- Email: [email protected]
Theory of carrier accumulation in organic heterojunctions
Accepted Manuscript Theory of carrier accumulation in organic heterojunctions Jun-ichi Takahashi PII:
S1566-1199(18)30559-7
DOI:
https://doi.org/10.1016/j.orgel.2018.10.044
Reference:
ORGELE 4960
To appear in:
Organic Electronics
Received Date: 31 August 2018 Revised Date:
28 October 2018
Accepted Date: 29 October 2018
Please cite this article as: J.-i. Takahashi, Theory of carrier accumulation in organic heterojunctions, Organic Electronics (2018), doi: https://doi.org/10.1016/j.orgel.2018.10.044. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Metal-Semiconductor Junction Organic Heterojunction
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Theory of Carrier Accumulation in Organic Heterojunctions
1Electronic
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Jun-ichi Takahashi, Materials Development Center, Idemitsu Kosan Co., Ltd.,
1280 Kami-izumi Sodegaura, Chiba, 299-0293, Japan
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Abstract
Even though organic light emitting diodes (OLED) have been achieving commercial
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successes, their device physics have been under debating. In this article, we develop a junction theory of organic heterojunctions, which describes the carrier accumulation dynamics in them. We derive an equation, which is the counterpart of the Mott-Schottky relation in the metal-semiconductor contact. We will show that the essence of the carrier transport control in organic devices is the control of the internal electric field and therefore the drift motion, whereas that in the semiconductors is the control of the carrier population by shifting the Fermi energy and therefore the diffusion motion.
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Tang’s invention of organic electronic devices with layered ultrathin layers of small organic molecules was a new paradigm of controlling the carrier transport in polaron
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conductors rather than only a finding of the substitutes of Si semiconductors.
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Key words: Organic Light Emitting Diode, Heterojunction, Mott-Schottky relation, Carrier accumulation, polaron conductor, quasiconductor.
_____________________________ a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
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Highlights A junction theory in organic heterojunctions is presented to describe the carrier accumulation dynamics in organic electronic devices. organic heterojunctions.
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The counterpart of the Mott-Schottky relation of the Schottky contact is given for The quasiconductor concept is proposed to enlighten the distinct features of polaron
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conduction than the carrier dynamics in semiconductors.
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1. Introduction It is said that the 20th century was the era of quantum mechanics. One of its most prosperous achievements was the development of semiconductor devices, which has
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been the basis of the technology of the modern society. The molecular electronics has progressed steadily behind the development of the Si technology. It was reported that polycrystalline powder of some aromatic molecules showed an electrical conductivity having the similar temperature dependence of the intrinsic semiconductors in 1950 [1]. A notable topic in the end of 70’s was the conductive polymers, which were typical band
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systems of one-dimensional semiconductor systems [2,3]. In 1986 when the end of the 20th century approached, Tang and Slyke presented a novel organic devices, the functionalities of which were separated in different ultrathin layers [4,5]. This
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innovative concept opened a new world of organic active electronic devices of not only diodes but also solar cells and FETs [6]. Nowadays, OLED has been studied extensively and regarded as a leading candidate of the display devices of the next generation. However, even though the OLED has already achieved commercial successes, our understanding of their device physics has been surprisingly poor. The development of semiconductor has been based on the fundamental research of the underlying physics: Wilson’s band theory [7], contact phenomena theory of Mott, Davydov and Schottky
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[8-10], photoeffect and tunneling research of Frenkel and Ioffe [11]. Their counterparts of organic devices have not been established well to forecast the device performance quantitatively. For example, let’s consider the dynamics of MIS capacitor. As it is well known, a voltage-controllable capacitor can be made using a metal-semiconductor
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contact [12]. Similarly, a voltage-controllable capacitor can be made also using a metal-organic contact. However, we have failed to achieve the controllable capacitors
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with single organic layer. At least two organic layers or bulkhetero structure are needed. Furthermore, we have shown, by the impedance spectroscopy, their carrier dynamics is quite different from that of metal-semiconductor (Schottky) contact [13]. For the Schottky contact, the insulating part is the charged depletion layer, where carriers are excluded from the neutral conductive region. On the other hand, for the organic heterojunctions, the insulating part must be the neutral region. Instead of the formation of the charged insulating depletion layer in Schottky contact, the conductive accumulation layer evolves in organic heterojunctions. Nevertheless, the device physics of the organic devices has been discussed under the same framework of the semiconductors. What is the meaning of the relation between the Schottky contact and the organic heterojunctions? 3
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In this article, we develop a junction theory, which describes the accumulation dynamics in the organic heterojunction. It is the counterpart for the polaron conductors of the junction theory for semiconductors. Based on the theory, we will discuss the essential nature, which distinguishes the organic devices from the Si semiconductor
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devices. 2. Theory
Because the OLEDs have at least two metal-organic contacts and several different
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organic layers to which different functionalities are assigned separately, the carrier injection and transport dynamics become complicated. Exhaustive efforts have been paid to analyze their dynamics of injection [14-16], transport [17, 18] and device
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properties [19-22]. However, it is not an easy task to have unified pictures of their interplays.
We have developed a method of Dynamic Modulus Plot (DMP) to analyze the carrier dynamics in layered organic devices [13]. Using the DMP method, we analyzed the simplest and the most basic device of ITO/NPD/Alq3/LiF/Al, which is made of a hole conducting and an electron conducting layers. This device seems to be the counterpart of the pn junctions and/or the Schottky contact in the semiconductor devices. However,
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there are quite differences from those of the pn junctions. (1) The equivalent circuit of the Schottky contact is a series connection of a resistor (R) and a capacitor (C), whereas that of the organic heterojunction is always the series connection of the parallel CR units and the C, which means dielectricity
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cannot be ignored at any time.
(2) The organic layers are neutral insulating ones at sufficiently large negative bias
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voltage, whereas the semiconductor layer of the Schottky contact is a neutral conductor.
(3) The carriers flow from the electrode into the organic layer in the case of organic heterojunctions, whereas that flows from the semiconductor to the electrode in the case of the Schottky contact.
The key point of the theory is that the bias voltage controls the space charge accumulation in the organic dielectrics. We must consider the potential balance among the space charge, the externally applied voltage and the polarization, whereas only the balance between the space charge potential and the externally applied voltage is taken into account in the Schottky contact. Before starting the discussion, it should be noted that the molecules discussed in this 4
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article are small molecules and usually they are used as amorphous states. Even though the band structure concept in organic materials is well established in the molecular crystals and conductive polymers [23, 24], the band structure exists hardly in these materials. Instead of the band structure, the isolated molecular orbitals delocalize at
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each molecule. The following discussion is not necessarily valid for conductive polymers and molecular crystal systems.
We define the coordinates as Fig.1. Region I is the dielectric layer of Alq3 with a
thickness of l, where spontaneous polarization, P=eEi, exists [25]. Region II and III are
the NPD layers, where the region II is the conductive part in which hole accumulates
and the region III is the one which remains to be insulating. The thickness of the
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accumulated region is t=d-l. The carrier distribution is governed by the Poisson
equation and the balance equation of the drift current and the diffusion current. 0=
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∆ =−
−
(1) (2)
, with charge density ρ, dielectric constant ε, conductivity σ=ρµ, mobility µ, and diffusion constant D. For one-dimensional configuration, ρ‘s in eq.(2) are replaced by ϕ using eq.(1) and we have an equation after integration,
, where
≡
=
(3)
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and A is a constant of integration. It is easy to get the general solution of
eq.(3) for constant µ and D. However, to calculate the solution in general form, which satisfies the boundary condition, is very tedious. For the simplicity of discussion, we set
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A to be zero in the following discussion. The solutions are.
ρ=2
or
ln"# − #$ % +
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ϕ=
(4-a)
( " ) * %+
ϕ=− #+
ρ=0
$
(4-b)
$
(5-a) (5-b)
From eq. (5-a) and (5-b), it is obvious that the above solutions are the cases without a current flow. The non-zero A solution will be necessary to describe the cases of a finite current flow, where electric-field-dependent mobilities must be taken into account. We set ϕ"0% = 0. From the continuity condition of the electric field and the potential, we obtain successively.
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"#% =
Region II:
".)
*%
( "#%
12
+
/0 #
=0
)
.)
*
*
(6-b)
−
/#
=
" )
*%
3 "#%
And then,
, where
Q = :.
"67 )68 %
4# = 2
=−
".)
3
=−
" )
*
*
−
/1
−
5
*
(8-a)
(8-b)
+
/1
−
" )
P#$ EQ ;
).
* %".) * %
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(
(7-b)
12 .)
=0 3 "#%
(7-a)
*
)
"# − 4% +
4 − #$ NO = L# M ? 1 − #$ 2
#$ = 1 +
.)
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3 "#%
.
+
( " ) * %+
"#% = 2 Region III:
(6-a)
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=-
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( "#%
Region I:
= ;"
(
−
3
−
(9)
(10)
/%
(11) (12-a)
*%
*%
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Eq.(9) is rewritten using the relation V = −
(12-b) 3 "=
− 4% +
3 "4%
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2 NOLR L P 2 12 ?1 − E− "= − 4% + ? + 1E = S + NOL NO 2 ; LON 1− 2 R
/1
(13)
, where t=d-l and e=E1-Ei . By combining eq.(12-a), (12-b) and (11). e=−
, where r =
5
5
C
?1 ± A1 + 4 D E
(14)
. Because e should be negative, the sign of the square root is taken as
positive. From the Einstein’s relation,
= GH. We define u = J
6
K
and we obtain,
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GH R =−4 X+1 ?12 ?1 − E − + E=S+ N X X−R Y
/1
(15)
The parameters in eq.(15) can be calculated experimentally from the DMP. As has been
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r = TUDJ .
Figure
(2-d)
are
the
plot
of
the
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and then
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discussed in ref.13, Q can be calculated from the DMP as Q = ρt = eq.(15)
using
the
data
of
ITO/NPD(60)/Alq3(100)/LiF/Al in ref.13. Eq.(15) reproduces the data the best when μis
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taken as 6.2x10-10 m2/Vs. Three terms in eq.(15) are shown separately. It is obvious that the first term, coming from the space charge in the region II, and the second term, coming from the electric field in the region III, are sufficiently small. At the same time,
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u in the third term is sufficiently smaller than l (not shown in the graph). The main contribution comes from the last term of Region I, Alq3 layer. Here, we assume that the first and the second terms can be neglected and the temperature is so low that u<
qel>>kT. The eq.(15) can be simplified as, 2Z[R1 =S+ O
/1
(16)
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Eq.(16) is the counterpart for the organic heterojunction of the Mott-Schottky relation of the Schottky contact [12]. It seems that the evaluated value of μ would be too small. However, it is not surprising because the value is the one at sufficiently low electric field so that the lack of the Poole-Frenkel effect will reduce the value than those reported
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3. Discussion
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using other methods [18].
The Mott-Schottky relation is well known as a standard method to evaluate the effective carrier density of the semiconductors [12]. It is often applied to evaluate the characteristics of the organic heterojunctions [26, 27]. However, such analysis needs careful consideration.
One must remember that the normal states of the organics are the neutral insulators, whereas those of the semiconductors are the neutral conductors. The characteristic voltage with physical meaning in the organic heterojunction should be the one at which the conductive region starts to evolve from the neutral insulating phase, where the applied voltage cancels the spontaneous polarization. That is contrast with the Schottky 7
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contact, where the characteristic voltage is the one at which the insulating region starts to evolve from the neutral conductive phase. In this case, the applied voltage cancels the difference between the Fermi level mismatching. Even though both are the voltages at which a charged region starts to evolve from the neutral phase, the equation forms of
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Mott-Schottky relation must become distinct depending on if the neutral phase is conductive or insulating.
The carrier transport in insulators has been investigated extensively in conjunction with the metal-oxide field effect transistor (MOSFET) technology. Carrier transport dynamics specific to the insulators have been established that their dynamics are
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governed by the electrode-limited conduction and the bulk-limited conduction [28]. At the same time, the junction dynamics of the organic heterojunctions also have distinct dynamics than those of semiconductors as is discussed above. The difference between
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the natures of the carrier transport dynamics through the junction and in the bulk calls for the revision of the carrier transport dynamics of step-by-step injection [29-31]. The revised scenarios are depicted in Fig.3.
In the case of p-type Schottky contact, the electric states of the semiconductors before making contact are neutral and conductive. When the metal (gray) – semiconductor (yellow) contact is formed, carriers diffuse through the contact due to the difference of the carrier population and immobile ions are left. The space charges of the immobile
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ions make an electric field, the drift current of which is in the opposite direction of the diffusion current. The space charge region of the immobile ions, the depletion layer (white), grows until the Fermi level of the semiconductor coincides with the metal work function (Fig.3-a). When the applied voltage compensates the built-in potential of the
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Schottky contact, the depletion layer disappears (Fig.3-b). Under positive bias voltage, the quasi-Fermi level becomes lower than the work function of the electrode metal. The
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carrier population in the semiconductor exceeds over that in the electrode and then diffusion current flows from the semiconductor to the electrode, which is sustained by the recombination at the interface [12]. On the other hand, in the case of the organic heterojunctions, the electric states of the organics before making a contact are neutral and insulating. When the contact is formed, a carrier accumulation layer appears instead of the charged insulating layer of Schottky contact [13]. When the bias voltage is increased, holes start to accumulate in the NPD layer at some voltage, which gives a semi-circle in DMP-c. The holes must be supplied externally for the formation of the accumulation region. We have shown that the finite number of the interface states are the source of the accumulated carriers rather than those injected from the electrode in the case of a typical OLED, 8
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ITO/NPD/Alq3/LiF/Al [13]. Full scenario of the voltage dependence is as follows. When the bias voltage is sufficiently low that the internal electric field is negative, the carriers are confined in the interface states. There are very few carries in each organic layer and they are insulating (white) (Fig.3-c). As the voltage is increased and when the flat level
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condition is achieved in the NPD layer, the holes start to diffuse into NPD layer. Because there is an energy barrier for holes at NPD/Alq3 interface and the negative electric field remains in Alq3 layer, the holes are dammed and the accumulation layer is formed (yellow) (Fig.3-d). When the bias voltage is increased further and the energy level of the Alq3 layer also becomes flat, the holes will overflow the barrier and diffuse
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into the Alq3 layer. At the same time, electrons will flow from the cathode and diffuse into the layer under the flat level condition in the Alq3 layer (Fig.3-e). Finally, when the voltage is sufficiently high that the internal electric fields in NPD and Alq3 layers direct
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from anode to cathode with finite strength, flows of holes and electrons are sustained by the electrode-limited injection process or the bulk-limited hopping process driven by the electric field [28]. Holes and electrons recombine and sink in the Alq3 layer (Fig.3-f). Here, the overflowed accumulation holes are not supplied directly from the electrode but from the interface states. The role of the injection from the electrode is to keep the thermal equilibrium at the interface states. This scenario can explain the behavior of the DMP of the OLEDs consistently.
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The dielectrics have been considered as the semiconductors with wide energy gap. In these systems, the carriers are the polarons existing on the trap states, which hop among the trap sites via the conduction paths of the band states. On the other hand, in the case of the organic dielectrics, the carriers exist as the molecular orbital states
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localized on each molecule, which hop among the adjacent molecular sites directly. The conduction in semiconductors is the limiting case of the carrier transport in delocalized
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Bloch states in band systems, whereas that in the organics is another limiting case of localized carrier states. As is discussed above, the carrier transport in organics can be controlled in an active manner by introducing the heterojunction similar to semiconductors. One must remember that the dynamics is derived from the same equation set, even though their dynamics are quite distinct. Therefore, the carrier dynamics in organics should be considered as the twins rather than the derivative of that of the semiconductors. Tang and Slyke’s invention was the way of controlling the carrier transport in the polaron conductors using heterojunctions of ultrathin layers. As discussed in this article, their innovation is the discovery of a parallel evolution of active electronic devices from the different class of electric materials rather than the discovery of the substitutes of Si 9
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semiconductors. Then we propose to call such a material class of polaron conductors as “quasiconductors” as the counterpart of the semiconductors.
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4. Conclusion The carrier accumulation dynamics is modeled by the Poisson equation and the current balance equation. In the case of the organic heterojunctions, the space charge region evolves from the neutral insulating state, whereas it does from the neutral conductive state in the case of semiconductor devices. This difference results different potential
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distribution and then the Mott-Schottky relation is revised. Based on the accumulation model and the ALCS model, a new carrier dynamics model in organic heterojunctions is
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proposed.
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References [1] H. Akamatsu and H. Inokuchi, J.Chem.Phys.18, 810 (1950). [2] C. K. Chiang, C. R. Fincher, Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis,
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S. C. Gau, and Alan G. MacDiarmid, Phys.Rev.Lett. 39, 1098 (1978). [3] C. K. Chiang, M. A. Druy, S. C. Gau, A. J. Heeger, E. J. Louis, A. G. MacDiarmid, Y. W. Park, and H. Shirakawa, J.Am.Chem.Soc. 100(3), 1013 (1978). [4] C. W. Tang, Appl.Phys.Lett. 48(2), 183 (1986).
[5] C. W. Tang and S. A. Van Slyke, Appl.Phys.Lett. 51, 913 (1987).
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[6] Mohan V. Jacob, Electronics 3, 594(2014). S. Ponomarenko and S. Kirchmeyer, Polymer Science, Ser. C, 56(1), 1 (2014). And references therein. [7] A. H. Wilson, Proc R Soc Lond A, 133(822), 458 (1931),
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[8] N. F. Mott, Math. Proc. Camb. Philos. Soc. 34, 568 (1938). [9] B. I. Davydov, , Zh. Eksp. Teor. Fiz. 9, 451 (1939). [10] W. Schottky, Z.Phys. 113,367 (1939)
[11] J. Frenkel, and A. Ioffe, Phys.Rev. 39(3), 530 (1932).
[12] S. M. Sze, Physics of Semiconductor Device, Wiley-Interscience，New York，2nd edition，1981
[13] J. Takahashi and H. Naito, Org. Electron. 61, 10 (2018).
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[14] H. Ishii, K. Sugiyama, E. Ito, and K. Seki, Adv. Mater., 11(8), 605 (1999). [15] S. Braun, W. R. Salaneck, and M. Fahlman, Adv. Mater. 21, 1450 (2009), [16] I. D.Parker, J. Appl. Phys. 75 (3), 1656 (1994). [17] N. Tessler, Y. Preezant, N. Rappaport, and Y. Roichman, Adv. Mater. 21, 27 (2009).
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[18] M. Bouhassoune, S. L. M. van Mensfoort, P. A. Bobbert, R. Coehoorn, Org. Electr. 10(3), 437 (2009).
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[19] H. Kleemann, B. Lu¨ssem, and K. Leo, J.Appl.Phys. 111, 123722 (2012). [20] Gert-Jan A. H. Wetzelaer and Paul W. M. Blom, NPG Asia Materials 6, e110 (2014).
[21] E. Tutiŝ, D. Berner, and L. Zuppiroli, J. Appl. Phys., 93(8), 4594 (2003). [22] M. Kühn, C. Pflumm, W. Jaegermann, E. Mankel, Org. Electr. 37, 336 (2016). [23] D. Schmeiβer, W. Jaegermann, Ch. Pettenkofer, H. Wachtel, A. Jimenez-Gonzales, J. U. von Schutz, H. C. Wolf, P. Erk, H. Meixner and S. Hünig. Solid State Commun. 81, 827 (1992). [24] S. Hasegawa, T. Mori, K. Imaeda, S. Tanaka, Y. Yamashita, H. Inokuchi, H. Fujimoto, K. Seki, and N. Ueno, J. Chem. Phys. 100, 6969 (1994).
[25] K. Osada, K. Goushi, H. Kaji, C. Adachi, H. Ishii and Y. Noguchi, Org. Electr. 58 , 313 11
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[26] F. Fabregat-Santiago, G. Garcia-Belmonte, I. Mora-Sero, and J. Bisquert, Phys.Chem.Chem.Phys., 13, 9083 (2011). [27] P. Stallinga, H. L. Gomes, M. Murgia, and K. Mullen, Org.Electr. 3, 43 (2002).
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[28] F. C. Chiu, Adv. Mater. Sci. Eng. Article ID 578168, (2014). [29] Y. Noguchi, N. Sato, Y. Tanaka, Y. Nakayama, and H. Ishii, Appl.Phys.Lett. 92, 203306 (2008).
[30] S. Berleb, W. Brütting, and G. Paasch, Org.Electro, 1, 41 (2000).
[31] S. Altazin, S. Züfle, E. Knapp, C. Kirsch, T.D. Schmidt, L. Jäger, Y. Noguchi, W.
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Brütting, B. Ruhstaller. Org. Electr. 39, 244 (2016).
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Figures.
FIG.1. The coordinate system used to calculate the potential distribution of the model
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device, ITO/NPD/Alq3/LiF/Al. A and B are the anode LiF/Al and the cathode ITO. Region I is the Alq3 layer and Region II and III are the NPD layer. The region I has a finite spontaneous polarization and the holes accumulate in a part of NPD layer, region II.
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The origin of x axis is taken as the anode-Alq3 interface. The thicknesses of each layer l,
d-l, s-d, are shown in the figure.
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FIG.(2-a)
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FIG.(2-b)
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FIG.(2-c)
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FIG.(2-d)
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FIG.2. The DMP-b of ITO/NPD(60)/Alq3(100)/LiF/Al (a), the voltage dependence of the relaxation frequency (b) and the thickness of the accumulation layer of the NPD layer (c). (d) is the Left Hand Side equations calculated using these values under the assumption of μ=6.2x10-10cm2/Vs. The three terms in eq.(15) are shown separately.
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Blue triangles are the first term in eq.(15), the contribution from region II, Green rectangles are the second one from region III. Red diamonds are the third one from
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region I, Alq3 layer. White circles are the sum of them. It is shown that potential shift in NPD layer (region II and III) is sufficiently smaller than that in Alq3 layer.
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FIG.3. The energy level scheme of the carrier transport dynamics in the p-type
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Schottky contact (a,b) and the organic heterojunction (c-f). In contrast with Fig.1, the layers ITO, NPD, Alq3 and (LiF)/Al are aligned from left to right in (c-f). Gray, white and yellow regions are the electrodes, insulating and conductive regions. + and – are the carriers. – in circles are the immobile ions. The red arrows are the direction of the
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carrier flow. See text for detail.
18
S1566-1199(18)30559-7
DOI:
https://doi.org/10.1016/j.orgel.2018.10.044
Reference:
ORGELE 4960
To appear in:
Organic Electronics
Received Date: 31 August 2018 Revised Date:
28 October 2018
Accepted Date: 29 October 2018
Please cite this article as: J.-i. Takahashi, Theory of carrier accumulation in organic heterojunctions, Organic Electronics (2018), doi: https://doi.org/10.1016/j.orgel.2018.10.044. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Metal-Semiconductor Junction Organic Heterojunction
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Theory of Carrier Accumulation in Organic Heterojunctions
1Electronic
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Jun-ichi Takahashi, Materials Development Center, Idemitsu Kosan Co., Ltd.,
1280 Kami-izumi Sodegaura, Chiba, 299-0293, Japan
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Abstract
Even though organic light emitting diodes (OLED) have been achieving commercial
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successes, their device physics have been under debating. In this article, we develop a junction theory of organic heterojunctions, which describes the carrier accumulation dynamics in them. We derive an equation, which is the counterpart of the Mott-Schottky relation in the metal-semiconductor contact. We will show that the essence of the carrier transport control in organic devices is the control of the internal electric field and therefore the drift motion, whereas that in the semiconductors is the control of the carrier population by shifting the Fermi energy and therefore the diffusion motion.
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Tang’s invention of organic electronic devices with layered ultrathin layers of small organic molecules was a new paradigm of controlling the carrier transport in polaron
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conductors rather than only a finding of the substitutes of Si semiconductors.
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Key words: Organic Light Emitting Diode, Heterojunction, Mott-Schottky relation, Carrier accumulation, polaron conductor, quasiconductor.
_____________________________ a)
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
1
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Highlights A junction theory in organic heterojunctions is presented to describe the carrier accumulation dynamics in organic electronic devices. organic heterojunctions.
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The counterpart of the Mott-Schottky relation of the Schottky contact is given for The quasiconductor concept is proposed to enlighten the distinct features of polaron
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conduction than the carrier dynamics in semiconductors.
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1. Introduction It is said that the 20th century was the era of quantum mechanics. One of its most prosperous achievements was the development of semiconductor devices, which has
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been the basis of the technology of the modern society. The molecular electronics has progressed steadily behind the development of the Si technology. It was reported that polycrystalline powder of some aromatic molecules showed an electrical conductivity having the similar temperature dependence of the intrinsic semiconductors in 1950 [1]. A notable topic in the end of 70’s was the conductive polymers, which were typical band
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systems of one-dimensional semiconductor systems [2,3]. In 1986 when the end of the 20th century approached, Tang and Slyke presented a novel organic devices, the functionalities of which were separated in different ultrathin layers [4,5]. This
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innovative concept opened a new world of organic active electronic devices of not only diodes but also solar cells and FETs [6]. Nowadays, OLED has been studied extensively and regarded as a leading candidate of the display devices of the next generation. However, even though the OLED has already achieved commercial successes, our understanding of their device physics has been surprisingly poor. The development of semiconductor has been based on the fundamental research of the underlying physics: Wilson’s band theory [7], contact phenomena theory of Mott, Davydov and Schottky
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[8-10], photoeffect and tunneling research of Frenkel and Ioffe [11]. Their counterparts of organic devices have not been established well to forecast the device performance quantitatively. For example, let’s consider the dynamics of MIS capacitor. As it is well known, a voltage-controllable capacitor can be made using a metal-semiconductor
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contact [12]. Similarly, a voltage-controllable capacitor can be made also using a metal-organic contact. However, we have failed to achieve the controllable capacitors
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with single organic layer. At least two organic layers or bulkhetero structure are needed. Furthermore, we have shown, by the impedance spectroscopy, their carrier dynamics is quite different from that of metal-semiconductor (Schottky) contact [13]. For the Schottky contact, the insulating part is the charged depletion layer, where carriers are excluded from the neutral conductive region. On the other hand, for the organic heterojunctions, the insulating part must be the neutral region. Instead of the formation of the charged insulating depletion layer in Schottky contact, the conductive accumulation layer evolves in organic heterojunctions. Nevertheless, the device physics of the organic devices has been discussed under the same framework of the semiconductors. What is the meaning of the relation between the Schottky contact and the organic heterojunctions? 3
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In this article, we develop a junction theory, which describes the accumulation dynamics in the organic heterojunction. It is the counterpart for the polaron conductors of the junction theory for semiconductors. Based on the theory, we will discuss the essential nature, which distinguishes the organic devices from the Si semiconductor
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devices. 2. Theory
Because the OLEDs have at least two metal-organic contacts and several different
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organic layers to which different functionalities are assigned separately, the carrier injection and transport dynamics become complicated. Exhaustive efforts have been paid to analyze their dynamics of injection [14-16], transport [17, 18] and device
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properties [19-22]. However, it is not an easy task to have unified pictures of their interplays.
We have developed a method of Dynamic Modulus Plot (DMP) to analyze the carrier dynamics in layered organic devices [13]. Using the DMP method, we analyzed the simplest and the most basic device of ITO/NPD/Alq3/LiF/Al, which is made of a hole conducting and an electron conducting layers. This device seems to be the counterpart of the pn junctions and/or the Schottky contact in the semiconductor devices. However,
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there are quite differences from those of the pn junctions. (1) The equivalent circuit of the Schottky contact is a series connection of a resistor (R) and a capacitor (C), whereas that of the organic heterojunction is always the series connection of the parallel CR units and the C, which means dielectricity
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cannot be ignored at any time.
(2) The organic layers are neutral insulating ones at sufficiently large negative bias
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voltage, whereas the semiconductor layer of the Schottky contact is a neutral conductor.
(3) The carriers flow from the electrode into the organic layer in the case of organic heterojunctions, whereas that flows from the semiconductor to the electrode in the case of the Schottky contact.
The key point of the theory is that the bias voltage controls the space charge accumulation in the organic dielectrics. We must consider the potential balance among the space charge, the externally applied voltage and the polarization, whereas only the balance between the space charge potential and the externally applied voltage is taken into account in the Schottky contact. Before starting the discussion, it should be noted that the molecules discussed in this 4
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article are small molecules and usually they are used as amorphous states. Even though the band structure concept in organic materials is well established in the molecular crystals and conductive polymers [23, 24], the band structure exists hardly in these materials. Instead of the band structure, the isolated molecular orbitals delocalize at
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each molecule. The following discussion is not necessarily valid for conductive polymers and molecular crystal systems.
We define the coordinates as Fig.1. Region I is the dielectric layer of Alq3 with a
thickness of l, where spontaneous polarization, P=eEi, exists [25]. Region II and III are
the NPD layers, where the region II is the conductive part in which hole accumulates
and the region III is the one which remains to be insulating. The thickness of the
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accumulated region is t=d-l. The carrier distribution is governed by the Poisson
equation and the balance equation of the drift current and the diffusion current. 0=
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∆ =−
−
(1) (2)
, with charge density ρ, dielectric constant ε, conductivity σ=ρµ, mobility µ, and diffusion constant D. For one-dimensional configuration, ρ‘s in eq.(2) are replaced by ϕ using eq.(1) and we have an equation after integration,
, where
≡
=
(3)
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+
and A is a constant of integration. It is easy to get the general solution of
eq.(3) for constant µ and D. However, to calculate the solution in general form, which satisfies the boundary condition, is very tedious. For the simplicity of discussion, we set
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A to be zero in the following discussion. The solutions are.
ρ=2
or
ln"# − #$ % +
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ϕ=
(4-a)
( " ) * %+
ϕ=− #+
ρ=0
$
(4-b)
$
(5-a) (5-b)
From eq. (5-a) and (5-b), it is obvious that the above solutions are the cases without a current flow. The non-zero A solution will be necessary to describe the cases of a finite current flow, where electric-field-dependent mobilities must be taken into account. We set ϕ"0% = 0. From the continuity condition of the electric field and the potential, we obtain successively.
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"#% =
Region II:
".)
*%
( "#%
12
+
/0 #
=0
)
.)
*
*
(6-b)
−
/#
=
" )
*%
3 "#%
And then,
, where
Q = :.
"67 )68 %
4# = 2
=−
".)
3
=−
" )
*
*
−
/1
−
5
*
(8-a)
(8-b)
+
/1
−
" )
P#$ EQ ;
).
* %".) * %
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(
(7-b)
12 .)
=0 3 "#%
(7-a)
*
)
"# − 4% +
4 − #$ NO = L# M ? 1 − #$ 2
#$ = 1 +
.)
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3 "#%
.
+
( " ) * %+
"#% = 2 Region III:
(6-a)
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=-
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( "#%
Region I:
= ;"
(
−
3
−
(9)
(10)
/%
(11) (12-a)
*%
*%
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Eq.(9) is rewritten using the relation V = −
(12-b) 3 "=
− 4% +
3 "4%
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2 NOLR L P 2 12 ?1 − E− "= − 4% + ? + 1E = S + NOL NO 2 ; LON 1− 2 R
/1
(13)
, where t=d-l and e=E1-Ei . By combining eq.(12-a), (12-b) and (11). e=−
, where r =
5
5
C
?1 ± A1 + 4 D E
(14)
. Because e should be negative, the sign of the square root is taken as
positive. From the Einstein’s relation,
= GH. We define u = J
6
K
and we obtain,
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2
GH R =−4 X+1 ?12 ?1 − E − + E=S+ N X X−R Y
/1
(15)
The parameters in eq.(15) can be calculated experimentally from the DMP. As has been
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r = TUDJ .
Figure
(2-d)
are
the
plot
of
the
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and then
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discussed in ref.13, Q can be calculated from the DMP as Q = ρt = eq.(15)
using
the
data
of
ITO/NPD(60)/Alq3(100)/LiF/Al in ref.13. Eq.(15) reproduces the data the best when μis
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taken as 6.2x10-10 m2/Vs. Three terms in eq.(15) are shown separately. It is obvious that the first term, coming from the space charge in the region II, and the second term, coming from the electric field in the region III, are sufficiently small. At the same time,
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u in the third term is sufficiently smaller than l (not shown in the graph). The main contribution comes from the last term of Region I, Alq3 layer. Here, we assume that the first and the second terms can be neglected and the temperature is so low that u<
qel>>kT. The eq.(15) can be simplified as, 2Z[R1 =S+ O
/1
(16)
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Eq.(16) is the counterpart for the organic heterojunction of the Mott-Schottky relation of the Schottky contact [12]. It seems that the evaluated value of μ would be too small. However, it is not surprising because the value is the one at sufficiently low electric field so that the lack of the Poole-Frenkel effect will reduce the value than those reported
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3. Discussion
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using other methods [18].
The Mott-Schottky relation is well known as a standard method to evaluate the effective carrier density of the semiconductors [12]. It is often applied to evaluate the characteristics of the organic heterojunctions [26, 27]. However, such analysis needs careful consideration.
One must remember that the normal states of the organics are the neutral insulators, whereas those of the semiconductors are the neutral conductors. The characteristic voltage with physical meaning in the organic heterojunction should be the one at which the conductive region starts to evolve from the neutral insulating phase, where the applied voltage cancels the spontaneous polarization. That is contrast with the Schottky 7
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contact, where the characteristic voltage is the one at which the insulating region starts to evolve from the neutral conductive phase. In this case, the applied voltage cancels the difference between the Fermi level mismatching. Even though both are the voltages at which a charged region starts to evolve from the neutral phase, the equation forms of
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Mott-Schottky relation must become distinct depending on if the neutral phase is conductive or insulating.
The carrier transport in insulators has been investigated extensively in conjunction with the metal-oxide field effect transistor (MOSFET) technology. Carrier transport dynamics specific to the insulators have been established that their dynamics are
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governed by the electrode-limited conduction and the bulk-limited conduction [28]. At the same time, the junction dynamics of the organic heterojunctions also have distinct dynamics than those of semiconductors as is discussed above. The difference between
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the natures of the carrier transport dynamics through the junction and in the bulk calls for the revision of the carrier transport dynamics of step-by-step injection [29-31]. The revised scenarios are depicted in Fig.3.
In the case of p-type Schottky contact, the electric states of the semiconductors before making contact are neutral and conductive. When the metal (gray) – semiconductor (yellow) contact is formed, carriers diffuse through the contact due to the difference of the carrier population and immobile ions are left. The space charges of the immobile
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ions make an electric field, the drift current of which is in the opposite direction of the diffusion current. The space charge region of the immobile ions, the depletion layer (white), grows until the Fermi level of the semiconductor coincides with the metal work function (Fig.3-a). When the applied voltage compensates the built-in potential of the
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Schottky contact, the depletion layer disappears (Fig.3-b). Under positive bias voltage, the quasi-Fermi level becomes lower than the work function of the electrode metal. The
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carrier population in the semiconductor exceeds over that in the electrode and then diffusion current flows from the semiconductor to the electrode, which is sustained by the recombination at the interface [12]. On the other hand, in the case of the organic heterojunctions, the electric states of the organics before making a contact are neutral and insulating. When the contact is formed, a carrier accumulation layer appears instead of the charged insulating layer of Schottky contact [13]. When the bias voltage is increased, holes start to accumulate in the NPD layer at some voltage, which gives a semi-circle in DMP-c. The holes must be supplied externally for the formation of the accumulation region. We have shown that the finite number of the interface states are the source of the accumulated carriers rather than those injected from the electrode in the case of a typical OLED, 8
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ITO/NPD/Alq3/LiF/Al [13]. Full scenario of the voltage dependence is as follows. When the bias voltage is sufficiently low that the internal electric field is negative, the carriers are confined in the interface states. There are very few carries in each organic layer and they are insulating (white) (Fig.3-c). As the voltage is increased and when the flat level
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condition is achieved in the NPD layer, the holes start to diffuse into NPD layer. Because there is an energy barrier for holes at NPD/Alq3 interface and the negative electric field remains in Alq3 layer, the holes are dammed and the accumulation layer is formed (yellow) (Fig.3-d). When the bias voltage is increased further and the energy level of the Alq3 layer also becomes flat, the holes will overflow the barrier and diffuse
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into the Alq3 layer. At the same time, electrons will flow from the cathode and diffuse into the layer under the flat level condition in the Alq3 layer (Fig.3-e). Finally, when the voltage is sufficiently high that the internal electric fields in NPD and Alq3 layers direct
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from anode to cathode with finite strength, flows of holes and electrons are sustained by the electrode-limited injection process or the bulk-limited hopping process driven by the electric field [28]. Holes and electrons recombine and sink in the Alq3 layer (Fig.3-f). Here, the overflowed accumulation holes are not supplied directly from the electrode but from the interface states. The role of the injection from the electrode is to keep the thermal equilibrium at the interface states. This scenario can explain the behavior of the DMP of the OLEDs consistently.
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The dielectrics have been considered as the semiconductors with wide energy gap. In these systems, the carriers are the polarons existing on the trap states, which hop among the trap sites via the conduction paths of the band states. On the other hand, in the case of the organic dielectrics, the carriers exist as the molecular orbital states
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localized on each molecule, which hop among the adjacent molecular sites directly. The conduction in semiconductors is the limiting case of the carrier transport in delocalized
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Bloch states in band systems, whereas that in the organics is another limiting case of localized carrier states. As is discussed above, the carrier transport in organics can be controlled in an active manner by introducing the heterojunction similar to semiconductors. One must remember that the dynamics is derived from the same equation set, even though their dynamics are quite distinct. Therefore, the carrier dynamics in organics should be considered as the twins rather than the derivative of that of the semiconductors. Tang and Slyke’s invention was the way of controlling the carrier transport in the polaron conductors using heterojunctions of ultrathin layers. As discussed in this article, their innovation is the discovery of a parallel evolution of active electronic devices from the different class of electric materials rather than the discovery of the substitutes of Si 9
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semiconductors. Then we propose to call such a material class of polaron conductors as “quasiconductors” as the counterpart of the semiconductors.
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4. Conclusion The carrier accumulation dynamics is modeled by the Poisson equation and the current balance equation. In the case of the organic heterojunctions, the space charge region evolves from the neutral insulating state, whereas it does from the neutral conductive state in the case of semiconductor devices. This difference results different potential
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distribution and then the Mott-Schottky relation is revised. Based on the accumulation model and the ALCS model, a new carrier dynamics model in organic heterojunctions is
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proposed.
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References [1] H. Akamatsu and H. Inokuchi, J.Chem.Phys.18, 810 (1950). [2] C. K. Chiang, C. R. Fincher, Jr., Y. W. Park, A. J. Heeger, H. Shirakawa, E. J. Louis,
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S. C. Gau, and Alan G. MacDiarmid, Phys.Rev.Lett. 39, 1098 (1978). [3] C. K. Chiang, M. A. Druy, S. C. Gau, A. J. Heeger, E. J. Louis, A. G. MacDiarmid, Y. W. Park, and H. Shirakawa, J.Am.Chem.Soc. 100(3), 1013 (1978). [4] C. W. Tang, Appl.Phys.Lett. 48(2), 183 (1986).
[5] C. W. Tang and S. A. Van Slyke, Appl.Phys.Lett. 51, 913 (1987).
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[6] Mohan V. Jacob, Electronics 3, 594(2014). S. Ponomarenko and S. Kirchmeyer, Polymer Science, Ser. C, 56(1), 1 (2014). And references therein. [7] A. H. Wilson, Proc R Soc Lond A, 133(822), 458 (1931),
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[8] N. F. Mott, Math. Proc. Camb. Philos. Soc. 34, 568 (1938). [9] B. I. Davydov, , Zh. Eksp. Teor. Fiz. 9, 451 (1939). [10] W. Schottky, Z.Phys. 113,367 (1939)
[11] J. Frenkel, and A. Ioffe, Phys.Rev. 39(3), 530 (1932).
[12] S. M. Sze, Physics of Semiconductor Device, Wiley-Interscience，New York，2nd edition，1981
[13] J. Takahashi and H. Naito, Org. Electron. 61, 10 (2018).
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[14] H. Ishii, K. Sugiyama, E. Ito, and K. Seki, Adv. Mater., 11(8), 605 (1999). [15] S. Braun, W. R. Salaneck, and M. Fahlman, Adv. Mater. 21, 1450 (2009), [16] I. D.Parker, J. Appl. Phys. 75 (3), 1656 (1994). [17] N. Tessler, Y. Preezant, N. Rappaport, and Y. Roichman, Adv. Mater. 21, 27 (2009).
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[18] M. Bouhassoune, S. L. M. van Mensfoort, P. A. Bobbert, R. Coehoorn, Org. Electr. 10(3), 437 (2009).
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[19] H. Kleemann, B. Lu¨ssem, and K. Leo, J.Appl.Phys. 111, 123722 (2012). [20] Gert-Jan A. H. Wetzelaer and Paul W. M. Blom, NPG Asia Materials 6, e110 (2014).
[21] E. Tutiŝ, D. Berner, and L. Zuppiroli, J. Appl. Phys., 93(8), 4594 (2003). [22] M. Kühn, C. Pflumm, W. Jaegermann, E. Mankel, Org. Electr. 37, 336 (2016). [23] D. Schmeiβer, W. Jaegermann, Ch. Pettenkofer, H. Wachtel, A. Jimenez-Gonzales, J. U. von Schutz, H. C. Wolf, P. Erk, H. Meixner and S. Hünig. Solid State Commun. 81, 827 (1992). [24] S. Hasegawa, T. Mori, K. Imaeda, S. Tanaka, Y. Yamashita, H. Inokuchi, H. Fujimoto, K. Seki, and N. Ueno, J. Chem. Phys. 100, 6969 (1994).
[25] K. Osada, K. Goushi, H. Kaji, C. Adachi, H. Ishii and Y. Noguchi, Org. Electr. 58 , 313 11
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[26] F. Fabregat-Santiago, G. Garcia-Belmonte, I. Mora-Sero, and J. Bisquert, Phys.Chem.Chem.Phys., 13, 9083 (2011). [27] P. Stallinga, H. L. Gomes, M. Murgia, and K. Mullen, Org.Electr. 3, 43 (2002).
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[28] F. C. Chiu, Adv. Mater. Sci. Eng. Article ID 578168, (2014). [29] Y. Noguchi, N. Sato, Y. Tanaka, Y. Nakayama, and H. Ishii, Appl.Phys.Lett. 92, 203306 (2008).
[30] S. Berleb, W. Brütting, and G. Paasch, Org.Electro, 1, 41 (2000).
[31] S. Altazin, S. Züfle, E. Knapp, C. Kirsch, T.D. Schmidt, L. Jäger, Y. Noguchi, W.
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Brütting, B. Ruhstaller. Org. Electr. 39, 244 (2016).
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Figures.
FIG.1. The coordinate system used to calculate the potential distribution of the model
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device, ITO/NPD/Alq3/LiF/Al. A and B are the anode LiF/Al and the cathode ITO. Region I is the Alq3 layer and Region II and III are the NPD layer. The region I has a finite spontaneous polarization and the holes accumulate in a part of NPD layer, region II.
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The origin of x axis is taken as the anode-Alq3 interface. The thicknesses of each layer l,
d-l, s-d, are shown in the figure.
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FIG.(2-a)
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FIG.(2-b)
15
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FIG.(2-c)
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FIG.(2-d)
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FIG.2. The DMP-b of ITO/NPD(60)/Alq3(100)/LiF/Al (a), the voltage dependence of the relaxation frequency (b) and the thickness of the accumulation layer of the NPD layer (c). (d) is the Left Hand Side equations calculated using these values under the assumption of μ=6.2x10-10cm2/Vs. The three terms in eq.(15) are shown separately.
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Blue triangles are the first term in eq.(15), the contribution from region II, Green rectangles are the second one from region III. Red diamonds are the third one from
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region I, Alq3 layer. White circles are the sum of them. It is shown that potential shift in NPD layer (region II and III) is sufficiently smaller than that in Alq3 layer.
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FIG.3. The energy level scheme of the carrier transport dynamics in the p-type
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Schottky contact (a,b) and the organic heterojunction (c-f). In contrast with Fig.1, the layers ITO, NPD, Alq3 and (LiF)/Al are aligned from left to right in (c-f). Gray, white and yellow regions are the electrodes, insulating and conductive regions. + and – are the carriers. – in circles are the immobile ions. The red arrows are the direction of the
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carrier flow. See text for detail.
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