In this article, we analyze the electric field dependence of the hole mobility in disordered poly(p-phenylene vinylene). The charge carrier mobility is obtained from Monte Carlo simulations. Depending on the field strength three regions can be identified: the percolation region, the correlation region, and the inverted region. Each region is characterized by a different conduction mechanism and thus a different functional dependence of the mobility on the electric field. Earlier studies have highlighted that Poole-Frenkel law, which appears in the correlation region, is based on the type of correlation caused by randomly distributed electric dipoles. This behavior is thus observed in a limited range of field strengths, and by studying a broader range of electric fields, a more fundamental understanding of the transport mechanism is obtained. We identify the electric fields determining the transitions between the different conduction mechanisms in the material and we explain their physical origin. In principle, this allows us to characterize the mobility field dependence for any organic material. Additionally, we study the charge carrier trapping mechanisms due to diagonal and off-diagonal disorder, respectively.

1.
J.
Wang
,
F.
Zhang
,
J.
Zhang
,
W.
Tang
,
A.
Tang
,
H.
Peng
,
Z.
Xu
,
F.
Teng
, and
Y.
Wang
, “
Key issues and recent progress of high efficient organic light-emitting diodes
,”
J. Photochem. Photobiol., C
17
,
69
-
104
(
2013
).
2.
D.
Wohrle
and
D.
Meissner
, “
Organic Solar Cells
,”
Adv. Mater.
3
,
129
(
1991
).
3.
J.
Garland
,
T.
Biegala
,
M.
Carmody
,
C.
Gilmore
, and
S.
Sivananthan
, “
Next-generation multijunction solar cells: The promise of II-VI materials
,”
J. Appl. Phys.
109
,
102425
(
2011
).
4.
X.
Guo
,
M.
Baumgarten
, and
K.
Müllen
, “
Designing π-conjugated polymers for organic electronics
,”
Prog. Polym. Sci.
38
,
1832
(
2013
).
5.
L.
Muccioli
,
G.
D’Avino
,
R.
Berardi
,
S.
Orlandi
,
A.
Pizzirusso
,
M.
Ricci
,
O.
Roscioni
, and
C.
Zannoni
, “
Supramolecular organization of functional organic materials in the bulk and at organic/organic interfaces: A modeling and computer simulation approach
,”
Topics in Current Chemistry
(
Springer
,
2013
), pp.
1
63
.
6.
R. A.
Marcus
, “
On the theory of oxidation-reduction reactions involving electron transfer. I
,”
J. Chem. Phys.
24
,
966
(
1956
).
7.
C.
Andrieu
,
A.
Doucet
, and
R.
Holenstein
, “
Particle Markov chain Monte Carlo methods
,”
J. R. Stat. Soc. B
72
,
269
(
2010
).
8.
M.
Jakobsson
,
M.
Linares
, and
S.
Stafström
, “
Monte Carlo simulations of charge transport in organic systems with true off-diagonal disorder
,”
J. Chem. Phys.
137
,
114901
(
2012
).
9.
J.
Brédas
,
D.
Beljonne
,
V.
Coropceanu
, and
J.
Cornil
, “
Charge-transfer and energy-transfer processes in pi-conjugated oligomers and polymers: A molecular picture
,”
Chem. rev.
104
,
4971
(
2004
).
10.
V.
Lemaur
,
D.
da Silva Filho
,
V.
Coropceanu
,
M.
Lehmann
,
Y.
Geerts
,
J.
Piris
, and
J.
Cornil
, “
Charge transport properties in discotic liquid crystals: A quantum-chemical insight into structure-property relationships
,”
J. Am. Chem. Soc.
126
,
3271
(
2004
).
11.
Y.
Olivier
,
V.
Lemaur
,
J.
Brédas
, and
J.
Cornil
, “
Charge hopping in organic semiconductors: Influence of molecular parameters on macroscopic mobilities in model one-dimensional stacks
,”
J. Phys. Chem. A
110
,
6356
(
2006
).
12.
F.
Castet
,
P.
Aurel
,
A.
Fritsch
,
L.
Ducasse
,
D.
Liotard
,
M.
Linares
, and
D.
Beljonne
, “
Electronic polarization effects on charge carriers in anthracene: A valence bond study
,”
Phys. Rev. B
77
,
115210
(
2008
).
13.
J.
Frenkel
, “
On pre-breakdown phenomena in insulators and electronic semi-conductors
,”
Phys. Rev.
54
,
647
(
1938
).
14.
S.
Novikov
, “
Hopping charge transport in organic materials
,”
Russ. J. Electrochem.
48
,
388
(
2012
).
15.
S.
Novikov
,
D.
Dunlap
,
V.
Kenkre
,
P.
Parris
, and
A.
Vannikov
, “
Essential role of correlations in governing charge transport in disordered organic materials
,”
Phys. Rev. Lett.
81
,
4472
(
1998
).
16.
Y.
Garstein
and
E.
Conwell
, “
High-field hopping mobility in molecular systems with spatially correlated energetic disorder
,”
Chem. Phys. Lett.
245
,
351
(
1995
).
17.
D.
Dunlap
,
P.
Parris
, and
V.
Kenkre
, “
Charge-dipole model for the universal field dependence of mobilities in molecularly doped polymers
,”
Phys. Rev. Lett.
77
,
542
(
1996
).
18.
D.
Dunlap
,
V.
Kenkre
, and
P.
Parris
, “
What is behind the E ?
,”
J. Imag. Sci. Tech.
43
,
437
(
1999
).
19.
S.
Novikov
and
A.
Vannikov
, “
Distribution of electrostatic potential in a lattice of randomly oriented dipoles
,”
JETP
79
,
482
(
1994
).
20.
S.
Novikov
and
A.
Vannikov
, “
Cluster structure in the distribution of the electrostatic potential in a lattice of randomly oriented dipoles
,”
J. Phys. Chem.
99
,
14573
(
1995
).
21.
H.
Bässler
, “
Charge transport in disordered organic photoconductors, a Monte Carlo simulation study
,”
Phys. Status Solidi B
175
,
15
(
1993
).
22.
W.
Jorgensen
and
J.
Tirado-Rives
, “
The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin
,”
J. Am. Chem. Soc.
110
,
1657
(
1988
).
23.
W.
Jorgensen
,
D.
Maxwell
, and
J.
Tirado-Rives
, “
Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids
,”
J. Am. Chem. Soc.
118
,
11225
(
1996
).
24.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
, “
GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation
,”
J. Chem. Theory Comput.
4
,
435
(
2008
).
25.
D.
van der Spoel
,
E.
Lindahl
,
B.
Hess
,
G.
Groenhof
,
A.
Mark
, and
H.
Berendsen
, “
GROMACS: Fast, flexible, and free
,”
J. Comput. Chem.
26
,
1701
(
2005
).
26.
E.
Lindahl
,
B.
Hess
, and
D.
van der Spoel
, “
GROMACS 3.0: A package for molecular simulation and trajectory analysis
,”
J. Mol. Model.
7
,
306
(
2001
).
27.
H.
Berendsen
,
D.
van der Spoel
, and
R.
van Drunen
, “
GROMACS: A message-passing parallel molecular dynamics implementation
,”
Comput. Phys. Commun.
91
,
43
(
1995
).
28.
S.
Nosé
, “
A molecular dynamics method for simulations in the canonical ensemble
,”
Mol. Phys.
52
,
255
(
1984
).
29.
W. G.
Hoover
, “
Canonical dynamics: Equilibrium phase-space distributions
,”
Phys. Rev. A
31
,
1695
(
1985
).
30.
M.
Parrinello
and
A.
Rahman
, “
Polymorphic transitions in single crystals: A new molecular dynamics method
,”
J. Appl. Phys.
52
,
7182
(
1981
).
31.
S.
Nosé
and
M.
Klein
, “
Constant pressure molecular dynamics for molecular systems
,”
Mol. Phys.
50
,
1055
(
1983
).
32.
R.
Mulliken
,
C.
Rieke
,
D.
Orloff
, and
H.
Orloff
, “
Formulas and numerical tables for overlap integrals
,”
J. Chem. Phys.
17
,
1248
(
1949
).
33.
A.
Hansson
and
S.
Stafström
, “
Intershell conductance in multiwall carbon nanotubes
,”
Phys. Rev. B
67
,
075406
(
2003
).
34.
D.
Dunlap
and
S.
Novikov
, “
Charge transport in molecularly doped polymers: A catalogue of correlated disorder arising from long-range interactions
,”
SPIE
3144
,
80
(
1997
).
35.
S.
Novikov
,
D.
Dunlap
, and
V.
Kenkre
, “
Charge carrier transport in disordered organic materials: Dipoles, quadrupoles, traps, and all that
,”
SPIE
3471
,
181
(
1998
).
36.
B.
Hartenstein
,
H.
Bässler
,
S.
Heun
,
P.
Borsenberger
,
M.
van der Auweraer
, and
F.
de Schryver
, “
Charge transport in molecularly doped polymers at low dopant concentrations: Simulation and experiment
,”
Chem. Phys.
191
,
321
(
1995
).
37.
V.
Kažukauskas
,
M.
Pranaitis
,
L.
Sicot
, and
F.
Kajzar
, “
Negative mobility dependence on electric field in poly(3-alkylthiophene)s
,”
Mater. Sci.
12
,
187
(
2006
).
38.
B.
Limketkai
,
P.
Jadhav
, and
M.
Baldo
, “
Electric-field-dependent percolation model of charge-carrier mobility in amorphous organic semiconductors
,”
Phys. Rev. B
75
,
113203
(
2007
).
39.
C.
Vijila
,
B.
Balakrisnan
,
C.
Huang
,
Z.
Chen
,
C.
Zhen
,
M.
Auch
, and
S.
Chua
, “
Non-dispersive hole transport in a novel trifluoromethyl-biphenyl substituted PPV derivative
,”
J. Phys.: Conf. Ser.
28
,
53
(
2006
).
40.
S.
Quan-Min
,
H.
Yan-Bing
,
L.
Jing
,
J.
Hui
, and
L.
Yun-Bai
, “
Hole transport properties of MEH-PPV at different excitation wavelengths
,”
Chin. Phys. Lett.
23
,
950
(
2006
).
41.
S.
Raj Mohan
,
M.
Singh
, and
M.
Joshi
, “
Negative field dependence of mobility in disordered organic thin films due to non-equilibrium charge transport
,”
Org. Electron.
11
,
1642
(
2010
).
42.
G.
Owen
,
J.
Sworakowski
,
J.
Thomas
,
D.
Williams
, and
J.
Williams
, “
Carrier traps in ultra-high purity single crystals of anthracene
,”
J. Chem. Soc., Faraday Trans. 2
70
,
853
(
1974
).
You do not currently have access to this content.