Nanotechnologies for electrical engineering
Course description
Nanotechnology consists in the investigation and manipulation of matter at a scale of 1 to 100 nanometers (a nanometer is equal to 1 billionth of a meter). It has broad applications across a number of fields including engineering, physics, chemistry, and biology. Examples of nanotechnology applications include nano-sensors, electronic and photonic components for information processing, displays, batteries, solar cells, etc.. The course covers an introduction to nanoscale transport phenomena, and to the light interaction and manipulation at the nanoscale and their applications to electrical engineering. If you are either a master or a PhD student at the University of Naples Federico II and you wish to know more about this course, or to better understand how this course may fit in your study plan, you can send a mail to prof. Forestiere carlo.forestiere@unina.it
Syllabus
- Elements of Quantum Mechanics: The origin of quantum theory. Black body radiation and quanta hypotheses, photoelectric effects, matter waves. Free wave packet. Phase velocity and group velocity. Schrodinger equation. Linear Operators. Dual, Hermitian, and Commuting Operators. Operators. Wave equation of a free particle. Particle in a scalar potential. Hamiltonian and Canonical Quantization. Probability density and normalization condition. Probability Current. Continuity equation. Mean Values. Time independent Schrodinger equation. Stationary Solutions of Schrodinger Equation. Infinite 1D potential well. Finite 1D potential well. Infinite 2D potential well. Tunneling through a rectangular barrier. Quantum dots.Postulates of Quantum Mechanics. Hilbert spaces. Physical states and “ket vectors”. Dual spaces and “bra” vectors. Scalar product. Eigenvalue problems and observable. Probability. Postulates concerning measurement. Wavefunction collapse. Heisenberg’s Uncertainty relations. The equation of motions: evolution operators and the Schrödinger Equation.
- Conduction in metals and semiconductors: The Drude theory of Metals. Assumption. DC electric conductivity of metals. AC electric conductivity. Dielectric function and plasma Frequency. Thermal Conductivity. Hall effect and magnetoresistance. Specific heat of a classical electron gas. The Sommerfeld theory of Metals. Ground state properties of a quantum electron gas. Density of states. Fermi-Dirac distribution. Specific heat of a classical electron gas. Failures of the Free Electron model. Bravais lattices and Primitive Vectors. Primitive cell and Wigner-Seitz cell. Lattices with a basis. Honeycomb lattice. The Reciprocal lattice. Brillouin zones. Bloch’s Theorem. Periodic (Born-van Karman) boundary conditions. Kronig-Penney model. Crystal Momentum. Energy Band Diagrams. Density of States. Semiclassical model. Filled Bands. Partially filled bands. Holes. Effective mass.
- Graphene and Carbon Nanotubes Josephson junction. Non-linear LC circuits. Charge - qubit circuits. Flux - qubit circuits. Phase - qubit circuits. Cooper - pair box. Transmon. Entangled qubits.
- Elements of Nanooptics: Localized surface plasmons (LSP). Solution of the quasi-electrostatic problem of a spherical particle in a uniform electric field: polarizability, resonance condition, electric fields. Electric field enhancement and its application. Sensitivity of the resonance to local variations of the refractive index. LSP sensors. Surface Plasmon Polaritons (SPP). Propagating surface wave at the interface between a metal and a dielectric. Excitation configurations: Otto / Kretschmann configurations; grating coupler. SPP sensors. Photonic Crystals (PC): optical modes in a 1D photonic crystal (transmission matrix and Bloch theorem). PC Point defects and cavities. Line defects and waveguides. Metamaterials. Natural and artificial materials: artificial atoms. Left-handed materials and negative refraction.
Prerequisites
Prior knowledge of quantum mechanics and solid state physics are helpful, but not required.
Textbooks
- A. Messiah, Quantum Mechanics, Dover
- D. Griffiths, D. Schroeter, Introduction to Quantum Mechanics (3rd ed.). Cambridge: Cambridge University Press (2018)
- Zagoskin A. M. Quantum Engineering: Theory and Design of Quantum Coherent Structures, Cambridge University Press, 2011.
- I. Mayergoyz, Quantum Mechanics for Electrical Engineers, World Scientific, 2016.
- N. W. Ashcroft, and N. D. Mermin. "Solid State Physics Harcourt College Publishers." New York (1976).
- Novotny, Lukas, and Bert Hecht. Principles of nano-optics. Cambridge university press (2012)
- J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade. "Molding the flow of light." Princeton Univ. Press, Princeton, NJ (2008)