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Charge transport in Disordered Organic Semiconductors
Eduard MeijerDago de LeeuwErik van VeenendaalTeun Klapwijk
Outline
• Introduction:Ordered vs. Disordered semiconductorsThe field-effect transistor
• Parameter Definition:Threshold voltage and Mobility
• Modelling the temperature dependence
• Temperature dependence of the field-effect mobility
• Field dependence of the conductivity
• Conclusions
Conductionband
Valenceband
Eg
Electronenergy
Holeenergy
Simplified band diagram of a
semiconductor
Ordered system:conduction takes placein the extended states
(CB&VB)
IntroductionOrdered Semiconductor
IntroductionDisordered Semiconductor
• Non equivalent sites• Variation in energy levels
• Localized states have a Gaussian distribution• Charge carriers hop between localized states
HOMO
LUMO
E
DOS
EF
EF
E
DOS
EF
E
DOS
The tail of the Gaussian is approximated by an Exponential
IntroductionDisordered Semiconductor
H. Bässler, Phys. Stat. Sol. B, 175, 15 (1993).M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B. 57, 12964 (1998)
IntroductionField-Effect Transistor
DS
Vds
Vg
+
organic semiconductor
++
• What moves?• How (fast) does it move?
Basic questions:
Sn
S
C6H13
n
Poly(2,5-thienylene vinylene) (PTV)
Poly(3-hexyl thiophene) (P3HT)
Pentacene
IntroductionField-Effect Transistor
-20 -15 -10 -5 0
0
2
4
6
8
Vg=-10 V
Vg=-15 V
Vg=-20 Vx10-5
I ds [A
]
Vds [V]
• P-type semiconductors
• Charge carrier densityis varied with applied Vg.
• Mobility ~ 10-3-10-1 cm2/Vs
Vds=-2 V
Vds=-30 V
pentacene
-35 -30 -25 -20 -15 -10 -5 0 510-1110-1010-910-810-710-610-510-410-3
I ds [A
]Vg [V]
IntroductionField-Effect Transistor
2 important characterization parameters:
• Charge carrier mobility (steepness of the Ids-Vg-curve)• Threshold voltage (position of the curve)
Standard MOSFET modeling is often used for the parameterextraction:
linear:
saturation: ( )2, 2 thgiFEsatd VVCLWI −= µ
( )thgidFElind VVCVLWI −= µ,
IntroductionField-Effect Transistor
But standard MOSFET analysis is not allowed, since:
• These are accumulation devices (no inversion observed)• No extended state transport• Non-constant density of states
Threshold voltage can not be definedMobility depends on the charge density
Parameter definition
{
Instead of the threshold voltagefor accumulation FETs the flatband voltage is important#
#Appl. Phys. Lett. 80, 3838 (2002)*Tanase et al. submitted.
0 2 4 6 8 101016
1017
1018
1019
1020
Gate
Semiconductor
Source Drainx
Au Au
n++Si
SiO2
ρ [cm
-3]
x [nm]
Vg=-10 V Vg=-19 V
Parameter definition
Assumption that all induced carriers move with one mobility is still found to be reasonable*:
µFE=L
WCiVds
∂Ids
∂Vg
Modelling the temperature dependence
We use a hopping model in an exponential density of states*(based on polyled modelling)
*M.C.J.M. Vissenberg and M. Matters, Phys. Rev. B. 57, 12964 (1998)
EF
E
DOS
=
00
exp)(TkE
TkNEg
BB
t
( )( ) 12
03
0
40
0
0
0
0
0
22
sin2
2
−
−
−
=TT
s
FBgi
B
s
TT
cs
Bsdds
VVCTkB
TT
TT
TkTT
TLq
WVIε
εα
π
εσε
Conductivity prefactorOverlap parameter between localized sites
Width of exponential distributionFlat-band voltage
Modelling the temperature dependence4 modelling parameters
Sn
Modelling the temperature dependencePTV
Modelling the temperature dependencePentacene
S
C6H13
n
Modelling the temperature dependenceP3HT
But what do these parameters mean?
→ Look at the temperature dependence in a different way
Modelling the temperature dependence
T0 [K] σ0[106S/m] α-1 [Å] VFB [V]PTV 382 5.6 1.5 1
Pentacene 385 3.5 3.1 1
P3HT 425 1.6 1.6 2.5
Typically observed: • Thermally activated behaviour• Ea depends on the amount of induced charge (Vg)
0 2 4 6 8 10 12 1410-810-710-610-510-410-310-210-1100101102
µ FE [c
m2 /V
s]
Vg=-25 V
Vg=-20 V Vg=-15 V Vg=-10 V Vg=-5 V
1000/T [K-1]
T0*=EMN/kB
µ0
Ea
Temperature dependence of the field-effect mobility
Appl. Phys. Lett. 76, 3433 (2000)
ln(µ0) ~ Ea→
Meyer-Neldel Rule*.
*W. Meyer and H. Neldel, Z. Tech. Phys. 18, 588 (1937).
0.0 0.1 0.2 0.30.1
1
10
100
pref
acto
r µ0 [
cm2 /V
s]
Ea [eV]
nS
kBT0*=38 meV for pentacenekBT0*=42 meV for PTV
Common intersection point at T0*:
−−=
*11exp0
00 TkTkE
BBaFE µµ
Temperature dependence of the field-effect mobility
Temperature dependenceDiscussion
. T ,T ,T
:forlinearity improved No
41
31
21
−−−
kBT0* ~ 40 meV for pentacene, PTV, P3HTC60 and sexithiophene*.
→ common origin?
What are µ0and T0* ?
+?
Jump rate from site to site
i , Ei
j , Ej
+
The energy for a hop is suppliedby phonons.
δ−
δυ=
δ−υ=υ
TkHexp
kSexp
TkGexp
BBB00
STHG with δ−δ=δ
Jump rate:
A. Yelon and B. Movaghar, Phys. Rev. Lett. 65, 618 (1990).D. Emin Phys. Rev. B 61, 14543 (2000).
Entropy change results in Meyer-Neldel rule
Temperature dependenceDiscussion
Etc.
Single phonon → attempt frequency ↑
Multi phonon → entropy ↑
ln(µ0) ~ Ea
A. Yelon and B. Movaghar, Phys. Rev. Lett. 65, 618 (1990).
Temperature dependenceDiscussion
Temperature dependenceDiscussion
+
Ea
+
Ea+
Single ormulti-phonon?
hω0 < Eahω0 > Ea
A. Miller and E. Abrahams, Phys. Rev. 120, 745 (1960). D. Emin Phys. Rev. Lett. 32, 303 (1974).
Field dependence of the in-plane conductivity
E
Glass
Au
Field dependence in PTV
0 1 2 3 4 5 6 710-13
10-12
10-11
10-10
10-9
10-8
10-7 209 K 187 K 170 K 156 K 145 K 135 K 125 K 115 K
σ
[S/c
m]
E1/2 [(V/µm)1/2]
Sn
Synth. Metals. 121, 1351 (2001).
0 2 4 6 8 1010-1310-1210-1110-1010-910-810-710-610-510-410-3
49MV/m34MV/m25MV/m15MV/m
σ [S
/cm
]
1000/T [K-1]
Field dependence in PTV
T0*
−+
∆−= F
TkTkB
Tk BBB *11exp0
0µµ
Field dependence of the mobility
−+
∆−= F
TkTkB
Tk BBB *11exp0
0µµ
For PTV: T0* 520 K
For P3HT: T0* 550 K
−−=
*11)(exp0
00 TkTkVE
BBgaFE µµ
For PTV: T0* 490 K
For P3HT: T0* 510 K
Related?#
#A. Peled, L. Schein, Phys. Scripta 44, 304 (1991).
• Hopping in an exponential DOS gives a reasonabledescription of the charge transport
• Meyer-Neldel rule is related to the Field dependence
• T0* found in MNR and the field-dependent mobility indicates a multiphonon process (entropy)
• Entropy considerations are important to describe the charge transport (polaron)
Conclusions
