nanostructured materials 0d: quantum dots 1d: nanowires 2d: superlattices and heterostructures...
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Nanostructured materialsNanostructured materials
• 0D: quantum dots0D: quantum dots• 1D: Nanowires1D: Nanowires• 2D: superlattices and heterostructures2D: superlattices and heterostructures• Nano-PhotonicsNano-Photonics• Magnetic nanostructuresMagnetic nanostructures• Nanofluidic devices and surfacesNanofluidic devices and surfaces
Copyright Stuart Lindsay 2009
Nanostructured materials derive their special properties from having one or more dimensions made small compared to a length scale critical to the physics of the process.
Copyright Stuart Lindsay 2009
Development of electronic properties Development of electronic properties as a function of cluster sizeas a function of cluster size
Each band has a width that reflects the interaction between atoms, with a bandgap between the conduction and the valence bands that reflects the original separation of the bonding ad antibonding states.
Electronic DOS and dimensionalityElectronic DOS and dimensionality
Size effects are most evident at band edges (semiconductor NPs).
DOS (dn/dE) as a function of dimensionality.
3D case is for free particles.
Copyright Stuart Lindsay 2009
k-space is filled with an uniform grid of points each separated in units of 2π/L along any axis.The volume of k-space occupied by each point is:
r-space: k-spacek-space:
V
drr 2 43
232
8
4 4
dkkL
V
dkk
k
3 2
L
3D DOS3D DOS
2
2
2Vk
dk
dn
m
kE
2
22
m
k
dk
dE 2
2
1
22222
2 2
22E
mEVm
k
mVk
dE
dk
dk
dn
dE
dn
Copyright Stuart Lindsay 2009
Density of states in a volume V per unit wave vector:
For a free electron gas:
2D DOS2D DOS
Constant for each electronic band
22
2
kA
dk
dn
22 Am
dE
dk
dk
dn
dE
dn
Copyright Stuart Lindsay 2009
m
k
dk
dE 2
8
1D DOS1D DOS
2
L
dk
dn
2
1
22
E
k
Lm
dE
dn
At each atomic level, the DOS in the 1D solid decreases as the reciprocal of the square root of energy.
Copyright Stuart Lindsay 2009
m
k
dk
dE 2
0 D DOS0 D DOS
In zero dimensions the energy states are sharp levels corresponding to the eigenstates of the system.
Copyright Stuart Lindsay 2009
0D Electronic Structures: 0D Electronic Structures: Quantum DotsQuantum Dots
Light incident on a semiconductor at an energy greater than the Light incident on a semiconductor at an energy greater than the bandgap forms an exciton, i.e. an electron-hole quasiparticle, bandgap forms an exciton, i.e. an electron-hole quasiparticle, representing a bound state.representing a bound state.
Excitons can be treated as “Bohr atoms”
2
2
0
2
4
1
r
e
r
mV
R
e.
mmREE
*h
*e
8111
2
2
2
220
Electronic Electronic energy gapenergy gap
*2
204
mer
When the size of the nanoparticle approaches that of an exciton, size quantization occurs.
Intrinsic band gap
NP radiusNP radius electrostaticcorrection
1-D Electronic Structures: Carbon Nanotubes1-D Electronic Structures: Carbon Nanotubes
Wrapping vectorWrapping vector: 2211 anann
Diameter: 0.0783nm 2122
21 nnnnd
The folding of the sheet controls the electronic properties of the The folding of the sheet controls the electronic properties of the nanotubes.nanotubes.
pz electrons hybridize to form π e π* valence and conduction bands that are separated by an energy gap of about 1V (semiconductor).
For certain high simmetry directions (the K points in the reciprocal lattice) the material behaves like a metal.
Conduction in CNTsConduction in CNTs
Apex: at this point CB meets VB for graphene sheets (metal-like behavior)
Allowed statesK
k wave vector perpendicular to the CNT long axis
D = diameter of the nanotube
The component of the wave vector perpendicular to the CNT long axis is quantized
D
nk
2
Metallic behavior: the allowed values of intersect the k points at which the conduction and valence bands meet.
CNTs can be either metals or semiconductors depending on their chirality..
k
Field effect transistor made from a single semiconducting CNT connecting source and drain connectors.
Semiconductor NanowiresSemiconductor Nanowires
• Ga-P/Ga-As p/n nanojunctions
Copyright Stuart Lindsay 2009
(IOP)
TEM imagesTEM images
Line profiles of Line profiles of the composition the composition
through the through the junction regionjunction region
17
2D Electronic Structures: 2D Electronic Structures: superlattices and heterostructuressuperlattices and heterostructures
Variation of electron energy in an MBE grown superlattice
SuperlatticeSuperlattice::alternating layers of small alternating layers of small bandgap semiconductors bandgap semiconductors (GaAs) interdispersed with (GaAs) interdispersed with layers of wide bandgap layers of wide bandgap semiconductors (GaAlAs).semiconductors (GaAlAs).
The thickness of each layer The thickness of each layer is considerably smaller is considerably smaller than the electron mean free than the electron mean free path.path.
Band splitting into sub-bands
Modulation of the structure on the length scale d (thickness of the layer in the superlattice) gives rise to the formation of new bands inside the original Brillouin zone .
Electrons can pass freely from one small bandgap region to another without scattering.
Resonant tunneling through different sub-bands
Negative differential resistanceNegative differential resistance: electrons slow down with increasing bias when approaching the first sub-band boundary (≈20mV).
Low scattering in 2-D means reaching zone boundaries at reasonable fields, accelerating electrons at the band edges.
Quantum Hall resistance of 2D electron gasQuantum Hall resistance of 2D electron gas
Magnetic quantization in 2D electron gas
A series of steps in the Hall resistance corresponding exactly at twice the Landauer frequency were observed.
2ne
hRH
Copyright Stuart Lindsay 2009
Electrons in a layer are accelerated by an applied magnetic field at a frequency::
m
eBC
von Klitzing resistancevon Klitzing resistanceNobel in Physics 1985Nobel in Physics 1985
Confinement on optical length scales Confinement on optical length scales PlasmonicsPlasmonics
2
130
r
rV
Small (d<<λ) metal particles exhibit a phenomenon called plasma plasma resonanceresonance, i.e. plasma-polariton resonance of the free electrons in the metal surface.
A resonant metal particle can capture light over a region of many wavelengths in dimension even if the particle itself is only a fraction of a wavelength in diameter (resonant antennasresonant antennas).
Free electrons in metals polarize excluding electric fields from the interior of the metal showing a negative dielectric constant.The polarizability of a sphere of volume V and dielectric constant εr is:
r
r
LL
V
)11(
10
6.1
2
2
11
1ln
2
11
1
b
a
e
e
ee
eL
For Ag =-2 at 400 nm, but resonance moves to 700 nm for a/b=6.
The resonance is tunable throughout the visible by engineering the particle shape.
When εr →-2 →∞
For d<<λ the resonant frequency is independent on the particle size, but depends on particle shape.
For a prolate spheroid of eccentricity e:2
2 1
a
be
where:
Plasmon enhanced optical absorptionPlasmon enhanced optical absorption
Placing a chromophore near a resonant metal nanoparticle:
Electric field surrounding a resonant nanoparticle
(E=Ez)
dye layerdye layer
Enhanced fluorescenceReduced decay times
The increased absorption cross section is accompanied by a decrease in fluorescence lifetime.
The plasmon resonance results in local enhancement of the electric field: doubling the electric field quadruples the light absorption.
A single dye molecule is only visible in fluorescence when the gold NP passes over it.
Enhanced fluorescence
25
Photonic engineeringPhotonic engineering
In quantum dots all of available gain is squeezed into a narrow bandwidth.
Performance of a solid-state laser material in various geometries.
Lasing effect: the gain of the laser medium must exceed the cavity losses.
Dashed lines: density of states
Modern semiconductor lasers are made from semiconductors heterostructures designed to trap excited electrons and holes in the optically active part of the laser.
3D3D
2D2D
1D1D
0D0D
Quantum dot laserQuantum dot laser
The QDs are chosen to have a bandgap that is smaller than that of the medium.
Excitons are stabilized in the optical cavity, because the electrons are confined to the low-energy part of the conduction band and the holes are confined to the top of the valence band.
Quantum dots of the right size can Quantum dots of the right size can place all of the exciton energies at place all of the exciton energies at the right value for lasing.the right value for lasing.
Optical cavityOptical cavity
Photonic crystals: Photonic crystals: concentrating photon energy into bandsconcentrating photon energy into bands
Copyright Stuart Lindsay 2009
Opalescent materials from colloidal crystal (polystyrene latex beads)
The concentration of modes into bands results in an increase in the density of states in the allowed bands, particularly near bands edges. Optical wavelengths require that materials should be structured on the half-micron scale.
Opalescence comes from sharp (Bragg) reflection in only certain Opalescence comes from sharp (Bragg) reflection in only certain directions.directions.
Bragg’s law
exthkl
inthkl
sinnd
cosnd
222
2
hkl = Miller indices of the colloidal crystal latticen = refraction indexdhkl = spacing between Bragg planes in the hkl direction
For a given spacing in some direction in the colloidal crystal lattice , For a given spacing in some direction in the colloidal crystal lattice , the wavelength of the reflected beam is given by the Bragg law.the wavelength of the reflected beam is given by the Bragg law.
intext sinnsin Colloidal particles spaced with polymer spacers
3D Photonic crystals3D Photonic crystals
Require “non spherical” atoms to give zero “structure factor” in directions where propagation must be suppressed
Photonic crystals convert heat into light! See Optics Letters 28 1909, 2003.
Optical dispersion in a crystal made by non spherical atoms. A 3D bandgap appear when structures are designed to have zero intensity in directions of allowed Bragg reflections.Repeat period is on the order of 30μm (3D optical bandgap in the far IR, limit of today technology).
Magnetic propertiesMagnetic properties
• DiamagnetismDiamagnetism:Zero-spin systems give rise to circulating currents that oppose the applied field (negative magnetic susceptibility, Larmor diamagnetism).
• ParamagnetismParamagnetism::Free-electrons are magnetically polarized by an external magnetic field (positive magnetic susceptibility, Pauli paramagnetism).
• FerromagnetismFerromagnetism::Spontaneous magnetic ordering due to electron-electron interactions.
Antiferromagnetism: polarization alternates from atom to atom. No net macroscopic magnetic moment arises.
Magnetic InteractionsMagnetic Interactions
• Exchange (electron-electron) interaction (many-particle wavefunction antisymmetry)
- atomic scales
• Dipole-dipole interactions between locally ordered magnetic regions
Dipole interaction energy grows with the volume of the ordered region. The size of the individual domains is set by a competition between volume and surface energy effects.
- hundreds of atoms to micron scales
• Magnetic Anisotropy energy
Magnetization interacts with angular momentum of the atoms in the crystal.
– many microns
Super-paramagnetic particlesSuper-paramagnetic particles
• Ferromagnetic domains, created by d-electrons exchange interactions, develop only when a cluster of iron atoms reaches a critical size (ca. microns).
The magnetic moment per atom decreases toward the bulk value as cluster size is increased.
Stable domains cannot be established in crystals that are smaller than the intrinsic domain size.
• Small particles can have very high magnetic susceptibility with permanent magnetic dipole.
Small clusters consisting of a single ferromagnetic domain follow the applied field freely (super-paramagnetismsuper-paramagnetism).
The magnetic susceptibility of superparamagnetic particles is orders of magnitude larger than bulk paramagnetic materials.
Ferromagnetic limitFerromagnetic limit
Magnetic response for particles of increasing
size (Gd clusters)
Superparamagnetic separationsSuperparamagnetic separations
Magnetic sorting of cells labeled with superparamagnetic beads
HM
z
BMF zz
)(0 MHB
Induced magnetic moment:
Magnetic force:
Particle were pulled to point of highest field gradient
Copyright Stuart Lindsay 2009
MFSMFS: microfabricated : microfabricated ferromagnetic strips ferromagnetic strips
Giant MagnetoresistanceGiant MagnetoresistanceMagnetic hard drives are based on a nanostructured device, called giant magnetoresistance sensorgiant magnetoresistance sensor..Albert Fert, Peter Grünbers Nobel Prize in Physics 2007
Hitachi hard drive reading headHitachi hard drive reading head
Co, magnetic layerCo, magnetic layer
NiFe alloy, magnetic layerNiFe alloy, magnetic layerAn easily re-alignable magnetizationAn easily re-alignable magnetization
Cu, electrically conducting layerCu, electrically conducting layerLayers have a width that is smaller than electron scattering length.
The magnetization on the surface The magnetization on the surface of the disk can be read out as of the disk can be read out as fluctuations in the resistance of fluctuations in the resistance of the conducting layer.the conducting layer.
For antiparallel magnetic layers both spin polarizations are scattered, giving rise to super-resistance (II).
Giant magnetoresistance occurs when the magnetic layers above Giant magnetoresistance occurs when the magnetic layers above and below the conductor are magnetized in opposite direction.and below the conductor are magnetized in opposite direction.
Electron scattering in magnetic media is strongly dependent on spin polarization.
When magnetic layers are parallely magnetized, only one spin polarization is scattered (I,III).
II IIII III III
NanofluidicsNanofluidics
Lu
Re
Fluid flow in small structures is entirely laminar and dominated by the chemical boundaries of the channel.
Reynolds numberReynolds number (Re), a dimensionless number quantifying the ratio of inertial to viscous forces that act on the volume of a liquid:
viscosity
density channel narrowest dimension
Re >> 1: turbulence regimeRe << 1: viscous regime
Re in a L=100nm channel with <u> = 1mm/s not exceeds 10-4
Flow in nanoscale channels is dominated by viscosity!
Fluids do not mix in a nanofluidic device.
The chemistry of the interface becomes critical and aqueous fluids will not generally enter a channel with hydrophobic surfaces.
u
Kinematic viscosityKinematic viscosity
For water: ν =1·10-6 m2s-1 (25°C) (25°C)
1-D Nanochannel devices 1-D Nanochannel devices
A significant stretching of large molecules can occur in a large ion gradient or electric field in a channel that is comparable to the radius of giration of the molecule..
Ex. Ex. A 17μm DNA (fully stretched length) is equivalent to 340 freely jointed segments each of 5 nm length.The relative giration radius is:
nmr 925340
It can be significantly extended in a channel of 100 nm diameter, It can be significantly extended in a channel of 100 nm diameter, owing to the strong interaction between the fluid and the wall.owing to the strong interaction between the fluid and the wall.
Tim
e
Mg ions introduced
DNA + cutting enzymes introduced
Microchannels
distance
DNA cutting starts
Fluorescently labeled DNA at various times
DNA is introduced through the microchannel and then transported through the nanochannels by an applied voltage.
Continous time course of the cutting process
Nanopores: 0D fluidic nanostructureNanopores: 0D fluidic nanostructure2-nm diameter holes: only a single DNA molecule can pass through it at a given time.
The passage of DNA molecules can be measured by the drops in currents that occur when a single DNA molecule occludes the hole.
Polystyrenebead
electrophoresiselectrophoresis
Optical tweezerOptical tweezer
Flow in Carbon NanotubesFlow in Carbon Nanotubes
42
The measured rate of water flow through 2nm-diameter CNTs was found to be 1000 times higher than predicted by classical hydrodynamics.
A. Fabrication of a layer of CNTs penetrating a silicon nitride membrane;
B. and C. SEM images before and after filling with silicon nitride;
D. Individual finished device:
E. An array of devices
2D Nanostructures:2D Nanostructures:Superhydrophobic surfacesSuperhydrophobic surfaces
BC
ACABccos
The angle formed by a tangent to a flat surface of a drop of water at the point of contact (contact anglecontact angle) is given in terms of the interfacial energies of the system by the Young equation:
γAB= air/surface interfacial tension
γAC= water/surface interfacial tension
γBC= air/water interfacial tension
Si Nanowires Coated Si surface(planar)
Coated nanostructured surface (rough)
Roughening on the nanoscale can greatly increase hydrophobicity.
1ccos Water/surface repulsion (large interfacial tension)
Water drop