bionano quantum wells, wires, and dots lecture 5

7/25/2019 BIONANO Quantum Wells, Wires, And Dots Lecture 5

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Quantum Wells, Wires, and

Dots


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Quantified semiconductors

Quantum confined semiconductorsinclude: quantum wells, which confine electrons or

holes in one dimension and allow freepropagation in two dimensions.

quantum wires, which confine electrons orholes in two spatial dimensions and allow free

propagation in the third. quantum dots, which confine electrons in all

three spatial dimensions


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Semiconductors


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Figure 9.2. Evolution of integrated circuit technology.


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Figure 9.3. Moore's law (data points are for INE!"s #icroprocessors$ the

pro%ections are &ased on the 22 echnology oad#ap I)2*2.


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Figure 9.+. rend of the #ini#u# feature si,e (22 echnology

oad#ap I)2*2.


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Figure 9.-. verage selling price per &it of /M #e#ory since 091-.


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Figure 9.. loc4 speed of #icroprocessors since 091-.


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Figure 9.1. 5art of the periodic ta&le showing the III6 I76 and 7 colu#ns.

he ele#ental se#iconductors )i and 8e &elong to colu#n I7.


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Figure 9.9. )che#atic representation of the or&ital #odel of a single

silicon ato#6 with its 0+ electrons of which the + valence electrons reside

in the outer#ost shell. he energy levels are shown to the right (not to

scale*.


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Figure 9.0. (a* etrahedral &onding of silicon in the dia#ond structure

showing the four nearest neigh&ors connected through covalent &onds$ (&*

2/ &ond #odel illustrating the sharing of the valence electrons &etween

nearestneigh&or silicon ato#s. Each line &etween the silicon core

represents one valence electron.


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Figure 9.00. (a* Energy levels in an isolated silicon ato# and (&* in a

silicon crystal of N ato#s6 illustrating the for#ation of energy &ands. he

valence &and contains +N states and can acco##odate all +N valence

electrons.


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Figure .0. )che#atic plot of the single particle energy spectru# in a &ul4

se#iconductor for &oth the electron and hole states on the left side of the

panel with appropriate electron (e* and hole (h* discrete :uantu# states

shown on the right. he upper para&olic &and is the conduction &and6 the

lower the valence.


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Figure 9.02. valence electron %u#ping across the energy gap in pure

silicon resulting in the generation of a free electron and hole in the crystal;

(a* energy &and #odel6 (&* &ond #odel.


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Figure 9.0.


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Figure 9.03. E=trinsic ntype silicon doped with 5 donor ato#s. (a*

Energy &and diagra# and (&* >ond #odel.


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Figure 9.0+. E=trinsic ptype silicon doped with > acceptor ato#s. (a*

Energy &and diagra# and (&* >ond #odel.


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Figure 9.0-. (a* )che#atic crosssectional view of a M?) capacitor$ (&*

Energy &and diagra# (not to scale* of the M?) capacitor under flat &and

conditions along the cross section '.


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Figure 9.01. urrent flow in a NM?) transistor6 illustrating the three

operating regions (linear6 triode and saturation*.


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Figure 9.23. )che#atic illustration of the effect of 8e ato#s6 i#planted in

a )i crystal6 on the strain of )ilicon. (Fro# ef. 2- &y per#ission of the

Institute of Electrical and Electronics Engineers. 2003 IEEE*


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Figure 9.2+. )caling of the physical gate dielectric thic4ness and effective

o=ide thic4ness (E?*6 &ased on data fro# the I)22. (Fro# ef. +

&y per#ission of the Institute of Electrical and Electronics Engineers.

2003 IEEE*


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Figure 9.2-. )che#atic cross sections; (a* conventional &ul4 M?)FE

and (&* dual gate FE.


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Figure 9.21. epresentation of e#erging technologies in a 3/ space of

speed6 si,e and cost263. (Fro# ef. 3 &y per#ission of the Institute of

Electrical and Electronics Engineers. 2003 IEEE*


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Figure 9.29. )che#atic crosssection of a car&on nanotu&e field effect

transistor (NFE*. (dapted fro# Ph. Avouris, Acc. Chem. Res. 35,

1026 (2002)with 4ind per#ission of 5h. vouris.*


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Quantum confinement in semiconductors

In an unconfined (ul!" semiconductor, an electron#hole pair is t$picall$

ound within a characteristic length called the %ohr e&citon radius. If the

electron and hole are constrained further, then the semiconductor's

properties change. his effect is a form of quantum confinement, and it is a

!e$ feature in man$ emerging electronic structures.

Quantum confined semiconductors include: quantum wells, which confine electrons or holes in one dimension

and allow free propagation in two dimensions. quantum wires, which confine electrons or holes in two spatial

dimensions and allow free propagation in the third.

quantum dots, which confine electrons in all three spatialdimensions


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he particle in a o& (or the infinite potential well or infinite square well" is a

simple ideali)ed s$stem that can e completel$ sol*ed within quantum

mechanics. he infinite potential well is a finite si)ed region in space (the o&"

with an infinite potential at its oundaries (the walls". + particle e&periences no

forces while inside the o&, ut as the walls are 'infinitel$ high', it is constrainedto remain in the o&. his is similar to the situation of a gas confined in a non#

porous container.

igure considers the -#dimensional case, where the motion of the particle is

considered onl$ in a single dimension # the direction of the quantum

confinement.
http://upload.wikimedia.org/wikipedia/commons/2/27/Infinite_potential_well.svg


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Quantum wells

+ quantum well is a potential well that confines particles, which were

originall$ free to mo*e in three dimensions, to two dimensions, forcing

them to occup$ a planar region. he effects of quantum confinement ta!e

place when the quantum well thic!ness ecomes comparale at the de%roglie wa*elength of the carriers (generall$ electrons and holes", leading

to energ$ le*els called energ$ suands, i.e., the carriers can onl$ ha*e

discrete energ$ *alues.


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Figure 1.2. )che#atic energy &and diagra# of 8as@8al=s

0=:uantu#

well. n electron (represented &y its wavefunction * can &e consideredas partially confined in the :uantu# well of width e:ual to the 8as

thic4ness. he &arrier height E is e:ual to the difference in the energiesof the &otto# of the conduction &and E

c

for the two layer #aterials. Ev

is

the energy of the top of the valence &and and Egap

is the &and gap energy.

Egap for

l=8a0=s

Egap for

8as

Ec

Ev

E

thic4ness of

8as layer


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Figure 1.3. 5recipitate particles of spacing acting as o&stacles todislocation #otion.

hard precipitate particles

dislocation


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Quantum wells

Quantum wells are formed in semiconductors $ ha*ing a material, li!e

gallium arsenide sandwiched etween two la$ers of a material with awider andgap, li!e aluminium arsenide. hese structures can e

grown $ molecular eam epita&$ or chemical *apor deposition with

control of the la$er thic!ness down to monola$ers.

%ecause of their quasi#two dimensional nature, electrons in quantum

wells ha*e a sharper densit$ of states than ul! materials. +s a result

quantum wells are in wide use in diode lasers, specificall$ lue lasers.

he$ are also used to ma!e /01s (/igh 0lectron 1oilit$

ransistors", which are used in low#noise electronics. Quantum well

infrared photodetectors are also ased on quantum wells, and are used

for infrared imaging.

%$ doping either the well itself, or preferal$, the arrier of a quantum

well with donor impurities, a two#dimensional electron gas (2D03" ma$

e formed.


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(a*

(&*

(c*

d

d

Figure 1.0. )che#atic representations of nanoco#posite #aterials with

characteristic length scale; (a* nanolayered co#posites with

nanoscale&ilayer repeat length $ (&* nanofila#entary (nanowire*co#posites co#posed of a #atri= with e#&edded fila#ents of nanoscale

dia#eter d$ (c* nanoparticulate co#posites co#posed of a #atri= with

e#&edded particles of nanoscale dia#eter d.


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Figure 1.. rans#ission electron #icrographs of &inary nanoparticle

asse#&lies. (a* Fe3?

+(+n#*Fe

-15t

+2(+n#* asse#&ly$ (&* Fe

3?

+(1n#*

Fe-1

5t+2

(+n#* asse#&ly$ Fe3?

+(02 n#* Fe

-15t

+2(+ n#* asse#&ly. (Fro#

ef. +A by permission of Macmillan Magazines Ltd.*


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Quantum wiresIn condensed matter ph$sics, a quantum wire is an electricall$ conducting wire,

in which quantum effects are affecting transport properties. Due to the

confinement of conduction electrons in the trans*erse direction of the wire,

their trans*erse energ$ is quanti)ed into a series of discrete *alues 04

(ground state energ$, with lower *alue", 0-,...

5ne consequence of this quanti)ation is that the classical formula for

calculating the electrical resisti*it$ of a wire is not *alid for quantum wires

(where 6 is the resisti*it$, l is the length, and + is the cross#sectional area of

the wire".

Instead, an e&act calculation of the trans*erse energies of the confinedelectrons has to e performed to calculate a wire's resistance. ollowing from

the quanti)ation of electron energ$, the resistance is also found to e

quanti)ed.


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Figure 1.-. )canning electron #icrograph of electrodeposited Feo

nanowires (the polycar&onate #atri= in which the wires were e#&edded

has &een co#pletely dissolved*.


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Quantum wires

he importance of the quanti)ation is in*ersel$ proportional to the diameter ofthe nanowire for a gi*en material.

rom material to material, it is dependent on the electronic properties,

especiall$ on the effecti*e mass of the electrons. In simple words, it means that

it will depend on how conduction electrons interact with the atoms within a gi*en

material.

Semiconductors show clear conductance quanti)ation for large wire trans*erse

dimensions (-44 nm" ecause the electronic modes due to confinement are

spatiall$ e&tended and thus the$ ha*e low energ$ separations. his means that

the$ can onl$ e resol*ed at cr$ogenic temperature (few !el*ins" where the

thermal e&citation energ$ is lower than the inter#mode energ$ separation.

or metals, quanti)ation corresponding to the lowest energ$ states is onl$

oser*ed for atomic wires. heir corresponding wa*elength eing thus

e&tremel$ small the$ ha*e a *er$ large energ$ separation which ma!es

resistance quanti)ation perfectl$ oser*ale at room temperature.


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7aron nanotues as quantum wiresIt is possile to ma!e quantum wires out of metallic caron nanotues,

at least in limited quantities. he ad*antages of ma!ing wires from

caron nanotues include their high electrical conducti*it$ (due to a high

moilit$", light weight, small diameter, low chemical reacti*it$, and high

tensile strength.

It has een claimed that it is possile to create macroscopic quantum

wires. With a rope of caron nanotues, it is not necessar$ for an$

single fier to tra*el the entire length, since quantum tunneling will allow

electrons to 8ump from strand to strand. his ma!es quantum wiresinteresting for commercial uses.


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Quantum dots+ quantum dot is a semiconductor whose e&citons are confined in all three

spatial dimensions. +s a result, the$ ha*e properties that are etween

those of ul! semiconductors and those of discrete molecules.

Different si)ed quantum dots emit different color light due to quantumconfinement.

QD were disco*ered $ 9ouis 0. %rus, who was then at %ell 9as and is now a chemistr$

professor at 7olumia ni*ersit$. he term Quantum Dot was coined $ 1ar! ;eed, who was

then at e&as Instruments and is now a professor of applied ph$sics at


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7olloidal s$nthesis of quantum dots

7olloidal semiconductor nanocr$stals are s$nthesi)ed from precursor compounds dissol*ed

in solutions, much li!e traditional chemical processes. he s$nthesis of colloidal quantumdots is ased on a three component s$stem composed of: precursors, organic surfactants,

and sol*ents. When heating a reaction medium to a sufficientl$ high temperature, the

precursors chemicall$ transform into monomers. 5nce the monomers reach a high enough

supersaturation le*el, the nanocr$stal growth starts with a nucleation process. he

temperature during the growth process is one of the critical factors in determining optimal

conditions for the nanocr$stal growth. It must e high enough to allow for rearrangement

and annealing of atoms during the s$nthesis process while eing low enough to promote

cr$stal growth. +nother critical factor that has to e stringentl$ controlled during nanocr$stal

growth is the monomer concentration. he growth process of nanocr$stals can occur in two

different regimes, =focusing> and =defocusing>. +t high monomer concentrations, the critical

si)e (the si)e where nanocr$stals neither grow nor shrin!" is relati*el$ small, resulting in

growth of nearl$ all particles. In this regime, smaller particles grow faster than large ones

(since larger cr$stals need more atoms to grow than small cr$stals" resulting in =focusing> ofthe si)e distriution to $ield nearl$ monodisperse particles. he si)e focusing is optimal

when the monomer concentration is !ept such that the a*erage nanocr$stal si)e present is

alwa$s slightl$ larger than the critical si)e. When the monomer concentration is depleted

during growth, the critical si)e ecomes larger than the a*erage si)e present, and the

distriution =defocuses> as a result of 5stwald ripening.


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Figure .3. !a Mer #odel for the growth stages of nanocrystals.


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Figure .+. )ynthetic apparatus for the preparation of nanocrystals.


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Figure .A. to#ic Force Microscope i#ages of 8e clusters on two types

of surfaces. 8raphite in the left two panels6 and )i?2in the right. he line

plots on the figure give vertical profiles of line cuts through the FM

i#ages directly a&ove and give the :uantitative si,e infor#ation.


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Figure .1.Illustration of a cross sectional view of Si quantum dotsformed in a glass matrix via ion implantation. Note that the randomarrangement and spherical shape of the quantum dot particles is

expected for quantum dots implanted in an amorphous media.


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Figure .9.Photoluminescence spectra from Si (400 keV, 1.53 x 1017

cm-2) implanted SiO2as implanted and after annealing at 950 and

1100 C. (From Ref. 4 by permission of the American Institute of

Physics.)


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Quantum dotshere are colloidal methods to produce man$ different semiconductors,

including cadmium selenide, cadmium sulfide, indium arsenide, and indium

phosphide. hese quantum dots can contain as few as -44 to -44,444atoms within the quantum dot *olume, with a diameter of -4 to ?4 atoms.

5ther methods for s$nthesis are also used. Indi*idual quantum dots can e

created from two#dimensional electron or hole gases present in remotel$

doped quantum wells or semiconductor heterostructures called lateral

quantum dots. he sample surface is coated with a thin la$er of resist. +

lateral pattern is then defined in the resist $ electron eam lithograph$. hispattern can then e transferred to the electron or hole gas $ etching, or $

depositing metal electrodes (lift#off process" that allow the application of

e&ternal *oltages etween the electron gas and the electrodes.

he energ$ spectrum of a quantum dot can e engineered $ controlling the

geometrical si)e, shape, and the strength of the confinement potential. +lso

in contrast to atoms it is relati*el$ eas$ to connect quantum dots $ tunnel

arriers to conducting leads, which allows the application of the techniques

of tunneling spectroscop$ for their in*estigation.

7onfinement in quantum dots can also arise from electrostatic potentials

(generated $ e&ternal electrodes, doping, strain, or impurities".


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Figure .0. )canning electron #icrograph of :uantu# dot patterns on a

8a)& surface induced &y rion sputtering with an ion energy of - e7.

he dots show a he=agonal ordering with a characteristic wavelength that

depends on ion energy. he insets show the corresponding distri&ution of

the nearestneigh&or distance. (Fro# ef. - &y per#ission of the

#erican 5hysical )ociety.*


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Quantum dots+n immediate optical feature of colloidal quantum dots is their coloration.

While the material which ma!es up a quantum dot defines its intrinsic energ$signature, the quantum confined si)e of the nanocr$stal is more significant at

energies near the and gap. hus quantum dots of the same material, ut with

different si)es, can emit light of different colors. he ph$sical reason is

quantum confinement effect.

he larger the dot, the redder (lower energ$" its fluorescence spectrum.

7on*ersel$, smaller dots emit luer (higher energ$" light. he coloration is

directl$ related to the energ$ le*els of the quantum dot.


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Quantum dotsQuantitati*el$ spea!ing, the andgap energ$ that determines the energ$ (and

hence color" of the fluoresced light is in*ersel$ proportional to the square of

the si)e of the quantum dot.

9arger quantum dots ha*e more energ$ le*els which are more closel$ spaced.

his allows the quantum dot to asor photons containing less energ$, i.e.

those closer to the red end of the spectrum. ;ecent articles in nanotechnolog$

and other 8ournals ha*e egun to suggest that the shape of the quantum dot

ma$ well also e a factor in the coloration, ut as $et not enough informationhas ecome a*ailale.

he lifetime of fluorescence is determined $ the si)e. 9arger dots ha*e more

closel$ spaced energ$ le*els in which the electron#hole pair can e trapped.

herefore, electron#hole pairs in larger dots li*e longer and thus these large

dots show a larger lifetime.


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luorescence emission spectra of 7de quantum dots of

different si)es.


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Quantum dots in iolog$In modern iological anal$sis, *arious !inds of organic d$es are used.

/owe*er, with each passing $ear, more fle&iilit$ is eing required of these

d$es, and the traditional d$es are often unale to meet the e&pectations. o

this end, quantum dots ha*e quic!l$ filled in the role, eing found to e

superior to traditional organic d$es on se*eral counts,

rightness (owing to the high quantum $ield"

stailit$ (much less photodestruction".

he impro*ed photostailit$ of quantum dots for e&ample, allows the

acquisition of man$ consecuti*e focal#plane images that can e

reconstructed into a high#resolution three#dimensional image. +nother

application that ta!es ad*antage of the e&traordinar$ photostailit$ ofquantum dot proes is the real#time trac!ing of molecules and cells o*er

e&tended periods of time. or single#particle trac!ing, the irregular lin!ing

of quantum dots is a minor drawac!.

IEI;530 Qd t t l


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IEI;530: Qdot anocr$stal

1ulticolor immunofluorescence imaging with QdotF secondar$ antiod$

con8ugates.9aminin in a mouse !idne$ section was laeled with an anti#laminin primar$

antiod$ and *isuali)ed using green#fluorescent QdotF ?G? Ig3. H07+1

(plateletendothelial cell adhesion moleculeJ 7D@-" was laeled with an anti

H07+1#- primar$ antiod$ and *isuali)ed using red#fluorescent QdotF G??

Ig3. uclei were stained with lue#fluorescent /oechst @@@C2.


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IEI;530 Qd t t l


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QdotF iocon8ugate is a generic term to descrie QdotF nanocr$stals coupled to

proteins, oligonucleotides, small molecules, etc., which are used to direct inding of the

quantum dots to targets of interest. 0&amples of QdotF iocon8ugates include

strepta*idin, protein +, and iotin families of con8ugates. QdotF iocon8ugates are oftenused as simple replacements for analogous con*entional d$e con8ugates when their

unique performance characteristics are required to achie*e optimal results.

1ost d$e con8ugates are s$nthesi)ed $ attaching one or more fluorophores to a single

iomoleculeJ howe*er, the large surface area afforded $ the nanocr$stal fluorophore

allows simultaneous con8ugation of man$ iomolecules to a single QdotF nanocr$stal.+d*antages conferred $ this approach include increased a*idit$ for targets, the

potential for cooperati*e inding in some cases, and the use of efficient signal

amplification methodologies. or e&ample, comining iotin#functionali)ed products

with the strepta*idin laels allows for successi*e enhancements in signal *ia

sandwiching (strepta*idiniotinstrepta*idinetc." following an initial laeling step.

Standard fluorescence microscopes are an e&cellent and widel$ a*ailale tool for the

detection of QdotF iocon8ugates. hese microscopes are often fitted with right white

light lamps and filter arrangementsJ QdotF nanocr$stals efficientl$ asor white light

using road e&citation filters, and the outstanding photostailit$ of QdotF iocon8ugates

allows the microscopist more time for image optimi)ation.


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7onclusions

Semiconductor materials can e miniaturi)ed in order to

achie*e discrete (quantum" electronic properties.

Quantum dots are electronicall$ confined in all three spatial

directions, that ma!es them accept and emit light of narrowl$defined energies.

5f all quanti)ed semiconductors, QDs are most often used

in iolog$.

bionano quantum wells, wires, and dots lecture 5

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