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
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
Why we are interested in “nano-material”?
Stages from free-space to nano-material
• Free-space
SchrÖdinger equation in free-space:
Solution: ,... 3 , 2 , 1 , / 2
l L l
k
1
) / (
i kr Et
k e 0 2 2 2 | | m k E t r t r t i
m , ,
Stages from free-space to nano-material
• Bulk semiconductor
SchrÖdinger equation in bulk semiconductor:
Solution:
Electron behavior: Bloch wave
t r t r t i r V
m 0 , ,
2 0 )] ( 2 [ ) ( ) ( 0
0 r V r lR V
r e r V 2
0 ()
k n ei kr Et
Stages from free-space to nano-material
• Nano-material
SchrÖdinger equation in nano-material:
with artificially generated extra potential contribution:
Solution: t r t r nano t i r V r V
m 0 , ,
2 0 )] ( ) ( 2 [ ) (r Vnano
k n r F
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
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
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
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
Why we are interested in “nano-material”?
Electrons in semiconductors: highly mobile, easily transportable and correlated, yet highly
scattered in terms of energy
Why we are interested in “nano-material”?
Electrons in semiconductors: easily controllable and accessible, yet poor inherent performance
Electrons in atomic systems: excellent inherent performance, yet hardly controllable or
Why we are interested in “nano-material”?
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
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
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
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).
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.
Electronic Properties
• Ballistic transport – a result of much reduced electron-phonon scattering, low temperature mobility in QW (in-plane direction) reaches a rather absurd value ~107cm2/s-V, with
corresponding mean free path over 100m
• Resulted effect – electrons can be steered,
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
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
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
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
Optical Properties
• Quantized energy level dependence on size (geometric dimension)
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
Applications
• Light source - QD lasers, QC (Quantum Cascade) lasers
• Light detector – QDIP (Quantum Dot Infrared Photo-detector)
• Electromagnetic induced transparency (EIT) – to obtain transparent highly dispersive materials
References
• Solid State Physics – C. Kittel, “Introduction to Solid State Physics”, Springer, ISBN: 978-0-471-41526-8
• 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, ISBN-0124096603
• On nano-material and device fabrication techniques – T. Steiner, “Semiconductor Nanostructures for Optoelectronic Applications”, Artech House, 2004, ISBN-1580537510
