Nanoscale and Quantum Effects

1
Nanoscale and Quantum Effects

• Behavior in nanoscale materials and structures
  can be remarkably different that in bulk
  materials.

Carbon nanotube
Thermal conductivity greater than diamond!!!
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The Four Regimes
Molecular regime very few atoms to thousands of
atoms, molecular chemistry/interaction
dominates Quantum regime quantum effects
(confinement) dominate Nanoscale regime some
quantum effects present, nanoscale features such
as interfaces, boundaries play a role, some
statistical analysis may be applied Bulk
macroscale properties, equations can be applied
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Nano/quantum Phenomena

• Chemical take advantage of large
  surface to volume ratio,
  interfacial
  and surface chemistry important,
  interatomic forces
  important
  systems too small for statistical analysis
• Electronic quantum confinement,
  bandgap engineering, change
  in density
  of states, electron tunneling
• Magnetic giant magnetoresistance
  by nanoscale multilayers,
  change in magnetic
  susceptibility

STM of dangling bonds on a SiH surface
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Nano/quantum Phenomena

• Mechanical improved strength hardness in
  light-weight nanocomposites and nanomaterials,
  altered bending, compression properties,
  nanomechanics of molecular structures
• Optical absorption and fluorescence of
  nanocrystals, single photon phenomena, photonic
  bandgap engineering
• Fluidic enhanced flow properties with
  nanoparticles, nanoscale adsorbed films important
• Thermal phonon confinement, increased
  thermoelectric performance of nanoscale
  materials, interfacial thermal resistance
  important, systems too small for statistical
  analysis, phonon tunneling

Fluorescence of quantum dots of various sizes
Phonon tunneling
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Chemical Phenomena

• Interatomic forces
• Stable crystals formed from ionic and covalent
  bonds
• Van der Waals forces interaction between closed
  shell molecules
• Thermodynamic processes are random if there are
  not enough atoms/molecules around to be
  statistically significant, then thermodynamics as
  we know it breaks down!

If the number of dangling bonds is significant,
the properties of the nanostructure of
nanocomposite can be affected!
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Magnetic Phenomena

• Giant magnetoresistance interfacial
  spin-dependent scattering between metallic and
  magnetic nanolayers enhanced by addition of
  a nano-oxide layer (NOL)
• Nanoparticle cluster (lt1000 Au
  atoms) magnetic moment of atoms interact
  and can force all the moments to
  align ? net moment of cluster

Giant magnetoresistance of a multilayer structure
as function of the thickness of a NiFe layer
Chen et al, J Appl Phys, Vol. 93, pp. 7699 7701
(2003)
Si
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Mechanical Phenomena

• Elastic modulus of nanostructured material
  increases when the grain size lt 5 - 50 nm
• Yield strength of nanostructured Cu is 400 MPa,
  six times higher than coarse-grained Cu

A, E Coarse-grain Cu B,C,D Nanostructured Cu
Elastic modulus vs. diameter of polypyrole
nanotubes
Engineering stress
Wang et al, Nature, Vol.418, pp. 912 915 (2002)
Cuenot et al, J Appl Phys, Vol. 93, pp. 5650
5655 (2003)
Engineering strain
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Fluidic Phenomena
1-2 monolayers H2O

• Adsorbed water films are everywhere!
• Nanoscale layers of fluids are affected
  by surface
  roughness, surface tension,
  frictional losses in ways
  very different
  from bulk fluids
• Long-chain molecules act more like
  soft solids (are
  more ordered)
• Fluids of molecular mixtures segregate
  themselves by size
• Nanometer-size liquid jets propagate
  over shorter
  distances than predicted
• Molecular fluids between rough surfaces
  are more liquid-like
  than between
  smooth surfaces

MD simulations of lubricant flow between two
solids
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Quantum Mechanics

• Quantization easily observed by spectral lines
• Important for analysis
• Schrödinger equation
• Particle in a box theory
• Heisenberg uncertainty principal
• Pauli exclusion principle
• De Broglie wavelength
• Band theory

Discrete electronic transitions in optical
absorption of CdSe nanocrystals of varying size
Murray et al, Ann Rev Mat Sci, Vol. 30, pp. 545
610 (2000)
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Optical Properties

• Optical properties determined by electron
  transitions in a material and light scattering
  effects
• In semiconductors, when the characteristic length
  scale exciton (electron hole) radius (a few
  nanometers) ? quantum confinement
• Novel optical properties!

Discrete electronic transitions in optical
absorption of CdSe nanocrystals of varying size
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Nanoscale Electron Conduction

• Scattering events electron with phonons or
  defects
• Mean free path/time strongly dependent on
• Impurity content
• Defect content
• Crystal structure
• Doping level
• Temperature
• When L l
• Scattering events affected
• Transport is ballistic
• Local thermodynamic equilibrium cannot be
  defined

l electron mean free path v electron
velocity t electron mean free
time
phonon
e-
defect
L gtgt l
Bulk
Nanoparticle
L l atomic spacing
L
?
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Electron Confinement

• Bulk electrons delocalized, electrons in a Fermi
  gas
• Nanoscale electrons confined, localized, density
  of states depends on dimensionality,
  electrostatic forces important
• Electron confinement ? quantized (discrete)
  energy states and standing waves!
• Quantum Mechanics Particle in a Box,
  Schrödinger Equation

Quantum corral Fe on Cu(111)
L gtgt ?
Bulk
Each quantum states contributes Ge
For quantization to be important,
?E gtgt kBT or
Nanoparticle/Quantum Dot
L ? atomic spacing
http//www.almaden.ibm.com/vis/stm/corral.html
?(e)metal 1 nm

?(e)semiconductor 100 nm
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Tunneling
Electron (the lion) has non-zero probability of
tunneling through the barrier! Adapted from
Walmsley, 1987
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Nanoscale Phonon Transport
Microscopic
Phonon confinement affects phonon density of
states, specific heat, thermal conductivity, etc.
l
Phonon discrete quantum of atomic vibrational
energy Wave propagation like propagation of
packet of phonons
What happens in a nanowire?
What happens at an interface?
material A, ?A, CA, vA
material B, ?B, CB, vB
boundary scattering
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Interfacial Thermal Effects
Interface nanoscale thin film!
Single interface considerations
Inelastic scattering
Elastic scattering
Specular interface
Diffuse scattering
Acoustic impedance mismatch (?AvA/ ?BvB)
Phonon spectra mismatch
Strain
Multiple interface considerations
Phonon wavelength tunneling
Phonon coherence length mini-band formation
Phonon tunneling
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Phonon Confinement
Nanoscale boundary scattering, surface phonon
modes
Quantum
scale phonon waveguide! density of states,
dispersion relation modified
Theoretical Calculation using
Landauer formula (1998)
Close-up of phonon cavity patterned in the
membrane
12 wirebonded pads converging to 60 nm thick Si
nitride membrane
4 thin film gold transducers act as phonon
waveguides
Phonon wavelength defines confinement ?(p) 1 -
10 nm
Quantum of phonon conductance
Schwab et al, Nature, Vol. 404, pp. 974 977
(2000)
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Measuring Confinement Effects

• Experiments that give information about the
  density of states, and therefore the
  dimensionality
• Photoemission spectroscopy
• Seebeck effect measurements
• Electron/hole concentration in semiconductors
• Optical absorption characteristics to determine
  dielectric constant
• NMR to give Fermi contact term
• de Haas-van Alphen effect

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Questions Remain

• In low-dimensional structures
• What are phonon-phonon relaxation times?
• How do the phonon and electron gases couple?
• What is the role of defects in transport?
• Can we design structures for very high or low
  thermal/electrical conductivities?
• How does the interface influence transport?
• How do electrons and phonons move through
  nanostructures?