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)