Charge Transport and Related Phenomena in Organic Devices

Noam Rappaport, Yevgeni Preezant, Yehoram Bar, Yohai Roichman, Nir Tessler

Microelectronic & Nanoelectronic Centers, Electrical Engineering Department, Technion, Haifa 32000, Israel

Oren Tal, Yossi Rosenwaks,Dept. of Physical Electronics, Faculty of Engineering, Tel Aviv

University, Tel Aviv 69978, Israel

Calvin K. Chan and Antoine KahnDept. of Electrical Engineering, Princeton University, Princeton NJ

08544, USA

Charge Transport

• Short Introduction

(or the things we tend to neglect)

• Simplified Device-Oriented Approach

• FETs (charge density & Electric Field)

• PN Diodes

• Thin film device

Highlight Inconsistencies

Hopping conduction model

• Conjugated segments “States”• Charge conduction non coherent hopping

x

What are the important factors?

1. Energy difference

2. Distance

3. Similarity of the Molecular structures

1. What is the statistics of energy-distribution?

2. What is the statistics of distance-distribution?

3. Is it important to note that we are dealing with molecular SC? Do we need to use the concept of polaron?

Detailed Equilibrium

1 1i j ij j i jif E f E f E f E

exp

j iij

ji kT

, 1 1 exp /i if E E kT

exp /

1

j i j iij j i

t

E E kT E EE E

else

0

exp / exp

1

j i j iij

E E kT E E

else

ijR

Anderson:

Ei

Ej

Polaron Picture

20 exp( )exp exp

2 2 8

0.4

j i j ibij

b

b

Er

kT kT kTE

E eV

0

exp / exp

1

j i j iij

E E kT E E

else

ijR

Anderson (Miller Abrahams)

E

QConfiguration co-ordinate

2

0

2 2max

0

exp

exp

E

E

k

C

Morphology or TopologySpatial (Off Diagonal) Disorder

20%

100%20%

H. Bassler, Phys. Stat. Solid. (b), 175,15, (1993)

Mean Medium Approximation

X0X0-X X0+X

Energy

Physical picture is GREATLY relaxed to allow for Charge Density and Electric Field effects is a single model Y. Roichman & Nir Tessler 2003

10-7

10-6

10-5

10-4

10-3

10-2

10-1

400 500 600 700 800 900

Mo

bilit

y (a

.u.)

(Electric Field)0.5 (V/cm)0.5

/kT

Mean Medium Approximation(at low charge density)

2 2 2 1/ 2exp 4 / 9 exp C E

C=2.5*10-4 =2

3

4

5

6

7

Dashed line – Fit using

Y. Roichman, et. al., Phys. Stat. Solidi a-201 (6), 1246-1262 (2004)

Mean Medium Approximation

=5kT

=4kT

=7kT

Pk =0.73-1.17 exp1.65

“Unified” percolation models predict much higher density dependence:2

0.73-1.17 2 exp1.65

10-5

10-4

10-3

10-2

10-6 10-5 10-4 10-3 10-2 10-1

Mob

ility

(a.

u.)

Relative Charge Density

Limitations of the MMA• Assumes equilibrium

– Can not model intrinsically non-equilibrium density of states (as exponential).

– Can not model a sample with preferential paths (percolation).

• Assumes that the sample is uniform on the length scale defined by the distance between contacts.

But it actually shares the assumptions used with any device model

Choose material that shows less mixed phases.

Shaked et. al., Adv mat, 15,913, 2003

Role of MW

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

0 5 10 15 20

Mob

ility

[cm

2 V-1

s-1]

Gate Voltage (V)

MW=1M

MW=2,8M

MW=0.1M

550 600 650 700 750 800600 650 700 750550 600 650 700 750

Wavelength (nm)

0.1M 1M 2.8M

550 600 650 700 750 800600 650 700 750550 600 650 700 750

Wavelength (nm)

0.1M 1M 2.8M

Eliminate parasitic currents

Close topology

10-3

10-2

10-1

100

101

102

-10 -8 -6 -4 -2

So

urce

Cu

rre

nt (

nA

)

Gate-Source Bias (V)

10-6

10-5

10-4

0.1110

10111012

Cha

rge

Mo

bili

ty (

cm2 v-1

s-1)

Insulator Potential Drop (V)

Charge Density (cm-2)

10-3

10-2

10-1

100

101

102

-10 -8 -6 -4 -2Sou

rce

-Dra

in C

urre

nt (

nA)

Gate-Source Voltage (V)

-1-2-4

-1-2

-4-8

-3

VDS=Mobility = ?

Need to account for:1. It is density dependent (varies

along the channel)2. Real DOS is not single

Gaussian (density dependence is “unknown”)

Develop a method for a general density dependence

Transistors

O. Katz, Y. Roichman, et. al, Semicond. Sci. Technol. 20, 90-94 (2005)

N. Tessler & Y. Roichman, Organic Elect., 2005.Vg

W

LSiO2

W

L

Insulator

Source Drain

ModelDeduced

MMARoichman et. al.

120meV

PercolationPasveer et. al.

Coehoorn et. al.

75meV

K= 0.38Pk

But the polymer is MEH-PPV

Extracting

1. Use low VDS

2. Do not use DS

GS

I

V

Field dependent at 2-3x103V/cm.A longer length scale, as in correlation, is required

-1

-4

10-6

10-5

10-4

0.1110

10111012

Cha

rge

Mo

bili

ty (

cm2v-1

s-1)

Insulator Potential Drop (V)

Charge Density (cm-2)

Can we use MMA

to describe LEDs too

Can we use Semiconductor Device model

to describe 100nm thick device?

hhhhh ndx

dDEnJ

Current continuity Eq.

To model LEDs we need to be able to predict the charge density distribution inside the device

charge density distribution inside a device is governed by D/

Y. Roichman and N. Tessler, Applied Physics Letters 80, 1948 (2002).

Generalized Einstein-Relation:

2Low 0µ µ exp 2.25c E

maxµ=µ (1+(tanh((p/0.05).^ ))µ /µ );Low Low

=0.73-1.17 1 exp 1 /1.65

3 /D DOSp P P

( 3)max 0µ 10 µ

Simple expression to fit them all

For the MMA model :

N. Tessler & Y. Roichman, Organic Elect., 2005.

10-5

10-4

10-3

10-2

10-1

0 200 400 600 800

(Electric Field)0.5

2x1014

1015

4x1016

1018

1019

Mob

ility

(a.

u.)

=7kT

Use General Einstein Relation to Model Junctions

• Semiconductor / Semiconductor (PN diode)

• Metal / Semiconductor (contact)

1aqV

kTe pJ x e

nK

1 / 2fn K

Ideality Factor:

0

0

1.2 1.61 1 / 2

f

T

TnT

T

Exponential DOS

1

1.5

2

2.5

3

3.5

4

30 40 50 60 70 80

100meV

130

=180meVId

ea

lity

Fa

cto

r

1/kT

Gaussian DOS

1

1.5

2

2.5

3

3.5

4

30 40 50 60 70 80

100meV

130

=180meVId

ea

lity

Fa

cto

r

1/kT

Gaussian DOS

Organic /Organic JunctionP N

N. Tessler & Y. Roichman, Organic Elect., 2005.

1

1.5

2

2.5

3

3.5

4

30 40 50 60 70 80

100meV

130

=180meV

Ide

alit

y F

act

or

1/kT

Gaussian DOS

1

1.5

2

2.5

3

3.5

4

30 40 50 60 70 80

100meV

130

=180meV

Ide

alit

y F

act

or

1/kT

Gaussian DOS

Model the contact to LED as a transport problem

Fimage UU

-ExUF max,eff

Energy

Distance , x

xo

Fimage UU

max,eff

Energy

Distance , x

xo

Im016age

qU

x

UBand

M

Poly

B M Poly

Model the contact to LED as a transport problem

Equilibrium at the contact interface defines the charge density on the organic side

Transport in contact region & bulk is modeled using semiconductor equations

e e e

dnJ qn E qD

dxq

E nx

Gaussian

nature

and D (or D/) are functions of density

Y. Preezant and N. Tessler, JAP 93 (4), 2059-2064 (2003).

Y. Roichman, et. al., Phys. Stat. Solidi a-201 (6), 1246-1262 (2004)

Model the contact to LED as a transport problem

Results:

We could reproduce effects of – barrier temperature ….BUT – each experiment required a different physical set of parameters to make the fit quantitative.

Take home message: 1. The Device Model doesn’t work well 2. The contact region and bulk may be governed by a different picture

Arkhipov – non equilibrium at the contact leads to injection that is limited by hops into a Gaussian DOS (1nm insulating gap will make it valid).

Baldo – The metal enhances disorder at the contact region only

V. I. Arkhipov, et. al., Phys. Rev. B 59 (11), 7514-7520 (1999).B. N. Limketkai and M. A. Baldo, Phys. Rev. B 71, 085207 (2005

Anything else could be wrong?

Are there Concerns Regarding LEDs

2

4ˆ ( , ) h

x Et

D tp x t e

22 0.026LL DX

V V

~10nm

100nm

Filaments ?

Curren

tTime

Time of flight measurement(excitation = step function)

t

But step function is better suited for the understanding of devices as it has the same steady state!

A linear part a dominant mobility

Transient measurement(in thin, 300nm, films)

0 1 2 3

0

2

4

manual mobility estimation 29k[a

.u.]

Sec

Rgnd29k Linear29k

Low excitation density

Hard to find a linear slope

Ph

oto

cu

rre

nt

Mobility Distribution

2

2 0

dV t V

I t A P q d g d t g de e e e e edd

V t

Saturated Pathways Unsaturated Pathways

1. Thick Films: V.I. Arkhipov, E.V. Emelianova, G.J. Adriaenssens, H. Bässler, J. of Non-Crystalline Solids 299-302 (2002)2. Thin Films (experimental): R. Österbacka et al., Synthetic Metals 139,811-813, 2003

Fitting with ModelTransient Fit to Measurement

Mobility Distribution Function

220

1 021

220

1 0 022

e

e eg foro e e

e eg foro e e

g

Intensity e (average) [cm2/(Vs)] Normalized CW QE

Low 1.87x10-9 1 Medium 3.6x10-9 0.6

High 6.6x10-9 0.3

Are there Concerns Regarding LEDs

2

4ˆ ( , ) h

x Et

D tp x t e

22 0.026LL DX

V V

~10nm

100nm

Filaments ?

Motion on a 3D grid

Note:

the “long jumps” are due to the cyclic conditions at Y & Z axis

Monte Carlo(Hopping in Gaussian DOS)

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6

Bro

ade

ning

at t

he o

utpu

t (n

m)

Applied Voltage (V)

Monte-Carlo

Drift-diffusion

6D kT

q

Conclusion

• Are all types of devices “seeing” the same microscopic physical picture? (don’t think so)

• New description for dispersive transport (Filaments, Stability?)

Thank You

2 2 2 2 1/ 20

2 2 2 1/ 20

4exp exp for 1.5

9

4exp exp 2.25 for 1.5

9

C E

C E

C=3x10-4 (cm/Vs)0.5

Spatial (Off Diagonal) Disorder

2 10;

0..3.26

0..0.2.3

a

a

a

x

y

0

1

2

4

5

6

0

6

1

1

1

5

5

5

44

4

443

33

3

333

2

2

2

2

2

2

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6

Nu

mbe

r o

f Site

s

Energy

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5 6

Num

ber

of S

ites

Energy

2 2 1/ 20

2 1/ 20

exp 2 / 3 exp for 1.5

exp 2 / 3 exp 2.25 for 1.5

C E

C E

C=3x10-4 (cm/Vs)0.5

hhhhh ndx

dDEnJ

Current continuity Eq.

To model LEDs we need to be able to predict the charge density distribution inside the device

f

h

hhh dE

dn

nD

1

Equilibrium conditions(existence of a Fermi level + constant temperature)

GeneralizedEinstein-Relation(Ashcroft, solid state physics)

charge density distribution inside a device is governed by D/

Y. Roichman and N. Tessler, Applied Physics Letters 80, 1948 (2002).