Nanostructured materials 0D: quantum dots 1D: Nanowires 2D: superlattices and heterostructures...

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