nanoprobes, spectroscopy and scattering gerard wegdam ... · (vu: solid state physics) nanoprobes,...

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Mark S. Golden 2003

A course given as part of the joint MA course given as part of the joint M.Sc. .Sc. programmeprogramme

Condensed Matter ScienceCondensed Matter Science

of the Universiteit van Amsterdamof the Universiteit van Amsterdamand the Vrije Universiteit.and the Vrije Universiteit.

Gerard Wegdam, Gerard Wegdam, Mark GoldenMark Golden, Jeroen Goedkoop,, Jeroen Goedkoop,Ekkes Brück, Ekkes Brück, Erika EiserErika Eiser

(UvA(UvA: WZI,: WZI, VHIVHI))

Andreas Borgschulte, Wiebke Lohstroh, (Bernard Dam)Andreas Borgschulte, Wiebke Lohstroh, (Bernard Dam)(VU(VU: solid state physics: solid state physics))

Nanoprobes, spectroscopy and scatteringNanoprobes, spectroscopy and scattering

Lecture 2: Optical probes


Overview of the courseOverview of the course

big introduction & beginning of optical probesbig introduction & beginning of optical probesoptical probes and inelastic electron scatteringoptical probes and inelastic electron scatteringphotoemission and related probesphotoemission and related probesxx--ray spectroscopiesray spectroscopieslab experimentslab experimentsscanning tunneling microscopy / spectroscopyscanning tunneling microscopy / spectroscopyoverspill: spectroscopyoverspill: spectroscopylab experimentslab experimentspreparing presentations: 'spectroscopy'preparing presentations: 'spectroscopy'student presentations: 'spectroscopy'student presentations: 'spectroscopy'lab experimentslab experimentsintroduction light/xintroduction light/x--ray scatteringray scatteringthin film xthin film x--ray reflectivity / diffractionray reflectivity / diffractionlab experimentslab experiments(3D) crystal structures from x(3D) crystal structures from x--ray diffractionray diffractionstructure in disordered systems & soft matterstructure in disordered systems & soft matterlab experimentslab experimentsdynamic light scattering and coherent xdynamic light scattering and coherent x--rays Irays Idynamic light scattering and coherent xdynamic light scattering and coherent x--rays IIrays IIlab experimentslab experimentspreparing presentations: 'scattering'preparing presentations: 'scattering'student presentations: 'scattering'student presentations: 'scattering'

Golden / GoedkoopGolden / GoedkoopGolden / GoedkoopGolden / GoedkoopGolden / GoedkoopGolden / GoedkoopGolden / GoedkoopGolden / Goedkoop

all of usall of usBorgschulteBorgschulte

--all of usall of us

you guys! you guys! all of usall of usall of usall of us

EiserEiserLohstrohLohstrohall of usall of us

BrückBrückEiserEiser

all of usall of usWegdamWegdamWegdamWegdamall of usall of us

you guysyou guysall of usall of us

Monday 01/09Monday 01/09Thursday 04/09Thursday 04/09Monday 08/09Monday 08/09Thursday 11/09Thursday 11/09Friday 12/09Friday 12/09Monday 15/09Monday 15/09Thursday 18/09Thursday 18/09Friday 19/09Friday 19/09Monday 22/09Monday 22/09Thursday 25/09Thursday 25/09Friday 26/09Friday 26/09Monday 29/09Monday 29/09Thursday 02/10Thursday 02/10Friday 03/10Friday 03/10Monday 06/10Monday 06/10Thursday 09/10Thursday 09/10Friday 10/10Friday 10/10Monday 13/10Monday 13/10Thursday 16/10Thursday 16/10Friday 17/10Friday 17/10Monday 20/10Monday 20/10Thursday 27/10Thursday 27/10

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Lecture 2Lecture 2

first 45 minutesfirst 45 minutes

dealing with the questions from last lecturedealing with the questions from last lecture

Overview of Lecture 2Overview of Lecture 2

hhνν, electron, neutron:, electron, neutron:

•• massmass

•• equation for E(equation for E(λλ))

•• λλ and momentum for E = 1, 10, 100, 1000 eVand momentum for E = 1, 10, 100, 1000 eV

questions (optical) from real lifequestions (optical) from real life

from 45from 45--60 minutes = break60 minutes = break


Lecture 2 continuedLecture 2 continued

60 60 -- 120 minutes (i.e. second hour)120 minutes (i.e. second hour)

Overview of Lecture 2Overview of Lecture 2

120 120 -- 180 minutes (i.e. third hour)180 minutes (i.e. third hour)

theoretical background:theoretical background:

basic terms, definitions, useful equations for optical basic terms, definitions, useful equations for optical spectroscopiesspectroscopies

(not enough time for derivations: see Ibach & L(not enough time for derivations: see Ibach & Lüth)üth)

minimini--breakbreakcase study:case study: spectroscopy of spectroscopy of fullerene Cfullerene C6060from INS, via IR, Raman, absorption of visible light, from INS, via IR, Raman, absorption of visible light, inelastic scattering of electrons, xinelastic scattering of electrons, x--ray spectroscopyray spectroscopy

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Lecture 2: Optical probesLecture 2: Optical probes

Optical properties:Optical properties: absorption, emission, amplification absorption, emission, amplification and modification of light and modification of light

prism

SHG

laser

window

mirror

glass fibre


pic: courtesy of ALStoday


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Case studies:Case studies:

'optical' probes'optical' probes

&&

(solid) C(solid) C6060



Case studies: CCase studies: C6060

introduction to fullerenes and Cintroduction to fullerenes and C6060 in particularin particular


•• materials familymaterials family•• physical propertiesphysical properties•• molecular and solid state structuremolecular and solid state structure•• basics of electronic structurebasics of electronic structure

examples from:examples from:

-- inelastic neutron scatteringinelastic neutron scattering-- infrainfra--red, Ramanred, Raman-- visible lightvisible light-- inelastic elecgtron scatteringinelastic elecgtron scattering-- VUV and soft xVUV and soft x--rayray

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truncated truncated icosahedronicosahedron

II hh symmetrysymmetry

....the roundest ....the roundest molecule in the molecule in the universeuniverse


FullerenesFullerenes

pure carbonpure carbon

made of 12 pentagonal faces and the rest = hexagonsmade of 12 pentagonal faces and the rest = hexagons


the third allotrope of carbon: diamond, graphite, the third allotrope of carbon: diamond, graphite, fullerenesfullerenes

essentially spessentially sp22 hybridised electronic basis hybridised electronic basis →→ conjugatedconjugated

pentagons pentagons →→ pyramidalisation angle pyramidalisation angle →→ curvaturecurvature

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Carbon in four Carbon in four dimensions.......dimensions.......

spsp22

spsp22

pure sppure sp22

pure sppure sp33



How many electrons does a carbon atom have ?How many electrons does a carbon atom have ?How many of them are in valence orbitals ?How many of them are in valence orbitals ?

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Conjugated Conjugated -- spsp22 -- carbon systemscarbon systems

C atom: 1sC atom: 1s222s2s222p2p22

spsp22 hybrids have 3 hybrids have 3 electrons availableelectrons availablefor for σσ bondingbonding

1 electron remains1 electron remainsin a in a ππ--orbital (2porbital (2pzz))


FullerenesFullerenes

pure carbonpure carbon

made of 12 pentagonal faces and the rest = hexagonsmade of 12 pentagonal faces and the rest = hexagons


the third allotrope of carbon: diamond, graphite, fullerenesthe third allotrope of carbon: diamond, graphite, fullerenes

essentially spessentially sp22 hybridised electronic basis hybridised electronic basis →→ conjugatedconjugated

pentagons pentagons →→ pyramidalisation angle pyramidalisation angle →→ curvaturecurvature

discovery: 1986. Kroto, Smalley, Curl. Nobel prize for chem.discovery: 1986. Kroto, Smalley, Curl. Nobel prize for chem.

breakthrough: 1990. Krbreakthrough: 1990. Kräätschmer & Huffman: carbon arc tschmer & Huffman: carbon arc method of production of g quantitiesmethod of production of g quantities

origin = astrophysics question re. interstellar absorption bandsorigin = astrophysics question re. interstellar absorption bands

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Why the interest ?Why the interest ?



PropertProperties of fullerenes as ies of fullerenes as ππ--electron systems electron systems

+ storage of+ storage ofgas or chargegas or charge

How does such a How does such a 'simple' system (no 'simple' system (no d or f electrons) d or f electrons) manage to display manage to display so many different so many different ground states of ground states of quantum electronic quantum electronic matter ? matter ?

Fundamental challengeFundamental challenge

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Carbon nanostructures: versatile nanoscale building blocksCarbon nanostructures: versatile nanoscale building blocks

field emitters in FPDsfield emitters in FPDsmolecular wiresmolecular wiresfield effect transistorsfield effect transistorssuper strong fibressuper strong fibresperfect SPM tipsperfect SPM tipslight emitting diodeslight emitting diodesmolecular switchesmolecular switchesphotovoltaic devicesphotovoltaic devices. . . .. . . .

nanotubesnanotubes

fullerenesfullerenes

polymerspolymers

small moleculessmall molecules/ monomers/ monomers


Molecular solidMolecular solid

NonNon--polar:polar:solid Csolid C6060

FCC close FCC close packingpacking


(111) surface

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Close packed structuresClose packed structures …..or nearly close packed

FCC HCP BCC

pics: [email protected]


atom missing



interstitial sitesinterstitial sites

How can we alter the properties of CHow can we alter the properties of C6060 ??

intercalationintercalation

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C60d = 0.7 nm

Li+ 0.076 nm

Na+ 0.1 nm

K+ 0.15 nm

Rb+ 0.16 nm

Cs+ 0.174 nm


What fits into the interstitial sites of solid CWhat fits into the interstitial sites of solid C6060 ??



Intercalation is only one of Intercalation is only one of three three ways to ways to engineer the properties of fullerenes.engineer the properties of fullerenes.

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ππ -- electronic structure of solid Celectronic structure of solid C6060

band gap

bandsbands

no. of allowed energy levels per unit vol. in the range E to E+δE

N(E):density of states:


HOMOHOMO

LUMOLUMO


What should nWhat should n--type intercalation do ?type intercalation do ?


partially fill the partially fill the LUMOLUMO--derived derived conduction conduction bandband

tt1u1u -- total six total six electronselectrons

Satpathy et al., PRB, 1992

e.g. Ke.g. KnnCC6060

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Solid CSolid C6060: not just a solid made up of 'fat' atoms....: not just a solid made up of 'fat' atoms....


very low energy degrees of very low energy degrees of freedom connected with freedom connected with rotations of the ballsrotations of the balls

librations etc.librations etc.

use use inelasticinelastic neutron scattering to neutron scattering to measure these . . . . . measure these . . . . .



2 meV2 meV 5 meV5 meV 13 meV13 meV 50 meV50 meV 180 meV180 meV

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INS: real dataINS: real data


Pintschovius et al., Rep. Prog. Phys. 57, 473 1996

comparison of comparison of CC6060 and Kand K33CC6060

intermolecularintermolecular

low E low E intramolecularintramolecular

high E high E intramolecularintramolecular



IRIR photons of energy 50 photons of energy 50 -- 200 meV200 meV

absorptionabsorption

reflectivityreflectivity

intraintra--molecular molecular phonons / vibronsphonons / vibrons

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IRIR a 60 atom molecule has 3na 60 atom molecule has 3n--6 = 174 6 = 174 internal vibrational modesinternal vibrational modes

consequence of high consequence of high IIhh symmetrysymmetry

(only 46 modes (only 46 modes allowed in total)allowed in total)

e.g. of selection rules e.g. of selection rules proves truncated icosohedral proves truncated icosohedral structurestructure!!

transmissiontransmissionCC6060 shows only 4 shows only 4 IRIR--active modes active modes ((FF1u1u))

1 2 3 41 2 3 4



RamanRaman inelastic light scatteringinelastic light scattering

Raman has different (symmetry) Raman has different (symmetry) selection rules w.r.t. IRselection rules w.r.t. IR

different vibrons visible (different vibrons visible (AAgg,, HHgg))

incoming laser light can be incoming laser light can be tuned to an electronic tuned to an electronic transition: transition: resonant Ramanresonant Raman

can be used to extract electron can be used to extract electron phonon coupling constant (phonon coupling constant (λλ))

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IRIR IR: also dynamics of the conduction electronsIR: also dynamics of the conduction electrons

insulators:insulators: phonons phonons visible at low visible at low energiesenergies

metal:metal: phonons phonons screened out, screened out, plasma plasma edgeedge visible here at visible here at ca. 300 meVca. 300 meV

Note also the huge Note also the huge phonon intensities in the phonon intensities in the doped systems !doped systems ! Iwasa & Kanewasu, PRB, 1995



IR of conduction electrons in metalsIR of conduction electrons in metals

nn generally so high that generally so high that ωωpp lies lies in UVin UV

thus metals usually only first thus metals usually only first transparent in UV range....transparent in UV range....

commonly used approach is the Drude dielectric function:commonly used approach is the Drude dielectric function:

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IRIR what does a plasma edge at 0.3 eV mean ?what does a plasma edge at 0.3 eV mean ?

Data: Iwasa & Kanewasu, PRB, 1995

KK33CC6060 is a 'poor' metal !is a 'poor' metal !

In fact is is In fact is is veryvery far from far from a simple, free electron a simple, free electron metal.....metal.....



IRIR KramersKramers--Kronig analysis: extract the optical Kronig analysis: extract the optical conductivity conductivity σσ((ωω))

Iwasa & Kanewasu, PRB, 1995

real real part of part of σσ((ωω))

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IRIR DrudeDrude--Lorentz fit of optical conductivity Lorentz fit of optical conductivity σσ11((ωω))

Iwasa & Kanewasu, PRB, 1995

interband interband transitiontransition

midmid--IRIR

DrudeDrude


Inelastic electron scatteringInelastic electron scatteringLecture 2: Optical probesLecture 2: Optical probes

EELSEELS

in transmissionin transmission

(bulk sensitive)(bulk sensitive)

in reflectionin reflection

(surface sensitive)(surface sensitive)

(bulk):(bulk):

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EELSEELSLecture 2: Optical probesLecture 2: Optical probes

measured quantity: loss functionmeasured quantity: loss function

KramersKramers--Kronig analysis (KKA) allows Kronig analysis (KKA) allows extraction of extraction of εε11((ωω) and ) and εε22((ωω))


Sohmen & Fink, PRB, 1992

EELS of CEELS of C6060


peaks in the loss function peaks in the loss function are are plasmonsplasmons

caused either by free caused either by free carriers or by interband carriers or by interband transitionstransitions

ππ plasmon at 6eVplasmon at 6eV

ππ ++ σσ plasmon at 26eVplasmon at 26eV

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Bulliard, Allen & Leach, CPL, 1993

EELS of CEELS of C6060


comparison of EELS in the solid comparison of EELS in the solid and gas phase, with visand gas phase, with vis--UV UV absorption in solutionabsorption in solution

interband transitions between interband transitions between occupied and unoccupied occupied and unoccupied molecular orbitals (MO's)molecular orbitals (MO's)


LDA band gap ca. 1.5 eVCC6060 'band gap' & excitons'band gap' & excitonsLecture 2: Optical probesLecture 2: Optical probes

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LDA band gap ca. 1.5 eV

CC6060 'band gap' & excitons'band gap' & excitonsLecture 2: Optical probesLecture 2: Optical probes

onset of optical absorption,

EELS etc. ca. 1.5 eV

Eopt=1.55 eV

OK ?OK ?NO !NO !


optical transition is an 'on-ball' (Frenkel) exciton

True 'transport' gapTrue 'transport' gap

EEggPESPES--IPESIPES= 3.5 eV= 3.5 eV

exciton BE ~ U = 1.5 eV

transport gap


EN-1 electrons - EN+1 electrons

PES IPESPES IPES

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these were examples of using spectroscopy to get

information on the energy (ω) and momentum (k or q)

dependence of:

librations

vibrations (phonons)

dynamics of 'free' electrons

electronic stransitions between localised levels



that's it for this week

x-ray's and C60 will be covered next week


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EXPERIMENTS - spectroscopy :

Date Group Exp.

5/9 1 optical absorption (WZI)

12/9 2 electron spec. (WZI)

3 STM (VU)

19/9 1 STM (VU)

2 optical absorption (WZI)

3 electron spectroscopy (WZI)

26/9 1 electron spectroscopy (WZI)

2 STM (VU)

3 optical absorption (WZI)


1= Wing 1= Wing Kiu + Kiu + SanneSanne

2= Anne 2= Anne Lisa + Lisa + JeroenJeroen

3 = Tracy, 3 = Tracy, Sven + Sven + EricEric


EXPERIMENTS - scattering :

Date Group Exp.

3/10 1 DLS (WZI)

2 thin film (VU)

3 XRD (WZI)

10/9 1 XRD (WZI)

2 DLS (WZI)

3 thin film (VU)

17/9 1 thin film (VU)

2 XRD (WZI)

3 DLS (WZI)


1= Wing 1= Wing Kiu + Kiu + SanneSanne

2= Anne 2= Anne Lisa + Lisa + JeroenJeroen

3 = Tracy, 3 = Tracy, Sven + Sven + EricEric

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Research papers :

these will be distributed in

next week's lectures (should

be Monday)


nanoprobes, spectroscopy and scattering gerard wegdam ... · (vu: solid state physics) nanoprobes,...

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