Current Applied Physics 5 (2005) 9–14

www.elsevier.com/locate/cap

Steady-state analysis for contact barrier effectsin metal/organic/metal structure using numerical bipolar

transport simulation q

Jung-Ho Lee a,*, No Gill Park b, Young Sik Kim c,*, Chung-Ha Suh a,Jae-Hoon Shim b,*, Young Kwan Kim d

a Department of Electronic Engineering, Hongik University, Seoul 121-791, South Koreab Research Institute of Science and Technology, Hongik University, Seoul 121-791, South Korea

c Department of Science, Hongik University, Seoul 121-791, South Koread Department of Chemical Engineering, Hongik University, Seoul 121-791, South Korea

Received 30 August 2003; accepted 23 December 2003

Available online 6 May 2004

Abstract

We have studied contact barrier effects in ITO/MEH-PPV/Al and Au/MEH-PPV/Au structure using band-theory-based bipolar

transport model that describes both injection limited and space charge limited current flow and the transition between them. Charge

injection into the organic material occurs by thermionic emission and by tunneling. The model calculations show a good description

of the measured I–V characteristics over a wide current range in both situations. In the ITO/MEH-PPV/Al structure with high

contact barriers >0.3 eV, the model shows that net injected charge was relatively small and the carrier density and the electric field

were nearly uniform. Thus, thermionic emission is the dominant mechanism at small bias in this regime because space charge effects

were not important. However, in the symmetric Au/MEH-PPV/Au structure with very low contact barrier �0.1 eV, the current flow

in the model is space charge limited and the electric field in the structure is highly non-uniform and parabolic-shaped energy profiles

were observed. We also confirm that our bipolar model analysis is more physical than single-carrier model analysis in which the

electric field in anode contact region has non-negligible negative value.

� 2004 Elsevier B.V. All rights reserved.

PACS: 73.61.Ph

Keywords: OLED; Device simulation; Contact barrier effect

1. Introduction

Organic light emitting diodes (OLEDs) have many

properties that make them attractive for electronicapplications. Specially, OLEDs are being developed for

application in flat panel displays [1–3]. There has been

much progress recently in understanding the device

qOriginal version presented at the 4th International Conference on

Electroluminescence of Molecular Materials and Related Phenomena

(ICEL4), 27–30 August 2003, Cheju Island, Korea.* Corresponding authors. Tel.: +82-2-320-1607; fax: +82-2-3142-

0335.

E-mail addresses: phile71@passmail.to, youngkim@wow.hongik.

ac.kr (Y.S. Kim).

1567-1739/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cap.2003.12.004

physics of OLEDs and their basic operating principles

[4–12]. OLEDs consist of a thin layer of luminescent

organic material between two metal electrodes. Under a

sufficiently large voltage bias, one contact injects elec-trons and the other injects holes. These charge carriers

move across the device and can recombine in the organic

material emitting light.

In order to understand the operation of an OLED, it

is required to study the injection, transport, and

recombination processes involved. There have been

extensive studies of charge injection and transport for

the single layer, single-carrier devices [7–12]. Here, wepresent calculation of single layer organic light emitting

diode characteristics using two carrier device model

which includes charge injection, transport, FN tunnel-

ing, and space charge effects in the organic material.

10 J.-H. Lee et al. / Current Applied Physics 5 (2005) 9–14

There are two characteristics of charge injectionbetween electrode and organic material. One is an

ohmic contact (OC). It is a junction between a metal

and organic material that does not limit the current

flow. It occurs when Schottky energy barrier between

two materials is below 0.3–0.4 eV. The other charac-

teristic is called an injection-limited contact (ILC). This

occurs when Schottky energy barrier between two

materials is over 0.4 eV. In an OC, space charge limitedhas great influence on charge mobility and inner electric

field becomes unstable. It is difficult to represent

equations of space charge limited region since we con-

sidered the mobility that is in proportion to carrier

diffusion and an electric field [13–17]. In an ILC, charge

injection characteristics have influenced on charge

mobility. Since the net injected charge density of this

region is relatively small, electric field and charge den-sity of inner device is nearly uniform and space charge

effects are negligible. In this case charge density is

almost constant so device current density can be

approximated by drift term.

Here, band-theory-based bipolar transport models

are formulated in Section 2. The key physical parame-

ters, such as electrical potential, electron density, and

hole density, are modeled by using classical collectiveequations. Other physical parameters are also consid-

ered and calculated in order to understand the internal

parameter profiles and determine the external parameter

quantities. For example, optical recombination rate

profile shows the peak position of exciton recombina-

tion. Schottky barrier lowering is calculated from con-

tact image force effect. Interface carrier transport

models such as thermionic emission, interface recombi-nation, and Fowler–Nordheim tunneling are provided

as a current boundary condition [18].

In order to compare the model results with experi-

mental measurements on device fabricated using the

electroluminescent polymer ploy[2-methoxy, 5-(20-ethyl-hexyloxy)-1,2-phenylene vinylene] (MEH-PPV) [19], we

simulated the device characteristics of ITO/MEH-PPV/

Al and Au/MEH-PPV/Au structure in Section 3 bychanging the contacts which can show either injection

limited behavior or space charge limited behavior. Also,

the difference between our model and the single-carrier

model is addressed. Finally, the conclusion is summa-

rized in Section 4.

2. Bipolar transport models

The transport of electrons and holes in organic device

can be solved by the continuity equation, with a drift–

diffusion equation, coupled to Poisson’s equation.

Energy level discontinuities at the organic hetero-junc-

tion can be used to produce an energy barrier that

blocks charge transport across the structure:

dJndx

¼ �qðG� RÞ; ð1Þ

dJpdx

¼ qðG� RÞ; ð2Þ

d2wdx2

¼ � qeðp � nÞ; ð3Þ

where Jn and Jp are the electron and hole current den-

sities, respectively. Electrostatic potential w are function

of the length of the device, q is the electric charge and e isthe static dielectric constant. The optical recombination

rate R is given by R ¼ cnp, where c ¼ 4pqlR=e is

Langevin recombination coefficient [20]. The generation

of electron hole pair (EHP) is given by G ¼ cnepe, wherene, pe is thermal equilibrium electron and hole carrier

density. Effective recombination mobility lR taken to be

larger either the hole mobility lp or the electron mobility

ln.In equilibrium, the electron density n and the hole

density p is represented to ne and pe using Maxwell–

Boltzmann statistics:

ne ¼ n0 expqw� q/F þ vC

kT

� �; ð4Þ

pe ¼ p0 exp�� qw� q/F þ vC þ Eg

kT

�; ð5Þ

where /F is the Fermi level in equilibrium and vC is the

electron affinity. T is the temperature in Kelvin and k is

the Boltzmann’s constant. n0 is molecule’s density ofstate and Eg is energy gap.

The drift–diffusion equations defining the electron

and hole currents, Jn and Jp are

Jn ¼ qln nE�

þ kTq

dndx

�; ð6Þ

Jp ¼ qlp pE�

� kTq

dpdx

�; ð7Þ

where the electric field is given by E ¼ �dw=dx, the

electron and hole mobility is given by ln ¼ ln0 expðE=E0Þand lp ¼ lp0 expðE=E0Þ, respectively. lp0 and ln0 is holeand electron mobility in zero electric field, respectively.

The equations are solved numerically using a Sharfetter–

Gummel spatial discretization method [21]:

Jpiþ1=2¼

kTlp

DxpiB

qwiþ1 � qwi

kT

� ��

� piþ1Bqwi � qwiþ1

kT

� ��; ð8Þ

Jniþ1=2¼ kTln

Dxniþ1B

qwiþ1 � qwi

kT

� ��

� niBqwi � qwiþ1

kT

� ��; ð9Þ

Table 1

Material parameters used in the simulation

Value Units

Relative permittivity of free space es 3.0 –

Temperature T 300 K

Low field electron mobility ln0 1.7· 10�8 cm2/V S

Low field hole mobility lp0 1.7· 10�6 cm2/V S

Electron affinity vC 2.9 eV

Boltzmann’s constant k 8.62· 10�5 eV/K

Electronic charge q 1.602· 10�19 C

Energy gap Eg 2.4 eV

Critical electric field E0 105 eV

J.-H. Lee et al. / Current Applied Physics 5 (2005) 9–14 11

where Dx ¼ xiþ1 � xi is differential mesh size, BðyÞ ¼y=ðexpðyÞ � 1Þ is function of Bernoulli.

At the metal/organic/metal contact, there are

boundary conditions. Firstly, total current is sum of

thermionic current from x ¼ 0 to L and back-flowing

interface recombination current and FN (Fowler–

Nordheim tunneling) current [18],

Jpð0Þ ¼ �qvrpðpe½Eð0Þ� � pð0ÞÞ � Jtpjx¼0

�� Jtp0jx¼0

�;

ð10Þ

JnðLÞ ¼ qvrnðne½EðLÞ� � nðLÞÞ þ Jtnjx¼L

�� Jtn0jx¼L

�; ð11Þ

where electron and hole’s effective recombination

velocity are vrn ¼ 16pelnðkT Þ2=q3, vrp ¼ 16pelpðkT Þ

2=q3

respectively.

And the hole and electron density of quasi-equilib-

rium in x ¼ 0, L is

pe½Eð0Þ� ¼ n0 exp��ubp � Dubp

kT

�; ð12Þ

ne½EðLÞ� ¼ n0 exp�� ubn � Dubn

kT

�; ð13Þ

where Schottky hole and electron electric potential

barrier are ubp, ubn. If ubp and ubn are negative electric

potential, there are barrier lowering by image force. In

this case the model also incorporates image force low-

ering of the barrier at contacts:

Dubp ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqEð0Þ=4pe

p; ð14Þ

Dubn ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqEðLÞ=4pe

p: ð15Þ

The Fowler–Nordheim currents take the form [18]

Jtpjx¼0 ¼ CpEð0Þ2 exp�� jp

Eð0Þ

�; ð16Þ

Jtnjx¼L ¼ CnEðLÞ2 exp�� jn

EðLÞ

�; ð17Þ

where constant coefficients are given by

Cp ¼ 3q2=8phðubp � DubpÞ; ð18Þ

jp ¼ 8pffiffiffiffiffiffiffiffiffi2qm

pðubp � DubpÞ

3=2=3h; ð19Þ

Cn ¼ 3q2=8phðubn � DubnÞ; ð20Þ

jn ¼ 8pffiffiffiffiffiffiffiffiffi2qm

pðubn � DubnÞ

3=2=3h; ð21Þ

The position independent of the total current

J ¼ Jp þ Jn is used to verify that steady-state has been

reached. At steady-state, one can obtain the recombi-

nation current Jr ¼ Jpð0Þ � JpðLÞ. These quantities are

related to the quantum efficiency gq ¼ QJr=J , and power

efficiency gp ¼ QðJr=JÞðEg=V Þ by multiplying the ratio

of radiative to total recombination. The ratio of radia-

tive to total recombination is Q ¼ 1=4 because of aquarter of the excitons forms are singlets.

3. Results and discussions

We present calculation of single layer organic light

emitting diode characteristics using two carrier device

model that includes charge injection, transport, FNtunneling, and space charge effects in the organic mate-

rial. In this paper, we applied the device model to organic

material device using MEH-PPV where hole is majority

carrier. When the energy level of electron and hole is

Ec ¼ 2:9 eV, Ev ¼ 5:3 eV respectively, the energy gap can

be 2.4 eV. Dielectric coefficient is e ¼ 3 and charge den-

sity is n0 ¼ 1021 cm�3. We use the hole mobility para-

meters l0 ¼ 1:7� 10�6 cm2/V s and E0 ¼ 1� 105 V/cmin order to compare experimental result (Table 1). The

temperature in all calculations is room temperature.

Fig. 1 shows a comparison of the calculated I–Vcharacteristics of a 120 nm thick ITO/MEH-PPV/Al to

measurements of Ref. [19]. Fig. 1(a) shows a log–linear

plot and Fig. 1(b) shows a linear–linear plot. The barrier

for electron injection to MEH-PPV from Al is about 1.4

eV and for hole injection from ITO about 0.5 eV, andthese values were used in the calculation. Because the

barrier for electron injection is much larger than for hole

injection, the current flow is dominated by holes. The

calculation gives a good description of the measured I–Vcharacteristics over a wide current range in this injection

limited situation.

Fig. 2 shows a comparison of calculated and mea-

sured I–V characteristics of a 110 nm thick Au/MEH-PPV/Au. Fig. 2(a) shows a log–linear plot and Fig. 2(b)

shows a linear–linear plot. The barrier for hole injection

from Au into MEH-PPV is 0.1 eV and that value was

used in the calculation. For such small injection barriers,

the current is space charge limited. The barrier for

electron injection from Au is 2.3 eV and there are

essentially no electrons in the device. The same hole

mobility parameters were used. The calculation gives areasonable description for the measured I–V character-

istics in this space charge limited situation.

0 5 10 15 20 250.0

0.5

1.0

1.5

2.0

2.5

0 5 10 15 20 251E-8

1E-5

0.01

10

Bias (V)

(b)(a)

J (A

/cm

2 )

Bias (V)

30

Fig. 1. Comparison of calculated (solid line) and measured (dotted line, from Ref. [19]) current density as a function of bias voltage for a 120 nm ITO/

MEH-PPV/Al device: (a) log–linear plot; (b) linear–linear plot.

0 20 40 60 80 100 120

1E13

1E14

1E15

1E16

Hol

e D

ensi

ty [1

/cm

3 ]

Position [nm](a) (b)

5 [V] 10 [V] 15 [V] 20 [V]

0 20 40 60 80 100

1E16

1E17

1E18

1E19

Hol

e D

ensi

ty [1

/cm

2]

Position [nm]

5[V] 10 [V] 15 [V]

Fig. 3. Calculated hole density as a function of position for (a) ITO/MEH-PPV/Al device, (b) Au/MEH-PPV/Au device.

6 7 8 9 10 11 12 13 14 150.0

0.5

1.0

1.5

2.0

2.5

5 6 7 8 9 10 11 12 13 14

0.1

1

Bias [V]

J (A

/cm

2 )

Bias [V]

(b)(a)

15 5

Fig. 2. Comparison of calculated (solid line) and measured (dotted line, from Ref. [10]) current density as a function of bias voltage for a 110 nm Au/

MEH-PPV/Au device: (a) log–linear plot; (b) linear–linear plot.

12 J.-H. Lee et al. / Current Applied Physics 5 (2005) 9–14

In Fig. 3, we show the calculated hole densities for

four bias voltages as a function of position for the ITO/

MEH-PPV/Al structure in Fig. 3(a) and the Au/MEH-

PPV/Au structure in Fig. 3(b). The bias voltages in Fig.

3(a) are 20, 15, 10, and 5 V. In Fig. 3(b), the bias volt-

ages are 20, 15, and 5 V. In both figures, the hole

0 20 40 60 80 100 120

0.5

1.0

1.5

Elec

tric

Fiel

d [1

06 V/c

m2 ]

Position [nm](a) (b)

5 [V] 10 [V] 15 [V] 20 [V]

0 20 40 60 80 1000.0

0.5

1.0

1.5

Elec

tric

Fiel

d [1

06V/

cm2 ]

Position [nm]

5 [V] 10 [V] 15 [V]

Fig. 4. Calculated electric field as a function of position for (a) ITO/MEH-PPV/Al device, (b) Au/MEH-PPV/Au device.

J.-H. Lee et al. / Current Applied Physics 5 (2005) 9–14 13

injecting contact is at the left. The hole density for the

device in the ITO/MEH-PPV/Al structure, which has

a high hole injection barrier, is nearly spatially cons-

tant. It increases rapidly with increasing bias, however,

it does not significantly influence the electric field in the

device. The hole density for the device in the Au/MEH-

PPV/Au structure, which has a 0.1 eV barrier to holeinjection, varies strongly with position. The hole densi-

ties change significantly with bias and they are large

enough to strongly influence the electric field in the

device.

Fig. 4 shows the calculated electric fields as a function

of position for the ITO/MEH-PPV/Al structure in Fig.

4(a) and the Au/MEH-PPV/Au structure in Fig. 4(b) at

the same bias voltages as in Fig. 3. For the ITO/MEH-PPV/Al structure, the electric field is an essentially

constant function of position, whereas for the device in

the Au/MEH-PPV/Au structure, the electric field is a

strongly varying function of position. For the device in

the ITO/MEH-PPV/Al structure, the electric field at the

hole injecting contact has the correct sign to lead to

image force lowering of the injection barrier. In the Au/

MEH-PPV/Au structure, however, the sign of the elec-tric field is reversed because of the high hole density near

a hole injection electrode, so it can not lead to image

force lowering of the injection barrier.

4. Conclusion

We have studied single layer OLEDs characteristics

using bipolar transport device model that includes charge

injection, transport, FN tunneling, and space charge ef-

fects in the organic material. In this paper, we applied the

device model to organic material device usingMEH-PPVwhere hole is majority carrier. The calculations include

carrier diffusion and field dependent mobilities and

therefore they do not reduce to the simple analytic form

often used to describe the space charge limited regime

which is derived for field independent mobilities and

neglecting diffusion. We considered cases in which the

energy barrier to injection of electrons is much larger

than that for holes so that holes dominate the current

flow in the device and the temperature in all calculations

is room temperature. The model calculations show a

good description of the measured I–V characteristics

over a wide current range in both structures.

In the ITO/MEH-PPV/Al structure with high contact

barriers >0.3 eV, the hole density in the model showsnearly spatially uniform. It increases rapidly with

increasing bias, however, it does not significantly influ-

ence the electric field. Thus, in the device the electric

field is an essentially constant function of position. At

high bias, the electric field at the hole injecting contact

has the correct sign to lead to image force lowering of

the injection barrier. Thus, the dominant mechanism is

thermionic emission at small bias, and tunneling at highbias in this regime.

In the symmetric Au/MEH-PPV/Au structure with

very low contact barrier �0.1 eV, the hole density varies

strongly with position. Also, the hole densities change

significantly with bias and they are large enough to

strongly influence the electric field in the device. At high

bias, the sign of the electric field is reversed because of

the high hole density near a hole injection electrode, so itcan not lead to image force lowering of the injection

barrier in this regime. We also confirm that our bipolar

model analysis is more physical than single-carrier

model analysis in which the electric field in anode con-

tact region has non-negligible negative value.

Acknowledgements

This research was supported by the 2004 Hongik

University Academic Research Support Fund.

References

[1] C.W. Tang, S.A. VanSlyke, Appl. Phys. Lett. 51 (1987) 913.

[2] J.H. Burroughes, D.D.C. Bradley, A.R. Brown, R.N. Marks, K.

Mackay, R.H. Friend, P.L. Burns, A.B. Holmes, Nature (Lon-

don) 347 (1990) 539.

14 J.-H. Lee et al. / Current Applied Physics 5 (2005) 9–14

[3] D. Braun, A.J. Heeger, Appl. Phys. Lett. 68 (1991) 1982.

[4] N.C. Greenham, R.H. Friend, Solid State Phys. 49 (1995) 1.

[5] D.V. Khramtchenkov, V.I. Arkhipov, H. Bassler, J. Appl. Phys.

81 (1997) 6954.

[6] Y.-H. Tak, H. Bassler, J. Appl. Phys. 81 (1997) 6963.

[7] E.M. Conwell, M.W. Wu, Appl. Phys. Lett. 70 (1997) 1867.

[8] P.W.M. Blom, M.J.M. deJong, S. Breedijk, Appl. Phys. Lett. 71

(1997) 930.

[9] I.H. Campbell, T.W. Hagler, D.L. Smith, Phys. Rev. Lett. 76

(1996) 1900.

[10] P.S. Davids, I.H. Campbell, D.L. Smith, J. Appl. Phys. 82 (1997)

6319.

[11] I.H. Campbell, P.S. Davids, D.L. Smith, N.N. Barashkov, J.P.

Ferraris, Appl. Phys. Lett. 72 (1998) 1863.

[12] B.K. Crone, P.S. Davids, I.H. Cambell, D.L. Smith, J. Appl. Phys.

87 (2000) 1974.

[13] D.M. Pai, J. Chem. Phys. 52 (1970) 2285.

[14] H. Bassler, Phys. Status Solidi B 175 (1993) 15.

[15] Yu.N. Gartstein, E.M. Conwell, Chem. Phys. Lett. 245 (1996)

351.

[16] D.H. Dunlap, P.E. Parris, V.M. Kenkre, Phys. Rev. Lett. 77

(1996) 542.

[17] H. Meyer, D. Haarrer, H. Naarmann, H.H. Hohold, Phys. Rev. B

52 (1995) 2587.

[18] R.H. Fowler, L. Nordheim, Proc. R. Soc. London 119 (1928)

173.

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

[20] V.N. Abakumov, V.I. Perel, I.N. Yassievich, Nonradiative

Recombination in Semiconductors, North-Holland, Amsterdam,

1991, p. 108.

[21] D.L. Scharfetter, H.K. Gummel, IEEE Trans. Electron Dev. ED-

16 (1969) 64.