Surface and Interface SciencePhysics 627; Chemistry 542

Lectures 14March 11, 2013

Experimental Studies of Electronic Properties:Photoemission

Angle Resolved PhotoemissionInverse Photoemission

Some photon mediated excitations in solids

Why use electrons to probe surfaces??

Primary emission is from the first few atomic layers

G = n2/a

Photoelectron Spectroscopy

VB

CLB

CLS

h

h2 > h

EF

EV

KE

Intensity

KE

Intensity

Valence BandPhotoemission

Core levelPhotoemission

Auger ElectronEmission

Photoemission from SolidsPhotoelectric Effect• Excite solid with monochromatic light • Measure KE- and angular-distribution of emitted electrons

[can be done as a function of excitation energy (hv)]

ENERGETICS: hv

EN EN-1

EK

Einit = hv + EN Efin = EN-1 + EK

Efin = Einit

EN-1 + EK = hv + EN

EK = hv – (EN-1 + EN)

EB = hv – EK

EB

Photoemission from SolidsCAUTION!!! Ionization Energy = Orbital Energy

• KOOPMANS’ THEOREM (result from Hartree-Fock Theory)

(EN-1[frozen] – EN)HF = i HF

(frozen does not include relaxation around hole)

• Consider correlations (absent in HF theory):Define correlation energy as follows:

where

and = relaxation energy =

So:

That is: = (Best HF) – (experiment)

iC

iRi

iB EEE (exp) i

NCi

NCiC EEE 1,,

HFNiNi EE 1i

RE

(exp)11,,iBHFN

iN

iNCNC

iC EEEEEE

iCE

Angle Integrated PhotoemissionEnergy Distribution Curve

5d36s2 2s22p2

23 eV

25 eV

42 eV

35 eV

Ta C

VB

4f7/24f5/2

4s

4p

Angle Integrated PhotoemissionEnergy Distribution Curve

Some Essentials of the TheoryHamiltonian for electrons in a solid:

)(2

rVmppHo

int

2

)(),(2

),( HHrVtrem

trApH oce

),(22

2int 2

2 trAppAAH mce

mce

If we: • Choose gauge where = 0

• Note that

• Keep only terms linear in ignore

Then:

This is modified when time varying EM Field is present:

Where:

AiAppA

A

pAH mce

int

Vector potential

Electric potential

A

pAAiAp

A

Some Essentials of the Theory

Transition rate for photoexcitation given by Fermi’s Golden Rule

)(2 2

ifimce

f EEpA

In UV, >> ao so A ~ spatially uniform over unit cell

)(2 2

ififmce EEpA

“Dipole Approximation”

• Consider as Bloch State in solid

• UV photon has very small momentum (compared to e-)

“k-conserving” optical transition

“vertical” transition in reduced zone scheme.

Direct Transition

k|| conservedupon emission from surface.

sin22||

kmEk

sin51.0|| kEk

k|| in Ang-1

Ek in eV

k

kdEkEkEkEpAEN fiffi

if32

))(())()((),(

kdEkEkEkEMEN fiffi

fi32

))(())()((),(

)(kMM fifi

mkkEkE ff 2

)()(22

)(),(,

2 EDMEN

ifif

)(),( iEDEN

From this we can calculate the number of electrons atEnergy E, given excitation energy

Or equivalently:

Now, some simplifying assumptions:

(Free electron-like final states) :

Neglecting energy dependence of Mfi

Photoemission spectrum proportional to Density of States

2(m - m’)ak(E) = 2(n – n’)

Graphene Graphene + H

Nature Materials 9, 315 (2010)

Topological Insulator: Bi2Se3

Nature 260, 1101 (2009)

Inverse Photoemission

Unoccupied Surface States and

Image Potential States

Energy alignment at Organic/oxide interfaces

Rangan et al., J. Phys. Chem. 114, 1139 (2010)