lecture 1: introduction metals, insulators and ...€¦ · metals, insulators and semiconductors...

1

Lecture 1: IntroductionLecture 1: Introduction

Metals: conduct electricity down to lowest T's

Non-metals: may conduct at ↑T, but cond. ↓ as T↓

Metals, insulators and semiconductorsMetals, insulators and semiconductors

Metallic and nonMetallic and non--metallic solidsmetallic solids

….. can be understood from filling of bands:

E

N(E)band gap

conduction bandvalence

band

E

N(E)Fermi level

EF


Conduction in systems with a band gapConduction in systems with a band gap


high T: ionic conductivity (e.g. NaCl)- low cond. cf. metallic conductivity

electronic cond. needs e- excited to the conduction band - thermal excitation (small gap)- optical excitation

= photoconductivity (Xerox)


Band picture works fairly wellBand picture works fairly well


ionic system- cation levels empty (e.g. Na+)

- anion levels full (e.g. Cl-)

molecular solid- gap between HOMO and LUMO

Egap

Interesting cases: partially filled orbitals

e.g. transition metal oxides such as ReO3 has (5d)1

metallicsometimes TM-O NOT metallic (interesting…!)


Many properties depend on thermal excitation of e- from ground state

No. particles in excited state at temperature T:

ni ∝ exp (- Ei / kT ) Boltzmann distribution

BUT

…….can't use Boltzmann for electrons in a solid !


Thermal excitation of electronsThermal excitation of electrons


Electrons obey the Pauli exclusion principle

Electrons are indistinguishable (exchange of electrons between two occupied levels does not lead to a different arrangement)


1 + exp [ (E - EF) / kT ]f (E) =

1 FermiFermi--DiracDiracdistributiondistribution


T=0: Fermi-Dirac distribution


1 + exp [ (E - EF) / kT ]f (E) =

1 FermiFermi--DiracDirac distributiondistribution

f(E

)

E

top filled level in band = EF

filled empty

these states determine a number of properties: e.g. electronic specific heat

Fermi-Dirac distribution can be measured directly using photoemission

f(E

)

Energy

T=0 < T1 < T2

increase T:

2


Thermal excitation of electronsThermal excitation of electronsFermiFermi--DiracDirac distributiondistribution

f(E

)

Energy

Width ca. 4 kT

4kT

room temp. 4kT is ca. 0.1 eV

Total width of bands often eV

only small no. of total e- are thermally excited

Fermi level is fundamental: it's the thermodynamic chemical potential for e- in the solid

Metals in contact: charge transferred till EF's are equal


SemiconductorsSemiconductors

Non metals

conduct via thermal excitation of carriers across gap


missing e- in valence band (holes)

e- in the conduction band

Egap ca. 1 eV



Fermi level now lies in the gapThermal excitation of electronsThermal excitation of electrons

VBCB

pure solid

n-type

p-type

Fermi-Diracdistribution

EF

EF

EF



Bottom of conduction band:

E - E F = E gap / 2

E - E F usually much larger than kT

exponent dominates

no. of exited electrons: n ∝ exp (-E gap / 2kT)


1 + exp [ (E - EF) / kT ]f (E) =

1

cf. intrinsic behaviour of pure materialsArhheniusbehaviour

A course given as part of the joint Masters programmeA course given as part of the joint Masters programme

Condensed Matter ScienceCondensed Matter Science

of the Universiteit van Amsterdamof the Universiteit van Amsterdamand the and the VrijeVrije Universiteit, Amsterdam.Universiteit, Amsterdam.

Mark Golden (Mark Golden (UvAUvA) & Bernard Dam (VU)) & Bernard Dam (VU)

Electronic Structure and Chemistry of SolidsElectronic Structure and Chemistry of Solids

Lecture 2: Spectroscopic Methods

Mark S. Golden, Van der Waals-Zeeman Institute, Universiteit van Amsterdam, Room 2.09, Valckenierstraat 65, 1018 XE Amsterdam, Tel.: 020 525 6363.

[email protected] http://www.science.uva.nl/research/wzi/cmp

Electronic Structure & Chemistry of Solids (2005)Electronic Structure & Chemistry of Solids (2005)

Book chapterBook chapter lecturer date(s)lecturer date(s)

• Introduction - MSG 30.10• Spectroscopic methods - MSG 03.11• Electronic energy levels and chem. bonding - BD 07.11, 10.11• Optics (not in Cox as such [i.e. better]) - BD 14.11• Elementary band theory - MSG 17.11, 21.11• The effects of electron repulsion - MSG 24.11, 28.12• Lattice distortions - BD 08.12• Defects, impurities and surfaces - BD 15.12• Questions and answers session - all 19.12

• Closing workshop with presentations - all 22.12.2005• Oral exams - all Jan. 2006

3

Question from Lecture 1: Intro, bonding, classification of solidQuestion from Lecture 1: Intro, bonding, classification of solidss

Discuss the different types of bonding encountered in the alkaliDiscuss the different types of bonding encountered in the alkali metal metal intercalated Cintercalated C6060 compound Kcompound K33CC6060..

This is a soThis is a so--called called fulleridefulleride, has an , has an f.c.cf.c.c structure and is a metal and a structure and is a metal and a superconductor (superconductor (TcTc 18K). There is charge transfer from the K atoms to the C18K). There is charge transfer from the K atoms to the C6060cages.cages.

© s

teph

en.h

eyes

@ch

em.o

x.ac

.uk

© J.W. Bullard, 1999

http://rs1.physik.uni-dortmund.de/sem/c60/kap6.htm

Lecture 2: checkLecture 2: check--up of Lecture 1 materialup of Lecture 1 material

Importance of solidsImportance of solids

Molecular solidsMolecular solidsIonic solidsIonic solidsCovalent solids Covalent solids Metallic solidsMetallic solids'Real', complex solids'Real', complex solids

Chemical classification of solidsChemical classification of solids

OrbitalsOrbitals in atoms, molecules and solidsin atoms, molecules and solidsBands and bondsBands and bonds

Electrons in solidsElectrons in solids

Metallic and nonMetallic and non--metallic solidsmetallic solidsThermal excitation of electronsThermal excitation of electronsSemiconductorsSemiconductors


OK ?

Lecture 2: Spectroscopic methodsLecture 2: Spectroscopic methods

IntoductionIntoduction: types of (electronic) spectroscopy: types of (electronic) spectroscopy

General principlesGeneral principlesApplications of PESApplications of PESInverse PESInverse PES

PhotoemissionPhotoemission

General principlesGeneral principlesApplications of xApplications of x--ray emission spectroscopyray emission spectroscopyXX--ray absorption spectroscopyray absorption spectroscopy

XX--ray spectroscopyray spectroscopy

Band gaps and Band gaps and excitonsexcitonsAbsorption and reflectivityAbsorption and reflectivityMetals Metals -- the plasma frequencythe plasma frequency

Optical propertiesOptical properties STM / STSSTM / STSGeneral principlesGeneral principlesApplications of STMApplications of STM

not in Cox

Bernard: later

Chapter 2: Spectroscopic MethodsChapter 2: Spectroscopic Methods

Spectroscopic methodsSpectroscopic methods

to understand the electronic properties, we need to to understand the electronic properties, we need to learn about the electrons in a solidlearn about the electrons in a solid

spectroscopy can tell us about what the electrons are spectroscopy can tell us about what the electrons are doing in real materials doing in real materials

energy

momentum

spin1023 electrons

EM-radiation electrons


A warmA warm--up 'competition':up 'competition':

take 2 minutes to write down as many spectroscopic take 2 minutes to write down as many spectroscopic methods as you can think of that involve the electronic methods as you can think of that involve the electronic and optical properties of a solidand optical properties of a solid

(using, for example electrons/radiation as incoming and (using, for example electrons/radiation as incoming and outgoing 'particles')outgoing 'particles')

1023 electrons

EM-radiation electrons


Types of spectroscopyTypes of spectroscopy

Probing particles:Probing particles: Method:Method: Information about:Information about:

Photon in, electron outPhoton in, electron out PES PES occupied statesoccupied states

Electron in , photon outElectron in , photon out IPESIPES unoccupied statesunoccupied states

Photon in, photon outPhoton in, photon outxx--raysrays XES, XES, RIXSRIXS occupied statesoccupied statesvisible light, IRvisible light, IR reflectivity,reflectivity, conduction electronconduction electron

ellipsometryellipsometry dynamicsdynamics

Photon inPhoton inxx--raysrays XASXAS unoccupied statesunoccupied statesvisible light, IRvisible light, IR absorptionabsorption band gap, defect statesband gap, defect states

Electron in, electron outElectron in, electron out EELSEELS collective excitationscollective excitations

Electron in Electron in oror electron outelectron out STM / STSSTM / STS occupied or unoccupied occupied or unoccupied states (local)states (local)

4

PES XPS IPES XAS AES EEPES XPS IPES XAS AES EELSLS

NN--11 NN--11 N+1N+1 N, N, can becan be≈≈ N+1N+1

N N NN--22

Chapter 2: Spectroscopic MethodsChapter 2: Spectroscopic Methods Chapter 2: Spectroscopic MethodsChapter 2: Spectroscopic Methods

photoemissionphotoemissionoror

photoelectron spectroscopyphotoelectron spectroscopy

conceptually very simpleconceptually very simple

Pedestrian guide to PESPedestrian guide to PES

KE = hν - BE binding energy of the electron in the crystal

kinetic energy of photoelectron in the vacuum

theoretical beginnings:theoretical beginnings:

Albert Einstein at beginning of 20th century (Albert Einstein at beginning of 20th century (→→ Nobel prize)Nobel prize)

experimental beginnings:experimental beginnings:

Heinrich Hertz at end of 19th centuryHeinrich Hertz at end of 19th century


step 1step 1

incoming photon causes an incoming photon causes an

optical transition in the solidoptical transition in the solid

'vertical' transition'vertical' transition

simplesimple

Three step model for PESThree step model for PES

purely phenomenological, but usefulpurely phenomenological, but useful


simplesimple


step 2step 2

transmission of the photoelectron through the solid transmission of the photoelectron through the solid

(towards surface)(towards surface)

energyenergy--loss processesloss processes

secondary electronssecondary electrons

inelastic mean free path, inelastic mean free path, λλ



simplesimple


step 3step 3

transmission of the photoelectron across the surface transmission of the photoelectron across the surface

and into the vacuumand into the vacuum

through surface potential barrierthrough surface potential barrier

kk⊥⊥ not conservednot conserved



5

Ener

gy

Ener

gy →→

(1)(1) (2)(2) (3)(3)3 step model3 step model

samplesample vacuumvacuum

ΦΦ

EEvv

EEFF

hhνν

photoexcitationphotoexcitation transport to transport to surfacesurface

transmission transmission across surfaceacross surface

secondary secondary electron electron cutcut--offoff


Kinetic energy Kinetic energy →→

Generic spectrumGeneric spectrum

←← Binding energyBinding energyhhνν--ΦΦsamplesample

hhνν--ΦΦspectrometerspectrometer00

00

hhνν--ΦΦsamplesample

e.g. VB e.g. VB of goldof goldEEFF


ΦΦsamplesample

'Fermi edge''Fermi edge'direct measure of direct measure of FermiFermi--DiracDiracdistribution:distribution:

PES is ionising spectroscopyPES is ionising spectroscopy

⇒⇒ in metals:in metals:

if if TTsamplesample low enough, the 10%low enough, the 10%--90% width of the Fermi edge 90% width of the Fermi edge ((≈≈FWHM Gaussian) measures the experimental energy resolutionFWHM Gaussian) measures the experimental energy resolution


'Fermi edge''Fermi edge'direct measure of direct measure of FermiFermi--DiracDiracdistribution:distribution:

PES is ionising spectroscopyPES is ionising spectroscopy

⇒⇒ in metals:in metals:

if if TTsamplesample low enough, the 10%low enough, the 10%--90% width of the Fermi edge 90% width of the Fermi edge ((≈≈FWHM Gaussian) measures the experimental energy resolutionFWHM Gaussian) measures the experimental energy resolution


Surface sensitivitySurface sensitivity cross section for inelastic scattering cross section for inelastic scattering of of photoelectonsphotoelectons during steps 2,3 is during steps 2,3 is HIGH !HIGH !

3λ = 3 nma few atomiclayers !

crystal

photons

KEe,vacuum = hν - BEe,crystal


IMFPIMFP


inelastic mean free inelastic mean free pathlengthpathlength, , λλ

λλ defined as path length after which transmitted signal = defined as path length after which transmitted signal = 1/e of original signal1/e of original signal

λλ::

•• KE dependentKE dependent

•• weakly material weakly material dependentdependent

'universal' curve'universal' curve

6


1) you need photons.....1) you need photons.....

light sourceslight sources

VUV photonsVUV photonsxx--ray photonsray photons

in the labin the lab

synchrotron radiationsynchrotron radiation

21 1486 21 1486 eVeV


3rd generation SR sources3rd generation SR sources

BESSY GmbH,BESSY GmbH,BerlinBerlinU125U125--1/PGM 1/PGM beamlinebeamline

Swiss Light Source,Swiss Light Source,PSI, PSI, VilligenVilligen, CH., CH.SIS SIS beamlinebeamline


3rd generation SR sources3rd generation SR sources

BESSY GmbH,BESSY GmbH,BerlinBerlinU125U125--1/PGM 1/PGM beamlinebeamline

Swiss Light Source,Swiss Light Source,PSI, PSI, VilligenVilligen, CH., CH.SIS SIS beamlinebeamline


intense, brilliantintense, brilliantselectable energyselectable energy

= monochromatic= monochromaticselectable selectable polarisationpolarisation

! VUV: too high E for lasers! VUV: too high E for lasers

! no windows possible! no windows possible

! reflecting optics! reflecting optics

synchrotronsynchrotronsourcessources

Synchrotron radiationSynchrotron radiation


1) you need to 1) you need to analyseanalyse the KE and the KE and θ,φ θ,φ

distribution of the photoelectrons.....distribution of the photoelectrons.....

7


PhotoemissionPhotoemission an advanced PES setan advanced PES set--up works like this:up works like this:

ultrahigh vacuum chamber

photon source

750 k750 k∈∈ Pic: Damascelli


what doeswhat does

photoemission measure ? photoemission measure ?


PESPES

ionising spectroscopyionising spectroscopy

no. of electrons vs. their binding energyno. of electrons vs. their binding energy

'direct' measure of occupied density of states: N(E)'direct' measure of occupied density of states: N(E)

[......ionisation cross sections, polarisation selection [......ionisation cross sections, polarisation selection rules....]rules....]

intensities of different bands in a PES spectrum are weighted by the cross-section of the atomic orbital which makes up the band

tabulated

PhotoionisationPhotoionisation cross sectionscross sections

radial part of the radial part of the wavefunctionwavefunction importantimportant

good match of initial and final state good match of initial and final state wavefunctionswavefunctions

optimal overlap:optimal overlap:

low low EEfinalfinal + extended |i> (e.g. C 2s, 2p)+ extended |i> (e.g. C 2s, 2p)

high high EEfinalfinal + + compact |i> (e.g. C1s)compact |i> (e.g. C1s)

→→ use to use to discriminate between different |i>discriminate between different |i>

final state ! final state ! (selected (selected via choice of via choice of hhνν))



examples (Cox and other) of examples (Cox and other) of photoemissionphotoemission


PES PES and XAS/IPESand XAS/IPES of Cof C6060

PES gives energy PES gives energy distribution of the filled distribution of the filled MO's......MO's......

......or the bands formed ......or the bands formed in the solidin the solid

gas phasegas phase

solid statesolid state

C60: molecular solid !

bands only slightly broader and shifted

8


PESPESgas phase vs. molecular solidgas phase vs. molecular solid

sharp MO's in gas phase molecule sharp MO's in gas phase molecule broadenbroaden due todue toband formation band formation in the solidin the solid

(not much for solid C(not much for solid C6060 ⇔⇔ superconductivity ?)superconductivity ?)

shiftshift to lower BE in solidto lower BE in solid

= = screeningscreening of 'hole' made by removing photoelectron.of 'hole' made by removing photoelectron.→→ in solid there is extra interin solid there is extra inter--site screening:site screening:

Solid = continuum, relative dielectric constant Solid = continuum, relative dielectric constant εεrr (molecular (molecular polarisabilitypolarisability). ). Insert charge Insert charge qq spread over radius spread over radius rr from vacuum into solidfrom vacuum into solid

→→ electrostatic polarisationelectrostatic polarisation. . For For rr ~ atom, ~ atom, ∆∆E of order 1 E of order 1 eVeV..


PESPESmetal metal -- valence band photoemission (UPS)valence band photoemission (UPS)

(generally) broad bands(generally) broad bandse.g. VB of aluminiume.g. VB of aluminium

inelastically scatteredelectrons

Fermi-Diraccutoff

E F

N(E) ∝ E½

free-electron band is a parabola


angle resolved photoemissionangle resolved photoemission

samplesample


metal metal -- angle resolved valence band photoemission (ARPES)angle resolved valence band photoemission (ARPES)

single crystalline sample

angle-reolved detection of photoelectrons

What physical quantities are measured in photoemission ?What physical quantities are measured in photoemission ?

Fermifunction

spectralfunction

vectorpotential(photons)

momentum(photoelectrons)

Spectral function:

the probablility of removing an electron of energy E andwavevector k from the interacting N-electron system

BUT the matrix element is always present:

dependence on photon energy, polarisation....


How to determine kHow to determine k||||

momentum component parallel to surface, pmomentum component parallel to surface, p||||

samplesample

KE=½mvKE=½mv22, p=, p=mvmv

KE=½pKE=½p22/m/m

p=(2mKE)p=(2mKE)½½

kk vector parallel to surface, kvector parallel to surface, k||||

θθ sin)2(sin ½|| mKEpp ==

θsin)/2( ½2|||| hh mKEpk ==

vertical transitions and kvertical transitions and k||||--conservation across surfaceconservation across surface


9

ARPESARPES

what about kwhat about k⊥⊥? ?

EEii

EEFF

EEkinkin

hhννΦΦ

EEVV

VV00

(w.r.t. bottom of band) electrons feel an attractive (w.r.t. bottom of band) electrons feel an attractive potential, Vpotential, V00 = E= EFF + + ΦΦ

inner potentialinner potential


ARPES for 2D systemsARPES for 2D systems

if kif k⊥⊥ not particularly important for the energy variation of not particularly important for the energy variation of the electronic states the electronic states

θθ sin)(512.0sin2|| eVEmEk kin

kin ==h

in Åin Å--11 in in eVeV in in degrees degrees


0.00.20.4Binding energy (eV) Momentum (Å-1)

0.3 0.4 0.5 0.6 0.7

EEnergy nergy DDistribution istribution CCurves I (k,E) urves I (k,E) MMomentum omentum DDistribution istribution CCurvesurves


StateState--ofof--thethe--art ARPES of a art ARPES of a high high TcTc superconductorsuperconductor BorisenkoBorisenko et al., PRBet al., PRB6464, 094513 (2001) , 094513 (2001)


ARPES data - equal footing in either in E or k

EDC - I (kx,ky,E) EDM - I (kx,ky,E)

MDM - I (kx,ky,E)

MDC - I (kx,ky,E)

A full picture of IA full picture of IPESPES vs. the 3D vs. the 3D kkxx, , kkyy, E, EBB spacespace

0.5

eV

(π,π)(π,0)

EF

MX

min max

X

X

YM

M

Bin

ding

ene

rgy

(eV

)

Momentum (Å-1 )

ky

kx

2

EF

BorisenkoBorisenko et al., PRBet al., PRB6464, 094513 (2001) , 094513 (2001)


Constant energy surfaces: E dependenceConstant energy surfaces: E dependence

KordyukKordyuk et al., 2000et al., 2000300K, 300K, hhνν = 21 = 21 eVeV


HTSCHTSC

10


time for a coffeetime for a coffee

Lifetimes contd.Lifetimes contd.

ττhh are of the order of 10are of the order of 10--1515 secondsseconds

PES is a PES is a FASTFAST probeprobe

ττhh << << ττee

energy widths in PES are energy widths in PES are dominated by hole lifetime:dominated by hole lifetime:

ee

hh


Self energy and the spectral functionSelf energy and the spectral function

Spectral function:Spectral function:

causes E shiftcauses E shift

causes width causes width ((LorentzianLorentzian))


imaginary part of the self energy


core level photoemissioncore level photoemission

Core level photoemissionCore level photoemission

xx--ray ray photelectronphotelectron spectroscopyspectroscopy

NN--11

"XPS""XPS"

core levels strongly core levels strongly localisedlocalised, thus , thus BE'sBE'sgive give elemental identificationelemental identification

chemical shiftschemical shifts give information on:give information on:

* chemical environment of emitter* chemical environment of emitter

* oxidation / valence / bonding state* oxidation / valence / bonding state

satellites satellites and/orand/or shake upshake up are the response of are the response of system to core system to core ionisationionisationangular distribution angular distribution (PhD, XPD) is a local, non(PhD, XPD) is a local, non--destructive structural probedestructive structural probe


PESPESphotoemission using xphotoemission using x--rays (XPS)rays (XPS)ionise either valence bands or core levelsionise either valence bands or core levelse.g. Nae.g. Na0.70.7WOWO33

BE of core level characteristic for element

11


PESPESXPS as ESCA XPS as ESCA ''EElectron lectron SSpectroscopy for pectroscopy for CChemical hemical AAnalysis'nalysis'

core level BE signals core level BE signals which elementwhich element

exact BE exact BE cancan give info give info about chemical about chemical environmentenvironment

surface sensitive surface sensitive chemical analysischemical analysis

C atoms in four different surroundings

L. K

arls

son,

Upp

sala


PESPESphotoemission using xphotoemission using x--rays (XPS)rays (XPS)e.g. Nae.g. Na0.70.7WOWO33

zoom inzoom in


PESPESusing using photoionisationphotoionisation crosscross--sectionssections

ionise either valence bands or core levelsionise either valence bands or core levelse.g. Nae.g. Na0.70.7WOWO33

hν = Al:Kα (1487eV) He I (21.2 eV)

VBVB


inverse photoemissioninverse photoemission


Inverse photoemissionInverse photoemission

sample a solidsample a solid

monochromatic electron beammonochromatic electron beam

fall into empty electronicfall into empty electroniclevels levels in the solidin the solid

measure:measure:intensity of emitted radiation (intensity of emitted radiation (BremstrahlungBremstrahlung) vs. ) vs.

KE of electrons, orKE of electrons, orintensity and energy of emitted radiation for intensity and energy of emitted radiation for

constant incoming electron energyconstant incoming electron energy

......also surface sensitive & lower resolution than PES......also surface sensitive & lower resolution than PES

sample

N+1N+1


Inverse photoemissionInverse photoemission

combination PES + IPES is powerfulcombination PES + IPES is powerful1) metals1) metals2) systems with gaps2) systems with gaps

N+1N+1NN--11

transporttransport gap

.....cf. excitonsdiscussed later

12


PES + IPESPES + IPES

N+1N+1NN--11

TM 3d bandTM 3d band

3d band filling ↑

3d band narrows


xx--ray absorption / emission ray absorption / emission & co.& co.


Core level spectroscopiesCore level spectroscopies

Core Core orbitalsorbitals not directly involved in bondingnot directly involved in bonding

→→ sharp, retain their atomic identitysharp, retain their atomic identityZZ, , angular momentum l angular momentum l

sitesite--selectiveselective & & symmetrysymmetry--selectiveselective spectroscopiesspectroscopies

monochromatic photons, tuned to core level transitionsmonochromatic photons, tuned to core level transitions

requires synchrotron radiationrequires synchrotron radiation


times have moved on since ESS was written....times have moved on since ESS was written....

synchrotron radiation sources have become synchrotron radiation sources have become commonplacecommonplace

XAS / EXAFS is XAS / EXAFS is widelywidely usedused

XES is enjoying a renaissance (SRXES is enjoying a renaissance (SR--excited)excited)

XAS & XESXAS & XES


xx--ray absorptionray absorption resonant IXSresonant IXS xx--ray emissionray emissionXASXAS RIXSRIXS XESXES

NN--11NNNN ≈≈ N+1N+1

unoccupied excitations vs. q occupied



Simple symmetry selection rulesSimple symmetry selection rules

XASXAS

1) 1s 1) 1s →→ 2p, 2p 2p, 2p →→ 3d3d

2) 1s 2) 1s →→ e.g. 2pe.g. 2pxx for for E E of of hhννinin parallel a axisparallel a axis

XESXES

1) 1s core hole 1) 1s core hole →→ filled from electrons from 2p (3p)filled from electrons from 2p (3p)

2) 2) analyseanalyse E E of of hhννoutout →→ e.g. 2pe.g. 2pxx electrons onlyelectrons only

dipole selction rule

Can be bulk sensitive, can cope well with insulators Can be bulk sensitive, can cope well with insulators ….life sciences….life sciences

13


PolarisationPolarisation--dependent XES: dependent XES: glycineglycine on Cu(110)on Cu(110)A. NilssonA. Nilsson(Uppsala & ALS)(Uppsala & ALS)


PolarisationPolarisation--dependent XAS: Srdependent XAS: Sr22CuOCuO33

O1s

O2p/Cu3d

formally Cu 3dformally Cu 3d99 + O 2p+ O 2p66

covalence (Cu3d/O2p covalence (Cu3d/O2p hybridisationhybridisation) leads to unoccupied O2p states: ) leads to unoccupied O2p states: 'intrinsic' hole states'intrinsic' hole states

Expect:Expect:

O(1):O(2) = 2O(1):O(2) = 2

XAS says = 1.8XAS says = 1.8

VVpdpd pushes pushes holes to holes to

peripheryperiphery



EXAFS: EXAFS: in XAS also scan hν far above the core threshold:

EExtended xtended XX--ray ray AAbsorption bsorption FFine ine SStructuretructure

Outgoing photoelectron = free electronOutgoing photoelectron = free electron

backback--scattering from surrounding atoms scattering from surrounding atoms →→ interferenceinterference


EXAFSEXAFS

Interference: outgoing and reflected waves Interference: outgoing and reflected waves →→ EXAFS wiggles EXAFS wiggles in the signal from the corein the signal from the core--ionisedionised sitesite

Depends on:Depends on:

wavelength of free electron statewavelength of free electron state KEKEpathlengthpathlength to and from surrounding atomsto and from surrounding atoms

EXAFS sensitive to local structureEXAFS sensitive to local structure::

sitesite--selectiveselective

long range order not necessary !long range order not necessary !


EXAFSEXAFS

O:K edge O:K edge (O1s)(O1s)

GeOGeO22 in:in:

glassyglassy

hexagonalhexagonal

tetragonal tetragonal

structuresstructures

Result:Result:local colocal co--ordination ordination like hexagonal like hexagonal

530 eV in absolute E scale


final states can be important in final states can be important in core level spectroscopiescore level spectroscopies

14



Watch out for the core hole !Watch out for the core hole !

IntraIntra--atomic interactions between core hole and other atomic interactions between core hole and other levels can mean that all DOSlevels can mean that all DOS--related info is lostrelated info is lost

e.g. atomic e.g. atomic multipletsmultiplets in TMin TM--LL2,32,3 XASXAS

If adequately dealt with theoretically, these effects can If adequately dealt with theoretically, these effects can be used elegantly be used elegantly →→

e.g. e.g. info on info on valencyvalency and and covalencycovalency ininTM and RE systemsTM and RE systems

Tm is Tm is purelypurelydivalentdivalent

4f4f1313

initial stateinitial state

air stableair stablePESPES Tm4dTm4d→→4f excitations4f excitations

Phys. Rev. Phys. Rev. LettLett., ., 7979, 3026 (1997), 3026 (1997)

Tm@CTm@C8282

Using final state Using final state multipletsmultiplets to determine to determine valenciesvalencies



scanning probe methodsscanning probe methodsnow……now……

….. finish off spectroscopic ….. finish off spectroscopic methods with STM/STSmethods with STM/STS

Pic: Crommie, Lutz, Eigler, IBM

Scanning probe microscopyScanning probe microscopy

(i) (i) thought up in 1980's thought up in 1980's ('86 Nobel prize ('86 Nobel prize BinnigBinnig & Rohrer, IBM)& Rohrer, IBM)(ii) (ii) simplesimple(iii)(iii) amazingly flexibleamazingly flexible

plus (bonus): plus (bonus): …..produces sexy, …..produces sexy, colourcolour imagesimages

Scanning tunneling microscopy (STM)

Scanning tunneling spectroscopy (STS)

Atomic force microscopy (AFM)

Magnetic force microscopy (MFM)

…your name….microscopy (XYM)


Basic principleBasic principle

tiptip

sample surfacesample surface

electronic tunneling from electronic tunneling from 'atomically' sharp tip'atomically' sharp tip

local forces tiplocal forces tip⇔⇔surface surface bend a flexible cantileverbend a flexible cantilever

oror

STM / STSSTM / STS AFMAFM laser


15

Scanning tunneling microscopy & spectroscopyScanning tunneling microscopy & spectroscopy

overlap of overlap of wavefunctionswavefunctions: : tip tip ↔↔ samplesample

picspics: Uni. Kiel: Uni. Kiel



picpic: Uni. Kiel: Uni. Kiel

Quantum mechanical tunneling current:Quantum mechanical tunneling current:

κκ -- barrier dep. barrier dep. constantconstant

dd -- distancedistance

For a metal, For a metal, κκ is ca. 1 Åis ca. 1 Å--11

move tip away by 1 Å….move tip away by 1 Å….

...current decreases by ca. 10x...current decreases by ca. 10x



picpic: Uni. Kiel: Uni. Kiel

Q: which electronic states are involved ?Q: which electronic states are involved ?

Q: which direction do the electrons tunnel ?Q: which direction do the electrons tunnel ?

A: those of A: those of bothboth tip and sample surfacetip and sample surface

--++

++

--

A: depends on the biasA: depends on the bias

unoccupied occupied statesunoccupied occupied states



Feedback loop: keep Feedback loop: keep II tt

constant while moving constant while moving tip in x and ytip in x and y

topologytopology

Feedback off: constant Feedback off: constant height and measure height and measure II tt

vs. vs. VV biasbias

spectroscopyspectroscopy

STMSTM

STSSTS


STM as tool for atomic sculpture…..STM as tool for atomic sculpture…..

The Start:The Start:

Xe atoms on a gold surface:

1) shove into place using the STM tip

2) image your art using the same tip

EiglerEigler et al. , IBM et al. , IBM AlmadenAlmaden

EiglerEigler & Schweitzer& SchweitzerNature Nature 344344, 524 (1990) , 524 (1990)


Quantum corralsQuantum corrals

Remember:Remember:even in 'topology' mode, STM

measures electronic states, notatomic positions

CrommieCrommie, Lutz, , Lutz, EiglerEigler, IBM , IBM AlmadenAlmaden

First build up the fenceFirst build up the fence

….. here Fe on Cu[111]….. here Fe on Cu[111]

Then see what's inside the corral…Then see what's inside the corral…

surface state = 2D electron gas

Science 262, 218 (1993)

Physics Today 46 17 (1993)


16

Atomic force microscopyAtomic force microscopy

A tool for nanotechnologyA tool for nanotechnology

Single wall carbon Single wall carbon nantubenantube with a kink with a kink →→SSingle ingle EElectron lectron TTransistorransistor

nownow

future….future….

Dekker group, Delft


MFM exampleMFM example

magnetic tip magnetic tip →→ magnetic magnetic constrastconstrast

ferromagnetic domainsferromagnetic domains

after 1 Tesla

amorphous-GdxFe1-x films

ferrimagnetic

Peters & Peters & GoedkoopGoedkoop

CMP-Group, WZI



That's all, folks......That's all, folks......

Questions on Spectroscopic methodsQuestions on Spectroscopic methods

1.1. What do we really What do we really measure measure experimentally in a PES experiment ?experimentally in a PES experiment ?

2.2. At what kinetic energy would the midpoint of a Au Fermi edge appAt what kinetic energy would the midpoint of a Au Fermi edge appear in ear in PES with PES with hhνν=38.0 =38.0 eVeV ??

3.3. Where does the surface sensitivity of PES come from ?Where does the surface sensitivity of PES come from ?

4.4. What factors contribute to the width of a feature in a PES experWhat factors contribute to the width of a feature in a PES experiment ?iment ?

5.5. How can we try and see which peaks in a PES spectrum come from wHow can we try and see which peaks in a PES spectrum come from which hich element/orbital ?element/orbital ?

6.6. What do we measure experimentally in an IPES experiment ?What do we measure experimentally in an IPES experiment ?

7.7. What is happening (microscopically) in an XAS experiment ? How cWhat is happening (microscopically) in an XAS experiment ? How could we ould we monitor this process ?monitor this process ?

8.8. To reproduce the dotted data of Cox's Fig 2.6 with XAS, which seTo reproduce the dotted data of Cox's Fig 2.6 with XAS, which set of core t of core level excitations should we measure ? Would this work ?level excitations should we measure ? Would this work ?

9.9. What do we measure experimentally in an XES experiment ? How areWhat do we measure experimentally in an XES experiment ? How are XES XES and PES related ? How are they different ?and PES related ? How are they different ?

10.10. How does EXAFS work ? Why not simply do diffraction ?How does EXAFS work ? Why not simply do diffraction ?


Stuff to do till coming Monday:Stuff to do till coming Monday:

i) prepare yourself to be able to i) prepare yourself to be able to present answers to the questions present answers to the questions about Ch. 2 at the blackboard at the about Ch. 2 at the blackboard at the start of Monday's lecture start of Monday's lecture

ii) please read chapter 3 before ii) please read chapter 3 before Monday !!Monday !!

lecture 1: introduction metals, insulators and ...€¦ · metals, insulators and semiconductors...

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