Carrier mobility of Si and Organic Materials

1

Organic SemiconductorEE 4541.617A

2009. 1st Semester

2009 5 12

K. C. Kao and W. Hwang, Electrical Transport in Solids, (Pergamon, New York, 1981), p.159

Changhee Lee, SNU, Korea1/41

Changhee LeeSchool of Electrical Engineering and Computer Science

Seoul National Univ. [email protected]

2009. 5.12.


2009. 1st Semester

Electron mobility of Si

Carrier mobility of Si and Organic Materials

hole mobility of Perylene hole mobility of MPMP


370 nm thick perylene crystal 8.7 um thick unordered layer of

MPMP ( sublimed).

2


2009. 1st Semester

d 2

Mobility Measurement Techniques

10 2−

)/( 2 Vscmμ 10 4− 10 6− 10 8− 100 102

TOFMobility in the bulk

d = 0.5~5 mm

FETMobility in a thin layer

d ~ 50 nm

τμ

Vd 2

=∴

Vdμ

τ2

=


d 0.5 5 mmOther 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).]……


2009. 1st SemesterMobility Measurement Techniques: Organic TFT


T. N. Jackson, Penn State U.

3


2009. 1st Semester

Light (hν)τ

μVd 2

=

Mobility measurement techniques: TOF-PC

Time-of-flight photoconductivityt =0

hυ------

++++++

------

++

+++

+0 < t < τ

------

+++++

+

t=τ

rren

t

g p y

N2 laser

VacuumCryostat

B/S

Sample

Si-PD

Trigger


t =0 t=τ

0 < t < τ

Time

Pho

tocu

r

OscilloscopeBias VPC

gg

TOF Signal

RL


2009. 1st SemesterTransport of charge carriers in organic materials

60

40

20

0

Phot

ocur

rent

(arb

. uni

ts)

100806040200

0.20

0.15

0.10

0.05

0.00hoto

curre

nt (a

rb. u

nits)

a-NPD Alq3

Gaussian transport Dispersive transport Fast

Slow

P 1.00.80.60.40.20.0

Time (μs)

Ph 806040200

Time (μs)

Dispersive transportGaussian transport

er D

ensi

ty

Trappingand release

Band States


Distance

Carr

ie

Localized states

Hopping

Deep trap

Ref.) Harvey Scher, Michael F. Shlesinger and John T. Bendler, Physics today, Jan. p.26 (1991)

4


2009. 1st SemesterMobility Measurement Techniques: Transient EL

30

25

20

rb.u

nit)

57V

Al

PPP15

10

5

0

Ligh

t (x

10-3

ar

500450400350300250200150100500

Time (x10-9 s)

57V

19V27V

39V

42V

46V52V

240

220

Mobility from the delay time

τ=d2/ μV

ITO glass

PMT


220

200

180

160

140

120

100

Tim

e Del

ay (n

s)

605040302010

1/V (x10-3 V-1)

Hole mobility

in the vacuum-deposited PPP:

ITO/PPP/Al: μ=4.5x10-6 cm2/Vs

G. W. Kang, C. H. Lee, W. J. Song, and C. Seoul, SPIE 4105, 362 (2001).


2009. 1st SemesterTransient EL Mobility vs TOF-PC mobility in Alq3


S. C. Tse, H. H. Fong, and S. K. So, J. Appl. Phys. 94, 2033 (2003)

For a thin layer of Alq3 (d<180 nm), it is found that td is affected by both the charging effect and carrier transit time through the Alq3 layer. For a thicker layer of Alq3 (d>200 nm), tdapproaches the intrinsic electron transit time through Alq3 .

5


2009. 1st SemesterSpace-charge-limited current

Hole only device

0.3 μm

d=0.13 μm

0.7 μm

OC1C10-PPV

Electron only device

3

2

89

dVJ roSCLC μεε=

d=0 22 m

ITO Au+

OC1C10-PPV-


d=0.22 μm 0.37 μm

0.31 μm12

1

+

+

∝ m

m

dVJ

(a)Ca Ca

Poly(dialkoxy-p-phenylene vinylene) (OC1C10-PPV)P. W. M. Blom M. J. M. de Jong, and J. J. M. Vleggaar, Appl. Phys. Lett. 68, 3308 (1996).


2009. 1st Semesterd

T it tiV R

++++++

Dark injection SCL transient current

Transient SCLC

Transit time Ohmic contact τ787.0=pt

PTPBpoly (tetraphenylbenzidine) PTPB

1.0

0.8

0.6

0.4i(t) (

arb.

uni

t)

Dark injection SCL transient currentτ787.0=pt

t


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

0.2

0.01.00.80.60.40.20.0

Time (ms)

787.0pt

=τ

TOF-PC

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

6


2009. 1st SemesterMobility Measurement Techniques: dark charge injection

ITO/300nm m-MTDATA/Ag with ITO biased positively.

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.

Etr μ

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

steady-state value.


M. Stossel et al, Phys. Chem. Chem. Phys.1, 1791 (1999)A. Many and G. Rakavy, Phys. Rev. 126, 1980 (1962)


2009. 1st Semester

nj.

Carrier injection efficiency

contact limiting-currentfor 1contact ohmicfor 1

current injected :efficiencyInjection

<=

=

ηη

ηSCLC

3

2

89

dVJ ro

SCLCμεε

=

Inje

ctio

n E

ffici

ency

ηin


Hol

e

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

7


2009. 1st SemesterMobility Measurement Techniques: TRM-SHG

Vscm /25.0 2=μ


T. Manaka, E. Lim, R. Tamura, M. Iwamoto, Nature Photon.1, 581 (2007).

T. Manaka, M. Nakao, D. Yamada, E. Lim and M. Iwamoto, Optics Express 15, 15964 (2008).


2009. 1st Semester

(1) Poole-Frenkel Model

Conduction band mxx =x

)(xV)(xV

Charge Transport in Disordered Organic Solids

EEePF

2/1

0

3

PF βπεε

φ =⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ

Conduction band

edge at ETunneling

PFφΔedge at E=0

Zero field (E=0) E≠0

x

eEx−x

e

oεπε4

2

−


Zero field (E 0) E≠0

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−=

TkE

TkEμF,T

B

PF

BPF expexp)( βμ EΔ : Activation energy at

E=0

: PF Mobility

: PF constant

PFμ

PFβ

0

3

PF πεεβ e

=

8


2009. 1st Semester

0

111TTTeff

−= : Empirical parameter

0T

(2) Gill’s modified Poole-Frenkel model

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ−=

effeff TkE

TkEμF,T

B

PF

BPF expexp)( βμ


PVKpoly-n-vinylcarbazole

(hole conductor)

Nn

O2N C

O

NO2


TNF2,4,6-trinitro-9-fluorenone

(electron acceptor)

NO2

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


2009. 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):

⎪⎬⎫

⎪⎨⎧

>−

−−= jiji

kTRvW εεεε

α ),exp()2exp( εεj


α = inverse localization length, Rij = distance between the localized states, εi = 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.

σLUMO

⎪⎭⎬

⎪⎩⎨

>=

ji

jijphij kTRvW

εεα

,1)2exp( εi

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

0

5

ε


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

HOMO σ-1 0 1 2 3 4 5-10

-5 TkTk BB

2σε−=∞

log (t/to)

TkB

ε

9


2009. 1st Semester

TkB

σσ =∧

Hole mobility of TAPC embedded in BPPC matrix


: Energetic disorder: Positional disorder: Constant 2 9x10-4 (cm/V)1/2

σ

CΣ


radiuson localizaticarrier anddistance site-inter average where

),/2exp()( 2

==

−=

o

ooo aμ

ρρ

ρρρρ

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

1.5)( ,32exp

32exp)(

1.5)( ,32exp

32exp)(

22

B

2

B

22

B

2

B

≥Σ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡Σ−⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

<Σ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡Σ−⎟⎟

⎠

⎞⎜⎜⎝

⎛

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

ETk

CTk

μE,T

ETk

CTk

μE,T

o

o

σσμ

σσμ

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

: High temperature limit of the mobilityC

oμ

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


2009. 1st Semester

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

methylphenylmethane (thickness~8.7 μm)

Hole mobility of MPMP



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

10


2009. 1st SemesterDisorder parameters• σ: The width of the DOS. Random distribution of both permanent and van der Waals dipoles lead to local fluctuations in electric potential increase σ 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. • Σ: The degree of positional disorder. Amorphous morphology of molecular solids or doped polymers lead to the variation in the intermolecular distances.

Disorder parameters

μ TAPC doped polystyrene >> μ 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 σ and Σ.• The elimination of random dipolar fields due to


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

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


2009. 1st SemesterDisorder parameters


A. Dieckmann, H. Bässler and P. M. Borsenberger, J. Chem. Phys. 99, 8136 (1993).

11


2009. 1st SemesterEffect of dipolar molecules on carrier mobilities

• Conduction through the dopant.• Mobility is strongly affected by the dipole moment of the dopant for holes and electrons


A. Goonesekera and S. Ducharme, J. Appl. Phys. 85, 6506 (1999)


2009. 1st SemesterTemperature dependence of the hole mobility of PPVs


P.W.M. Blom, M.C.J.M. Vissenberg, Materials Science and Engineering 27, 53-94 (2000)

12


2009. 1st Semester

⎩⎨⎧ <

=+−

−− τα

α

tttt ,

(t)J )1(

)1(

ph

(4) Scher-Montroll dispersive transport model

Trapping

Band Statesα−≈Ψ tt)(Continuous time random walk (CTRW)


⎩ >+ τα tt ,)1(ppp gand release

Localized statesDeep trap

oTT

=α

Disappearance of plateau

hoto

curr

ent Slope = -(1-

α)

log

i ph

ατ1

)(EL

∝


Time

t =0 t =τ Time

Ph

Slope = -(1+α)

log tt =0 t =τ

Scher and Montroll, Phys. Rev. B 12, 2455 (1975)


2009. 1st Semester

ατ1

)(EL

∝

Scher-Montroll model of dispersive transport

)45.01( −−t

)45.01( +−t2.2 45.011

=

=α


H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975)

13


2009. 1st SemesterDispersive Transport in a-Selenium


G. Pfister, Phys. Rev. Lett. 36, 271 (1976)


2009. 1st Semester


14


2009. 1st SemesterCharge –voltage characteristics of organic semiconductors

Injection limited

Thermionic emission]1)[exp( −=

TkeVJJ

Bs )exp(2*

TkeTAJB

bns

φ−=

Current

Bulk Limited

Ohmic (Doped semiconductor)EepJ μ=

Tunneling)exp(2

EbEJ −

≈qh

qmb3

)(28 2/3* φπ=


Bulk Limited

SCLC (undoped semicond. or Insulator)

3

2

89

dVJ roSCLC μεε=


2009. 1st Semester

PPV

AuITO

V=0

V>0

Space-charge-limited current (SCLC)

velocitydensity)charge(JSCLC ×≈

Space-charge-limited current (SCLC)

OLED acts as a capacitor

V>0

V>>0

+

PPV

AuITO +

+

++

+++++

2

2

)( )area

(

velocity density)charge(

VdVV

d

Ed

CVJ

ro

ro

SCLC

μεε

μεε

μ

⋅⋅⋅=

×⋅

=

ερ

−=2

2

dxVd

potentialField ~ 0 at contact


+

PPV Au

ITO +

++

++

+++

+

+

++

+++++

3 dro=

3

2

89

dVJ roSCLC μεε=

xd

ohmic

SCLC

15


2009. 1st SemesterOhmic Contact (1)

field. applied external no is theresince

,0 :equation flowCurrent

. :equationPoisson

dxdnF - qDqnJ

qndxdF

==

=

μ

ε

figurerightin theconditionboundarytheFrom

log

used. isrelation Einstein thewhere

,

pp

0.Fdx

Tkq

nn

qTk

μD

FdxTk

qFdxDμ

ndn

x

Bs

B

B

=∴

=

==∴

∫:cathodevirtual


law.Boltzmann i.e., ],exp[

figure,right in thecondition boundary theFrom

0

Tkχ)ψ(x)-(φnn

.Fdxqχ)ψ(x)-(φ

B

ms

x

m

−−=∴

−=− ∫ .dxdV 0

:cathode virtual

=


2009. 1st Semester

when0conditionboundarytheusingand

)2( gmultiplyinafter sidesboth gIntegratin

].exp[22

2

2

χφψdψdxdψ

Tkχ)ψ(x)-(φnqnq

dxdFq

dxψd

B

ms

−==

−−−=−=−=

εε

Ohmic Contact (2)

)}].2

{exp(sin2

)[2

exp()2(W

regionon accumulati theof width the givesequation thisgIntegratin

]}.exp[]{exp[2)(

,when 0condition boundary theusing and

12/12

22

Tkφ

Tkχφ

NqTk

Tk)φ(

Tkχ)ψ(x)-(φTknq

dxdψ

χφψdx

B

m

Bc

B

B

m

B

mBs

−−−

−=

−−−

−−=

==

− ϕπε

ϕε


).2

exp()2(2

W

, levelenergy discrete ain confined trapsshallow containing torssemiconducFor

).2

exp()2(2

W

,4 If

2/12

2/12

TkEχφ

NqTk

ETkχφ

NqTk

Tkφ

B

t

t

B

t

Bc

B

Bm

−−≈

−≈

>−

επ

επϕ

16



.)()( :equation flowCurrent

.)]()([)( :equationPoisson

density trapoffunction on Distributi

xFxpqJ

xpxpqdx

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

p

t

t

μεε

ρ

=

+==

=oφ'ieV

'x

aeV

0 :electrode Virtual'

==xxdx

dφ

2)(

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

,0)(For

.exp ,)()(

)()(q

2222

xJxF

xJxFxFxFJdx

xFddx

xdFxF

xp

]Tk

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

pq

pp

t

B

Fv

E

E pt

p

pu

l

εμεμ

μ

=∴

===−∴==

=

−== ∫ ElectrodeOrganic semiconductor

Electrode


law.Gurney -Mott .89

)( condition,Boundary

.)(

3

20

dVJ

.dxxFV

xxF

p

d

p

εμ

εμ

=

=

=∴

∫

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)


2009. 1st Semester

ITO/PPV/Au hole-only devices

3

2

89

dVJ roSCLC μεε=

3&/1050iFit 26− V

Space-charge-limited current

3 & /105.0usingFit 26 =×= rVscm εμ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −Δ−=

effB

PFo exp)(

TkFEμF,T βμ



17


2009. 1st Semester

ofonset or the law sOhm' from departure theofonset The

.89

such thatt predominan isspecimen theinside carriers free generated thermallyofdensity theif holds law sohm' field, lowAt

3

2

ppo

o

dV

dVqp

p

εμμ >>Jlog


Vat V

ansit timecarrier tr when theplace takes

regime SCL the toohmic thefromn transitio theTherefore,

.or 89

89

V

have eequation w thisgrearranginBy

.98V when place takesconduction SCL the

2

t

dt

2

2

opop

o

d

qpd

dqp

τ

ττσε

με

μ

ε

=

≈==

=

Ω

Ω

Ω

VJ ∝

2VJ ∝


. timerelaxation dielectric the toequalely approximat is

V

do

p

σετ

μ

=

Ω

K. C. Kao and W. Hwang, Electrical Transport in Solids, (Pergamon, New York, 1981), p.159

t.predominan is conduction SCLC ,At t.predominan is conduction ohmic ,At

dt

dt

ττττ

<>

ε

2

98V dqpo=Ω

Vlog0


2009. 1st Semester

,equation Continuity

. timerelaxation dielectric d σετ

Jt

)p(pq o

o

⋅−∇=∂+∂

=


ignored. becan term2nd the, timerelaxation dielectric the tocomparable

timeain specimen over theuniformly spreads p and If

.)(

).()(Jby given iscurrent where

d

2

μσετ

εμ

μ

qp

pp

pDpqp

tp

ppqDFppqt

o

o

pp

oppo

∂

=

<

∇+−=∂∂

∴

+∇−+=∂


m.equilibriuestablish -re carrier to for the required time theof measure a is

.exp0 .)(

dτ

τεμ

)(-t/)p(tp(t)pqp

tp

dpo ==∴−≈

∂∂

∴

18


2009. 1st Semester

,)(/1

)()(density charge Trapped

)()(),(levelsenergy discrete multipleor singlein confined Traps

xpNxSNxp

xSEENxEh

tt

tt

tt

θ

δ

+≈

−=


trapsofon distributi spatial uniform-non Ignoring

.89

. where

)(/1

3

2

dVθJ

eNNg

θ

xpN

efftroSCLC

kTE

t

vpt

tt

t

μεε

θ

=

=

+

−

ECB


.89

,

3

2

dVθJ

ddpp

pθ

troSCLC

efft

t

μεε=

=+

=

EVB

Discrete trap levels




19


2009. 1st Semester

DOS

Energy

Space-charge-limited current: analytic solutionkT

EE

cf

Fc

eNn−

−=

ccE

FDkT

EEt

t dEEfeTk

Nn∞−

−−

= ∫ )(


EC (ELUMO)

EF

t

c

kTEE

tt e

kTNEG

−−

=)(

Et

Fc

Fc

kTEE

t

EkT

EE

tB

t

tB

eN

dEeTk

N

Tk

−−

∞−

−−

∞

=

≈ ∫

∫

T 1


tkT

Exponential trap distribution

TTm

Nn

NNn

Nn

t

m

c

ft

TT

c

ftt

t

=

=≈∴1

)()(


2009. 1st Semester

NJN

dxdFF

xFxnqJNnqNxqnxnxnq

dxxdF

mtm

f

m

c

f

o

t

o

t

o

tf

=

=

≈≈+

=

/1/1

/1

.)()(

.)()( :equation flowCurrent

.)()()]()([)( :equationPoisson

μεεεεεε Jlog

LawGurneyMott


.dxxFV

NqJN

mmxF

xNqJNF

mm

Nqdx

d

m

c

mm

o

t

m

co

tmm

co

∫=

+=∴

=+

∴

++

+

0

11

1

/11

)( condition,Boundary

.)()1()(

.)(1

)(

μεε

μεε

μεε

3

2

dV

89J

LawGurney -Mott

εμ=


. ,)1

()112( 12

111

TTm

dV

Nmm

mmNqJ t

m

mm

t

omc

m =++

+= +

++− εεμ

ΩV Vlog0TFLV

.)12

1)(1()(

SCLC Trapped Ohmic112

mm

m

v

o

ro

t

mm

mm

NpNqdV

+

Ω +++

=

⇒

εε .])12

1()1(89[

SCLC free-Trap SCLC Trapped

11

12

−+

+++

=

⇒

mmm

v

mt

roTFL m

mm

mNNqdV

εε

20


2009. 1st Semester

Ca/PPV/Ca electron-only devices


Trap-limited SCLCTrap-free SCLC




2009. 1st Semester

. ,

SCLC limited-Trap

12

1

TTm

dVNNJ t

m

mm

tv =∝ +

+−μ

318

eV 15.0≈tE

SCL current with an exponential trap distribution

3-18 cm10≈tN

Changhee Lee, SNU, Korea40/41P. E. Burrows, Z. Shen, V. Bulovic, D. M. McCarty, S. R. Forrest, J. A. Cronin and M. E. Thompson, J. Appl. Phys. 79, 7991

(1996).

21


2009. 1st SemesterTrap-limited SCL current with field-dependent μ


W. Brütting, S. Berleb and A. G. Mückl, Org. Electronics 2, 1 (2001)

Carrier mobility of Si and Organic Materials

Documents

Transcript of Carrier mobility of Si and Organic Materials