Fermi Level
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This document discusses the position of the Fermi level in intrinsic and extrinsic semiconductors. It begins by defining the intrinsic Fermi level position in an intrinsic semiconductor. It then describes how the Fermi level shifts in n-type and p-type extrinsic semiconductors due to the introduction of donor and acceptor dopants. Equations are provided for calculating the intrinsic carrier concentration and extrinsic carrier concentrations in n-type and p-type materials.
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This document discusses transmission lines and the conditions required for distortionless transmission. It notes that losses in transmission lines can occur due to I2R loss, skin effect, and crystallization. Distortion can arise from amplitude distortion, attenuation distortion, and phase distortion. The conditions for distortionless transmission are that the attenuation constant must be zero and the phase velocity must be independent of frequency. This requires that the line's inductance and capacitance per unit length satisfy LG/RC=1/2. The document also examines propagation constants and phase velocity for lossless transmission lines. It provides examples of calculating phase velocity, propagation constant, and phase wavelength for given line parameters.
Quantum Hall Effect
The document summarizes a lecture on the quantum Hall effect. It defines the quantum Hall effect as a phenomenon where the resistance of a quantum well system is quantized under low temperature and high magnetic field conditions. It then provides calculations to show that the quantum Hall resistance is quantized and equal to h/q^2, where h is Planck's constant and q is the elementary charge. Finally, it discusses how the quantization occurs due to the formation of discrete energy levels called Landau levels in the presence of a magnetic field.
Telegrapher's Equation
This document discusses transmission lines and the Telegrapher's equation. It begins by introducing transmission lines and their parameters such as resistance, inductance, conductance and capacitance per unit length. It then derives the Telegrapher's equation that describes voltage and current on a transmission line. It shows how the equation can be used to find the propagation constant and solve for voltage and current as a function of position and time. It also discusses phase velocity and provides examples of calculating attenuation constant, phase constant, and phase velocity for different transmission line scenarios.
Dielectrics
This document discusses the topic of electrostatics and dielectrics in the Electromagnetic Theory course. It defines a dielectric as a material where charge displacement occurs in an external electric field rather than free motion of charges. Dielectrics are classified as polar or nonpolar depending on whether they have a permanent dipole moment. The types of polarization in dielectrics are electronic, orientation, and ionic polarization. Key concepts discussed include polarization density, polarization charge density, the relationship between polarization and electric field through susceptibility and relative permittivity, atomic polarizability, and the relationship between polarization and electric displacement. An example problem calculates the polarization given the electric displacement.
Capacitor
1) The document discusses different types of capacitors including parallel plate, cylindrical, and spherical capacitors. Equations for electrostatic potential and electric field are derived for each type.
2) Examples problems are worked out on determining the capacitance of a parallel plate capacitor when a dielectric slab is inserted, and the capacitance of a coaxial cylindrical capacitor with dielectrics of different permittivities in each region.
3) Key equations presented include the capacitance of parallel plate, cylindrical, and spherical capacitors in terms of their geometric parameters and dielectric properties.
Electrical Properties of Dipole
1) An electric dipole is formed when two equal but opposite charges are separated by an infinitesimal distance. The dipole moment is defined as the product of the charge magnitude and the distance between them.
2) The electrostatic potential and electric field due to a dipole can be expressed in terms of the dipole moment. The potential and field decrease with increasing distance from the dipole.
3) A torque is experienced by a dipole when placed in an external electric field, with the torque being proportional to the cross product of the dipole moment and the electric field.
Application of Gauss' Law
This document contains lecture notes on electrostatics and the application of Gauss' law from a course on electromagnetic theory taught by Arpan Deyasi. It defines line charge density, surface charge density, and volume charge density. It then uses Gauss' law to derive expressions for the electric field and potential due to different charge distributions, including line charges, surface charges on a ring and plane, and volume charges in a cylinder and sphere. Example problems are worked through applying Gauss' law to find electric fields and potentials for these various charge distributions.
Fundamentals of Gauss' Law
This document discusses Gauss's law and related electromagnetic theory concepts taught in a course. It provides:
1) An overview of Gauss's law, which states that the total outward electric flux through a closed surface is equal to the total charge enclosed divided by the permittivity of the medium.
2) Derivations and proofs of Gauss's law using calculus theorems like divergence theorem.
3) Applications of Gauss's law to problems involving charge distributions and electric field calculations.
4) Discussions of related concepts like Gauss's law in polarized media, current continuity equation, relaxation time, and Poisson's equation.
5) Example problems demonstrating the application of these electromagnetic theory principles.
Fundamentals of Coulomb's Law
This document discusses Coulomb's law and some key concepts in electrostatics, including:
- Coulomb's law describes the electrostatic force between two point charges, being directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
- The electric field intensity and electric flux density are introduced.
- Properties of the electric field such as it being irrotational are examined.
- The electrostatic potential is defined and its relationship to the electric field is explored.
Vector Integration
This document discusses vector calculus theorems including Stokes' theorem and the divergence theorem. Stokes' theorem relates the line integral of a vector field around a closed curve to the surface integral of the curl of the vector field over any surface bounded by the curve. The divergence theorem relates the volume integral of the divergence of a vector field over a volume to the surface integral of the vector field over the boundary surface of that volume. The document provides proofs of these theorems and examples of their applications to problems involving conservative vector fields and evaluating integrals.
Scalar and vector differentiation
This document discusses a course on electromagnetic theory taught by Arpan Deyasi. It covers topics related to vector differentiation, including the vector differential operator in Cartesian, cylindrical and spherical coordinates. It also covers differentiation of scalar functions, including calculating gradients, directional derivatives and finding normals to surfaces. Finally, it discusses differentiation of vector functions, specifically divergence, which represents the volume density of the net outward flux from a vector field.
Coordinate transformation
The document discusses various coordinate transformations between Cartesian, cylindrical, and spherical coordinate systems. It provides the transformation equations for scalar and vector variables between these coordinate systems. Examples are included to demonstrate transforming between Cartesian and cylindrical coordinates for points in both scalar and vector form. The key topics covered are the four types of coordinate transformations, the transformation equations, and examples to illustrate the transformations.
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Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
An improved modulation technique suitable for a three level flying capacitor ...
This research paper introduces an innovative modulation technique for controlling a 3-level flying capacitor multilevel inverter (FCMLI), aiming to streamline the modulation process in contrast to conventional methods. The proposed
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Fermi Level
- 1. Course: Electronic Devices paper code: EC301 Course Coordinator: Arpan Deyasi Department of Electronics and Communication Engineering RCC Institute of Information Technology Kolkata, India 8/4/2020 1Arpan Deyasi, RCCIIT Topic: Fermi Level (Intrinsic and Extrinsic)
- 2. 8/4/2020 Arpan Deyasi, RCCIIT 2 Position of Fermi level In intrinsic semiconductor 0 0n p= exp exp C FI C FI V V E E N kT E E N kT − − − − F FIE E=
- 3. 8/4/2020 Arpan Deyasi, RCCIIT 3 Position of Fermi level 2 expC C V FI V N E E E N kT + − = 1 1 ( ) ln 2 2 V FI C V C N E E E kT N = + +
- 4. 8/4/2020 Arpan Deyasi, RCCIIT 4 Position of Fermi level 3/2* * C e V h N m N m = 3/2 2 2 * 2 e C m kT N h π = 3/2 2 2 * 2 h V m kT N h π =
- 5. 8/4/2020 Arpan Deyasi, RCCIIT 5 Position of Fermi level * * 1 3 ( ) ln 2 4 h FI C V e m E E E kT m = + + 1 ( ) 2 FI C VE E E α= + + * * h em m>
- 6. 8/4/2020 Arpan Deyasi, RCCIIT 6 Position of Fermi level EC EV EFI EFI α Intrinsic Fermi level is not at the middle of forbidden region (EC+EV)/2 (EC+EV)/2 1 ( ) 2 FI C VE E E α= + +
- 7. 8/4/2020 Arpan Deyasi, RCCIIT 7 Intrinsic Carrier Concentration 2 0 0in n p= 2 exp exp C FI i C FI V V E E n N kT E E N kT − = − − × −
- 8. 8/4/2020 Arpan Deyasi, RCCIIT 8 Intrinsic Carrier Concentration 2 exp C V i C V E E n N N kT − − 2 exp g i C V E n N N kT = −
- 9. 8/4/2020 Arpan Deyasi, RCCIIT 9 Intrinsic Carrier Concentration exp 2 g i C V E n N N kT − * * ( , , )i e h gn f m m E=
- 10. 8/4/2020 Arpan Deyasi, RCCIIT 10 Extrinsic Carrier Concentration (n-type) Consider n-type semiconductor ND: Donor concentration 0exp C F C D E E N n N kT − − == exp C F C D E E N N kT − =
- 11. 8/4/2020 Arpan Deyasi, RCCIIT 11 exp C FI C i E E N n kT − − = Extrinsic Carrier Concentration (n-type) exp C FI C i E E N n kT − =
- 12. 8/4/2020 Arpan Deyasi, RCCIIT 12 Extrinsic Carrier Concentration (n-type) exp F FI i D E E n N kT − = exp expC FI C F i D E E E E n N kT kT − − =
- 13. 8/4/2020 Arpan Deyasi, RCCIIT 13 Extrinsic Carrier Concentration (n-type) ln D F FI i N E E kT n = + ND EF EFI ni=ND EC
- 14. 8/4/2020 Arpan Deyasi, RCCIIT 14 Extrinsic Carrier Concentration (p-type) Consider p-type semiconductor NA: Acceptor concentration 0exp F V V A E E N p N kT − − == exp F V V A E E N N kT − =
- 15. 8/4/2020 Arpan Deyasi, RCCIIT 15 Extrinsic Carrier Concentration (p-type) exp FI V V i E E N n kT − − = exp FI V V i E E N n kT − =
- 16. 8/4/2020 Arpan Deyasi, RCCIIT 16 Extrinsic Carrier Concentration (p-type) exp expFI V F V i A E E E E n N kT kT − − = exp FI F i A E E n N kT − =
- 17. 8/4/2020 Arpan Deyasi, RCCIIT 17 Extrinsic Carrier Concentration (p-type) ln A F FI i N E E kT n = − NA EF EFI ni=NA EV