first principles studies of the electronic structure of organic

First Principles Studies of the Electronic Structure of Organic Semiconductors and Interfaces

Sahar Sharifzadeh

Molecular Foundry, Lawrence Berkeley National Lab

2010 User Meeting

Jeff Neaton

Leeor Kronik (Weizmann)

Ariel Biller (Weizmann)

MF theory group

Computational resources:

National Energy Research Scientific Computing Center (NERSC) Scientific cluster support (SCS) at LBL MF IT division

Financial support DOE NanoHub NSF BASF ISF

Eric Isaacs

Biwu Ma

Electronic Structure and Device Performance

B. Ma, et al., Proc. SPIE , (2009);

C.E. Mauldin, et al., ACS Appl. Mater. Interfaces, 4, 2627(2010).

Donor Layer

PEDOT:PSS

Ag

ITO Glass

C60BCP

∆∆∆∆

HOMO

HOMO

LUMO

LUMO

Donor C60

Computational Methods

Kohn-Sham DFT within standard approximations

Shortcomings for the study of organics

Poor description of highly localized electrons

No VdW interactions Ground state theory -- No electron-hole interactions

Excited states

Ionization potential and electron affinity of molecules obtained as

total energy differences within DFT (∆SCF)

Many-body perturbation theory

Geometry optimization with GGA-PBE

Lattice vectors of crystals kept at experimental value

Many-body Perturbation Theory

Addition/removal energies via the GW approximation

Excitation energies obtained as first order correction to DFT

ε

V==Σ WGW,knVknknEknEE DFT

xc

GWA

n

DFT

n

GWA

n

vvvv−Σ+= )(

kkk

Hybertsen and Louie, Phys. Rev. 34, 5390 (1986).



S.G. Louie, in Topics in

Computational Materials Science, (World Scientific, Singapore, 1997)


Rohlfing and Louie, PRL 81 2312 (1998).

Optical excitation energies via the solution of the BSE

Solution for two-particle correlation function:

Electron-hole interactions explicitly accounted for

can get exciton binding energy

(Eck− Evk

)Avck

S+ vck

′ v ′ c ′ k

∑ Keh

′ v ′ c ′ k A′ v ′ c ′ k

S=Ω

SAvck

S


Excitation energies obtained as first order correction to DFT

ε

V==Σ WGW,knVknknEknEE DFT

xc

GWA

n

DFT

n

GWA

n

vvvv−Σ+= )(

kkk

)( BSE

gap

GW

gap EE −=∆

Outline

Electronic Level alignment at donor-acceptor interfaces

Excited states in bulk organic crystals

S.S., A. Biller, L. Kronik, J.B. Neaton

E.B. Isaacs, S.S., B. Ma, J.B. Neaton

Practical Applications

HORIBA Scientific

Thin-film transistors

Shimada et al., Jap. J. App. Phys. 47, 184 (2008)

Spintronics

Pentacene PTCDA

Photovoltaics

Derouiche and Djara, Solar Energy Materials & Solar Cells 91, 1163 (2007)

Existing ExperimentsPentacene PTCDA

Hill, et al., Chem. Phys. Lett. 327, 181 (2000).,Amy, et al., Organic electronics 6, 85 (2005).

Pentacene on Au

Spectroscopy

Park, et al. APL 80, 2872 (2002), Bulović, et al., Chem. Phys. 210, 1 (1996)

UPS/IPES

Optical

Absorption

Previous Theoretical StudiesPentacene PTCDA

Tiago,et al., PRB 67, 115212 (2003)]

Pentacene crystal

Dori,et al., PRB 73, 195208 (2006)

PTCDA molecule

Hummer et al., Modern Physics Letters B 20, 261 (2006)]

Pentacene crystal

GW Bandstructure GW DOS Absorption Spectra

Prototypical Organic Crystals

Pentacene (C22H14)

Triclinic, space group

2 molecules/unit cell

1P

PTCDA (C24H8O6)

Monoclinic, P2/m space group

2 molecules/unit cell

C

H

O

HOMO/LUMO Energies of Molecules and GW

Pentacene

HOMO

LUMO

Evac = 0

DFT-PBE GW ∆SCF expt.

HOMO

LUMO

HOMO/LUMO Energies of Molecules and GW

PTCDA

DFT GW ∆SCF expt.

Evac = 0

HOMO

LUMOLUMO

HOMO

Calculated gap agrees well with reported results: Dori,et al., PRB 73, 195208 (2006)

Agrees well with previous studies: Tiago,et al., PRB 67, 115212 (2003)]

Energ

y (e

V)

Pentacene Crystal Band-structure and

Density of States

2.2 eV2.4 eV

GW

-Corre

cte

d D

ensity

of S

tate

s

0.7

0.4

Along k

Γ X Y Γ Z E Z

HOMO-LUMO Gaps and Polarization

)1

(2

~2

ε

ε −

R

qP

PEEmolecule

gap

Crystal

gap *2−=Molecule represented by

a sphere in dielectric medium

3/1

cellunit

4

3*

2

V

=

πR

4.7 eV 2.7 eV

Isolated molecule Bulk crystal

HOMO

LUMO

HOMO

LUMO

4.5 eV 2.2 eV

HOMO

LUMO

Isolated molecule Bulk crystal

HOMO

LUMO

(2.1) (2.3)+P

-P

Comparison with Photoemission

De

nsity o

f sta

tes Broadened GW-corrected DOS

Uncertainties in interpreting photoemission data

• For PTCDA, definition of gap varies from 2.5 - 4.0 eV•Correction to gap for surface v. bulk polarization:0.6 eV•Controversy on whether the edge or peak value of orbitals should be taken • Correction to gap for vibrational effects: 0.2 eV

Energy (eV)

2.88

4.0

UPS IPESHill, et al., Chem. Phys. Lett. 327, 181 (2000).

Zahn, et al., Chem. Phys. 325, 99 (2006).

Krause, et al. New J. Phys. 10, 085001 (2008).

The Optical Gap and Delocalized Nature of the

Exciton

Lowest-energy excitation is π π*

Optical gap (eV) Molecule Crystal

Pentacene

GW/BSE 2.2 1.7*

Expt. 2.3 1.8

PTCDA

GW/BSE 2.7 2.2

Expt. 2.6 2.2

GW/BSE within 0.1 eV of experiment!

*Agrees well with previous studies: Tiago,et al., PRB 67, 115212 (2003)]

X

|Ψe|2

Pentacene Crystal

Previous theoretical predictions ∆∆∆∆ = 0.1- 0.6 eV for pentacene crystal

Nayak and Periasamy, Organic electronics 10, 1396 (2009); M.L. Tiago,et al., PRB 67, 115212 (2003);K. Hummer et al., Modern Physics Letters B 20, 261 (2006)

∆∆∆∆ = 0.6 eV for PTCDA crystalNayak and Periasamy, Organic electronics 10, 1396 (2009)

Experimental estimates

∆∆∆∆ = 0.4-1.6 eV for pentacene crystalAmy, et al., Organic electronics 6, 85 (2005)

∆∆∆∆ = 0.3-1.8 eV for PTCDA crystalHill, et al., Chem. Phys. Lett. 327, 181 (2000); Zahn, et al., Chem. Phys. 325, 99 (2006);

Krause, et al. New J. Phys. 10, 085001 (2008)

The Exciton Binding Energy

PTCDA:

• Molecule: 2.0 eV

• Crystal: 0.5 eV

Pentacene:

• Molecule: 2.3 eV

• Crystal: 0.5 eV ~ 1/ε * 2.3 eV ~ 1/ε * 2.0 eV

Exciton binding energy (∆) = Eopt – EHOMO-LUMO

Conclusions I

GW/BSE accurate in describing excited states in organics

Electrostatic model for addition/removal energies is reasonably accurate for describing bulk polarization

Exciton binding energy

Predicted to be ~0.5 eV for both pentacene and PTCDA

~1/ε * exciton binding energy of the molecule

Simple electrostatics can be applied to extrapolate energetics of other solid-state organic systems from single molecule calculations

Can use ∆SCF to get HOMO/LUMO gaps of molecules

4.7 2.7

Can We Explain Variations in VOC?

Voc ~ ECT?

B. Ma, et al., Proc. SPIE 21, 1413 (2009);

C.E. Mauldin, et al., ACS Appl. Mater.

Interfaces 4, 2627(2010).4Ta-SubPc

4Tp-SubPc

2Ta-SubPc

2Tp-SubPc

SubPc-A

The Charge Transfer Energy and Voc

crystal

Acceptor

erface

Donor

erfaceE ∆−−= intintCT EAIP

HOMO

HOMO

LUMO

LUMO

Donor Acceptor

ECT

A Simple Estimate of the Charge Transfer Energy

Non-linear relationship IP-EA one order of magnitude larger than VOC

HOMO

LUMO

Acceptor

HOMO

LUMO

Donor

~Voc?

Incorporation of Crystal Effects with Electrostatics

?EAIP~VOC

Acceptor

crystal

Donor

crystal −

PIPIP moleculecrystal −= PEAEA moleculecrystal −=

The Exciton Binding Energy is Morphology-Dependant

rcrystal

ε

1~∆

crystal

Acceptor

crystal

Donor

crystalCTE ∆−−= EAIP~VOC


rcrystal

ε

1~∆

crystal

Acceptor

crystal

Donor



crystal

Acceptor

crystal

Donor


rcrystal

ε

1~∆

r ~ 6.9 Å

∆ ~ 0.52 eV

4~

LUMO and HOMObetween charge ofCenter ~

ε

r

Correlation Between VOC and ECT


crystal

Acceptor

crystal

Donor


rcrystal

ε

1~∆

r ~ 12.2Å

∆ ~ 0.27 eV

r ~ 13.3 Å

∆ ~ 0.30 eVr ~ 6.9 Å

∆ ~ 0.52 eV

4~

LUMO and HOMObetween charge ofCenter ~

ε

r

pentacene/C60 interfaceYuanping Yi, et al., JACS, 131, 15777 (2009).

Excellent Correlation Between VOC and ECT

Excellent correlation between ECT and Voc Need model for interface morphology

Conclusions II Studied the interface between C60 and a variety of novel donor materials

for OPV

Calculated charge-transfer excitation energy correlates well with measured open-circuit voltage once morphological considerations are incorporated

We predict that crystalline systems have a smaller Voc than amorphous ones due to larger exciton binding energy

Future work Beyond the Mulliken limit description: neutral excitation energies with TDDFT

Better understanding of interface morphology either experimentally or through theoretical models

HOMO

HOMO

LUMO

LUMO

first principles studies of the electronic structure of organic

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