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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).