Syllabus
Unit 1
Learning Objectives
In the unit-1, students will learn the
1. Many electron wavefunctions and exchange-correlation effects
2. Basic ideas behind the Kohn-Sham equations
3. Fundamentals of Density Functional Theory and density approximations
Electronic Structure: Electron-Electron Interactions: Born-Oppenheimer approximation Hartree-Fock approximation, exchange and correlation effects, Kohn-Sham Equations, Local Density Approximation (LDA), generalized gradient approximation (GGA). Realistic Calculations in Solids: Pseudopotentials and Orthogonalized Planes Waves (OPW), Plane wave method. Electronic Structure of selected materials – Metals, Semiconductors, Semimetals.
Unit 2
Learning Objectives
In the unit-2, students will learn the
1. Classification of materials based on magnetic property
2. Quantum theories of magnetism
3. Local and Band contributions to ferromagnetism and Domain theory
Diamagnetism and Paramagnetism: Langevin theory of diamagnetism and paramagnetism, Quantum theory of diamagnetism of mononuclear systems, quantum theory of paramagnetism: Rare earth ions, Hund rules, crystal field splitting, paramagnetic susceptibility of conduction electrons.
Ferromagnetism and antiferromagnetism: Ferromagnetic order: Heisenberg Model – exchange, Stoner theory, Hubbard model, Kondo effect, temperature dependence of saturation magnetization, Ferrimagnetic order: Curie temperature and susceptibility of ferrimagnets, antiferromagnetic order, susceptibility below Neel temperature, ferromagnetic domains.
Unit 3
Learning Objectives
In the unit-3, students will learn
- Properties of Superconductors
- Macroscopic and microscopic theories and classifications of superconductors
- To explain the flux quantization and Josephson effects
Superconductivity: Meissner effect, Phenomenological theory: London’s equations, Thermodynamics of Superconductors, Landau-Ginzburg Free Energy, Type I and Type II superconductors, Microscopic Theory of Superconductivity: BCS theory and its prediction. Experimental detection of Bandgap, flux quantization, Josephson effects, application: SQUID. High Temperature Superconductors.
Unit 4
Learning Objectives:
In the unit-4, students will learn the
- Classification of semiconductors, doping process
- Transport behaviour of the carriers in semiconductors
- Formation of P-N junctions and semiconductor low dimensional structures
Semiconductors: energy band structure, intrinsic and extrinsic semiconductors, Effective mass, carrier concentration, Hydrogenic model of impurity levels, law of mass action, Compensated doping, Degenerate Semiconductors, Fermi levels of intrinsic and extrinsic semi-conductors, Temperature dependent conductivity and mobility, Direct and indirect gap semiconductors, Hall effect, p-n junctions: theory of I–V characteristics, Ohmic contact and Schottky-barrier, Heterostructures, quantum Hall effect.
Unit 5
Learning Objectives:
In the unit-5, students will learn the
- Concepts of polaritons and Polarons
- Details of Plasma frequency, plasmons and anomalous skin effect
- Optical absorptions in semiconductors, excitons, and luminescence
Optical properties of solids: Kramers – Kronig relations; Sum rules, Dielectric function for ionic lattice, Polaritons, Polarons, Dielectric function for free electron gas; loss spectroscopy. Optical properties of metals- Plasmons, skin effect and anomalous skin effect. Free carrier absorption in semiconductor and Excitons: Interband transition – direct and indirect transition, Mott- Wannier excitons, Frenkel excitons, Luminescence.
Objectives
Pre-requisites: Basic knowledge of crystal physics, quantum mechanics and electromagnetic theory.
Course objectives:
- To learn the quantum many body systems and calculation of energy bands in solids
- To differentiate the various magnetism and the quantum theories of magnetic origin in solids
- To understand the superconducting phenomena and differentiate the Type I and Type II superconductors
- To study the electron and hole behavior, mobility, effective masses in semiconductors
- To learn the doping process, Fermi energy levels and junction formations
- To understand the optical properties of metals, semiconductors, and insulators
Course Outcomes:
On completion of the course, students will be able to:
CO1. Acquire comprehensive understanding on the basics of electronic band structure calculations
CO2. Describe various magnetic phenomena and the origin of magnetic ordering in solids
CO3. Understand the properties of superconductors and the theories of superconductivity
CO4. Explain the carrier dynamics in semiconductors and junction formations.
CO5. Describe the optical properties of different solids
Skills: Problem solving skills as well as computational skills of the students in analyzing the various properties of solid-state materials will be improved through assignments, quizzes, and presentations.
CO-PO Mapping
|
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PSO1 |
PSO2 |
PSO3 |
| CO1 |
2 |
3 |
3 |
1 |
|
3 |
2 |
|
| CO2 |
3 |
3 |
2 |
1 |
|
3 |
3 |
|
| CO3 |
3 |
3 |
|
|
|
3 |
1 |
|
| CO4 |
3 |
3 |
2 |
|
|
3 |
2 |
|
| CO5 |
3 |
3 |
2 |
|
|
3 |
2 |
|
Evaluation Pattern
| Assessment |
Internal |
External Semester |
| Periodical 1 (P1) |
15 |
| Periodical 2 (P2) |
15 |
| *Continuous Assessment (CA) |
20 |
| End Semester |
50 |
*CA – Can be Quizzes, Assignments, Projects, and Reports. Justification for CO-PO Mapping
| Mapping |
Justification |
Affinity level |
| CO1-PO1 |
Students enrich advance knowledge on the formation of band structure of solids in CO1, which may be assigned a medium affinity with PO1. |
2 |
| CO1-PO2 |
Learns develop the analytical skills and critical thinking of using different approaches for the electronic band structure determination of solids and hence it can be given a maximum affinity with PO2 |
3 |
| CO1-PO3 |
Student understands the usage of different theories and models to solve complex electronic energy levels in solids and so a maximum affinity level is mapped with PO3. |
3 |
| CO1-PO4 |
In CO4, students are exposed to DFT, exchange and correlation functions used in the current research computing of bandstructure calculations. It builds confidence in students to take up computational research and hence it is mapped a minimum affinity with PO4. |
3 |
| CO1-PSO1 |
PSO1 is related to develop curiosity and inquisitiveness among students to look at fundamental problems. As CO1 matches highly with PSO1 it is given maximum affinity level |
3 |
| CO1-PSO2 |
As CO1 equips the students in enhancing their analytical skills of determining the energy level of solids, it is mapped with maximum level affinity to PSO2. |
2 |
| CO2-PO1 |
CO2 improves the fundamental physics of magnetism. Since PO1 is related to the knowledge in fundamental sciences, CO2 is mapped with maximum affinity of 3 to PO1. |
3 |
| CO2-PO2 |
Problems corresponds related to various magnetic parameters (CO2) will be solved by students which improves the analytical skills and critical thinking as mentioned in PO2. So, |
3 |
| CO2-PO3 |
In CO2, students will gain the understanding and analyzing the type of magnetism exhibited in solids, so it is mapped with a minimum affinity to PO3. |
2 |
| CO2-PO4 |
Students get exposed to basic analysis of hysteresis loop of different solid samples, the magnetic origin and so they will gain confidence in the basic research of magnetic materials. Hence CO2 is assigned a minimum affinity to PO4. |
1 |
| CO2-PSO1 |
In CO2, as the learners will develop curiosity in solving the magnetic hysteresis of solids, magnetic origin etc., which highly matches with the described PSO1 and so it is mapped with a maximum affinity level of 3 |
3 |
| CO2-PSO2 |
As students develop the analytical skills of determining the magnetic properties in solids which equips them to do independent research. Hence, a high affinity level of 3 is given in the mapping of CO2-PSO2. |
3 |
| CO3-PO1 |
In CO3, students develop knowledge on the fundamentals of superconductivity. Since PO1 is related to acquiring strong knowledge in basic science, CO2 is given maximum affinity of 3 when mapped with PO1. |
3 |
| CO3-PSO2 |
Students improve their analytical skills in finding solutions to the problems with respect to superconducting phenomena. PO2 is related to developing the analytical skills involving fundamentals of basic sciences. So, the CO2- PO2 mapping is given an affinity level of 3. |
3 |
| CO3-PSO1 |
In CO3, students develop interest of determining coherence length, penetration depth etc.. and so the mapping of CO3 with PSO1 is given a high affinity level |
3 |
| CO3-PSO2 |
In CO3, students develop basic knowledge on the working of SQUID. The mapping with PSO2 is given a minimum affinity as CO3 covers the fundamentals alone. |
1 |
| CO4-PO1 |
Students learn the fundamentals of Semiconductor devices in CO4 which highly matches with PO1. The mapping of CO4-PO1 is given a maximum affinity level |
3 |
| CO4-PO2 |
Students develop problem solving skills related to carrier mobilities, effective masses, Fermi levels etc.. Hence, the mapping of CO4 with PO2 is given a maximum affinity of 3. |
3 |
| CO4-PO3 |
In CO4, learners are exposed to fundamental understanding of quantum hall effect, semiconductor quantum structures which maps with PO3 with medium affinity level. |
2 |
| CO4-PSO1 |
In CO4, Students gain knowledge of solving problems regarding semiconductor carriers, Fermi levels, p-n junctions etc. Hence, the mapping of CO4 with PSO1 is given a maximum affinity of 3. |
3 |
| CO4-PSO2 |
Gaining knowledge of the formation of p-n junctions, quantum wells gives students fundamental platform to understand research in the device fabrications. The affinity with PSO2 is given a medium level. |
2 |
| CO5-PO1 |
In CO5, students get benefited the learning of optical properties of solids and hence it is mapped with high affinity to PO1 |
3 |
| CO5-PO2 |
Students develop analytical thinking and problem solving with respect to absorptions and luminescence in solids (CO5) and so it is given maximum affinity with PO2. |
3 |
| CO5-PO3 |
In CO5, learners gain the fundamentals of excitons, plasmons, absorption co-efficient which prepares them to analysis the complex problems in optical properties of various materials and thus it is mapped with PO3 with a medium affinity level. |
2 |
| CO5-PSO1 |
In CO5, students enrich their scientific knowledge on the optical properties of different solids and so it is assigned a maximum affinity with PSO1. |
3 |
| CO5-PSO2 |
In CO5, students develop the analysis of plasmons, excitons, types of transitions, defects emissions and hence it may be mapped with PSO2 with a medium affinity |
2 |
