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Theoretical Spectroscopy
Patrick Rinke
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin - Germany
Materials Theory Lecture
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 1
Excited States in (Material) Science – Are Ubiquitous
Theoretical SpectroscopyExperiment/Spectroscopy
appropriate?
accurate?
Material Properties + Applications
appropriate?
accurate?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 2
Excited States in (Material) Science – Are Ubiquitous
Theoretical SpectroscopyExperiment/Spectroscopy
appropriate?
accurate?
Material Properties + Applications
appropriate?
accurate?
photoemission DFT+G W0 0
from
first
principles
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 2
Band structures: photo-electron spectroscopy
- -
-
-
+
Photoemission
hn
GW
- -
-
Inverse Photoemission
-
-
hn
-
GW
- -
-+
Absorption
-
hn
BSETDDFT
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 3
Experimental: angle-resolved photoemission spectroscopy
photoemission: photon in – electron out
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 4
Experimental: angle-resolved photoemission spectroscopy
ARPES
=+1qo
Binding Energy (eV)8 6 4 2 0
Masaki Kobayashi, PhD dissertation
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 5
Experimental: angle-resolved photoemission spectroscopy
ARPES
=+1qo
Binding Energy (eV)8 6 4 2 0
Masaki Kobayashi, PhD dissertation
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 5
ARPES vs GW : the quasiparticle concept
Quasiparticle:
single-particle like excitation
A ( )k
e spectralfunction
e
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 6
ARPES vs GW : the quasiparticle concept
Quasiparticle:
single-particle like excitation
Ak(ǫ) = ImGk(ǫ) ≈Zk
ǫ− (ǫk + iΓk)
ǫk : excitation energyΓk : lifetimeZk : renormalisation
A ( )k
e quasiparticle-peak
ek
qp
Gk
e
The aim is to calculate the Green’s function G!
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 6
Green’s function and screening
-
-
-
-
-
---
--
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 7
Green’s function and screening
-
-
-
-
-
-
--- -
-
-
--
+
ejected
system polarizes
tt-
-- -
- -
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 7
Green’s function and screening
-
-
-
-
-
-
---
-
-
-
-
-+- -
-
-
--
+
ejected
system polarizes
tt tt
polarization is
time-dependent
hole is screened dynamically
-
--
--
- -
- -
W (r, r′, t) =
∫
dr′′ε−1(r, r′′, t)
|r′′ − r′|
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 7
Green’s function and screening
-
-
-
-
-
-
---
-
-
-
-
-+- -
-
-
--
+
ejected
system polarizes
tt tt
polarization is
time-dependent
hole is screened dynamically
-
--
--
- -
- -
quasiparticle
W (r, r′, t) =
∫
dr′′ε−1(r, r′′, t)
|r′′ − r′|
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 7
GW Approximation - Screened Electrons
-
-
-
-
-
-+
-
--
G: propagator
W
GS=GW :
W: screened
Coulomb
Self-Energy
ΣGW (r, r′, t) = iG(r, r′, t)W (r, r′, t)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 8
G0W0 Approximation in Practise
1 start from Kohn-Sham calculation for ǫKSs and φKS
s (r)
2 KS Green’s function:
G0(r, r′; ǫ) = lim
η→0+
∑
s
φKSs (r)φKS∗
s (r′)
ǫ− (ǫKSs + iη sgn(Ef − ǫKS
s ))
3 GW : χ0 = iG0G0 → W0 = v/(1− χ0v) → Σ0 = iG0W0
4 G0W0: ǫqps = ǫKSs + 〈s| Σ(ǫqps ) |s〉 − 〈s|vxc|s〉
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 9
GW Approximation - Screened Electrons
-
-
-
-
-
-+
-
--
G: propagator
W
GS=GW :
W: screened
Coulomb
Self-Energy: Σ = Σx + Σc
Σx = iGv:◮ exact (Hartree-Fock) exchange
Σc = iG(W − v):◮ correlation (screening due to other electrons)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 10
On the importance of screening – Silicon
ǫqpnk = ǫLDAnk + 〈φnk|Σx +Σc(ǫ
qpnk)− vxc|φnk〉
exp: 1.17 eV
Hartree-Fock (exchange-only) gap much too large
Screening is very important in solids!
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 11
ARPES – GW: wurtzite ZnO
H L A G K M G
Ener
gy r
elat
ive
to(e
V)
EF
0
-2
-4
-6
ZnO G W0 0
@OEPx(cLDA)
Yan, Rinke, Winkelnkemper, Qteish, Bimberg, Scheffler, Van de Walle,
Semicond. Sci. Technol. 26, 014037 (2011)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 12
G0W0 Band Gaps
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Experimental Band Gap [eV]
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
The
oret
ical
Ban
d G
ap [
eV]
LDAOEPx(cLDA)OEPx(cLDA) + G
0W
0
CdS
zb-GaNZnO
ZnS
CdSe
ZnSe
InNGe
wz-GaN
Rinke et al. New J. Phys. 7, 126 (2005), phys. stat. sol. (b) 245, 929 (2008)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 13
Nitrides (Al,In,Ga)N – Areas of (potential) Application
LEDs and Laser Diodes
High Frequency, High Power(e.g. HEMT)
Photovoltaics
Water Splitting
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 14
Group-III nitrides
(potential) applications
solid state lighting
photovoltaics
RGB projectors
until ∼2006
debate over gap of InN
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 15
Band gap of InN
1016
1017
1018
1019
1020
1021
carrier concentration (cm-3
)
0.40.60.81.01.21.41.61.82.02.22.4
Ega
p+E
F (eV
)
Wu et alHaddad et alIoffe InstituteBriot et alTansley and FoleyRF sputteringDC sputteringButcher et alSugita et al
Figure adapted from Butcher and TansleySuperlattices Microstruct. 38, 1 (2005)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 16
How can first principles calculations contribute?
Proposed reasons for band gap variation e.g. Butcher and Tansley Superlattices Microstruct. 38 (2005)
high carrier concentration ⇒ Moss-Burnstein effect
impurities, point defects, trapping centers
non-stoichiometry
formation of oxides and oxynitrides
metal inclusions, formation of metal clusters
First principles approach:
Density-functional theory (DFT) (ground state)
◮ atomistic control◮ stoichiometric, defect and impurity free structures
many-body perturbation theory in the GW approximation (excited state)
◮ method of choice for calculation of band gaps in solids
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 17
InN – GW band structure and Moss-Burstein effect
M/8|k
[110]|
0.0
0.5
1.0
1.5E
nerg
y [e
V]
Γ A/4|k
[001]|
w-InN
1020
1019
1018
1017
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 18
InN – GW and Moss-Burstein effect
1016
1017
1018
1019
1020
1021
carrier concentration (cm-3
)
0.60.81.01.21.41.61.82.02.2
Eg(n
) (e
V)
parabolic (meff
=0.07 m0)
G0W
0@OEPx(cLDA)
P. Rinke et al. APL 89, 161919 (2006)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 19
Group-III nitrides
(potential) applications
solid state lighting
photovoltaics
RGB projectors
now
debate over gap of InNsettled
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 20
Future Technologies – Organic Electronics
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 21
Hybrid inorganic/organic systems (HIOS)
ZnO/PTCDA organic electronics
organic field effect transistors (OFET)
organic light emitting diodes (OLED)
organic photovoltaic cells (OPVC)
. . .
Hybrid inorganic/organic interfacesare omnipresent!
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 22
Hybrid inorganic/organic systems (HIOS)
ZnO/PTCDA
ZnO/p-sexiphenyl(courtesy of S. Blumstengel)
organic electronics
organic field effect transistors (OFET)
organic light emitting diodes (OLED)
organic photovoltaic cells (OPVC)
. . .
Hybrid inorganic/organic interfacesare omnipresent!
hybrid electronics
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 22
Hybrid inorganic/organic systems (HIOS)
ZnO/p-sexiphenyl(courtesy of S. Blumstengel)
Combine the best of two worlds...
inorganic materials:
stable crystal structures
good growth control
high charge carrier mobilities
organic materials:
strong light-matter coupling
large chemical space gives diverserange of properties
... or more!
great potential for:
synergies between different materials
new physics at interface
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 23
Potential for new physics at HIOS
solid organic
HIOS
Potential for new interface morphologies.
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 24
Open questions at HIOS
-
polaronic-
band-like?
What is the nature of charge carriers?
New quasiparticles?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 25
Open questions at HIOS
valence band
conduction band
molecular states
-
HOMO
LUMO
-free carrier
What does the notion of “state” imply?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 26
Open questions at HIOS
valence band
conduction band
molecular states
-
HOMO
LUMO
- polaron
??
-
-
polaron?
free carrier?
+ polaron ??
What does the notion of “state” imply?
How do “states” line up energetically?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 26
Open questions at HIOS
valence band
conduction band
molecular states
-
HOMO
LUMO
- polaron
??
-
-
polaron?
free carrier?
hybrid state?
+ polaron ??
What does the notion of “state” imply?
How do “states” line up energetically?
Do hybrid “states” form?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 26
Molecules on surfaces – a challenge for first principles
The objective is:
to develop an atomistic understanding of (nano)materials
!"#"$%&'()*$$
$$$$$$$$$$$$$+,$$
$$$$$$$$$$$$$$$$-,.$
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 27
Molecules on surfaces – a challenge for first principles
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 27
Molecules on surfaces – a challenge for first principles
State-of-the-art for interfaces: density-functional theory (DFT)
local-density approximation (LDA)
generalized gradient approximation, e.g. PBE functional
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 27
Molecules on surfaces – a challenge for first principles
Beyond state-of-the-art:
advanced density functionals e.g. hybrid functionals or RPA
Green’s function methods e.g. GW
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 27
Molecules on surfaces – a challenge for first principles
!"#$%&'(#'&)*+,#"&-)*(./+)#0-)*(1')2',#3(
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 27
Level alignment at HIOS
conductionband
valenceband
molecularstates
EF
EIB: lectrone i bnjection arrier
HIB: oleh i bnjection arrier
injection limited current:
j ∝ AT 2 exp
(
−charge injection barrier
kBT
)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 28
Molecular levels at a surface
gas phasesurface
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 29
Molecular levels at a surface
gas phasesurface
+
electronaffinity (EA)
ionizationpotential (IP)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 29
Molecular levels at a surface
gas phasesurface
+
EA
IP
-
-
-
-
image effect
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 29
Molecular levels at a surface
gas phasesurface
+
EA
IP
-
-
-
-
image potentials
classical image potential:
metal: −1
4zsemiconductor/insulator: −
ε− 1
4(ε+ 1)
1
zε: dielectric constant
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 29
Molecular levels at a surface
gas phaseadsorbed
+
EA
IP
-
-
-
-
renormalization
+
classical image potential:
metal: −1
4zsemiconductor/insulator: −
ε− 1
4(ε+ 1)
1
zε: dielectric constant
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 29
The screened Coulomb interaction W
Work with screened coulomb interaction:
W (r, r′, t) =
∫
dr′′ε−1(r, r′′, t)
|r′′ − r′|
ε(r, r′′, t): dielectric function
The challenge is to calculate W (r, r′′, t) from first principles!
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 30
The screened Coulomb interaction W
Work with screened coulomb interaction:
W (r, r′, t) =
∫
dr′′ε−1(r, r′′, t)
|r′′ − r′|
ε(r, r′′, t): dielectric function
The challenge is to calculate W (r, r′′, t) from first principles!
we use random-phase approximation (RPA) for W :
= + + + ...
v: bare Coulomb interaction
c0: Kohn-Sham polarizability
W
formally scales with (system size)4
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 30
From screening to quasiparticle energies
-
-
-
-
-
-+
-
--
G: propagator
W
GS=GW :
W: screened
Coulomb
Quasiparticle energies: G0W0 scheme
electron addition and removal energies
correction to DFT eigenvalues ǫDFT
nk :
ǫqpnk = ǫDFT
nk +ΣG0W0
nk (ǫqpnk)− vxcnk
includes image effect
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 31
GW for surfaces – CO on NaCl
Na ClOC
HOMO-LUMO gap of CO:
gap/eV LDA G0W0 Exp.@LDA
free CO : 6.9 15.1 15.8∗
CO@NaCl: 7.4 13.1∗Constants of Diatomic Molecules (1979),
Phys. Rev. Lett. 22, 1034 (1969)
surface polarization significant here
C. Freysoldt, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 103, 056803 (2009)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 32
GW for surfaces – CO on Ultrathin NaCl on Ge
CO
NaCl
Ge
Supported ultrathin films are novel nano-systems withunexpected features (PRL 99, 086101 (2007))
Additional electrons/holes on CO see two interfaces
Will the CO gap depend on NaCl thickness?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 33
GW for surfaces – CO on Ultrathin NaCl on Ge
12.512.612.712.8
G0W
0@LDA
2 3 4NaCl layers
7.47.57.67.77.8
DFT-LDA
5σ-2
π∗ spl
ittin
g (e
V)
3.03.13.23.33.4
2π∗
2 3 4NaCl layers
-2.1-2.0-1.9-1.8-1.7
5σ
G0W
0 cor
rect
ions
(eV
)Polarization at NaCl/Ge interface gives layer-dependent CO gap
⇒ molecular levels can be tuned by polarization engineering:◮ interesting for molecular electronics and quantum transport
C. Freysoldt, P. Rinke, and M. Scheffler, PRL 103, 056803 (2009)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 34
Molecules on surfaces – a challenge for first principles
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 35
Electron gas at TTF/TCNQ interface
TTF and TCNQ crystals have
large band gap
but 2 dimensional electron gasobserved at interface
Nat. Mat. 7, 574 (2008)
What is the origin?
TTF
TCNQ
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 36
Electron gas at TTF/TCNQ interface
-3 -2 -1 0 1 2 3E-E
F [eV]
0
20
40
DO
S
DFT-PBE density of states
DFT-PBE:
predicts metallic interface
0.12 e/molecule charge transferto TCNQ
in seeming agreement withexperiment
TTF
TCNQ
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 36
TTF/TCNQ dimer at infinite separation
TTF TCNQ
EAIP
exp PBE expPBE
4.0
6.7
9.5
7.0
5.6
2.81.0
!
IP(TTF) > EA(TCNQ)
erroneous charge transfer
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 37
Ionisation Potential, Electron Affinity and (Band) Gaps
Could use total energy method to compute
ǫs = E(N ± 1, s)− E(N)
Ionisation potential: minimal energy to remove an electron
I = E(N − 1)− E(N)
Electron affinity: minimal energy to add an electron
A = E(N)− E(N + 1)
(Band) gap: Egap = I −A
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 38
∆SCF versus eigenvalues for finite systems
∞≈≈
data courtesy of Max Pinheiro
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 39
Ionisation Potential, Electron Affinity and Band Gap
so what about ∆SCF for excitations?
∆SCF: ǫs = EDFT(N)− EDFT(N ± 1, s)
reasonably good for I and A of small finite systems
but:
most functionals suffer from delocalization or self-interaction error(Science 321, 792 (2008))
⇒ the more delocalized the state, the larger the error
only truely justified for differences of ground states◮ ionisation potential, electron affinity◮ excited states that are ground states of particular symmetry
difficult to find excited state wavefunction (density)
excited state density is not unique
separate calculation for every excitation needed◮ not practical for large systems or solids
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 40
TTF/TCNQ dimer at infinite separation
culprit: self-interaction error in PBE
add Hartree-Fock (HF) exchange to removeself-interaction
⇒ PBE0-like hybrid functional:
Exc(α) = α(EHFx − EPBE
x ) + EPBEc
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 41
TTF/TCNQ dimer at infinite separation
0 0.2 0.4 0.6 0.8 1 α
-2
0
2
4
∆[e
V]
Experiment
PBE0(α)
artificial charge transfer
PBE0-like hybrid functional:
Exc(α) = α(EHFx − EPBE
x ) + EPBEc
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 41
TTF/TCNQ dimer at infinite separation
0 0.2 0.4 0.6 0.8 1 α
-2
0
2
4
∆[e
V]
Experiment
PBE0(α)
artificial charge transfer
How to choose α?
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 41
Performance of G0W0
TTF TCNQ
S
CH
H
NC
EA
IP
expG0W0 exp G0W0
6.7 6.7
9.5 9.7
3.7
-0.7
2.8
C6H4S4
all values in eV
C12H4N4
4.6
Exp.: JACS 112, 3302 (1990), J. Chem. Phys. 60, 1177 (1974),Adv. Mat. 21,1450 (2009),Mol. Cryst. Liquid Cryst. Inc. Nonlin. Opt. 171, 255 (1989)
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 42
TTF/TCNQ dimer – implications for interface
no charge transfer, but small charge rearrangement
2D electron gas not due to charge transfer
HOMO
LUMO
PBE optimal !
electron density difference
optimal-α calculations for interface in progress
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 43
Molecules on surfaces – a challenge for first principles
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Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 44
Molecules on surfaces – a challenge for first principles
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!
!
!
!
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 44
Acknowledgements
GW for surfaces
Christoph Freysoldt
Nitrides
Abdallah QteishMomme WinkelnkemperJorg Neugebauer
GW in FHI-aims
Xinguo Ren
Support and Ideas
Matthias Scheffler
TTF-TCNQ
Viktor AtallaMina Yoon
gwst code
Rex Goby
FHI-aims code
Volker Blumthe whole FHI-aims developer team
Patrick Rinke (FHI) Theoretical Spectroscopy TU Berlin 2012 45