photo-physics rené janssen -...

1

Photo-physics

René Janssen

Photo: Heliatek GENERATION

ORGA|NEXT|GENERATION &

IAP-FS2 & SOLLIANCE

WINTERSCHOOL

Organic Photovoltaics : from materials

to modules

UHasselt – 27-28 January 2015

Some basics of photochemistry

±

±

C C

H

H H

H

A B / C D E F

Ethylene

2 electrons and 2 levels : 6 configurations

2

Six configurations: Four energy levels

JE 2)S( 0

JE 2)S( 2

KJE )S( 1

KJE )T( 1

S2

S1

S0

T1

2K

This is a general result: The singlet excited state is higher in energy than the

corresponding triplet state.

The reason is the exchange energy which lowers the repulsion energy for two

parallel electron spins as compared to antiparallel spins.

A

B

F

C D E

3

Excited states in a molecular picture

S2

S1

S0

T1

S2S1S0 T1

State diagramMolecular orbital diagram

4

Fluorescence and phosphorescence spectra

400 450 500 550 600 650 700 750 800 850

Inte

sity

/nm

441

467

501

541

586

790710

O O

OO

S

S

O O

OO

S

S

Fluorescence

Phosphorescence

S0

S1

T1

2.81 eV

1.75 eV

Dorothee Wasserberg, J. Phys. Chem. B. 2005, 109, 4410-4415

2K = 1.06 eV

5

Two-layer organic p/n solar cell

GlassITO

p-type

n-type

Au

light

+

-

exciton dissociation into

+ and – charge carriers

C. W. Tang, Appl. Phys. Lett. 1985, 48, 183.

absorption

electron

transfer

donor acceptor

6

A-D* D+ A*DA

Electron transfer reactions

A molecule in the excited state has lower oxidation potential and a

higher electron affinity.

Many people call

this hole transfer.

I do not.

7

S0 S0

Donor Acceptor

S1

S1

CT

Electron transferElectron transfer

How can we determine (estimate) ECT?

How important is ECT for solar cells?

State diagram

acceptordonor

HOMO

HOMO

LUMO

LUMO~ECT

Orbital diagram

Dirk Veldman, Adv. Funct. Mater. 2009, 19, 1939

Efficiency in organic solar cells

8

Gibbs free energy for charge separation

sref0

2

ccs0

2

redox1111

84)A()D(

rr

e

R

eEEeGCSS

Weller equation:

change in free energy for charge separation as function of the polarity

of the solvent and the distance between donor and acceptor

Eox(D) oxidation potential of donor determined in solvent with ref

Ered(A) reduction potential of acceptor determined in solvent with ref

Rcc center-to-center distance from donor and acceptor

e electron charge

r + radius of D+ ion

r − radius of A- ion

40 permittivity of vacuum

s relative permittivity of solvent in which electron transfer occurs

ref relative permittivity of solvent used to determine Eox(D) and Ered(A)

separation solvation energy

9

CS Charge separation

CR Charge recombination

Electron transfer processes

What determines the rate of the CS and CR reactions?

10

Rate of electron transfer reactions D*A D+A- :

Marcus theory

According to the Marcus theory of

electron transfer, the rates of electron

transfer depend on:

1. The Gibbs free energy for charge

separation

2. The distance between donor and

acceptor

3. The reorganization energy : The

energy cost incurred by molecular

rearrangements of donor, acceptor,

and medium

0G

RTGet ek /‡

is the transmission coefficient

frequency by which the transition

state is approached

D*A

D+A-

0G

‡G

11Image: Atkins 7th Ed.

12

electron transfer can only occur at q*

is a measure of the probability that

DA D+A- occurs at q*

electron transfer occurs by tunneling

through the barrier V

tunneling is proportional to the square of

where HDA describes the coupling of the

electronic wavefunctions

RTGet ek /‡

DDAADA HH

rDADA eHH

202

r is the edge-to-edge distance of D and A

Electron tunneling

0DAH is for r = 0

Image: Atkins 7th Ed.

13

4

20‡

G

G

The Gibbs energy of activation

s

2cc0

2

s

11111

2

1

4

nRrr

e

Reorganization energy i + s

Internal reorganization energy i

Solvent reorganization energy s

The reorganization energy is

defined as the energy required to

"reorganize" the system structure

from initial to final coordinates,

without making the charge transfer.

0G

‡G

Image: Atkins 7th Ed.

14

RT

G

RTh

Hk DA

et

‡21

32

exp4

2

The Marcus expression for the rate of electron transfer

Activation energy

Rate for electron transfer:

4

20‡

G

G

rHH DADA exp2

02Coupling

What makes a solar cell efficient?

II. Quantum efficiency

Or how many photons are converted into electrons and collected?

III. Energy efficiency

Or what is the final (chemical) potential of the electrons generated?

I. Absorption efficiency

Or how many photons are absorbed?

Shockley-Queisser limit: ~33% efficiency for a single junction cell

15

16

+

−

+

−

ccexdisabs

Quantum efficiency

+−

+−

+− = exction

17

60

0

1)rsteroF(

DAET

R

Rk

),(1

)rsteroF(6

0

0jiET EEf

R

Rk

ij

ijB

ij

ji

EE

EETk

EE

EEf

1

exp),(

K. Feron, Int. J. Mol. Sci. 2012, 13, 17019

Hopping process in which excitons move

from molecule to molecule in a Gaussian

distribution of states

Exciton transport in organic semiconductors

For singlet states

Thermally activated from i → j

18

700 800

cw

-0.08 « -0.07 ns

-0.07 « -0.01

+0.03 « +0.07

+1.55 « +2.65

+0.34 « +1.03

700 800

BMBPPV 8K

sens corr

lexc=622nm

Inte

nsity

Wavelength (nm)

95% 5%

Time-resolved fluorescence at T = 8 K

S. C. J. Meskers, Chem. Phys. 2000, 260, 415

Spectrum exhibits a red shift in time

Relaxation of excitons

0.06 eV

19

Exciton diffusion

The exciton diffusion length is de L defined as 22 rL

where r is the distance between the location of

exciton creation and exciton annihilation

The diffusion constant for Förster energy transfer in 3 dimensions:

0

60

34

3

4

RCD

C is the chromophore density

is a constant between 0.30 and 0.56

0

2

iq

rD qi = 2, 4, or 6, for 1, 2, or 3 dimensional diffusion.General

In 1D 1/qi = 1/2 because a diffusing exciton has a 50%

chance of going in one direction or its opposite.

For 2D and 3D, 1/qi changes to 1/4 and 1/6, respectively,

by analogous reasoning.

20

An organic dye with a small fluorescence Stokes shift and high quantum

yield can easily possess a critical radius R0 ∼ 5 nm for self-transfer.

If the concentration of such a dye could be raised to C ∼ 1 molecule/nm3

the equation predicts that diffusion lengths on the order of 100 nm should

be observable.

30

3/236.6 RCL

Estimate of exciton diffusion length

In practice exciton diffusion length is much less: ~5-10 nm

Combining: 30

32

03

466 R

CDL

K. A. Colby J. Phys. Chem. A 2010, 114, 3471

21

L variation with the dimensionless disorder parameter kBT

Disorder explains the small L

S. Athanasopoulos, Phys. Rev. B. 2009, 80, 195209

Assume

s = 0.060 eV

kBT = 0.026 eV

Then L = 10 nm

22

+-

+

-

+-

active part

of the cell

excitons created here

are lostexcitons created here

are lost

Organic double layer p/n cell is limited by the exciton diffusion length

20 nm

-

light

metal electrode

transparent electrode

glass

+- 100 nm

A. J. Heeger et al., Science 1995, 270, 1789

R. H. Friend et al., Nature 1995, 376, 498

nanoscopic mixing of donor and acceptor to

overcome ~10 nm exciton diffusion length

absorption

electron

transfer

donor acceptor

Bulk-heterojunction solar cells

23

Pump 488 nm

Pump 630 nm

Photoinduced hole and electron transfer

h+

e-

0.5 1.0 1.5 2.0 2.5

1.2

0.8

0.4

0.0

-0.4

-0.8

488 nm

630 nm

-T

/T

Energy (eV)

0.3

0.2

0.1

0.0

-0.1

-0.2

MDMO-PPV

PCBM

P. A. van Hal, Appl. Phys. A. 2004, 79, 41. 24

Photoinduced absorption

Photoinduced

bleaching

25

Neutral

S = 0

P4

P2

P3

P1

Polaron

S = ½

N

P1 and P2 are allowed transitions

P3 and P4 are symmetry forbidden transitions

Formation of radical cation (polaron)

creates two sub gap transitions

E(P1) < E(P2) < E (N)

−e−

Polaron absorption

bg

au

bg

au

bg

au

bg

au

26

-5 0 5 10 15

510 nm

T

/T (

a.u

.)

Time delay (ps)

670 nm

-250 0 250 500 750 1000 1250

510 nm

T

/T (

a.u

.)

Time delay (ps)

670 nm

Pump 510 nm

Pump 670 nm

Sub-picosecond hole and electron transfer in the blend

Probe 1.27 eV = 970 nm

P. A. van Hal, Appl. Phys. A. 2004, 79, 41.

MDMO-PPV

PCBMh+

e-

27

10 100 1000 10000 1000001E-5

1E-4

1E-3

0.01

0.1

t-

Laser power (mW): :

0.13 0.46

1.2 0.50

0.6 0.54

T

/T

Time delay (ns)

Long-lived charges in such blends

MDMO-PPV/PCBM blend (1:4)

T. Offermans, J. Chem. Phys. 2003, 119, 10924

PCBM

MDMO-PPV

Use the external quantum efficiency

of the cell

hν

K. Vandewal, Adv. Funct. Mater. 2008, 18, 2064

Eg defined as the onset of the EQE

28

The charge-transfer (CT) state can be excited directly

e-h+

0 100 200

-0.50

-0.25

0.00

En

erg

y (

eV

)

R e-h

(Å)

Charges may circumvent the

potential barrier by choosing a

path involving low energy sites

E = 0 Ed=0.48 eV

E = 0.01 V/nm Ed= 0.35 eV

Ed

~10 Å

T. Offermans, J. Chem. Phys. 2003, 119, 10924

T. Offermans, Chem. Phys. 2005, 308, 125

+

-

29

Electron and hole are Coulombically bound!

+-

It may:

1. Recombine to the ground state via photoluminescence

2. Dissociate into free charges

3. Recombine to a triplet state

4. Recombine to the ground state via a radiation less process

30

DA

DA*

D+A−

CR : slow

CS : fast

What can happen to this CT state?

600 650 700 750 8000.0

0.5

1.0

x 600x 550

Wavelength / nm

PL

Em

issio

n

PFTBT+

PCBM−

PFTBT

PCBM

CT

D. Veldman. J. Am. Chem. Soc. 2008, 130, 7721

Charge transfer luminescence

31

S0

S1

CT

PFTBT PCBM

hν

PCBM-PFTBT+

PCBM

PFTBT

PCBM wt.% in PFTBT:

20 50 80AFM

TEM

20 50 80

0 20 40 60 80

0

1

2

3

4

5

PCBM wt. %

Estim

ate

d e

ffic

ien

cy (

%)

650 700 750 8000

5

10

15

20

PL

Em

issio

n /

10

5 C

ou

nts

Wavelength / nm

PCBM (wt. %)

5

10

20

35

50

65

80

CT emission

D. Veldman, J. Am. Chem. Soc. 2008, 130, 7721 32

PFTBT

PCBM

Dissociation into free charges

Solar cell efficiency

Larger PCBM domains

33

Increasing PCBM concentration: more “free” charges

Increasing CT emission yield

+-

+-

+-

The presence of nanocrystalline domains with high local carrier mobility of

at least one component in an organic heterojunction may explain the

efficient dissociation of charge transfer states into free charge carriers.

How do charges escape from their attraction?

D. Veldman, J. Am. Chem. Soc. 2008, 130, 7721

Processed without DIO

Jsc= 6.1 mA/cm2

Voc= 0.69 V

FF = 0.41

PCE = 1.7 %

Intimate blend

Processed with DIO

Jsc= 7.6 mA/cm2

Voc= 0.63 V

FF = 0.52

PCE = 2.5 %

Phase separation

400 500 600 700 800 900 1000 11000.0

0.1

0.2

Absorb

ance

Wavelength [nm]

PCPDTBT:PCBM

diiodooctane

no additive

-0.2 0.0 0.2 0.4 0.6

-5.6

-2.8

0.0

2.8

Bias [V]

Curr

ent density [

mA

/cm

2]

D. Di Nuzzo, Adv. Mater. 2010, 22, 4321

Solar cells based on PCPDTBT:PCBM

34

PCPDTBT

PCBM PCPDTBT

S0S0

S1

S1

T1

Free charges

T11.5

0

0.5

1

2

En

erg

y (

eV

)

SCT

TCT

Tn

1.40 eV

0.95 eV

1.18 eV

35

Photophysics of PCPDTBT:PCBM blends

PCBM PCPDTBT


700 800 900 1000 1100 1200 13000

2

4

6

8

10

12

exc

=600 nm

PCPDTBT

PCPDTBT:PCBM (1:1)

PL

in

ten

sity (

co

un

ts)

/ 1

03

Wavelength(nm)

1/20

PL quenched by

charge transfer to PCBM

36

CT

emission

Fluorescence of PCPDTBT:PCBM blends


0.5 1.0 1.5 2.0-2

-1

0

1

2

phase separated

intimate blend

Energy (eV)

-T

/T x

10

4

0.57

T = 80 K

exc = 830 nm

Intimate blend

1 peak at 0.96 eV → triplets

Phase separated blend

2 peaks at 0.88 eV and < 0.3 eV → charges

37

Morphology affects the photophysics

Photoinduced absorption of PCPDTBT:PCBM blends

+-


PCBM PCPDTBT

S0S0

S1

S1

T1

Free charges

T11.5

0

0.5

1

2

En

erg

y (

eV

)

SCT

TCT

Tn

In intimate blends no

long lived charges are found.

The only surviving state is a triplet.

38

Recombination to the PCPDTBT triplet state


e- h+

COLD

e- h+

HOT

e-

h+

To what extend are these charge transfer states really bound?

Does their dissociation require additional energy?

39

The binding energy of the interfacial CT state?

S1

S1

CT1

T1

T1

GS

CS1

S0

1.0

0.0

0.5

1.5

2.0

A D CT D+-A－ CS D+ … A－

Fre

e e

ne

rgy (

eV

)

40Well: there are rather different views on this issue……..

Hot or cold: that is the question!

Pump-push-probe experiments

A. Bakulin, Science, 2012, 335, 1340 41

Pump-push-probe experiments

Charge separation in efficient organic photoconversion systems occurs through

hot-state charge delocalization rather than energy-gradient-driven intermolecular

hopping.

A. Bakulin, Science, 2012, 335, 1340 42

IR photons promote

bound charge pairs to

delocalized band states.

This increases the

photoconductivity

1.5 2.0 2.5 3.0

10-3

10-2

10-1

100

annealed

EQ

E /

EQ

E (

2.3

4e

V)

Photon Energy (eV)

+0.4 V

0.0 V

-2.0 V

P3HT

No effect of photon energy on the field dependence of the EQE.

No influence of excess energy in charge generation.

T. van der Hofstad, Adv. Energy Mater. 2012, 2, 1095 43

PCBM

Glass

ITO

PEDOT:PSS

Active layer

LiF / Al

h+

e-P3HT

PCBM

CT

A

No energy dependence of normalized EQE

The internal quantum efficiency (IQE) is essentially independent of whether or not

D, A or CT states with an energy higher than that of CT1 are excited.

The best materials systems show an IQE higher than 90% without the need for

excess electronic or vibrational energy.

MEH-PPV:PC61BM PBDTTPD:PC61BM

K. Vandewal, Nature Mater. 2014, 13, 63 44

No need for excess energy

R. A. Marcus, J. Phys. Chem. 1989, 93, 3078

K. Vandewal, Phys. Rev B. 2010, 81, 125204

Marcus theory

45

Absorption s(E)

kT

EE

kT

f

EE

s s

4exp

4

1)(

2CT

kT

EE

kT

fEEI fI

f

4exp

4)(

2CTEmission rate If(E)

Absorption and emission spectra from a CT state

46

0.5 1.0 1.5 2.0 2.5

0.0

0.2

0.4

0.6

0.8

1.0

Norm

aliz

ed inte

nsity

Energy (eV)

0.5 1.0 1.5 2.0 2.5

10-4

10-3

10-2

10-1

100

Norm

aliz

ed inte

nsity

Energy (eV)

kT

EE

kT

f

EE

s s

4exp

4

1)(

2CT

kT

EE

kT

fEEI fI

f

4exp

4)(

2CT

Linear plot Semi-logarithmic plot

ECT

ECT

Shape of the absorption and emission spectra from a CT state

ECT = 1.5 eV, =0.25 K, T = 295 K

Absorption Emission

47K. Vandewal, Phys. Rev B. 2010, 81, 125204

Shape of the absorption and emission spectra from a CT state

Experimental curves can be directly fitted to Marcus theory

Relation between EL and CT absorption

Absorption and emission from the CT state are related,

not only spectrally but also in intensity

K.Vandewal, Phys. Rev B. 2010, 81, 125204 48

S0 S0

donor acceptor

S1

S1

CT

How important is ECT for solar cells? It should be related to the Voc !

State diagram

acceptordonor

HOMO

HOMO

LUMO

LUMO

Orbital diagram

D. Veldman, Adv. Funct. Mater. 2009, 19, 1939

Because Voc is related to the effective gap (page 248)

and the free energy is too (page 134).

49

ECT

~ECT

Energy efficiency in organic solar cells

K. Vandewal, Adv. Funct. Mater. 2008, 18, 2064

Note that in this equation Eg is the onset of the CT absorption (see page 254)

50

Evidence for relation of Voc and ECT

V43.0oc q

EV

g

51

ECT

0.1 eV

0.5 eV

ground state

excited state

charged state

photon energy

qVoc

Egap

photon energy

D. Veldman, Adv. Funct. Mater. 2009, 19, 1939

at room temperature

and 1 sun

Minimum energy loss

eV6.0oc qVEg

thermal decay

Jablonski state diagram of an organic solar cell

Here ECT was taken as the

maximum of the CT emission

0

5

10

(Theore

tical) E

ffic

iency

[%

]

2.0 1.5 1.0

Optical band gap energy [eV]

EQE = 0.65

FF = 0.65

So we may hope

for ~11%

0.6

0.7

0.8

D.Veldman, Adv. Funct. Mater. 2009, 19, 1939

R. A. J. Janssen, Adv. Mater. 2013, 25, 1847

Energy loss (eV)

Eg– qVoc

If you are optimistic and take EQE = 0.80 and FF = 0.80, the maximum would be 17%

52

Ultimate efficiency for single junction cells

At T = 0 K, ECT and Voc are the same

K. Vandewal, Phys. Rev B. 2010, 81, 12520453

54

2000 2005 2010 20150

2

4

6

8

10

12

Eff

icie

ncy (

%)

single junction

tandem junction

Efficiencies polymer solar cells

R. A. J. Janssen & J. Nelson, Adv. Mater. 2013, 25, 1847

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