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Nonlinear Optics and Quantum Optics
April 10, 2007
Nonlinear Optics and Quantum Optics, Vol. 37, pp. 239–247
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Energetic Disorder at the Interface Between
Disordered Organic Material and Metal
Electrode
S. V. NOVIKOV1 AND G. G. MALLIARAS2
1
A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Moscow 119991, Russia
2
Materials Science and Engineering, Cornell University, Ithaca, NY 14853–1501
The physics of organic disordered materials is dominated by the effects
of energetic disorder. We show that image forces reduce the electrostatic
component of the total energetic disorder near an interface with a
metal electrode. Typically, the standard deviation of energetic disorder
is dramatically reduced at the first few layers of organic semiconductor
molecules adjacent to the metal electrode. This means that the use
of bulk disorder parameters (such as standard deviation of disorder)
for description of the energetic disorder at the interface is poorly
justified even in the case of identical spatial and chemical structure of
the organic material at the interface and in the bulk of the transport
layer. Implications for charge injection into organic semiconductors
are discussed.
Key words: metal/organic interface, energetic disorder, charge carrier injection
INTRODUCTION
The performance of any organic electronic device depends to a very large
extent on effective carrier injection [1]. For this reason injection in organic
devices is a field of active study. Recently, it was recognized that energetic
disorder in organic materials used in today’s devices affects the injection
efficiency [2–4]. First, disorder was shown to increase injection and, second,
it was proposed as a major reason for the unusually weak temperature
dependence of the injected current [5, 6].
The injection properties of metal/organic interfaces depend on the
properties of a thin organic layer directly contacting with the metal. It is
well known that the structure of this interface layer is typically different
from the bulk structure of the organic material. For this reason we may
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suspect that the variance σi2 of the energetic disorder at the interface differs
from the variance σb2 of the disorder in the bulk of the organic material.
In literature [2–4], a calculation of the effect of energetic disorder on the
injection has been carried out using bulk disorder parameters (basically, its
variance σb2 ). To some extent this could be explained by lack of any detailed
knowledge of the structure of the interface layer. In addition, experimental
data of temperature dependence of the injected current seem to supports the
idea that σb ≈ σi [5]. At the same time, it is well known that frequently a
surface dipole layer is formed directly at the interface, providing an abrupt
leap in carrier energy in the range of 0.3–1.0 eV [7]. It is reasonable to
assume that such a layer has some degree of disorder and, thus, induces
additional energetic disorder in neighboring layers of organic materials [6].
The magnitude of this energetic disorder should decay while going away
from the interface, so σi > σb , but this magnitude is completely unknown;
in the calculations carried out in Ref. [6] very speculative parameters have
been used to estimate σi . In some situations we cannot neglect absorption
of the additional components at the interface (for example, in the case of
spin casting) or its modification because of the chemical reaction between
the electrode material and the molecules of organic material. This means
that the structure of the few layers of organic materials closest to the
electrode could be very different from the bulk structure of the organic
transport layer. Hence, we cannot expect that σi should be the same as σb .
ENERGETIC DISORDER AT THE INTERFACE:
GENERAL CONSIDERATION
In this paper we are going to show that the problem of inequality of σi and
σb has an additional twist, because in organic devices sandwiched between
conducting electrodes the bulk disorder itself depends on the proximity
to the electrode. A well-known fact is that a significant part of the total
energetic disorder in organic materials has an electrostatic origin. For polar
materials this is the dipolar disorder [8–10], while for non-polar materials
it is the quadrupolar disorder [11]. Estimations show that for the dipolar or
quadrupolar energetic disorder the corresponding values of σ are pretty close
to 0.05–0.1 eV for reasonable values of dipolar and quadrupolar moments
and intermolecular distances [8–11]. At the same time, a vast amount
of experimental data indicates that the mobility temperature dependence
in disordered organic materials requires values of σ in this very range
[12]. Next, the modern explanation for the Poole-Frenkel mobility field
dependence log µ ≈ const + bE1/2 in polar organic materials relates it to
the particular spatial behavior of the energy-energy correlation function
C(r) = <U (r)U (0)> ∝ 1/r that arises because of the dipolar contribution to
the total random carrier energy U (r) [9] (here the angular brackets denote
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the average over dipole locations and orientations). By measuring of b
we can calculate the dipolar contribution to the total σ , and again, this
contribution is a significant part of the total σ [13]. We can reasonably
assume that in a typical situation a very significant (in fact, dominant)
part of the total energetic disorder in the bulk of organic materials is of
electrostatic origin. Our major goal in this paper is to demonstrate that the
electrostatic disorder at the vicinity of metal/organic interface differs from
the bulk disorder far away from the electrode.
Indeed, the electrostatic energetic disorder in organic materials is directly
proportional to the disorder in the spatial distribution of electrostatic potential,
generated by randomly situated and oriented dipoles or quadrupoles. In
organic layers sandwiched between conducting electrodes this spatial
distribution must obey a boundary condition at the electrode surface: at this
surface the potential should be a constant. Thus, at the electrode surface
there is no energetic disorder at all, irrespectively to how disordered is the
material in the organic layer. This means that the magnitude of the dipolar
or quadrupolar disorder increases while going away from the interface,
asymptotically reaching its bulk value. Here we assume that there is no
significant increase of the dipolar or quadrupolar disorder directly at the
interface (i.e., a disordered surface dipole layer is absent). Now we are
going to support this general idea with the calculation of the variance of
the dipolar disorder in the vicinity of a conducting electrode.
DIPOLAR ENERGETIC DISORDER AT THE INTERFACE:
CALCULATION
Let us consider the simplest model of a rigid disordered polar organic
material where the randomly oriented (and orientationally uncorrelated)
point dipoles occupy the sites of a simple cubic lattice with the lattice
scale a [8, 10]. We consider the vicinity of a metal electrode located at
z = 0, so the lattice occupies the half-space z > 0 with the first lattice
layer having distance a/2 from the electrode plane. Charge carrier energy
at any site m is the sum
φ(rm , rn ),
(1)
U (rm ) = e
n=m
where φ(r,rn ) is the electrostatic potential, generated by the dipole, located
at the site n. In the case of an infinite medium without electrodes
pn (r − rn )
φ(r, rn ) =
,
(2)
ε |r − rn |3
where ε is the dielectric constant of the medium and pn is the dipole
moment, while at the presence of the electrode the contribution of the
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image forces should be taken into account
φ(r, rn ) =
pn (r − rn ) pin (r − rin )
+ 3 ,
ε |r − rn |3
ε r − rin (3)
here pin = (− pnx , - pny , pnz ) is the image dipole located at rin = (x n ,
yn , −z n ). The variance of the disorder is
e2 p2 c 1
rn2 − z 2
1
2
2
σ (z) =< Um >=
+
+
,
3ε2 z >0 |rn − z|4
|rn + z|4
|rn − z|3 |rn + z|3
n
(4)
where c is the fraction of sites occupied by dipoles (details of the calculations
are provided in Ref. [14]). The lattice site with rn = z = (0, 0, z) is excluded
from the sum (4). Note that σ (0) = 0, as it should be, because if the
electrostatic potential is a constant for z = 0, then there is no electrostatic
disorder at this plane, no matter how many dipoles occupy the half-space
z > 0. Far away from the electrode [8]
σ 2 (∞) = σb2 =
e2 p2 c 1
e2 p2 c
≈ 5.51 2 4 .
2
4
3ε r =0 rn
ε a
(5)
n
We can perform an approximate analytical summation in Eq. (4) by
replacing the sum with the integral in close analogy to the method, used
in Ref. [15] (again, details of the calculations are provided in Ref. [14])
4πe2 p2 c
a0 2
2
−2z/a0
σ (z) = σb 1 −
1−e
.
(6)
, σb2 =
2z
3ε2 a 3 a0
Here a cut-off a0 ≈ a has been introduced to remove the divergence
for short distances. This cut-off is equivalent to the exclusion of the site
with rn = z in Eq. (4). To obtain an agreement between the bulk σb in
Eq. (6) and the corresponding exact value for the lattice model in Eq. (5)
we have to set a0 = 0.76 a [16]. This choice of a0 leads to a remarkably
good agreement between the approximate analytic expression (6) and the
result of the direct summation according to Eq. (4) in the whole range of
distance from the interface (see Figure 1). A visual comparison between
the typical distribution of the carrier random energy U (r) in the bulk of
polar organic material and at the layer of organic material nearest to the
electrode is shown in Figure 2.
DIPOLAR ENERGETIC DISORDER AT THE INTERFACE:
EFFECT ON CHARGE INJECTION
Note that for the transport sites situated within a distance of 5–6 lattice
sites to the interface, the amplitude of energetic disorder is significantly
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ENERGETIC DISORDER AT THE INTERFACE
1
0.8
σ2(z)/σ2b
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0.6
0.4
0.2
0
0
5
10
15
20
z/a
FIGURE 1
Dependence of σ 2 (z) on z: the solid line present the result of Eq. (6) for a0 = 0.76a,
while the squares correspond to the direct summation using Eq. (4).
FIGURE 2
Distribution of the carrier random energy U (r) in the bulk of the organic material (a) and
in the organic layer closest to the electrode (b). Black spheres indicate the sites with
U > 0, while the white ones indicate sites with U < 0, and the radius of the sphere is
proportional to the absolute value of U . Sites with |U | < 0.3 ep/εa 2 are not shown for the
clarity sake. Note the significant decrease of the amplitude of the disorder at the interface.
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decreased in comparison to its bulk value. Yet this very thin layer is of
crucial importance for injection in organic devices. We anticipate that the
reduction of σ should significantly affect the dependence of the injection
current density on temperature in comparison with the treatment with
σ (z) = const for any theory of charge injection into disordered organic
materials [2–4].
Let us illustrate the effect of the reduction of σ for the theory, suggested
in the paper by Arkhipov et al. [3], where the direct analytic formula for
injection current density makes the calculation relatively straightforward.
According to this model, the injected current density is
∞
J∝
∞
dz 0 exp(−2γ z 0 )wesc (z 0 )
dU Bol(U )g[U0 (z 0 ) − U ],
−∞
d
U0 (z 0 ) = −
2
e
− eEz 0 ,
4εz 0
(7)
where Bol(U ) = exp(-U /kT) for U > 0 and Bol(U ) = 1 otherwise, and
wesc (z) is the probability for a carrier to avoid the surface recombination
z0
wesc (z 0 ) =
d
∞
d
0 (z)
dz exp − UkT
dz exp
0 (z)
− UkT
.
(8)
Here E is the applied electric field, g(U ) is the density of states in the
organic material (a Gaussian density of states is usually assumed), γ is the
inverse localization radius, is the interface barrier, and d is the minimal
distance, separating the electrode surface and the first layer of the organic
material. A natural generalization of the Eq. (7) to our case is straightforward:
we have to let the density of states g depend on z through the Eq. (6). We
performed the calculation using parameters provided in Ref. [5] for the
injection of holes from the Ag electrode into poly-dialkoxy-p-phenylene
vinylene: = 0.95 eV, γ = 0.33 A−1 , E = 5 × 105 V/cm, σb = 0.11 eV,
and d = 12 A (it was assumed that d = a). Note that all these parameters
were used in Ref. [5] for the comparison between the experimental data and
Eq. (7) not as fitting parameters, but have been measured independently.
The result of the calculation is shown in Figure 3. A transformation of the
curve occurs as anticipated: because of the smaller σ at the interface, the
temperature dependence of the injected current becomes stronger and does
not agree with experimental data anymore. In fact, the agreement between
the experimental points and the curve, calculated using Eq. (7) for σ (z) =
const, is not as perfect as it appears to be, because we have to expect that
d < a is a better choice for the minimal distance to the electrode (a is the
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ENERGETIC DISORDER AT THE INTERFACE
0
-1
log10(JT/J300)
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-2
-3
-4
-5
3
4
5
1000/T, K
6
7
-1
FIGURE 3
Plot of the temperature dependence of the injected current density JT (normalized by the
corresponding density J300 for 300 K) for the injection of holes from the Ag electrode into
poly-dialkoxy-p-phenylene vinylene, calculated using Eq. (7) for σ (z) = const (solid lines)
and σ (z), calculate by Eq. (6) (broken line), correspondingly. The squares indicate the
experimental points from Ref. [5]. The upper solid line has been calculated for d = a/2,
and the lower one for d = a, correspondingly.
intersite separation). For d < a the curve, calculated by Eq. (7) for σ (z) =
const, goes up (see Figure 3, the upper solid curve), and the agreement
worsens. Additionally, small distances to the electrode are very important
in the integral (7), so the use of the macroscopic ε in Eq. (7) is dubious.
Again, the decrease in ε moves the curve for σ (z) = const in Figure 3
upwards.
All these reservations notwithstanding, if we believe that the model of
Arkhipov et al. [3] is valid, then the significant discrepancy between the
lower broken line and the experimental points in Figure 3 seems to be an
indication of the need to introduce an additional disorder (with σ ≈ 0.1 eV)
at the interface. The possible source of this additional disorder could be
the surface dipole layer. From this point of view, the experimental results,
provided in Ref. [5] and connected to our consideration, in fact support
the idea of a disordered surface dipole layer: we clearly need additional
disorder at the interface to compensate the decrease in the electrostatic
disorder, provided by the bulk molecules.
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Possible generalizations (taking into account the possible additional
spatial disorder at the interface, roughness of the metal/organic interface) do
not change our main conclusion that the electrostatic part of the energetic
disorder in organic materials, provided by molecules in the bulk of the
material, is significantly suppressed at the interface.
If a disordered surface dipolar layer is indeed formed at the interface,
the picture suggested in this paper has to be modified. In this case the
magnitude of the total energetic disorder could decrease with the increase
of the distance to the electrode, or it could still increase, depending on the
relative amplitudes of the bulk and surface contributions. Yet in any case,
the result of this paper should be taken into account if the amplitude of
the total disorder at the interface is estimated.
CONCLUSION
In conclusion, we have shown that the electrostatic energetic disorder that
provides the dominant part of the total energetic disorder in the bulk of
organic semiconductors decreases dramatically in the neighborhood of a
metal electrode. The ramification of this study is that disorder parameters
derived from bulk measurements do not describe first few layers near
the metal even in the most favorable case when the spatial and chemical
structure of the material at the interface is exactly the same as in the bulk.
As a result, simple models that predict enhancement of charge injection in
organic semiconductors due to presence of disorder need to be reexamined.
ACKNOWLEDGEMENTS
This work was supported by the ISTC grant 2207 and RFBR grants
05-03-33206 and 03-03-33067. The research described in this publication
was made possible in part by Award No. RE2-2524-MO-03 of the U.S.
Civilian Research & Development Foundation for the Independent States
of the Former Soviet Union (CRDF).
REFERENCES
[1] Scott, J. C. (2003). Metal–organic interface and charge injection in organic electronic
devices. J. Vac. Sci. Technol. A, 21, 521–531.
[2] Gartstein, Y. N., and Conwell, E. M. (1996). Field-dependent thermal injection into
a disordered molecular insulator. Chem. Phys. Lett., 255, 93–98.
[3] Arkhipov, V. I., Emelianova, E. V., Tak, Y. H., and Bässler, H. (1998). Charge injection
into light-emitting diodes: Theory and experiment. J. Appl. Phys., 84, 848–856.
[4] Burin, A. L., and Ratner, M. A. (2003). Charge Injection into Disordered Molecular
Films. J. Polymer Sci. B, 41, 2601–2621.
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247
[5] Van Woudenbergh, T., Blom, P. W. M., Vissenberg, M. C. J. M., and Huilberts,
J. N. Temperature dependence of the charge injection in poly-dialkoxyp-p-phenylene
vinylene. Appl. Phys. Lett., 79, 1697–1699.
[6] Baldo, M. A., and Forrest, S. R. (2001). Interface-limited injection in amorphous
organic semiconductors. Phys. Rev. B, 64, 085201.
[7] Ishii, H., Sugiyama, K., Ito, E., and Seki, K. (1999). Energy Level Alignment and
Interfacial Electronic Structures at Organic/Metal and Organic/Organic Interfaces. Adv.
Mater., 11, 605–625.
[8] Novikov, S. V., and Vannikov, A. V. (1995). Cluster Structure in the Distribution
of the Electrostatic Potential in a Lattice of Randomly Oriented Dipoles. J. Phys.
Chem., 99, 14573–14576.
[9] Dunlap, D. H., Parris, P. E., and Kenkre, V. M. (1996). Charge-Dipole Model for
the Universal Field Dependence of Mobilities in Molecularly Doped Polymers. Phys.
Rev. Lett., 77, 542–545.
[10] Dieckmann, A., Bässler, H., and Borsenberger, P. M. (1993). An assessment of the
role of dipoles on the density-of-states function of disordered molecular solids. J.
Chem. Phys., 99, 8136–8141.
[11] Novikov, S. V., and Vannikov, A. V. (2001). Charge Carrier Transport in Nonpolar
Disordered Organic Materials: What Is the Reason for Poole-Frenkel Behavior? Mol.
Crystals and Liquid Crystals, 361, 89–94.
[12] Borsenberger, P. M., and Weiss, D. S. (1997). Organic Photoreceptors for Imaging
Systems. New York: Marcel Dekker.
[13] Novikov, S. V., Dunlap, D. H., Kenkre, V. M., Parris, P. E., and Vannikov, A. V.
(1998). Essential Role of Correlations in Governing Charge Transport in Disordered
Organic Materials. Phys. Rev. Lett., 81, 4472–4475.
[14] Novikov, S. V., and Malliaras, G. G. (2005). Energetic disorder at the metal/organic
semiconductor interface. 20/07/2005, from http://arxiv.org/abs/cond-mat/0506762
[15] Novikov, S. V., and Vannikov, A. V. (2001). Charge induced energy fluctuations in
thin organic films: effect on charge transport. Synth. Metals, 121, 1387–1388.
[16] Dunlap, D. H., and Novikov, S. V. (1997). Charge transport in molecularly doped
polymers: a catalogue of correlated disorder arising from long-range interactions,
Proc. SPIE Int. Soc. Opt. Eng. 3144, 80–89.
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