lecture2-18NOV2012

Nanotechnology

Quantum Confinement Bulk Solid Quantum Well Quantum Wire Quantum Dot

3D2D1D0DNanostructures

Quantum Confinement3-DAll carriers act as free carriers in all three directions2-D or Quantum WellsThe carriers act as free carriers in a plane1-D or Quantum WiresThe carriers are free to move down the direction of the wire0-D or Quantum DotsSystems in which carriers are confined in all directions (no free carriers)

Nanostructures

STRUCTURESPATIAL DIMENSIONCONFINEMENT DIMENSIONBulk30Surface/ Film (Quantum Well)21Nanotubes, -wires (Quantum wire)12Nano-particles, clusters (Quantum dots)03

Density of States (DOS)No. of states with energy < E : Density of states (n = dimension) :

Quantum Wells, Wires and DotsQuantum WellWireDot

Bulk Quantum Wells

Quantum Wires and Dots

3D DOSDensity of states in a volume V per unit wave vector:For a free electron gas:

2D DOSConstant for each electronic band

*1D DOSAt each atomic level, the DOS in the 1D solid decreases as the reciprocal of the square root of energy.

0 D DOSIn zero dimensions the energy states are sharp levels corresponding to the eigenstates of the system.

Energy Bands

Energy BandsWhen atoms come together to form a solid, their valence electrons interact due to Coulomb forces; they feel the electric field produced by their nucleus and that of the other atoms. From Heisenberg's uncertainty principle, the electrons constrained to a small volume, experience an increase in their energy state. This would imply that the electrons are promoted into the forbidden band gap.From the Pauli exclusion principle, the number of electrons that can have the same properties is limited (energy level included). In semiconductors and insulators, the valence band is filled, and no more electrons can be added.

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BandsAs a result, the valence electrons form wide bands when in a solid state. The bands are separated by gaps, where electrons cannot exist. The precise location of the bands and band gaps depends on the atom, the distance between atoms in the solid, and the atomic arrangement.

The energy corresponding to the highest filled state is the Fermi energy, Ef. Metal (copper half filled energy band) Metal (magnesium 3s and 3p bands overlap) Insulator (filled valence band separated by a wide band gap from an empty conduction band) semiconductor (filled valence band separated by a narrow band gap from an empty conduction band) Conduction band - a partially filled or empty energy bandValence band the highest partially or completely filled bandElectron Structures in Solids at 0 K.

Copper vs Magnesium[Ar] 3d10 4s1 [He] 2s2 2p6 3s2

Band gap EnergyWhen light shines on crystalline silicon, electrons within the crystal lattice may be freed. But only photons (packets of light energy) with a specific level of energy can free electrons in the semiconductor material from their atomic bonds to produce an electric current.This level of energy (band gap energy) is the amount of energy required to dislodge an electron from its covalent bond and allow it to become part of an electrical circuit. To free an electron, the energy of a photon must be at least as great as the band gap energy. Photons with more energy than the band gap energy will expend that extra amount as heat when freeing electrons.

InsulatorsIn insulators there are no free electrons to move throughout the material. Interatomic bonding is ionic or strongly covalent. The valence electrons are tightly bonded, highly localized and not free to scatter throughout the crystal. The band-gap is large, the valence band is full, and the conduction band is empty.* Insulators: -- wide band gap (> 2 eV) -- few electrons excited across band gapEnergyfilled bandfilled valence bandfilled statesGAP

*SemiconductorsIn semiconductors, bonding is predominantly covalent (relatively weak). These electrons are more easily removed by thermal excitation. The band-gap is smaller, the valence band is full, and the conduction band is empty.

*Conduction & Electron Transport Metals (Conductors):-- for metals, empty energy states are adjacent to filled states. two types of band structures for metals thermal energy excites electrons into empty higher energy states. - partially filled band - empty band that overlaps filled band

*Charge Carriers in Insulators and SemiconductorsTwo types of electronic charge carriers:

Free Electron negative charge located in conduction band energy level greater than Ef

Hole positive chargevacant electron state in the valence band Move at different speeds - drift velocities

Metals Electron StatesFor metals, little energy is required to promote electrons into the low-lying empty states. Energy provided by an electric field is sufficient to excite large numbers of electrons into the conduction band.

Energy (Eg) required to promote electrons from the valence band to the conduction band.Free Electrons

The magnitude of the band gap determines the differences between insulators, s/cs and metals.

The excitation mechanism of thermal is not a useful way to promote an electron to CB even the melting temperature is reached in an insulator.

Even very high electric fields is also unable to promote electrons across the band gap in an insulator.Insulators :CB (completely empty)VB (completely full)Eg~several electron voltsWide band gaps between VB and CB

When enough energy is supplied to the e- sitting at the top of the valance band, e- can make a transition to the bottom of the conduction band. When electron makes such a transition it leaves behind a missing electron state. This missing electron state is called as a hole. Hole behaves as a positive charge carrier.Magnitude of its charge is the same with that of the electron but with an opposite sign.Semiconductor energy bands at room temperatureForbiddenenergy gap [Eg]Full valancebandEmpty conductionband+e-+e-+e-+e-energy

Metals :CBVBCBVBNo gap between valance band and conduction bandTouching VB and CB Overlapping VB and CBThese two bands looks like as if partly filled bands and it is known that partly filled bands conducts well.This is the reason why metals have high conductivity.

Free Electron Theory

He was working prior to the development of quantum mechanics, so he began with a classical model:

Positive ion cores within an electron gas that follows Maxwell-Boltzmann statistics

Following the kinetic theory of gases- the electrons in the gas move in straight lines and make collisions only with the ion cores no electron-electron interactions.Drude Conduction

He envisioned instantaneous collisions in which electrons lose any energy gained from the electric field.The mean free path was approximately the inter-ionic core spacing.Model successfully determined the form of Ohms law in terms of free electrons and a relation between electrical and thermal conduction, but failed to explain electron heat capacity and the magnetic susceptibility of conduction electrons.

Classical Free Electron TheorySaliant PointsA solid is composed of atomsValance electrons are free to move like molecules of perfect gasCollide with positive ion core and other free electronsCollisions are elastic Electron velocities obey M-B statisticsUniform electric field

Ohms LawExperimental observation:E

Drude modelSuccessFailureVerify Ohms law Electrical and thermal conductivities of metalsOptical properties of metalsDerive Wiedemann-Franz lawSpecific heat of metals Variation of conductivity at low tempConductivity of SC and Insulators Photoelectric effect, Compton effect and Black body radiation

Diffusive Transport

Mean free path Mean free path: the average distance the electron travels between collision

Effective Mass

The Concept of Effective Mass :Comparing Free e- in vacuumAn e- in a crystalIn an electric field mo =9.1 x 10-31

Free electron massIn an electric field

In a crystal m = ?

m* effective massIf the same magnitude of electric field is applied to both electrons in vacuum and inside the crystal, the electrons will accelerate at a different rate from each other due to the existence of different potentials inside the crystal.

The electron inside the crystal has to try to make its own way.

So the electrons inside the crystal will have a different mass than that of the electron in vacuum.

This altered mass is called as an effective-mass.

What is the expression for m*Particles of electrons and holes behave as a wave under certain conditions. So one has to consider the de Broglie wavelength to link partical behaviour with wave behaviour.Partical such as electrons and waves can be diffracted from the crystal just as X-rays .Certain electron momentum is not allowed by the crystal lattice. This is the origin of the energy band gaps.n = the order of the diffraction = the wavelength of the X-rayd = the distance between planes = the incident angle of the X-ray beam

The energy of the free e- is related to the k free e- mass , m0 is the propogation constantThe waves are standing wavesThe momentum is (1)(2)By means of equations (1) and (2)certain e- momenta are not allowedby the crystal. The velocity of the electron at these momentum values is zero.The energy of the free electron can be related to its momentum momentumkEnergyE versus k diagram is a parabola.

Energy is continuous with k, i,e, all energy (momentum) values are allowed.

E versus k diagramorEnergy versus momentum diagrams

To find effective mass , m*We will take the derivative of energy with respect to k ;Change m* instead of mThis formula is the effective mass of an electron inside the crystal. m* is determined by the curvature of the E-k curve

- m* is inversely proportional to the curvature

Positive and negative effective massThe sign of the effective mass is determined directly from the sign of the curvature of the E-k curve.

The curvature of a graph at a minimum point is a positive quantity and the curvature of a graph at a maximum point is a negative quantity.

Particles(electrons) sitting near the minimum have a positive effective mass.

Particles(holes) sitting near the valence band maximum have a negative effective mass.

A negative effective mass implies that a particle will go the wrong way when an extrernal force is applied.

Direct-band gap s/cs (e.g. GaAs, InP, AlGaAs)+e-VBCBEk

Mass like charge is a very basic property of electrons and holes. The mass of electrons in a semiconductor may be different than its mass in vacuum.

Effective mass concept

Ballistic Conduction

Ballistic ConductionNo scattering Device dimensions are extremely small (L < li)

Transport Regimes

Since submicron structures can now be fabricated on length scales SMALLER than the average impurity spacing in semiconductors it is possible to study electron transport in a number of different REGIMES

In DIFFUSIVE conductors the mean free path is much SMALLER than the sample dimensions and DISORDER scattering dominates

In a QUASI-BALLISTIC conductor the mean free path and device size are COMPARABLE

A BALLISTIC conductor contains NO impurities and so the dominant source of electron scattering is at the device BOUNDARIES

This parameter is a measure for the distance the electron travels before its phase is randomized

Phase Coherence Length

le : Elastic mean-free pathL : Device sizel: Phase-breaking length F: Fermi wavelength (nm)

Classical conductance: L >> electron mean free pathD>> lF, electron wavelengthG changes continuously as D.ConductanceDG (G0)MacrowiresVI

Quantum conductance: L < electron mean free path ballistic transport (no collisions).D~ lF, electron wavelength wave nature of electron important.D ~ lF ~ 1-3 !G (G0)DD=lFD=lF/2NanowiresConductance Quantized!-1

Quantized Conductance

Due to ballistic transport in low- dimensional electron systems Quantized Conductance

Compound Semiconductor Nanostructures

In addition to group IV elements, compounds of group III and group V elements, and also compounds of group II and group VI elements are often semiconductors.

The common feature to all of these is that they have an average of 4 valence electrons per atom.

One example of a compound semiconductor is gallium arsenide, GaAs. In a compound semiconductor like GaAs, doping can be accomplished by slightly varying the stoichiometry, i.e., the ratio of Ga atoms to As atoms.

A slight increase in the proportion of As produces n-type doping, and a slight increase in the proportion of Ga produces p-type doping. Compound Semiconductors

Compound SemiconductorsIIIV

The table below list some semiconducting elements and compounds together with their bandgaps at 300 K

Material Direct / Indirect BandgapBand Gap Energy at 300 K (eV) Elements C (diamond) Ge Si Sn Indirect Indirect Indirect Direct 5.47 0.66 1.12 0.08 Groups III-V compounds GaAs InAs InSb GaP GaN InN Direct Direct Direct Indirect Direct Direct 1.42 0.36 0.17 2.26 3.36 0.70 Groups IV-IV compounds -SiC Indirect 2.99 Groups II-VI compounds ZnO CdSe ZnS Direct Direct Direct 3.35 1.70 3.68

Growth and structure of semiconductor quantum wells Heterostructure made by epitaxial growth technique: MBE and MOCVDSingle quantum well A single GaAs/AlGaAs quantum well. It is formed in the thin GaAs layer sandwiched between AlGaAs layers which have a large band gap. d is chosen so that the motion of the electrons in the GaAs layer is quantized in z direction. The lower figure shows the spatial variation of the conduction band (C.B) and the valence band (V.B) that corresponds to the change of composition. The band gap of AlGaAs is larger. The electrons and holes in GaAs layer are trapped by the potential barriers at each side by the discontinuity in the C.B and V.B. These barriers quantize the states in the z direction, but the motion in x, y plane is still free.

Superlattices

SuperlatticesTraditionalepitaxial structureComposition modulationsalong epitaxial layer(Could be induced via strain-configuration coupling.)

GaAs / AlGaAs multiple quantum well (MQW) or superlattice The distinction between them depends on the thickness b of the barrier separating the quantum wells. MQWs have lager b value, the individual quantum wells are isolated from each other. Superlattices, by contrast, have much thinner barriers, the quantum wells are thus coupled by tunnelling through the barrier, and new extended states are formed in the z direction. MQW or superlattice Growth and structure of semiconductor quantum wells

MBE Self-assembled NCsInitial stage InAs (7% mismatch) grows layer-by-layer 2D mechanism.Strained layer wetting layerWhen amount of InAs exceeds critical coverage (misfit > 1.8% ), 3D islands are formedStranski-Krastanow 3D growth

What are Quantum Dots?Quantum dots are semiconductor nanocrystals that are so small they are considered dimensionless.Quantum dots range from 2-10 nanometers (10-50 atoms)in diameter.

Quantum dotWhat is quantum dot? is a semiconductor whose excitons are confined in all three spatial dimensions. Consequently, such materials have electronic properties intermediate between those of bulk semiconductors and those of discrete molecules

Researching fields: have studied quantum dots in transistors, solar cells, LEDs, and diode lasers. They have also investigated quantum dots as agents for medical imaging and hope to use them as qubits

Colloidal quantum dots irradiated with a UV light. Different sized quantum dots emit different color light due to quantum confinement.WHY? HOW?

Characteristics of Quantum DotIn addition to such tuning, a main advantage with quantum dots is that, because of the high level of control possible over the size of the crystals produced, it is possible to have very precise control over the conductive properties of the materialThis equates to higher frequencies of light emitted after excitation of the dot as the crystal size grows smaller, resulting in a color shift from red to blue in the light emitted. Generally, the smaller the size of the crystal, the larger the band gap, the greater the difference in energy between the highest valence band and the lowest conduction band becomes, therefore more energy is needed to excite the dot, and concurrently, more energy is released when the crystal returns to its resting state.

Researchers at Los Alamos National Laboratory have developed a wireless device that efficiently produces visible light, through energy transfer from thin layers of quantum wells to crystals above the layers.Optical Propertiesquantum dots of the same material, but with different sizes, can emit light of different colors. The physical reason is the quantum confinement effect.

The larger the dot, the redder (lower energy) its fluorescence spectrum. Conversely, smaller dots emit bluer (higher energy) light. The coloration is directly related to the energy levels of the quantum dot.

As with any crystalline semiconductor, a quantum dot's electronic wave functions extend over the crystal lattice. Similar to a molecule, a quantum dot has both a quantized energy spectrum and a quantized density of electronic states near the edge of the band gap.

Applications of Quantum Dots

Quantum dots are unique class of semiconductor because they are so small, ranging from 2-10 nanometers (10-50 atoms) in diameter. At these small sizes materials behave differently, giving quantum dots unprecedented tunability

Quantum Dots - A tunable range of energies Because quantum dots' electron energy levels are discrete rather than continuous, the addition or subtraction of just a few atoms to the quantum dot has the effect of altering the boundaries of the bandgapChanging the length of the box changes the energy levels

Relative size of quantum dots

With quantum dots, the size of the band gap is controlled simply by adjusting the size of the dot

Quantum Dot Applications

LEDs (light emitting diodes); solid state white light, lasers, displays, memory, cell phones, and biological markers.

Biological marker applications of quantum dots have been the earliest commercial applications of quantum dots.

In these applications, quantum dots are tagged to a variety of nanoscale agents, like DNA, to allow medical researchers to better understand molecular interactions. (The Next Big Thing is Really Small, Jack Uldrich with Deb Newberry, p. 81)

Nanoparticles of cadmium selenide (quantum dots) glow when exposed to ultraviolet light. When injected, functionalized quantum dots can target cancer tumors. The surgeon can see the glowing tumor, and use it as a guide for more accurate tumor removal.

Quantum dots, visible under UV light, have accumulated in tumors of a mouse.

Self AssemblyThe principle behind bottom-up processing.Self assembly is the coordinated action of independent entities to produce larger, ordered structures or achieve a desired shape.Found in nature.Start on the atomic scale.

Self Assembly Nano TechnologySelf assembly can be defined as a coordinated actions of independent entities under local control of driving forces to produce a large, ordered structures or to achieve a desired group effect.The driving force of self assembly is usually based on an interplay of thermodynamics and kinetics.-- Chemically Controlled Self-assembly-- Physically Controlled Self-assembly-- Flip-up Principles and Spacer Techniques

Chemically Controlled Self AssemblyDeposition of loaded diblock copolymer micelles One block is soluble in toluene and the other is insoluble. Spherical micelles of copolymer molecular are formed in toluene These micelles are loaded with compounds such as HAuCl4 and deposited on planar substrate. Oxygen plasma treatment pyrolyses the polymer and turn precursor into nano Au particles with short range regular pattern

Physically Controlled Self Assembly Film deposition method using Stranski Krastanov Growth. Followed by initial layer by layer growth, island-like nano dots are formed to reduce the elastic strain energy (see next session) This technique can also combined with Lithography. Layer 2 can be conventionally patterned. Then alternative Layer 1 and 2 deposit can lead to a perfect SiGe islands at specific location.

NanodotsEach nanodot can hold one bit of information.10 Trillion dots per square inch.13 nm high80 nm wideSelf Assembled Nanodots

SAQDs - Electronic Structure z xy z x,y For SAQDs - z-axis confinement is generally much stronger than transverse quantisation x,y (Ez>>Exy) QD states are often approximated as a 2D Harmonic oscillator potential Fock-Darwin states2D state0D states~ HO like potentialQW like potential(2)(4)(6)n=1n=2n=3(2)(4)(6) Orbital character of QD states similar to atomic systems The shells n=1,2,3 - often termed s,p,d,.. in comparison with atomic systems DEe0-e1~50-70meV, DEh0-h1~20-30meV, Exciton BE ~30meV Dipole allowed optical transitions Dn=0 Single X transitions observable in absorption experiment PL requires state filling spectrosopy excitons interact

Self Assembled Quantum DotsHost: GaAs 5.653 Quantum Dot: InAs 5.867 Stranski- Krastanov growthGaAs

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