Electrical Properties of Organic Semiconductors

(1)

Changhee Lee, SNU, Kore

0/25

EE 430.859 2014. 1^st Semester

2014. 4. 17.

Changhee Lee

School of Electrical and Computer Engineering Seoul National Univ.

[email protected]

Electrical Properties of Organic Semiconductors

(2)

Changhee Lee, SNU, Kore

1/25

EE 430.859 2014. 1^stSemester

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.

T

n

μ

T ) 

_o ^

 (

Band-like transport of carriers.

Carrier mobility is limited by scatterings with phonons, impurities, etc.

(3)

2/25

EE 430.859 2014. 1^st 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

 

 



  



 A k T

k

B

ET



 4

) t 2 exp (

as, described be

can , k rate, (hopping)

transfer -

electron the

limit, rature

high tempe in the

theory Marcus

cal semiclassi the

to According

2

ET

(4)

3/25

EE 430.859 2014. 1^stSemester

Electron mobility of Si

Carrier mobility

e & h mobility of organic materials Applied voltage

Band-like conduction

Delocalized 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)

(5)

Changhee Lee, SNU, Kore

4/25

EE 430.859 2014. 1^st Semester

TOF

Mobility in the bulk d = 0.5~5 m

FET

Mobility in a thin layer d ~ 50 nm

 

V d

²





V d

  

²

Mobility Measurement Techniques

10

^²

)

/ ( cm

²

Vs

 10

4

10

^⁶

10

^⁸

10

⁰

10

²

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).]

……

(6)

Changhee Lee, SNU, Kore

5/25

EE 430.859 2014. 1^stSemester

d

Transit time Ohmic contact

V R

+ + + + + +



787 .

 0

t

p

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. unit)

1.0 0.8

0.6 0.4

0.2 0.0

Time (ms)

Dark injection SCL transient current

 787 .

 0 tp

787 . 0

tp

 

TOF-PC

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

Transient SCLC

(7)

6/25

EE 430.859 2014. 1^stSemester

Mobility Measurement Techniques : dark charge injection

E t

_tr

d

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

8 9

d

J

_SCLC 



_o



_r

 V

(8)

Changhee Lee, SNU, Kore

7/25

EE 430.859 2014. 1^st Semester

Hole Injection Ef ficiency 

inj.

Hole Injection Barrier (eV)

M. Abkowitz, J. S. Facci, J. Rehm, J. Appl. Phys. 1998, 83, 2670.

Carrier injection efficiency

contact limiting

- current for

1

contact ohmic

for 1

current injected

: efficiency Injection







 SCLC 3

2

8 9

d

J

_SCLC

 

^o



^r

 V

(9)

8/25

EE 430.859 2014. 1^st Semester

Conduction band edge at E Tunneling



PF



(1) Poole-Frenkel Model

Conduction band edge at E=0

Zero field (E=0) E≠0

x

m

x 

x )

( x V

 eEx x

e

o





4



2

) ( x V

 



 

 



 



 



 k T

E T

k μ E

F,T

B PF B

PF

exp exp

)

( 



Charge Transport in Disordered Organic Solids

 E : Activation energy at E=0 : PF Mobility

: PF constant



PF



PF 0

3

PF



  e

E e E

PF 2

/ 1

0 3

PF



   



 



 



(10)

9/25

EE 430.859 2014. 1^stSemester

0

1 1

1

T T

T

_eff

  T

₀

: Empirical parameter

(2) Gill’s modified Poole-Frenkel model

PVK

poly-n-vinylcarbazole (hole conductor)

TNF

2,4,6-trinitro-9-fluorenone (electron acceptor)

N

n

O₂N C O

NO₂

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

Charge Transport in Disordered Organic Solids

 





 





 





 



 





eff

k T

E T

k μ E

F,T

B PF B

PF

exp exp

)

( 



(11)

10/25

EE 430.859 2014. 1^stSemester

(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, R_ij= 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



Charge Transport in Disordered Organic Solids















 

 



j i

j i j i ij

ph

ij v R kT

W  



 

 

, 1

), ) exp(

2

exp( _i_j

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

-1 0 1 2 3 4 5

-10 -5 0 5

T k T

k_B _B

2

^  

log (t/t

_o

)

T k_B



T k T

T

o o

o 3

2 , exp

2 



 











 



 







(12)

11/25

EE 430.859 2014. 1^stSemester

Bassler’s Gaussian Disorder Model

T k_B

^  

radius on

localizati carrier

and

distance site

- inter average where

), / 2 exp(

)

( ²







o

o o

o a

μ



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) (

, 3 exp

exp 2 )

(

1.5) (

, 25 . 2 3 exp

exp 2 )

(

2 2

B 2

B

2

B 2

B



 





















  



 



















 









 





















  

 



















 







T E C k T

μ k E,T

T E C k T

μ k E,T

o o



 



 

(13)

Changhee Lee, SNU, Kore

12/25

EE 430.859 2014. 1^stSemester

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

MPMP

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

(thickness~8.7 m)

Charge Transport in Disordered Polymers

Hole mobility of MPMP

(14)

Changhee Lee, SNU, Kore

13/25

EE 430.859 2014. 1^stSemester

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.

(15)

14/25

EE 430.859 2014. 1^st Semester

Electron and hole mobilities of anthracene

Influence of impurity on the carrier mobility

(16)

15/25

EE 430.859 2014. 1^st Semester

Doping reduces carrier mobility and affects I-V-EL characteristics.

Ref. H.H. Fong et al.

Chem. Phys. Lett. 353 (2002) 407

Mobility – Doping Relation

(17)

16/25

EE 430.859 2014. 1^st Semester

Charge –voltage characteristics of organic semiconductors

Current

Injection limited

Bulk Limited

SCLC (undoped semicond. or Insulator)

3 2

8 9

d J

_SCLC

 

_o



_r

 V

Ohmic (Doped semiconductor) E

ep J  

Thermionic emission

] 1 )

[exp( 

 k T

J eV J

B

s ^* ²

exp( )

T k T e

A J

B bn s



 

Tunneling

)

2

exp(

E E b

J  

qh q b m

3

) ( 2

8 

^*



³^/²



(18)

17/25

EE 430.859 2014. 1^st Semester

Carrier injection at the contact

o

F effect e

Schottky



4



3

] 

1 )

[exp( 

 nk T

J eV J

B s

)

2

exp(

*

T k T e

A J

B s bn



 

2

* 2 3

* *

) A/cm /K

m 120( m

4 

 h k A  em

ⁿ ^B

)

2

exp(

E E b

J

_s

 

Thermionic Emission

Fowler-Nordheim Tunneling

effective Richardson constant for thermionic emission

qh q b m

3

) (

2

8 

^*



³^/²



(19)

18/25

EE 430.859 2014. 1^st Semester

Carrier Injection : Fowler-Nordheim Tunneling

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

(20)

19/25

EE 430.859 2014. 1^st Semester

)

2

exp(

E E b

J

_s

 

/3qh )

(q m*)

(2 8

b  

^1/2



^3/2

Fowler-Nordheim Tunneling

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

Carrier Injection : Fowler-Nordheim Tunneling

(21)

20/25

EE 430.859 2014. 1^st Semester

PPV

Au ITO

V=0

V>0

V>>0 +

PPV

Au ITO +

+ + +

+ + + +

+

PPV

Au

ITO + + +

+ +

+ + +

+ +

+ + ++

+

Space-charge-limited current (SCLC)

3 2 2

) (

area ) (

velocity density)

charge (

d V

d V V

d d E

CV J

r o

r o SCLC





 











 







3 2

8 9

d J

_SCLC

 

_o



_r

 V

Space-charge-limited current (SCLC) OLED acts as a capacitor



 

2



2

dx V d

potential

d x ohmic

SCLC Field ~ 0 at contact

(22)

21/25

EE 430.859 2014. 1^st Semester

SCLC: no trap

law.

Gurney -

Mott

8 . 9

) ( condition,

Boundary 2 . )

(

2 . )]

( [ )]

0 (

[ )]

( [ 2 .

)]

( [ )

) ( ( 2

, 0 ) ( For

. exp

, ) ( )

(

.) ( ) ( :

equation flow

Current

)] . ( )

( ) [

( : equation Poisson

density trap

of function on

Distributi

3 2

0

2 2

d J V

. dx x F V

J x x

F

J x x

F x

J F dx

x F d dx

x x dF

F

x p

T ] k [ E N

p(x) dE

E h(E,x)f x

p

x F x p q J

x p x

p q dx

x dF (E)S(x).

N h(E,x)

p

d p

p p

t

B F v

E

E p

t

p

t t

u p l



  



















 





The distance W_a between the actual electrode surface and

the virtual anode (-dV/dx=F=0) is so small that we can assume F(x=W_a 0)=0 for simplicity.

(no trap)



ⁱo^'

eV

'

x

eVa

Electrode

Organic semiconductor Electrode 0

: electrode Virtual

'



xx

dx d

(23)

22/25

EE 430.859 2014. 1^st Semester

DOS Energy

E

_C

(E

_LUMO

) E

_F

t c

kT E E

t

t t

e

kT E N

G

 

 ) (

Exponential trap distribution

E

kT E E c f

F c

e N n

 



t F c

F c

c c

kT E E t

E kT

E E

t B

t E

kT FD E E

t B

t t

e N

dE T e

k N

dE E

f T e

k n N

 





 





 









) (

T m T

N N n

n

t

m c f t

T T

c f t

t ^t





 ( ) ( )

¹

SCLC: exponential trap density

(24)

23/25

EE 430.859 2014. 1^st Semester

.

, 1 )

( 1 )

1

( 2

₂ ₁

1 1

1

T m T

d V N

m m m

N m q

J

_m ^t

m m

t m o

c

m







^

 

^

 

^_

. dx ) x ( F V

condition, Boundary

. N )

q ( J N )

m ( m ) x ( F

. x N )

q ( J F N

m m

. N )

q ( J N dx

) x ( F dF

.) x ( F ) x ( n q J : equation flow

Current

. N )

( n qN )

x ( )] qn

x ( n ) x ( n [ q dx

) x ( dF : equation Poisson

d

m c m

m

o t

m / c o

m t m

m / c o

m t /

f

m / c f o

t o

t f









 







 

 





 







 



 



 



0

1 1 1

1 1

1

1 1

V



log V

J log

0

3 2

d V 8 J 9

Law Gurney -

Mott





SCLC: exponential trap density

(25)

24/25

EE 430.859 2014. 1^st Semester

(a) Hole only device

(b) Electron only device

3 2

8 9

d J_SCLC  _o_rV

d=0.22 m

0.37 m

0.31 m ² ¹

1



 ^m_m

d J V

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

(26)

25/25

EE 430.859 2014. 1^stSemester

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