Energy band structure and electrical conductivity mechanisms of metals and semiconductors
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Solid-state physics; energy band structure; electrical conductivity; semiconductors; extrinsic semiconductors; intrinsic semiconductors; in-depth analysis.
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1.atomic structure
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3.semiconductor and its type
Unit 1.pdf
1. The document provides information on molecular structure and bonding theories including atomic and molecular orbitals, linear combination of atomic orbitals, molecular orbital diagrams of diatomic molecules like N2, O2 and F2, π molecular orbitals of butadiene and benzene, and crystal field theory.
2. Key concepts covered include how molecular orbitals are formed from the overlap and combination of atomic orbitals, bonding and anti-bonding molecular orbitals, and how molecular orbital diagrams can be used to explain bonding properties.
3. Crystal field theory is introduced as explaining the color, magnetic properties and other characteristics of crystalline substances based on interactions between the d-orbitals of metal ions and ligand ions or molecules
thesis
This document provides an introduction to the thesis which focuses on aspects of symmetry, disorder and the Josephson effect in d-wave superconductors. Some key points:
- The thesis studies d-wave superconductors where the gap function changes sign in certain crystal directions, in contrast to conventional s-wave superconductors where the gap is isotropic.
- For a disordered d-wave superconductor, numerical, perturbative and field theoretical methods are used to calculate the density of states, finding it follows a sublinear power law at low energies.
- The Josephson effect in d-wave superconductors is investigated using a tunneling Hamiltonian approach to understand experiments on bicrystal junctions
Spintronics
Spintronics also known as spin electronics, is the study of the intrinsic spin of the electron and its associated magnetic moment, in addition to its fundamental electronic charge, in solid-state devices
Periodicity introduction unit 1
The document is an introduction to periodicity for A-level chemistry students. It discusses the organization of the periodic table by atomic number into rows and columns. It also summarizes trends in various atomic properties across period 3, including atomic radius decreasing due to nuclear charge, ionization energy generally increasing due to nuclear charge but with exceptions, electrical conductivity decreasing for nonmetals with no delocalized electrons, electronegativity increasing with nuclear charge, and melting point generally increasing for metals due to metallic bonding but decreasing for nonmetals due to weaker van der Waals forces.
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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.
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- 1. 12/17/2019 1 Energy Band Structure And Electrical Conductivity Mechanisms of Metals And Semiconductors 1 Krishna Jangid PhD Student Department of Engineering Physics
- 2. Energy band structure of Metals and Semiconductors Formation of band (Metal) Categorization of materials 2
- 3. 𝑓 𝐸 = 1 ⅇ 𝐸−𝐸 𝐹 𝑘 𝐵 𝑇+1 Energy band structure of Metals and Semiconductors 3
- 4. Energy band structure of Metals and Semiconductors Metals Semiconductors/Insulators 4 Overlapping of bands in Mg Bands in Silicon
- 5. Electrical conductivity of metals 𝐹 = 𝑚 ⅆ𝑣 ⅆ𝑡 = ℏ ⅆ𝑘 ⅆ𝑡 = −ⅇ𝐸 𝛿𝑘 = − ⅇ𝐸𝑡 ℏ 𝑗 = 𝑛𝑞𝑣 = 𝑛ⅇ2 𝜏 𝐸 𝑚 𝑗 = 𝜎𝐸 𝜌 = 𝑚 𝑛ⅇ2 𝜏𝜎 = 𝑛ⅇ2 𝜏 𝑚 𝑣 = ℏ𝑘 𝑚 𝜏 is the collision time 5 Fermi sphere under the influence of Force F
- 6. Factors affecting conductivity in metals Scattering of electrons by Phonons Normal scattering Umklapp scattering Electrons Role of Pauli exclusion principle Imperfections Temperature Phonon concentration Scattering 𝝈 Scattering 𝝆 6
- 7. Electrical conductivity of semiconductors Intrinsic semiconductors where, 𝑁𝐶 = 2 2𝛱𝑚 𝑛 ∗ 𝑘𝑇 ℏ2 3/2 Concentration of electrons in the conduction band 𝒏 = 𝐸 𝐶 ∞ 𝐷𝑒 𝐸 𝑓𝑒 𝐸 ⅆ𝐸 𝒏 = 𝑁𝑐 exp − 𝐸𝑐 − 𝐸 𝐹 𝑘𝑇 𝒏𝒊 = 2 2𝜋𝑘𝑇 ℎ2 3 2 𝑚 𝑛 ∗ 𝑚 𝑝 ∗ 3 4 exp −𝐸𝑔 2𝑘𝑇 where, mn* and mp* are the effective mass of electrons and holes 7 Electron concentration dependence on temperature: (a) Ge; (b) Si
- 8. Electrical conductivity: ln 𝜎 = − 𝐸 𝑔 2𝑘 1 𝑇 + 3 2 ln 𝑇 + constant𝝈 = 𝜎 𝑛 + 𝜎 𝑝 = ⅇ𝑛𝑖 𝜇 𝑛 + 𝜇 𝑝 = ⅇ 𝜇 𝑛 + 𝜇 𝑝 2 2𝜋𝑘𝑇 3/2 ℎ3 𝑚 𝑛 ∗ 𝑚 𝑝 ∗ 3 4 exp −𝐸𝑔 2𝑘𝑇 Intrinsic semiconductors (cont.) Mobilities were assumed to be independent of temperature As scattering of electrons affects conductivity 8 Electrical conductivity vs Temperature
- 9. Extrinsic semiconductors Electrical conductivity: 𝜎 = ⅇ𝑛𝜇 𝑛 • Mobilities were assumed to be independent of temperature. • Nd is assumed to be constant. 𝜎 = ⅇ𝜇 𝑛 𝑁𝑑 𝑁𝑐 1 2 exp −𝐸𝑔 2𝑘𝑇 𝒍𝒏 𝝈 = −𝐸𝑔 2𝐾 1 𝑻 + 1 2 ln 𝑵 𝒅 𝑁𝑐 + constant Concentration of electrons in the conduction band Carrier concentration: 𝒏 = 𝑵 𝒅 𝑁𝐶 1 2 exp −𝐸𝑔 2𝐾𝑻 9 Carrier concentration dependence over temperature Conductivity dependence over temperature
- 10. References • Solid state physics by Puri and Babbar. • Introduction to solid state physics by Charles kittel. • Nanotechnology: Understanding Small Systems by Ben Rogers. • NPTEL videos.
- 11. Questions.. 10