Kausik Majumdar’s Group
Quantum Electronics Laboratory
Indian Institute of Science
Quantum Electronics Laboratory IISc
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E3 220: Foundations of nanoelectronic devices (3:0)

Lecture hour: Tuesdays and Thursdays, 10:00-11:30
Venue: ECE 1.08

This is a graduate level introductory course on the quantum mechanical foundations required to grasp principles of modern solid state devices. There is no prerequisite for this course.

First meeting in ECE 1.08 on August 8, 2023 (Tuesday) at 10:00.

Module 1: Introduction

Module 2-4: Mathematical foundations of quantum mechanics - Hilbert space, observables, operators and operator algebra, commutators, bra and ket notation, representation theory, change of basis.

Module 5-8: Postulates of quantum mechanics, uncertainty principle, coordinate and momentum representation, quantum dynamics using unitary operator, Schrodinger and Heisenberg pictures, stationary states, time evolution.

Module 9-11: Free particle, wave packet, Hydrogen atom, Excitons.

Module 12-14: Electrons in solids - Drude and Sommerfield model, k-space quantization from periodic boundary condition, density of states, Fermi energy, derivation of Fermi-Dirac distribution, chemical potential and its relation with Fermi level.

Module 15-21: Crystal lattice, Reciprocal lattice space, Brillouin zone, Electron levels in periodic potential with BVK boundary condition, Bloch theorem and its proof, Bandstructure, Crystal momentum, band velocity, density of states, effective mass, bandstructure examples in common semiconductors (Si, Ge, III-V) and implications to device physics.

Module 22-24: Semiclassical theory of electron dynamics in periodic lattice, Bloch electrons and wave packets, Comments on the model including validity, conductivity of perfect crystal, conservation of energy, current carrying capability by empty, filled and partially filled bands, introduction to the concept of holes.

Module 25-30: Principles of operation of MOSFET, concept of top of the barrier, Short channel effects, Quantum effects in MOSFET - Coupled Poisson-Schrodinger equations and iterative solutions, quantization in MOSFET channel, quantum capacitance, Tunneling, One dimensional barrier transmission problem, Gate oxide tunneling, Direct source to drain tunneling, Band-to-band tunneling.

Module 31-34: Lattice vibrations, one dimensional chain of atoms, effect of introduction of a basis, acoustic and optical branches, quantum theory of linear harmonic oscillators, creation and annihilation operators, quantization of energies, phonons, phonon bandstructure and density of states, effects in devices due to electron-phonon scattering.

Module 35-37: Quantization of angular momentum, Ladder operators, possible eigenvalues of total angular momentum and its components, electron spin, Pauli spin matrices, spin-orbit coupling.

E3 280: Carrier transport in nanoscale devices (3:0)

Lecture hour: T Th 8:30-10:00

This is a graduate level course on carrier transport in solid state devices. Both semi-classical and quantum transport principles are covered in the course. The students are recommended to attend E3 220 (Foundations of Nanoelectronic Devices) before taking this course.

Module 1: Introduction

Module 2-5: Review of basic quantum mechanics, crystal structure and Brillouin zone, electrons in crystalline solids, momentum space, Energy band structure in semiconductors, quantum confinement, semi-classical electron dynamics in perfect crystal.

Module 6: Scattering of electrons, Derivation of Fermi Golden Rule.

Module 7-11: Concept of scattering rate and relaxation time, scattering by ionized impurity, different types of phonon scattering and calculation of corresponding relaxation times, electron-electron scattering, electron scattering for confined carriers, surface roughness scattering.

Module 11-14: Concept of distribution function - equilibrium versus non-equilibrium, Boltzmann transport equation(BTE) - derivation and implication, Relaxation time approximation, solution of BTE, special cases, numerical solutions, validity of BTE, coupled electrical and thermal transport.

Module 15-18: Quantum transport - conduction quantization, current flow in a one-level model, different regimes of transport including self-consistent field and Coulomb blockade, current carrying modes in quantum wire and 2D electron gas, ballistic versus non-ballistic transport.

Module 19-24: Open system versus closed system, concept of level broadening, Formal treatment of open system, coherent transport using Green's function, ballistic current in a two-terminal device.