Electrical Properties of Organic Semiconductorsocw.snu.ac.kr/sites/default/files/NOTE/9222.pdf · 2018. 1. 30. · 0/25 Changhee Lee, SNU, Kore 전자물리특강 EE 430.859 2014

Changhee Lee, SNU, Kore0/25

전자물리특강EE 430.859

2014. 1st Semester

2014. 4. 17.

Changhee LeeSchool of Electrical and Computer Engineering

Seoul National Univ. [email protected]

Electrical Properties of Organic Semiconductors



2014. 1st Semester

Electron mobility of Si

Charge Transport in Si and Organic Crystals

Electron mobility of Perylene

370 nm thick perylene crystal

R. W. I. de Boer, M. E. Gershenson, A. F. Morpurgo, and V. Podzorov, phys. stat. sol. (a) 201, 1302 (2004).

Rubrene crystal: The angular dependence of the mobility measured at room temperature.

nTμT o)(

Band-like transport of carriers.Carrier mobility is limited by scatterings with phonons, impurities, etc.



2014. 1st Semester

Polaron hopping

Rate of Charge Transfer

The rate of charge transfer is limited by the reorganiztion of the molecules.

T = temperature; λ = reorganization energy; t = transfer integral

TkAk

BET

4

)t2(exp

as, described becan ,k rate, (hopping)transfer -electron the limit, raturehigh tempe in the theory Marcus calsemiclassi the toAccording

2

ET



2014. 1st Semester

Electron mobility of Si

Carrier mobility

e & h mobility of organic materialsApplied voltage

Band-like conductionDelocalized electron

Lattice vibration(phonon)

Scattered electron

Hopping conduction

Lattice vibration

Localized electron

Hole mobility of MPMP

bis(4-N,N-diethylamino-2-methylphenyl)-4-

methylphenylmethane (thickness~8.7 m)

P. M. Borsenberger, L. Pautmeier and H. Bässler, J. Chem. Phys. 95, 1258 (1991)



2014. 1st Semester

TOFMobility in the bulk

d = 0.5~5 m

FETMobility in a thin layer

d ~ 50 nm

Vd 2

Vd

2

Mobility Measurement Techniques

10 2

)/( 2 Vscm 10 4 10 6 10 8 100 102

Other mobility measurement techniques• Dark injection in the space-charge limited current regime• I-V characteristics of space charge limited current • Transient EL• SHG measurement [T. Manaka, E. Lim, R. Tamura, M. Iwamoto, Nature Photon.1, 581–584 (2007).]……



2014. 1st Semester

d

Transit time Ohmic contact

V R

++++++

787.0pt

Dark injection SCL transient current

M. Abkowitz, J. S. Facci, and M. Stolka, Appl. Phys. Lett. 63, 1892(1993).

PTPB

poly (tetraphenylbenzidine) PTPB

1.0

0.8

0.6

0.4

0.2

0.0

i(t) (

arb.

uni

t)1.00.80.60.40.20.0

Time (ms)

Dark injection SCL transient current787.0pt

787.0pt

TOF-PC

S.C. Tse, S.W. Tsang, and S.K. So, J. Appl. Phys. 100, 063708 (2006).

Transient SCLC



2014. 1st SemesterMobility Measurement Techniques: dark charge injection

Edttr

786.0

In a monopolar and single-layer configuration, the carrier transit time is shorter than in the absence of space-charge effects due to the enhancement of the electric field at the leading edge of the carrier packet.

The transient current overshoots its steady-state value by a factor of 1.21 and starts at 0.44 times the steady-state value.

A. Many and G. Rakavy, Phys. Rev. 126, 1980 (1962) M. Abkowitz, J. S. Facci, J. Rehm, J. Appl. Phys. 1998, 83, 2670.

3

2

89

dVJ roSCLC



2014. 1st Semester

Hol

e In

ject

ion

Effi

cien

cy

inj.

Hole Injection Barrier (eV)M. Abkowitz, J. S. Facci, J. Rehm, J. Appl. Phys. 1998, 83, 2670.

Carrier injection efficiency

contact limiting-currentfor 1contact ohmicfor 1

current injected :efficiencyInjection

SCLC

3

2

89

dVJ ro

SCLC



2014. 1st Semester

Conduction band edge at E

Tunneling

PF

(1) Poole-Frenkel Model

Conduction band edge at E=0

Zero field (E=0) E≠0

mxx x

)(xV

eExx

e

o4

2

)(xV

TkE

TkEμF,T

B

PF

BPF expexp)(

Charge Transport in Disordered Organic Solids

E : Activation energy at E=0

: PF Mobility

: PF constantPF

PF

0

3

PF e

EEePF

2/1

0

3

PF



2014. 1st Semester

0

111TTTeff

: Empirical parameter0T

(2) Gill’s modified Poole-Frenkel model

PVKpoly-n-vinylcarbazole

(hole conductor)

TNF2,4,6-trinitro-9-fluorenone

(electron acceptor)

Nn

O2N C

O

NO2

NO2

W. D. Gill, J. Appl. Phys. 43, 5033 (1972).


effeff TkE

TkEμF,T

B

PF

BPF expexp)(



2014. 1st Semester

(3) Bassler’s Gaussian Disorder Model• The energy of each site is distributed in accordance with the Gaussian distribution• Energies of adjacent sites are uncorrelated and motion between sites is Markovian (no phase memory)• The transition rates for phonon-assisted tunneling (Miller and Abrahams):

= inverse localization length, Rij = distance between the localized states, i = energy at the state i.• Since the hopping rates are strongly dependent on both the positions and the energies of the localized states, hopping transport is extremely sensitive to structural as well as energetic disorder.

H. Bässler, Phys. Status Solidi B 175, 15 (1993).

LUMO

HOMO


ji

jiji

ijphij kTRvW

,1

),exp()2exp( i

j

A. Miller, E. Abrahams, Phys. Rev. 120 (1960) 745. Hopping

-1 0 1 2 3 4 5-10

-5

0

5

TkTk BB

2

log (t/to)

TkB

kT

TT

oo

o 32 ,exp

2



2014. 1st SemesterBassler’s Gaussian Disorder Model

TkB

radiuson localizaticarrier anddistance site-inter average where

),/2exp()( 2

o

ooo aμ

H. Bässler, Phys. Status Solidi B 175, 15 (1993).M. Stolka, J. F. Janus and D. M. Pai, J. Phys. Chem. 88, 4707 (1984).

: Energetic disorder: Positional disorder: Constant ~2.9x10-4 (cm/V)1/2

: High temperature limit of the mobility

C

o

Hole mobility of TAPC embedded in BPPC matrix

P. M. Borsenberger, L. Pautmeier and H. Bassler, J. Chem. Phys. 94, 5447 (1991).

1.5)( ,exp32exp)(

1.5)( ,25.2exp32exp)(

22

B

2

B

2

B

2

B

ETk

CTk

μE,T

ETk

CTk

μE,T

o

o



2014. 1st Semester

P. M. Borsenberger, L. Pautmeier and H. Bässler, J. Chem. Phys. 95, 1258 (1991)

MPMPbis(4-N,N-diethylamino-2-methylphenyl)-4-

methylphenylmethane (thickness~8.7 m)

Charge Transport in Disordered Polymers

Hole mobility of MPMP



2014. 1st Semester

Disorder parameters• : The width of the DOS. Random distribution of both permanent and van der Waals dipoles lead to local

fluctuations in electric potential increase s by an amount proportional to the square root of the dipole concentration and to the strength of the dipole moment. reduce the carrier mobility. The smaller dipolar interaction is better for the carrier transport.

• : The degree of positional disorder. Amorphous morphology of molecular solids or doped polymers lead to the variation in the intermolecular distances.

P. M. Borsenberger and H. Bässler, J. Chem. Phys. 95, 5327 (1991).

Disorder parameters

TAPC doped polystyrene >> TAPC doped polycarbonate

Dipole moment:• TAPC [1,1-bis(di-4-tolylaminophenyl)cyclohexane] = 1.0 D• PC (bisphenol-A-polycarbonate) = 1.0 D• PS (polystyrene) = 0.1 D

• Larger dipolar interaction increases both and .

• The elimination of random dipolar fields due to static dipole moments of PC reduces both and and thereby increases the mobility.



2014. 1st Semester

Electron and hole mobilities of anthracene

Influence of impurity on the carrier mobility



2014. 1st Semester

Doping reduces carrier mobilityand affects I-V-EL characteristics.

Ref. H.H. Fong et al. Chem. Phys. Lett. 353 (2002) 407

Mobility – Doping Relation



2014. 1st SemesterCharge –voltage characteristics of organic semiconductors

Current

Injection limited

Bulk Limited

SCLC (undoped semicond. or Insulator)

3

2

89

dVJ roSCLC

Ohmic (Doped semiconductor)EepJ

Thermionic emission]1)[exp(

TkeVJJ

Bs )exp(2*

TkeTAJB

bns

Tunneling)exp(2

EbEJ

qh

qmb3

)(28 2/3*



2014. 1st SemesterCarrier injection at the contact

o

FeeffectSchottky4

3

]1)[exp( Tnk

eVJJB

s

)exp(2*

TkeTAJB

bns

22*

3

** /KA/cm )

mm120(4

h

kemA Bn

)exp(2

EbEJs

Thermionic Emission

Fowler-Nordheim Tunneling

effective Richardson constant for thermionic emission

qhqmb

3)(28 2/3*



2014. 1st SemesterCarrier Injection : Fowler-Nordheim Tunneling

I. D. Parker, J. Appl. Phys. 75, 1656 (1994).



2014. 1st Semester

)exp(2

EbEJs

/3qh)(q m*) (28b 3/21/2

Fowler-Nordheim Tunneling

I. D. Parker, J. Appl. Phys. 75, 1656 (1994).

Carrier Injection : Fowler-Nordheim Tunneling



2014. 1st Semester

PPV

AuITO

V=0

V>0

V>>0

+

PPV

AuITO +

++

+

+++++

+

PPVAu

ITO +

++

++

+++

+

+++

++++

+

Space-charge-limited current (SCLC)

3

2

2

)( )area

(

velocity density) charge(

dV

dVV

d

Ed

CVJ

ro

ro

SCLC

3

2

89

dVJ roSCLC

Space-charge-limited current (SCLC)

OLED acts as a capacitor

2

2

dxVd

potential

xd

ohmic

SCLC

Field ~ 0 at contact



2014. 1st SemesterSCLC: no trap

law.Gurney -Mott .89

)( condition,Boundary

.2)(

.2)]([)]0([)]([ .2)]([)()(2

,0)(For

.exp ,)()(

.)()( :equation flowCurrent

.)]()([)( :equationPoisson

density trapoffunction on Distributi

3

20

2222

dVJ

.dxxFV

xJxF

xJxFxFxFJdx

xFddx

xdFxF

xp

]Tk

E[Np(x)dEEh(E,x)fxp

xFxpqJ

xpxpqdx

xdF(E)S(x).Nh(E,x)

p

d

p

pp

t

B

Fv

E

E pt

p

t

t

pu

l

The distance Wa between the actual electrode surface and the virtual anode (-dV/dx=F=0) is so small that we can assumeF(x=Wa 0)=0 for simplicity.

(no trap)

o'ieV

'x

aeV

ElectrodeOrganic semiconductor

Electrode

0 :electrode Virtual'

xxdx

d



2014. 1st Semester

DOS

Energy

EC (ELUMO)

EF

t

ckT

EE

t

tt e

kTNEG

)(

Exponential trap distribution

E

kTEE

cf

Fc

eNn

t

Fc

Fc

cc

kTEE

t

EkT

EE

tB

t

E

FDkT

EE

tB

tt

eN

dEeTk

N

dEEfeTk

Nn

)(

TTm

Nn

NNn

Nn

t

m

c

ft

TT

c

ftt

t

1

)()(

SCLC: exponential trap density



2014. 1st Semester

. ,)1

()112( 12

111

TTm

dV

Nmm

mmNqJ t

m

mm

t

omc

m

.dx)x(FV condition,Boundary

.)NqJ()N

mm()x(F

.x)NqJ(NF

mm

.)NqJ(N

dx)x(dFF

.)x(F)x(nqJ :equation flow Current

.)Nn

(qN)x(qn)]x(n)x(n[qdx

)x(dF :equation Poisson

d

m

c

mm

o

t

m/

co

tmm

m/

co

tm/

f

m/

c

f

o

t

o

t

o

tf

0

11

1

11

11

1

1

1

V Vlog

Jlog

0

3

2

dV

89J

LawGurney -Mott

SCLC: exponential trap density



2014. 1st Semester

(a) Hole only device

(b) Electron only device

3

2

89

dVJ roSCLC

d=0.22 m 0.37 m

0.31 m12

1

m

m

dVJ

0.3 m

d=0.13 m

0.7 m

ITO Au

OC1C10-PPV

+

(a)

OC1C10-PPV

Ca Ca

-

P. W. M. Blom M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 3308 (1996).

SCLC: an example



2014. 1st Semester

P. W. M. Blom M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 3308 (1996).

ITO Au

OC1C10-PPV

+

SCLC: comparison with other models

Documents

Electrical Properties of Organic Semiconductorsocw.snu.ac.kr/sites/default/files/NOTE/9222.pdf · 2018. 1. 30. · 0/25 Changhee Lee, SNU, Kore 전자물리특강 EE 430.859 2014