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### Introduction to Nano-materials

As part of ECE-758 – Introduction to Nanotechnology

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

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

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

Stages from free-space to nano-material

- Free-space

SchrÖdinger equation in free-space:

Solution:

Electron behavior: plane wave

Stages from free-space to nano-material

- Bulk semiconductor

SchrÖdinger equation in bulk semiconductor:

Solution:

Electron behavior: Bloch wave

Stages from free-space to nano-material

- Nano-material

SchrÖdinger equation in nano-material:

with artificially generated extra potential contribution:

Solution:

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

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

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

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

Why we are interested in “nano-material”?

Electrons in semiconductors: highly mobile, easily transportable and correlated, yet highly scattered in terms of energy

Electrons in atomic systems: highly regulated in terms of energy, but not mobile

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 accessible

Why we are interested in “nano-material”?

- Answer: take advantage of both semiconductors and atomic systems – Semiconductor quantum dot 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
- Increased confinement reduces the extent of the electron and hole states and thereby reduces the dipole moment

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

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!

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) state are bounded inside the nano-structure.

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

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, deflected and focused in a manner very similar to optics, as an example, Young’s double slit diffraction was demonstrated on such platform

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

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

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

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.)

Optical Properties

- Quantized energy level dependence on size (geometric dimension)
- Resulted effect – tuning of optical gain/absorption spectrum

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)

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
- Ballistic electron devices
- Tunneling electron devices
- Single electron devices

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
- 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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