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Introduction to Nano-materials
As part of ECE-778 – Introduction to
Nanotechnology
1
Outline
• What is “nano-material” and why we are interested in it?
• Ways lead to the realization of nano-materials
• Optical and electronic properties of nano-materials
• Applications
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What is “nano-material” ?
• Narrow definition: low dimension semiconductor
structures including quantum wells, quantum wires, and
quantum dots
• Unlike bulk semiconductor material, artificial structure in
nanometer scale (from a few nm’s to a few tens of nm’s,
1nm is about 2 mono-layers/lattices) must be introduced
in addition to the “naturally” given semiconductor
crystalline structure
3
Why we are interested in “nano-material”?
• Expecting different behavior of electrons in their
transport (for electronic devices) and correlation (for
optoelectronic devices) from conventional bulk material
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Stages from free-space to nano-material
• Free-space
SchrÖdinger equation in free-space:


2
(
 )  r ,t  i  r ,t
2m0
t
Solution:
 k  e

i ( k r  Et /  )
1
 2
2


 |k |
k  2l / L, l  1,2,3,... E 
2m0
Electron behavior: plane wave
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Stages from free-space to nano-material
• Bulk semiconductor
SchrÖdinger equation in bulk semiconductor:



2

[
  V0 (r )]  r ,t  i  r ,t
2m0
t
e2

 

V0 (r )  V0 (r  lR)
V0 (r )  
r
Solution:
 2
2


 |k |
i ( k r  Et /  )

E
 nk  e
nk
2meff
Electron behavior: Bloch wave
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Stages from free-space to nano-material
• Nano-material
SchrÖdinger equation in nano-material:
 2




[
  V0 (r )  Vnano (r )]  r ,t  i  r ,t
2m0
t
with artificially generated extra potential contribution:

Vnano (r )
Solution:
 nk  e
iEt / 


Fn ,k (r ) nk
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Stages from free-space to nano-material
Electron behavior:
Quantum well – 1D confined and in parallel plane 2D
Bloch wave
Quantum wire – in cross-sectional plane 2D confined and
1D Bloch wave
Quantum dot – all 3D confined
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A summary on electron behavior
• Free space
– plane wave with inherent electron mass
– continued parabolic dispersion (E~k) relation
– density of states in terms of E: continues square root
dependence
• Bulk semiconductor
– plane wave like with effective mass, two different type of
electrons identified with opposite sign of their effective mass, i.e.,
electrons and holes
– parabolic band dispersion (E~k) relation
– density of states in terms of E: continues square root
dependence, with different parameters for electrons/holes in
different band
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A summary on electron behavior
• Quantum well
– discrete energy levels in 1D for both electrons and holes
– plane wave like with (different) effective masses in 2D parallel
plane for electrons and holes
– dispersion (E~k) relation: parabolic bands with discrete states
inside the stop-band
– density of states in terms of E: additive staircase functions, with
different parameters for electrons/holes in different band
• Quantum wire
– discrete energy levels in 2D cross-sectional plane for both
electrons and holes
– plane wave like with (different) effective masses in 1D for
electrons and holes
– dispersion (E~k) relation: parabolic bands with discrete states
inside the stop-band
– density of states in terms of E: additive staircase decayed
functions, with different parameters for electrons/holes in
different band
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A summary on electron behavior
• Quantum dot
– discrete energy levels for both electrons and holes
– dispersion (E~k) relation: atomic-like k-independent discrete
energy states only
– density of states in terms of E: -functions for electrons/holes
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Why we are interested in “nano-material”?
Free electrons (electrons in vacuum): highly mobile hence
transportable, all in one status, with kinetic energy but no
potential energy
Electrons in atomic systems: having multiple status with
different potentials, immobile hence untransportable, with
potential energy but no kinetic energy (excluding the
kinetic energy for orbiting)
Electrons in semiconductors: having multiple status with
different potentials, mobile hence transportable, with both
potential and kinetic energies, yet having scattered
energy levels at each status
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Why we are interested in “nano-material”?
Electrons in atomic systems: in highly regulated status,
possible to achieve accurate result, yet hardly accessible
and controllable
Electrons in semiconductors: easily accessible and
controllable, yet in poorly regulated status – any
manipulation can hardly lead to an accurate result
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Why we are interested in “nano-material”?
• Answer: take advantage of both semiconductors and
atomic systems – low dimensional semiconductor
material (or nano-material), i.e.,
semiconductor quantum wells
semiconductor quantum wires
semiconductor quantum dots
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Why we are interested in “nano-material”?
• Detailed reasons:
– Geometrical dimensions in the artificial structure can be tuned to
change the confinement of electrons and holes, hence to tailor
the correlations (e.g., excitations, transitions and
recombinations)
– Relaxation and dephasing processes are slowed due to the
reduced probability of inelastic and elastic collisions (much
expected for quantum computing, could be a drawback for light
emitting devices)
– Definite polarization (spin of photons are regulated)
– (Coulomb) binding between electron and hole is increased due
to the localization
– Increased binding and confinement also gives increased
electron-hole overlap, which leads to larger dipole matrix
elements and larger transition rates
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Ways lead to the realization of nano-material
• Required nano-structure size:
Electron in fully confined structure (QD with edge size d), its allowed
(quantized) energy (E) scales as 1/d2 (infinite barrier assumed)
Coulomb interaction energy (V) between electron and other charged
particle scales as 1/d
If the confinement length is so large that V>>E, the Coulomb interaction
mixes all the quantized electron energy levels and the material
shows a bulk behavior, i.e., the quantization feature is not preserved
for the same type of electrons (with the same effective mass), but
still preserved among different type of electrons, hence we have
(discrete) energy bands
If the confinement length is so small that V<<E, the Coulomb
interaction has little effect on the quantized electron energy levels,
i.e., the quantization feature is preserved, hence we have discrete
energy levels
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Ways lead to the realization of nano-material
• Required nano-structure size:
Similar arguments can be made about the effects of
temperature, i.e., kBT ~ E?
But kBT doesn’t change the electron eigen states, instead,
it changes the excitation, or the filling of electrons into
the eigen energy structure
If kBT>E, even E is a discrete set, temperature effect still
distribute electrons over multiple energy levels and dilute
the concentration of the density of states provided by the
confinement, since E can never be a single energy level
Therefore, we also need kBT<E!
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Ways lead to the realization of nano-material
• Required nano-structure size:
The critical size is, therefore, given by V(dc)=E(dc)>kBT (25meV at room
temperature).
For typical III-V semiconductor compounds, dc~10nm-100nm (around
20 to 200 mono-layers).
More specifically, if dc<10nm, full quantization, if dc>100nm, full bulk
(mix-up).
On the other hand, dc must be large enough to ensure that at least one
electron or one electron plus one hole (depending on applications)
are bounded inside the nano-structure.
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Ways lead to the realization of nano-material
• Current technologies
– Top-down approach: patterning  etching  re-growth
– Bottom-top approach: patterning  etching  selective-growth
– Uneven substrate growth: edge overgrowth, V-shape growth,
interface QD, etc.
– Self-organized growth: most successful approach so far
– Wafer bonding
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Electronic Properties
• Ballistic transport – a result of much reduced electronphonon scattering, low temperature mobility in QW (inplane direction) reaches a rather absurd value
~107cm2/s-V, with corresponding mean free path over
100m
• Resulted effect – electrons can be steered, deflected
and focused in a manner very similar to optics, as an
example, Young’s double slit diffraction was
demonstrated on such platform
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Electronic Properties
• Low dimension tunneling – as a collective effect of
multiple nano-structures, resonance appears due to the
“phase-matching” requirement
• Resulted effect – stair case like I-V characteristics, on
the down-turn side, negative resistance shows up
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Electronic Properties
• If excitation (charging) itself is also quantized (through,
e.g., Coulomb blockade), interaction between the
excitation quantization and the quantized eigen states
(i.e., the discrete energy levels in nano-structure) brings
us into a completely discrete regime
• Resulted effect – a possible platform to manipulate
single electron to realize various functionalities, e.g.,
single electron transistor (SET) for logical gate or
memory cell
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Optical Properties
• Discretization of energy levels increases the density of
states
• Resulted effect – enhances narrow band correlation,
such as electron-hole recombination; for QD lasers, the
threshold will be greatly reduced
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Optical Properties
• Discretization of energy levels reduces broadband
correlation
• Resulted effect – reduces relaxation and dephasing,
reduces temperature dependence; former keeps the
electrons in coherence, which is very much needed in
quantum computing; latter reduces device performance
temperature dependence (e.g., QD laser threshold and
efficiency, QD detector sensitivity, etc.)
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Optical Properties
• Quantized energy level dependence on size (geometric
dimension)
• Resulted effect – easy tuning of optical gain/absorption
spectrum
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Optical Properties
• Discretization of energy levels leads to zero dispersion at
the gain peak
• Resulted effect – reduces chirp, a very much needed
property in dynamic application of optoelectronic devices
(e.g., optical modulators or directly modulated lasers)
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Applications
• Light source - QD lasers, QC (Quantum Cascade) lasers
• Light detector – QDIP (Quantum Dot Infrared Photodetector)
• Electromagnetic induced transparency (EIT) – to obtain
transparent highly dispersive materials
• Ballistic electron devices
• Tunneling electron devices
• Single electron devices
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References
•
The first to read – F. Owens and C. Poole Jr., “The Physics and Chemistry
of Nanosolids”, Wiley-Interscience, 2008, ISBN-978-0-470-06740-6
•
On solid state physics – C. Kittel, “Introduction to Solid State Physics”,
Springer, ISBN-978-0-471-41526-8
•
On basic quantum mechanics – L. Schiff, “Quantum Mechanics”, 3rd Edition,
McGraw Hill, 1967, ISBN-0070856435
•
On nano-material electronic properties – W. Kirk and M. Reed,
“Nanostructures and Mesoscopic Systems”, Academic Press, 1991, ISBN0124096603
•
On nano-material and device fabrication techniques – T. Steiner,
“Semiconductor Nanostructures for Optoelectronic Applications”, Artech
House, 2004, ISBN-1580537510
•
On nano-material optical properties – G. Bryant and G. Solomon, “Optics of
Quantum Dots and Wires”, Artech House, 2005, ISBN-1580537618
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