. Electron drift under an electric field is depicted, showing the electron gaining kinetic energy as potential energy decreases while
The document discusses the transition from discrete atomic energy levels to energy bands in crystalline solids. As atoms come together to form a crystal lattice, the discrete energy levels of individual atoms broaden and overlap, forming continuous bands of allowed energies separated by forbidden gaps. Electrons near the top of the valence band can be excited into the conduction band, where they behave as free particles able to move through the solid and conduct electricity. Covalent bonding between atoms is also explained using the concept of energy bands.
This document provides an overview of solid state physics concepts including the structure of solids, crystal structures, lattice structures, unit cells, Miller indices, and band theory. It begins by defining crystalline and amorphous solids based on the arrangement of atoms. Crystalline solids have long-range order while amorphous solids are randomly arranged. Key concepts covered include space lattices, Bravais lattices, unit cells, and Miller indices for describing plane orientations in crystal structures. The document also introduces band theory concepts such as conduction bands, valence bands, forbidden gaps, and the Kronig-Penney model for explaining electron behavior in periodic potentials. Intrinsic and extrinsic semiconductors are defined based on
It is a notes of Bohr-Sommerfeld atomic model for graduate students.
For more information on this topic, kindly visit our blog at;
https://jayamchemistrylearners.blogspot.com/2022/04/bohr-sommerfeld-model-chemistrylearners.html
Introduction
Formation Of Bond.
Formation Of Band.
Role Of Pauli Exclusion Principle.
Fermi Dirac Distribution Equation
Classification Of Material In Term Of Energy Band Diagram.
Intrinsic Semiconductor.
a)Drive Density Of State
b)Drive Density Of Free Carrier.
c)Determination Of Fermi Level Position
Extrinsic Semiconductor.
a) N Type Extrinsic Semiconductor
b) P Type Extrinsic Semiconductor
Compensated semiconductor.
E Vs. Diagram.
Direct and Indirect Band Gap.
Degenerated and Non-degenerated.
PN Junction.
1. An intrinsic semiconductor is chemically pure with no impurities added. In an intrinsic semiconductor, the numbers of electrons and holes are equal at thermal equilibrium.
2. The Fermi level of an intrinsic semiconductor lies in the middle of the bandgap as the probabilities of occupation in the conduction and valence bands are equal.
3. Intrinsic semiconductors have low conductivity that depends on temperature as current is controlled by the generation and recombination of a small number of electrons and holes.
1) The document discusses energy band theory and how it relates to the electrical properties of semiconductors, insulators, and metals. It explains that semiconductors have a small forbidden band gap between the valence and conduction bands, allowing thermal or electromagnetic excitation of electrons.
2) The concept of effective mass is introduced, where electrons in a crystal lattice behave as if they have a different mass than free electrons due to the crystal potential. Effective mass depends on the curvature of electron energy-momentum diagrams.
3) Direct and indirect band gap materials are distinguished based on whether the minimum of the conduction band and maximum of the valence band occur at the same or different crystal momentum values.
This document provides an overview of intrinsic and extrinsic semiconductors. It begins with an introduction to crystalline solids and classifications of solids as conductors, insulators, or semiconductors. It then discusses intrinsic semiconductors, how increasing temperature generates electron-hole pairs, and how conductivity increases with temperature. Extrinsic or doped semiconductors are introduced, including n-type and p-type semiconductors created by adding donor or acceptor impurities. The document explains how doping increases the number of charge carriers and conductivity.
This document provides an introduction to semiconductors. It discusses the atomic structure of semiconductors like silicon and how covalent bonding forms between atoms. Semiconductors have energy bands with gaps between the valence and conduction bands. Doping semiconductors by adding impurities can produce either N-type or P-type materials. When a P-type and N-type material come into contact, electrons and holes diffuse across the junction, forming a depletion region that inhibits current flow in one direction. Diodes are formed from the junction between P-type and N-type materials and allow current to flow in only one direction.
Fisika Modern 15 molecules andsolid_semiconductorjayamartha
The document discusses the band theory of solids and its application to semiconductors, insulators, and metals. It explains that semiconductors have energy bands separated by a forbidden band gap, unlike metals where the bands overlap. At low temperatures, semiconductors behave as insulators as the bands are fully occupied, but at room temperature thermal energy excites a few electrons into the conduction band allowing conduction. This document also discusses effective mass and direct and indirect band gap materials.
Fisika Modern 15 molecules andsolid_semiconductorjayamartha
The document discusses semiconductor materials and their electrical properties. It explains that semiconductors have electrical conductivity between metals and insulators. The electrical properties of semiconductors can be understood using band theory, where electrons occupy allowed energy bands separated by forbidden gaps. At low temperatures, semiconductors behave as insulators as their valence bands are full and conduction bands are empty, but at room temperature some electrons gain enough thermal energy to cross the gap. This allows both holes and electrons to contribute to electrical conduction in semiconductors.
The document discusses computational methods for calculating the electronic band structure of solids, including:
1) The tight-binding approximation, which uses atomic orbitals as basis wave functions and can accurately reproduce band structures of many solids.
2) The cellular method and Wigner-Seitz approximation, which divide the crystal into unit cells centered on each atom to solve the Schrodinger equation.
3) Modern methods like the augmented plane wave method and pseudopotential method, which assume different potentials and wave functions to more accurately model band structures.
Electronic spectra of metal complexes-1SANTHANAM V
This document discusses electronic spectra of metal complexes. It begins by relating the observed color of complexes to the light absorbed and corresponding wavelength ranges. It then discusses the use of electronic spectra to determine d-d transition energies and the factors that affect d orbital energies. Key terms like states, microstates, and quantum numbers are introduced. Configuration, inter-electronic repulsions described by Racah parameters, nephelauxetic effect, and spin-orbit coupling are explained as factors that determine the splitting of energy levels. Russell-Saunders and j-j coupling are outlined as approaches to describe spin-orbit interactions in light and heavy elements respectively.
Fisika Modern (15) molecules andsolid_semiconductorjayamartha
The document discusses semiconductor materials and their electrical properties. It explains that semiconductors have electrical conductivity between metals and insulators. The electrical properties of semiconductors can be understood using band theory, where electrons occupy allowed energy bands separated by forbidden bands. At low temperatures, semiconductors behave as insulators as their valence band is full and conduction band is empty, but at room temperature some electrons gain enough energy to cross the band gap. This allows both holes and electrons to contribute to electrical conduction in semiconductors.
Semiconductors have properties between conductors and insulators due to their small energy band gap. Band theory explains the allowed energy levels for electrons in solids. Intrinsic semiconductors have few charge carriers that are generated thermally, while extrinsic semiconductors have impurities that generate majority carriers. The Hall effect demonstrates the behavior of charge carriers in a magnetic field and can determine carrier type and concentration. Semiconductors are used widely in electronic devices like diodes, transistors, sensors and solar cells due to their small size, low power needs, and long lifespan.
Diploma i boee u 1 electrostatic and capacitanceRai University
- Static electricity is an imbalance of electric charges within a material that remains until the charge is able to move away through a current or discharge. It is contrasted with current electricity which flows through conductors.
- A capacitor is composed of two conductive plates separated by a non-conductive dielectric. It is used to store electric charge electrostatically and has applications in many electronic devices. The capacitance of a capacitor depends on the plate area, distance between plates, and the dielectric material.
- Electric flux is defined as the electric field strength multiplied by the area over which it acts. It represents the number of electric field lines passing through a surface and has units of volt-meters.
This document provides an introduction to nano-materials. It defines nano-materials as artificial semiconductor structures with dimensions on the nanometer scale, including quantum wells, wires, and dots. Electron behavior changes from plane waves in free space, to Bloch waves in bulk semiconductors, to discrete energy levels in low-dimensional nano-structures. Nano-materials are of interest because they allow tailoring of electronic and optical properties by controlling geometric confinement. Common fabrication methods include lithography and self-organized growth to achieve sizes less than 100nm for full quantum confinement effects. Nano-materials demonstrate properties like ballistic transport, tunneling, and quantized energy levels that enable applications in light sources, detectors, and electronic devices
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2. ENERGY BAND DIAGRAM
• A Energy band diagram is a diagram plotting various key electron energy levels as a function
of some spatial dimension
• The bands can be thought of as the collection of the individual energy levels of electrons
surrounding each atom.
• The wavefunctions of the individual electrons, however, overlap with those of electrons
confined to neighboring atoms.
• The main feature of the energy band is that the electron’s energy states of electronics are
stable in different ranges. So, the level of energy of an atom will change in conduction bands
& valence bands.
3. ENERGY BAND DIAGRAM OF SEMICONDUCTOR
• The best examples of semiconductors are Silicon (Si) & Germanium (Ge) which
are the most used materials.
• The electrical properties of these materials lie among semiconductors as well
as insulators.
• The valence band is totally filled however the forbidden gap among these
bands is minute that is 1eV.
• The forbidden gap of Ge is 0.72eV and Si is 1.1eV.
4.
5. E-K DIAGRAM
An E-k diagram shows characteristics of a particular semiconductor material.
• It shows the relationship between the energy and momentum of available
quantum mechanical states for electrons in the material.
6. • The band gap (EG), which is the difference in energy between the top of the
valence band and the bottom of the conduction band.
• The effective mass of electrons and holes in the material. This is given by the
curvature of each of the bands.
• This diagram indicates how the actual electron states are equally spaced in k-
space. Which means that the density of states in E (ρ(E)ρ(E)) depends on the
slope of the E-k curve.
7. ENERGY BAND FORMATION :QUALITATIVE MODEL
• For an isolated atom we assume that the potential well is rectangular of width L and then we
showed that if you solve the energies for the electrons from Schrodinger equation you get
this kind of EK relation.
• This is a Schrodinger equation which depends only on the space we have removed the time
dependent time part because this is how we solved the Schrodinger equation.
• Where this k is related to the electronic energy the solution of this equation is as shown here
consists of a combination of 2 complex exponentials. And if you impose a boundary condition
corresponding to a rectangular well
8.
9. • So therefore they have developed different energies and since there are so
many electrons their energies are very close to each other and so the allowed
energies becomes a band.
• This approach of developing the allowed energy bands from discreet levels of
isolated atoms is referred to as the bloch, tight binding or Linear combination
of atomic orbitals approach.
13. • This form of representation of E-k diagram is referred to as period zone
representation.
• So the E-k relation is being shown for several periods even though it is
periodic and you can probably show that information only in one of the
periods and then the same thing will apply to other periods.
14. UTILITY OF E-K RELATION
• The utility of E-k relation is the E-k relation can be used to get crystal momentum because the
force on electron in a crystal is equal to the time derivative of the product h cross K.
• So, this implies hk is conserved in the interaction of electron with a force or other entities
and that is the reason why it is called a momentum namely the crystal momentum.
• However, it is not the true instantaneous momentum. Since the true instantaneous
momentum is mass of the electron multiplied by velocity of the electron.
18. • For the case of Gallium Arsenide similar approach gives you the conductivity and density of states
effective mass. The reason in this case ml and mt are both identical and = 0.067 m0. So, you see if you
compare it with silicon the effective mass of electron in Gallium Arsenide is much smaller.
• So electron feels much lighter in presence of Gallium Arsenide crystal potential as compared to silicon
crystal potential.
• And that is why the mobility of electron in Gallium Arsenide is very high if you apply force because the
mass is small the electron gains a high acceleration or high drift velocity in Gallium Arsenide as
compared to silicon.
19.
20. • So the E0 variation is obtained from the drift efficient modal formula. So, here the relation between E0
and psi is E0/q = constant -psi or gradient of E0/q is E.
• Electron affinity is obtained from the E-k diagram and crystal potential. So, chi can be a function of x if
the crystal potential is varying with x as it happens in a heterostructure or compositionally graded
structure.
• So, if the doping varies in a semiconductor the function of x for example the energy gap can change as
the function of x. Energy gap can also change if the composition is varying as a function of x.