Nanophysics
Contents
Part
2: Structure and stability of nanoparticles and nanoclusters
Part
3: Electrons in confinement
Part
2: Structure and stability of nanoparticles and nanoclusters
Part
3: Electrons in confinement
Course outline
*starred content, only conclusion is examinable
Pre-requisites
Quantum mechanics (QMI and QMII):
De Broglie Wavelength of Matter
Heisenberg uncertainty principle,
Schrodinger equation and its solutions for
Infinite Square well potential,
Simple harmonic oscillator
Central field potential such as coulomb potential in hydrogen atoms,
Pauli Exclusion Principle, Origin of periodic table of elements
Fermi’s golden rule, transition matrix element for interaction with light absorption
Part 1:
Introduction
Introduction to Nanoscale and Nanophysics
Study of physical laws behind the phenomena at nanoscale
Nanoscale is the crossover of bulk-like effect and atomic like effect, strong
Size dependence expected for many physical properties
Scaling law and its breakdown
Scaling laws show the physical properties as a function of size
The breakdown is either because the physics behind the law is no long valid or the
materials parameters are no longer size-invariant. The breakdown can be characterized
by characteristic energy or characteristic length
Characteristic energy (thermal energy ~kT)
Characteristic length (depends on the physical property concerned)
More examples throughout the course
Nanofabrication (additional research required, question 2 of Week 3-4 problem sheet)
Top-down approach: fabrication of nanostructure by cutting bulk materials into
desired structure
Bottom up approach: fabrication of nanostructure by assembling pre-existing
building blocks
Nanocharacterization (additional research required)*
Far field techniques: diffraction limited resolution
Near field technique
Part 2:
Structure and stability of nanoparticles and nanoclusters
Surface effect in nanosystem
Estimate of surface-to-volume ratio, huge surface area of finely divided matter.
Surface energy of nanoparticles, broken bond model for crystalline materials
Scaling laws of melting temperature of nanoparticles*
Minimization of surface energies
Spherical liquid drop
Faceted crystallites due to surface energy anisotropy (Truncated octahedron)
Non-crystalline faceted packing (decahedron and icosahedrons)
Nanoclusters and magic number effects
Electronic origins of magic number effect
Electronic shell model, analogy of multi-electron atoms (periodic table structure
of elements) and multi-nucleon nuclei.
Geometric origin of magic number effect
Closed surface layers in compact nanoparticles (noble gas clusters and large alkali
metal clusters), different magic number sequence for different nanostructures
Closed shell structure (carbon nanoclusters such as C60, C70, C60 and carbon nanotube)
Part 3:
Electrons in confinement
Review of Electrons in Solids
Many interacting particle nature of electrons in solid state*
Quantum independent particle approximation*
Classical independent particle approximation (Drude metals)
Low dimensional systems
Definitions:
Quantum Well: electron wavefunction is confined in one direction
Quantum wires: electron wavefunction confined in two directions
Quantum dots: electron wave functions confined in all three directions.
Density of states (DOS) of independent particles in 3D, 2D, 1D and 0D materials
Shell structure of the electron energy levels, origin of electronic magic numbers
Review of Semiconductor Physics
Nearly free electron systems: distinction of metals, semiconductors and insulators
Envelope approximation for electrons at the bottom of the conduction band and holes at the
top of the valence band of a two band model, Concept of effective mass*
Absorption and luminescence
Interband transition and intraband transition, matrix element
Low dimensional semiconductors
Reduced Mass and Joint density of states
Selection rule for interband transitions in semiconducting quantum wells:
for (envelope)
wavefunctions (Week7 problem)
Selection rule for intraband (or intersubband) transitions in semiconducting quantum wells:
for (envelope)
wavefunctions (Week7 problem)
Application: wavelength tunable solid state lasers based on quantum nanostructure.
Excitons
Definition: A bound state of an electron and a hole in a semiconductor or an insulator and
can be produced by exciting electrons from the valence band. It is an example
of failure of independent particle approximation due to the neglect of the
strong coulomb interaction
Hydrogenic model:
Can model exciton in the same way as electrons in a hydrogenic atom, except the
bare coulomb interaction is reduced by dielectric screening of the ions and the mass
of the particles is replaced by the reduced mass of exciton, with corresponding
effects on the binding energy and orbital size
Exciton confinement:
Weak, intermediate and strong, depending on the competition between space
confinement and Coulomb confinement
Part 4:
Nanoplasmonics
Review of electrodynamics
Wave equations for light in vacuum as well as in a dielectric media
Dielectric function,
Definition,
Model function for optical response of free electron metals (Drude model)
Lorentz oscillator model for interband transition
Non-Drude like optical response in metals, semiconductors and insulators
(Question in week 7)
Bulk Plasmon
Definition: longitudinal collective charge oscillation about its equilibrium position
Volume Plasmon energy
for undampled free electron metals
In general, given by the condition for bulk Plasmon:
.
Relation to optical property of metals
Dipole Plasmon in a nanoparticle:
Definition:
Uniform displacement of valence electron charge density in a sphere
Dipole plasmon energy
for an undamped free electron metal sphere,
reduced from bulk value due to depolarization factor
In general system, given by the condition for exciting dipole Plasmon in a sphere:
.
In deformed sphere, different dipole plasmon energies along different axes
due to difference in depolarization factors
Applications:
Nanoscale metal inclusion in glass
Strong light scattering at plasmon resonance can be used to induce dichrotic
colors in glass (Roman Lycurgus cup, stained glass etc.)
Plasmonics
the concentration and transport of light energy in sub-wavelength structure
Part 5:
Nanoelectronics
Review of charge transport in solids
Drude model of conduction of free electron by diffusive scattering,
drift velocity, phase velocity, mean free path for inelastic scattering
Semi-classical theory of conduction by diffusive scattering, phase velocity = Fermi velocity
Characteristic lengths for novel conduction mechanisms
Mean free path for inelastic scattering below which Ballistic conduction may occur
resistivity is independent of the length of the system
De Broglie Wavelength below which the system acts as a waveguide for the wavefunction,
quantum conductance per 1D wavefunction
Tunnelling and STM*
Tunnelling possible when the insulating gap is the same order as the decay length of
electron waves inside the gap
Tunnelling current is exponentially dependent on gap distance, resulting in a highly
sensitive control of the gap distance, used in scanning tunnelling microscopy
to detect the electronic distribution.
Tunnelling rate is also proportional to the available of electrons in the emitting
materials and the empty states in the receiving material.
The differential of tunnelling current as a function of bias voltage gives the
local density of states of electrons (Scanning Tunnelling Spectroscopy).
Example, direct imaging of spatial distribution and energy levels of electrons confined
within an artificial corral.
Coulomb blockade and single electron transistor*
Operation of a field effect transistor
Charging energy in nanostructure
Lifetime of single charge and minimum tunnelling resistance
Operation and application of single electron transistor
Supplementary materials (ppt files)
Pdf files of ppt for
Lecture 2: Nanocharacterization
Problem sheets
Recommended books
Charles Kittel ‘Introduction to Solid State Physics’, Wiley 2004
Edward L. Wolf ‘Nanophysics and Nanotechnology’, Wiley-VCH 2006
Gabor L. Hornyak, Joydeep Dutta, Harry F. Tibbals and Anil K. Rao ‘Introduction to Nanoscience’, CRC Press
Bart Van Zeghbroeck, Principles of Semiconductor Devices, Colarado University
Web reference materials:
Part 1:
introduction
Power of ten http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
Richard P Feynman, “There’s plenty of room at the bottom”, in Miniaturization, edited by H.D. Gilbert (Reinhold, New York, 1961) http://www.its.caltech.edu/~feynman/plenty.html
Feynman’s prize http://www.quniverse.sk/buzek/zaujimave/p257_s.pdf
Zettl’s nanomotor http://www.physics.berkeley.edu/research/zettl/projects/NEMS.html
Part 2:
Structure and stability of nanoparticles and nanoclusters
T.P.Martin (1996) ‘Shells of Atoms’, Physics Report, 273, p199-241
Part 3:
Electrons in confinement
Luminescence of quantum dots: http://www.youtube.com/watch?v=ohJ0DL2_HGs
Red emitting quantum well laser http://www.astro.cf.ac.uk/research/pm/researchareas/?page=red
Part 4:
Nanoplasmonics
Part 5:
Nanoelectronics
Single electron transistor http://physicsworld.com/cws/article/print/1420