# 1 Introduction to Nano-materials As part of ECE-758 – Introduction to Nanotechnology.

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Introduction to Nano-materialsAs part of ECE-758 Introduction to Nanotechnology

OutlineWhat is nano-material and why we are interested in it?Ways lead to the realization of nano-materialsOptical and electronic properties of nano-materialsApplications

What is nano-material ?Narrow definition: low dimension semiconductor structures including quantum wells, quantum wires, and quantum dotsUnlike bulk semiconductor material, artificial structure in nanometer scale (from a few nms to a few tens of nms, 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-materialFree-space Schrdinger equation in free-space:

Solution:

Electron behavior: plane wave

Stages from free-space to nano-materialBulk semiconductor Schrdinger equation in bulk semiconductor:

Solution:

Electron behavior: Bloch wave

Stages from free-space to nano-materialNano-material Schrdinger equation in nano-material:

with artificially generated extra potential contribution:

Solution:

Stages from free-space to nano-materialElectron 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 behaviorFree spaceplane wave with inherent electron masscontinued parabolic dispersion (E~k) relationdensity of states in terms of E: continues square root dependence

Bulk semiconductorplane wave like with effective mass, two different type of electrons identified with opposite sign of their effective mass, i.e., electrons and holesparabolic band dispersion (E~k) relationdensity of states in terms of E: continues square root dependence, with different parameters for electrons/holes in different band

A summary on electron behaviorQuantum welldiscrete energy levels in 1D for both electrons and holesplane wave like with (different) effective masses in 2D parallel plane for electrons and holesdispersion (E~k) relation: parabolic bands with discrete states inside the stop-banddensity of states in terms of E: additive staircase functions, with different parameters for electrons/holes in different band

Quantum wirediscrete energy levels in 2D cross-sectional plane for both electrons and holesplane wave like with (different) effective masses in 1D for electrons and holesdispersion (E~k) relation: parabolic bands with discrete states inside the stop-banddensity of states in terms of E: additive staircase decayed functions, with different parameters for electrons/holes in different band

A summary on electron behaviorQuantum dotdiscrete energy levels for both electrons and holesdispersion (E~k) relation: atomic-like k-independent discrete energy states onlydensity 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 localizationIncreased binding and confinement also gives increased electron-hole overlap, which leads to larger dipole matrix elements and larger transition ratesIncreased confinement reduces the extent of the electron and hole states and thereby reduces the dipole moment

Ways lead to the realization of nano-materialRequired 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

Ways lead to the realization of nano-materialRequired nano-structure size:

Similar arguments can be made about the effects of temperature, i.e., kBT ~ E?

But kBT doesnt 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

Ways lead to the realization of nano-materialRequired 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 dc100nm, 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-materialCurrent technologiesTop-down approach: patterning etching re-growthBottom-top approach: patterning etching selective-growthUneven substrate growth: edge overgrowth, V-shape growth, interface QD, etc.Self-organized growth: most successful approach so far

Electronic PropertiesBallistic 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, Youngs double slit diffraction was demonstrated on such platform

Electronic PropertiesLow 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 PropertiesIf 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 PropertiesDiscretization 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 PropertiesDiscretization 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 PropertiesQuantized energy level dependence on size (geometric dimension)

Resulted effect tuning of optical gain/absorption spectrum

Optical PropertiesDiscretization 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)

ApplicationsLight source - QD lasers, QC (Quantum Cascade) lasersLight detector QDIP (Quantum Dot Infrared Photo-detector)Electromagnetic induced transparency (EIT) to obtain transparent highly dispersive materialsBallistic electron devicesTunneling electron devicesSingle electron devices

ReferencesSolid 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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