we
Journal of	JET v°iume 12 (2°19) p.p. n~37
Issue 4, December 2019 Type of article 1.01
Technology	www.fe.um.si/en/jet.html
THE EXTERNAL BIAS-DEPENDENT ELECTRIC FIELD AT HOLE-INJECTING ELECTRODE/a-NPD JUNCTION AND ITS RELATIONSHIP TO GAUSSIAN DISORDERED INTERFACE STATES
OD ZUNANJE NAPETOSTI ODVISNO ELEKTRIČNO POLJE OB STIKU VRZELI VBRIZGAJOČE ELEKTRODE/a-NPD IN POVEZAVA Z NEUREJENIMI ENERGIJSKIMI STANJI VMESNE PLASTI
Bruno Cvikl R
Keywords: electrode/organic electric field, contact affected hole mobility, organic interface disorder parameters
Abstract
An alternative interpretation of two different sets of published temperature-dependent current-voltage a-NPD (i.e. N,N'-Di(1-naphthyl)-N,N'-diphenyl-(1,1'-biphenyl)-4,4'-diamine) organic semiconductor data is presented. The measurements are described in terms of the hole drift current density expressed with two parameters: the electric field at the hole-injecting interface, Eint, and, fflmax, the hole mobility determined by the measured current density at the maximum value of the externally applied electric field, Ea, in a given experiment. The former parameter, depending on the contact résistance, may be a function of Ea but the latter is Ea independent, The fixed value of Eint signifies the occurrence of the space charge limited current, SCLC, within the electrode/a-NPD structures
R Corresponding author: Professor Emeritus Bruno Cvikl, PhD., University of Maribor, Maribor, Slovenia and Jožef Stefan Institute, Ljubljana, Slovenia, E-mail address: bruno.cvikl@ijs.si
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and the contact is ohmic. Then, the calculated weak bias-dependent hole drift mobility, a function of Eint, equals the well-known exponential bias-dependent mobility, and saturates. The data not displaying SCLC characteristics are used for the calculation of Eint dependence on the applied field, Ea. It is shown that the quasi-ohmic contacts cause Eint to become a strong double-valued function of the externally applied electric field, Ea, described in terms of the distorted, inverted, high order parabola. The corresponding bias-dependent hole drift mobility is non-exponential and evolves on a considerably lower level than in SCLC cases. It is found that a sufficiently increased Ea alters the quasi-ohmic contact/a-NPD region into the ohmic one. A simple model of a thin, net hole charged, electrode/a-NPD interface enables the relationship between the deduced interfacial electric field, Eint, and the Ea dependent Gaussian width, ct, as well as the energy shift of its peak, 9, along the negative binding energy is to be investigated. The current-voltage method appears to be a helpful expedient for the investigation of the electric field at hole-injecting electrode/organic interfaces.
Povzetek
Članek podaja alternativno fizikalno interpretacijo dveh primerov v literaturi objavljenih temperaturno odvisnih meritev gostote toka v odvisnosti od pritisnjene napetosti na vzorcih a-NPD (i. e. N,N'-Di(1-naftil)-N,N'-difenil-(1,1'-bifenil)-4,4'-diamin) organskega polprevodnika. Meritve gostote toka vrzeli so v pričujočem članku popisane z dvema parametroma: z jakostjo električnega polja, Eint, na vmesni plasti elektroda/organski polprevodnik kjer se vrzeli vbrizgavajo v organski medij in, |max, mobilnost vrzeli, ki je določena z izmerjeno gostota toka pri maksimalni vrednosti zunanje električne poljske jakosti, Ea, danega eksperimenta. Parameter, Eint, ki je funkcija kontaktne napetosti, lahko zavisi še od Ea, toda drugi parameter je od Ea neodvisna konstanta. Nespremenjena vrednost Eint z vrednostjo Ea podaja obstojt. im. omejenega toka zaradi prostorskega naboja, SCLC, v vzorcu a-NPD s čimer je tedaj električni kontakt opredeljen kot ohmski stik. V tem primeru je izračunana, šibko Ea, odvisna mobilnost vrzeli podana z dobro poznano eksponentno odvisnostjo, ki vodi do nasičenja mobilnosti vrzeli. Eksperimentalni podatki, ki ne zadoščajo merilom SCLC so uporabljeni za izračun odvisnosti Eint od zunanjega polja Ea. Izkaže se, da zaradi kvazi-ohmskega kontakta postane Eint dvolična funkcija zunanjega pritisnjenega polja Ea, ki zavzame obliko skrivljene in invertirane parabole višjega reda. Temu ustrezna mobilnost vrzeli se izraža v ne-eksponentni formi is zavzame vrednosti, ki so bistveno pod nivojem vrednosti izračunane v primerih opredeljenih z SCLC značilnostmi. V delu je pokazano, da je mogoče z dovolj velikim zunanjim poljem, Ea, preoblikovati kvazi-ohmski kontakt v ohmskega. Poenostavljeni model tenke, z vrzeli nasičene, vmesne plasti elektroda/a-NPD omogoča proučevanje vzajemnega odnosa med električnim poljem vmesne plasti Eint in od Ea odvisno širino Gaussove funkcije razmazanosti energijskih stanj vrzeli v organskem polprevodniku in pa energijski pomik le-te vzdolž negativne vezavne energije. Eksperimentalna metoda gostota toka - napetost se izkaže, kot nadvse ustrezna metoda za raziskave električne poljske jakosti z vbrizganimi vrzeli odlikovane vmesne plasti stika elektrode/organski polprevodnik.
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The externalbias-dependent electric field at hole-injecting ele ctrode/
a-NPD junction and its relationship to Gaussian disordered interface states
1 INTRODUCTION
All organic semiconductor electrical devices are developed with the aim that the resistance between the injecting (and ejecting) charges from the suitable electrode into the organic is minimized. Improvements in the resistance of the electrode/organic semiconductor contact result in considerably improved device performances on account of advances of the charge carrier mobility. The science of so-called contact engineering [1-7] crucially contributes to the optimized performance of the distinct organic devices that are in use. The charge mobility | is an involved function of the externally applied electric field, Ea, the temperature T, and the charge carrier density, p, providing that the injection barrier between the charge-injecting electrode and the contacting organic semiconductor is as small as possible. The charge mobility is most commonly inferred by the current-voltage, j - Va, experiments in which the stead- state current density, j, through the electrode/organic/metal structures as a function of the externally applied DC electric field, Ea = Va/L, is measured. Here Va is the applied voltage over the two electrodes and L is the thickness of the organic medium between them. The prerequisite for its successful determination is the existence of ohmic contacts between the charge injecting electrode/organic interfaces. The current through such a structure is then the space charge limited current, SCLC, and only under this condition the data then provide the fully reliable charge-carrier mobility [3, 8, 9]. The criteria for the occurrence of SCLC are based on the effects of the electric field-dependent charge mobility, organic layer thickness and charge-injection barrier height as extensively discussed by Wang et. al. [8, 9]. It was concluded that these condition should be fulfilled prior to the measurements; otherwise the obtained results apparently "have no meaning" [9]. In cases of non-ohmic contacts the current density no longer exhibits the SCLC behavior. A thorough investigation into the reproducibility problem of the mobility measurements in organic semiconductors that concludes with the recommendations regarding the device preparation, fabrication, measurement and analyses in order to ensure the most trustworthy results has been reported recently by Blakesley et al. [10].
The above-stated works and others that have followed provide evidence that under identical conditions the hole mobility of a given organic substance is a function of the electrode material utilized for injection of holes. Evidently, the cause that influences the hole mobility ought to be related to the electric field at the hole-injecting interface. This expectation is explicitly expressed in the form of the steady-state non-zero electric field at the charge-injecting electrode/organic interface, Eint, that is a parameter in the extended Mott-Gurney space charge limited current model [11]. The second parameter of the stated law is the maximum value of the charge mobility, |max, (in [11] inappropriately termed effective mobility |eff as will be discussed later) that is in a given current-voltage experiment determined from the current density measured (exclusively) at the maximum value of Ea. The parameter |max is consequently bias independent. It should be stressed that both parameters are related to the charge drift mobility, |d, which is the quantity of great practical interest. As shown in [11], the SCLC fits in various organic samples based on the extended Mott-Gurney law are characterized by the external bias independent, parameter Eint, see for instance Fig. 1 and Fig. 2 of [11]. In cases of poor ohmic contacts the current density is no longer of the SCLC type, which commonly occurs (at least) within the initial part of the interval of the externally applied electric field Ea > 0.1 MV/m say, see Figs. 3, and 4 of [11]. The SCLC is in the extended Mott-Gurney formulation described in terms of a non-zero constant Eint, which is independent of the externally applied electric field, Ea. This was empirically verified by the independent SCLC analyses based upon the well-known Mott-Gurney expression incorporating
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the exponential bias dependent mobility [11]. As seen, there the SCLC predictions of Eqs. (1), and (2) considerably overshoot the j-V data within the initial part of the respective Ea interval. In contrast to this, it was found that in cases of a non-ohmic metal/organic contact, the concave SCLC curve formulated by the extended Mott-Gurney model can always be made to intersect (at least) the first and the last current-voltage measuring point of a giving Ea interval.
Recently, a particularly interesting current-voltage temperature and thickness dependent hole transport measurements within the various electrode/a-NPD (i.e., N,N'-Di(1-naphthyl)-N,N'-diphenyl-(1,!'-biphenyl)-4,4'-diamine) organic thin diode devices have been published by Rohloff et al. [12] and van Mensfoort et al. [13]. In [13] it was determined that Mott-Gurney law with the exponential bias-dependent mobility could not account for their data. Consequently, the given set of current density measurements, [13], on a ITO/a-NPD/Pd hole only organic structure, offers the information related to the current density deviation from the expected SCLC behavior. In contrast to this, for the hole only PEDOT:PSS/a-NPD/ TCTA/MoO3/Al organic structures the occurrence of SCLC has been determined by j-V measurements as reported by Rohloff et al. [12]. Here PEDOT:PSS denotes poly(3,4-ethylenedioxythiophene):polystyrene sulfonate and TCTA is an abridged notation for tris(4-carbazoyl-9-ylphenyl)amine. It is evident that in case of the stated organic structures prepared with chemically identical organic semiconductor a-NPD that the observed difference in the hole current density (between the samples of equal thickness and at similar temperature) should be related to the different hole injecting electrodes. The data of [12], and [13] then provide an opportunity to arrive at some additional information of not-yet understood processes that occur at the hole-injecting electrodes/a-NPD interfaces. In this respect, the investigation of the electric field at the hole-injecting electrodes/a-NPD interface, Eint, a parameter of the extended Mott-Gurney law [11], seems to be most convenient.
This is the purpose of the presented work. Namely, as written above, Eint is in an organic structure related to the charge drift mobility, |d and no detail knowledge exists in the literature about its relationship to the non-SCLC current density, j. The later process occurs due to the non-ideal electrode/organic contact. The explicit knowledge of Eint dependence on the externally applied field Ea (note that in SCLC cases Eint, is a constant, [11]) should then provide additional illumination of the charge transport processes and by this on the expected performance of a given organic structure. It will be shown that the current density deviation from the SCLC behavior in a-NPD hole transporting electrode/organic structures occurs on account of the external bias dependence of the electric fields, Eint, at hole injecting contacts, which detrimentally affects the hole drift mobility.
It is known, and [12] and [13] offer support to the claim that the interface between the electrode and the organic substance plays a crucial role in the charge transfer between the stated two media. It primarily depends on the relative alignment of molecular energy states in the organic to the Fermi level of the electrode giving rise to the energy barrier at the interface.
On account of a low density of free charge within the organic bulk, the electric field applied between the two electrodes results in a charge imbalance at the organic side of the charge injecting interface. The imbalance may be particularly large if the electrical contacts are ideal ohmic. The SCLC, the space charge limited current through the metal/organic/metal structure at a given applied electric field, Ea, is determined by the ability of the charge injecting electrode to continuously supply excess charges to the interface in the amount exceeding the steady current through the organic that is limited by space charge in its interior [14, 15]. On account of the interaction between the adsorbed organic molecules and the electrode the additional energy
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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states develop at the contact that depend on the method of the organic deposition, the organic crystallinity, and on number of other possible factors, The complex array of resultant energy barriers on the interface represents a cause that a portion of injected charges, the ones with insufficient energies accumulate (become trapped) in it. The free excess charge supplied by the contact the net trapped holes on those parts of a-NPD molecules that constitute the interface the charge on the organic side of the interface that compensate the built-in voltage, the charge at the electrode/organic contact and other possible sources of charge all contribute to the resultant electric field within the a-NPD organic.
The electrode/organic interface charging, i.e. the charge transient processes, before the steady state current is established is most suitable investigated by the time-resolved electric-field-induced optical second-harmonic generation, EFISHG, method [16, 17]. With the stated technique the electric fields in organic layers can be selectively and directly probed [16, 17]. In comparison to the EFISHG method it will be shown that the current-voltage method is suitable for the investigation of the steady state electric field at the charge injecting interface. It will be shown that the electric field at the hole injecting interface, Eint, as used in this paper represents the magnitude of the resulting vector £int = Ea + Ech at the position of the interface. Here Ech stands for the magnitude of the (steady state) electric field due to all other, unspecified, sources of charge and Ea, is the externally applied (steady state) electric field over the device.
It is noted that the authors of [12] and [13] have successfully interpreted their measurements in terms of the drift-diffusion theory of the hole mobility subjected to the charge hopping among the energy states described by the static, uniform, Gaussian energetic disorder in a-NPD organic bulk [18]. Assuming the hopping hole transport within the Gaussian distribution of disordered energy levels in the organic the authors have shown that the Gaussian disorder model (GDM)
[19],	reproduces the measurements well. This model takes into account the hole mobility described as a known function of the hole density, the electric field, the temperature, and the Gaussian width, ct. Likewise, it was shown that the correlated Gaussian disorder model (CDM)
[20]	also accounts for the data well. The CDM model contains additional description of the site energy correlated disorder due to the randomly oriented dipoles and may be viewed as an upgrade of the GDM description. No direct interaction between the hole-injecting electrodes and the a-NPD organic has been considered.
In [21] the charge transfer from the electrode into the density of states within the organic bulk has been considered and suggested that the spread of the disordered energy states near the interface appeared to be correlated with the charge mobility. This important question is presently also addressed and the relationship between the bias-dependent Eint (the principle cause of affecting the hole drift mobility) and the disordered energy states within the organic part of the interface is established on the basis of a simple interface model constructed upon the findings of Oehzelt et al., [22].
This paper is organized as follows:
In Sec. 2, a brief presentation of the extended Mott-Gurney law is given and the method of Eint extraction is presented. It is shown that the original Mott-Gurney law describing SCLC is valid for Eint = c Ea, where c is an electrode/organic specific constant. A simple model is presented by which the compatibility of the deduced results with Gaussian energetic disorder in organic is established. In Sec. 3.1, the predictions of the hole drift current density, j, are compared to the published current-voltage data of [12]. It is shown that the forward biased (i.e. Al at the positive
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potential) PEDOT:PSS/a-NPD(100 nm)/TCTA(5 nm)/MoO3/Al structure displays SCLC characteristics only for Ea exceeding a given temperature-dependent threshold value within the respective Ea interval of measurements. Within the SCLC region, characterized by the constant Eint, the calculated Ea dependence of the hole drift mobility, |d, coincides with the prediction of the well-known exponential dependent hole mobility. This is the region of good ohmic contact. The small current density deviation from the SCLC characteristic is used to calculate the Ea dependence of Eint, and to investigate its effect on the hole drift mobility. Based upon the simple model the relationship between the deduced Eint and the hole transport within the Gaussian distribution of disordered energy states within the organic side of the interface is demonstrated and characterized. In Section 3.2 the absence of SCLC characteristics for all temperature-dependent current-voltage measurements on the ITO/a-NPD/Pd organic structure of [13] is determined. The strong bias dependence of Eint is evaluated and the detrimental effect of its Ea dependence on the drift hole mobility is demonstrated. In Sec. 4 the conclusions drawn are presented.
On the basis of the results presented here the current/voltage method might be of interest also in the area of contact engineering.
2 THE EFFECT OF THE ELECTRODE/ORGANIC CONTACT ON CURRENT-VOLTAGE DATA
It was shown in [11] that the extended Mott-Gurney law describes the steady state current density within the single layer metal/organic structure that originates due to the externally applied DC electric field, Ea, and reflects the complicated electrode/organic processes, which directly govern the charge transport. These processes have generally been neglected in the analyses of current-voltage measurements from which the charge mobility is most often extracted.
Throughout this work, the hole-injecting electrode at the positive potential, Va, is considered at the origin of the frame of reference and the cathode is placed at the position x = L, where L is the thickness of the organic layer. The general expression of the hole drift current density is then expressed by the extended Gurney-Mott law, [11], that explicitly considers the charge-injecting interface of a given metal/organic structure and reads,
where, j is the (steady state) current density, g, is the relative permittivity of the organic layer, g0 is the permittivity of vacuum, Ea = Va/L, is the externally applied DC electric field over the organic structure and |d is Ea dependent charge carrier drift mobility, defined as,
J - SSoM-d
(2.1)
^d
ßmax 2
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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(l -! (if)2 + f£ ■-! (if)4 +3 (i*03 - T (TO? 1 (2-21
18 2 V Ea /	64 4 V Ea /	8\£a/Jl
The charge drift mobility, |d, depends on the organic morphology, intrinsic and extrinsic impurities, method of deposition, strengths of the charge-phonon interactions that determine the charge drift transport among the disordered energy states of the organic bulk, etc.
The stated model is characterized by two distinct, independent physical parameters; (a) the nonzero electric field at the charge injecting electrode/organic interface, Eint, [11] that is in this work investigated as a function of the externally applied electric field, Ea, and (b) the maximum value of the charge mobility |max as measured in a given experiment..Evidently, in the (forbidden limit) Eint = 0, see [11], Eq. (2.1) would have reduced into the original Mott-Gurney law, [14]. It is characterized by the charge density singularity, [14] at the charge-injecting interface. By postulating the existence of the non-zero electric field at the charge-injecting electrode/organic interface, Eint # 0, this deficiency is remedied, [11]. It can be noted, however, that for the ratio Eint/Ea = c, where c is a given constant 0 < c < 1 the charge drift mobility Eq. (2.2) is Ea independent. Simple rearrangements of terms then result in the expression,
9
J = | ^ £0 M 7J	(2 3)
where the so called effective charge mobility, [14], identified as 8 |d/9, is bias Va independent. Eq. (2.3) represents the original version of Mott-Gurney law that describes the SCLC condition of the drift current density within the given organic semiconductor. As seen, Eq. (2.3) is in fact valid when the non-zero ratio Eint/Ea is a given constant, i.e. Eint # 0, and represents a particular example of Eq. (2.1).
However, it has been realized that the charge mobility, Eq. (2.3) is in fact on the externally applied electric field, Ea, dependent parameter, [23]. With the current-voltage measurements of large number of organic semiconductors it was empirically determined that | may be suitably formulated in terms of the phenomenological exponential bias-dependent charge mobility given by,
^ =	e^ V11	(2.4)
The last two expressions taken together traditionally describe the SCLC (i.e. the maximum steady current density that a given electrode/organic structure may sustain) and are very often used in current-voltage experiments for experimental determination of the charge mobility, [8-10]. It was shown, [11] that the general expression for hole current density j, Eq. (2.1), leads to SCLC only under the condition that Eint is Ea independent quantity in which case the contact is defined as ohmic. The deviation of the given current density from the shape of SCLC curve is then reflected in a bias dependence of Eint (remember that |max is fixed since it is for a given organic structure extracted from the maximal value of the current density, jmax, as obtained at maximum Ea). The bias dependence of Eint is determined in two steps. Initially, the (fixed) parameters EintSCLC, and |max, are determined so that the trial SCLC fit, Eq. (2.1), intersects the first and the last current
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density points of the given Ea interval of measurements. With |max known the bias dependence of Eint is then described by the (positive) roots of Eq. (1) evaluated successively for each experimentally determined pair (j, Ea). Note that the first and the last current density points are measured at two different values of Ea. Both points are characterized by identical value of Eint = EintSCLC, Consequently, Eint is a double valued function of the parameter Ea in all cases in which the current density defies the SCLC description.
The relationship exist among the electric field at the charge-injecting electrode/organic interface, Eint, the externally applied electric field, Ea, and the electric field at the site of the interface due all other charges present within the organic, Ech. It is deduced by observing that the resultant electric field within the organic layer is, E = Ea + £ch see [16]. Written explicitly for the (thin) charged electrode/organic interface placed at the coordinate origin x = 0 the spatial dependent internal electric field, E(x), is then equal to
V
E(x) = k2nt + 2 KEa) x 1 2 = Ea + Ech(x)
L	£ £q Mmax J
(2.5)
Note that the interfacial electric field, Eint, is incorporated within the left term. Consequently, Ech(x) then represents the resultant electric field within organic due to all other sources except Eint. Since the hole-injecting interface is at the position x = 0, it immediately follows that,
Eint = Ea + Ech	(2.6)
where Ech(x = 0) = Ech. Consequently, current-voltage experiments directly provide the interfacial electric field, Eint, see Eq. (2.1), and with Eq. (2.6) its relation to the electric field at the site of the interface that results from the distribution of other charges existing within the organic is presented.
The compatibility of the current-voltage data analyses using the above-presented method with the notion of the charge transport within the Gaussian disordered energy states in the organic is illustrated by virtue of a simple model described below.
Lange et al. [21], have reported that the band bending in organics may be explained by the transfer of charge from the electrode into the tail of Gaussian distribution of energy states, DOS, which extends into the organic charge transport gap. The space charge formed by occupation of tail states strongly modulates the width of Gaussian energetic disorder at the electrode-organic contact and in such a way appears to affect the charge mobility. Since, as shown presently, the bias dependence of the hole drift mobility is greatly influenced by the electric field at the hole-injecting electrode/a-NPD interface it remains to show that the hole drift mobility (or equivalently the electric field Eint) and the Gaussian energetic disorder at the electrode/a-NPD contact are mutually interrelated. To show this, a simple physical model is constructed. It is assumed that the interface may be represented as a plane sheet of uniformly distributed holes that occupy the disordered energy states at the organic side of the contact. Specifically, Oehzelt et al. [22], have determined that in thermal equilibrium in absence of the externally applied electric field, Ea = 0, the nonzero charge density is spontaneously induced at the metal/organic contact. This fact triggers a shift of the central position of the Gaussian energetic disorder in the direction of the increased (negative) binding energy [22]. The prediction has been verified by Whitcher et al. [24, 25], and Khoshkho et al. [26]. More specifically, Beck et al., [27], have with
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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the infrared spectroscopy method determined (at Ea = 0) that the charge at the Mo3/CBP interface where CBP denotes (4,4'-bis(N-carbazolyl)-1,1'-biphenyl) organic semiconductor decays to a very small value already within about 3 nm into the CPB organic bulk.
With an extension of the ideas of [22] to cases in which the externally applied electric field is non-zero, Ea # 0, it was already possible: (a) to show that the room temperature linearly increasing electric field at the hole-injecting ITO/P3HT (i.e. poly(3-hexylthiopene)) interface leads to the negative field hole mobility, [28], and (b) to provide the evidence of the relationship between the linearly dependent interfacial electric field and the Gaussian energetic disorder, ct, within the narrow region of the P3HT organics close to the hole-injecting metal/organic interfaces [28].
In order to investigate the relationship between the Ea dependent electric field at the hole-injecting electrode/organic interface and the Gaussian energetic disorder in the organic a simple model has been constructed, [28]. Considering the interface as a thin, laterally infinite, uniformly charged plane (in presence of steady electric fields) than from the Gauss law ££0§ElntdS = q(Pt + Vf) it follows that Eint = yint/(2££0). Here pt, and pf are the (number) densities of trapped and free charge on the interface and yint denotes the interface charge density per unit area. In parallel to [28] and elaborating the approach of [22] and [27], it is now assumed that L* nm thick, laterally unlimited, organic layer in contact with an electrode is covered by an excess hole (areal) density that is in the first approximation equal to q p L* P(E) = 2 g g0 Eint, where P(E) is the probability that the disordered interfacial energy states are populated. The width L* chosen in this work, is the distance from the electrode/organic contact into the organic bulk at which the induced interface charge density is reduced to a small value, see Fig. 2a of [22], and Fig. 2 of [27]. The holes within the layer represent the seat of the interfacial electric field, Eint. The holes populate the disordered energy states within the organic interface, which are described in terms of Gaussian distribution function characterized by its width, ct, and the energy shift, 9. The stated relationship then reads,
eu = sn* rexp1"'	(2.7)
2 € €q C V2S J— 1+eXp[	]	1 '
K I
where EH is the highest occupied molecular orbital (HOMO), and EF is the Fermi level. In this work the energy shift, 9, and the width of the Gaussian, ct, are assumed to be implicit functions of the externally applied electric field, Ea. Evidently, the stated two parameters are fixed for constant Eint (SCLC conditions) but in case of the external bias-dependent Eint their bias dependence should vary in a particularly coordinated way on account that Eint is then a double-valued function of Ea. It is noted that Eq. (2.7) is: (a) independent of the hole mobility, and (b) that the product q p L*, the interface (areal) hole charge density plays the role of the scaling factor only. For reference the number of charged molecules per unit area the (saturation) value of p L* = 8x1013 cm-2 is in [27] deduced from the measurements.
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3 RESULTS AND DISCUSSION
3.1 The PEDOT: PSS/a-NPD(100 nm)/TCTA(5 nm)/MoO3/Al current-voltage data of Ref. [12]
The room temperature j-V measurements of the PEDOT:PSS/a-NPD(100 nm)/MoO3/Al organic structure of [12] were reported to exhibit unexpected behavior. The work functions of PEDOT:PSS is 5.1 eV, the HOMO level of the amorphous a-NPD is at 5.4 eV (i.e., the hole barrier between the two is then 0.3 eV) and the work function of MoO3 is placed at 6.86 eV, [12]. Contrary to the expectations it was found that the hole current density in the reverse direction (Pedot:PSS contact at the positive potential) exceeds the hole current in forward direction of bias, i.e., when the Al contact is at a positive potential. The authors report, [12] that the current density symmetry in the forward and backward direction of current is established by the deposition of 5 nm thick tris(4-carbazoyl-9-alphenyl)amine (TCTA) interlayer between the a-NPD and the MoO3/Al electrode.
The stated current density asymmetry effect will now be tentatively explained. In the reverse direction of bias, the barrier at PEDOT:PSS/a-NPD junctions appears to be small enough for the hole SCLC to take effect. However, the Al contact at the positive potential results in an unexpectedly weak current density, an effect that may be explained by the finding of Matsushima et al., [29]; in their study of the effect of the molybdenum trioxide layer placed between the ITO and a-NPD organic on the hole current transport the authors of [29] provide evidence that, under the stated polarity, the a-NPD/MoO3 interface becomes charged. Specifically, it is claimed that a-NPD boundary layer of the interface is charged positively while the MoO3 one negatively. Such a charged layer then detrimentally affects the hole injection from the MoO3/Al electrode. It is a fact that with the 5 nm thick TCTA layer between the a-NPD organic and the positively biased MoO3/Al electrode, [12], the SCLC regime is activated in the stated organic structure. This observation evidently supports the conjecture of Matsushima et al., [29], that in the forward direction of bias the a-NPD/MoO3 interface becomes charged. If this is indeed so, it may be clarified by the time-resolved electric-field-induced optical second-harmonic generation, EFISHG, investigation in combination with the steady current voltage measurements of the type as reported recently by Nishi et al. [16].
The forward hole current (positive potential at Al) within the PEDOT:PSS/a-NPD(100 nm)/TCTA(5 nm)/MoO3/Al organic structure was reported to be of the SCLC type, [12]. Then it is expected that from calculated curve with the bias-independent electric field, Eint, Eq. (2.1), at the hole-injecting TCTA/ a-NPD interface, should describe the data well. Consequently, the room temperature T = 295 K measurements, [12], are compared to the SCLC fit predicted by Eq. (2.1) (solid triangles) that connects the first and the last data point of the L = 100 nm thick sample (solid hexagons). In all calculations reported here the relative dielectric constant g = 3. The parameters of this initial (trial) SCLC fit are found to be: the maximum hole mobility is |max = 3.7x10-8 m2/Vs and the interfacial electric field is Eint = 1.5 MV/m, see Fig. 1. As seen in Fig. 1 an excellent fit to the T = 295 K data of [12] is indeed obtained but only within the range say, Ea > 1.0x107 V/m, Fig. 1. Thus, within the interval 10.0 MV/m < Ea < 25.0 MV/m the electric field at the hole-injecting interface (Eint = 1.5 MV/m), is constant and the bias dependence of the current density, j, is governed by the product |d Ea2. The hole drift mobility |d is weakly bias-dependent within the stated interval, as will be shown later. The fact that a clear disagreement between the SCLC fit and the data is observed within the interval of the applied electric field, 0.194x107 V/m < Ea
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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< 1.0x107 V/m, Fig. 1, signifies that the Al/MoO3/TCTA/5 nm)/a-NPD(100 nm)/PEDOT:PSS organic structure (Al at the positive bias Va) is not barrier-free within the stated Ea interval.
For the Al electrode (at the origin of the frame of reference) at positive bias, Va > 0 then follows that within the interval 1.94 MV/m < Ea < 25.0 MV/m the interfacial field Eint < Ea, see Fig 2. This fact demonstrates that the (organic side of) the hole-injecting interface is exposed to an additional (steady) electric field in the opposite direction of Ea. This electric field due to the space charge and other charge sources (Eint is excluded) is denoted as Ech. In fact, it will be observed that the relationship Eint < Ea, is valid for all cases reported here even for non-SCLC current density conditions. Consequently, for the particular structure under investigation TCTA/a-NPD is identified as the hole-injecting interface, and it is feasible that the space charge and perhaps also the a-NPD/PEDOT:PSS interface represent a positively charged source of the (steady-state) interfacial electric field, Ech, acting in the opposite direction to Ea. The stated organic structure represents then a particular example of an organic bilayer, [16]. The resulting steady-state electric field at the hole-injecting interface TCTA/a-NPD is equal to Eint = Ea - Ech, see Eq. (6), in agreement with the experimental fact that Eint < Ea. The Eint represents the electric field at the TCTA/a-NPD contact that is directed towards the cathode in the positive direction of the x-axis.
The stated difference between the trial SCLC fit and the data within 1.94 MV/m < Ea < 10.0 MV/m interval will now be analyzed. As seen, Fig. 1, the initial current density point jinit = 15.75 A/m2 at Ea = 1.94 MV/m and likewise j = 1079.35 A/m2 at Ea = 10. 0 MV/m, are both characterized by already deduced SCLC parameters Eint = 1.5 MV/m, and |max = 3.7x10-8 m2/Vs. Following the procedure described in Sec. 2 the bias-dependent interfacial electric field, Eint, within the stated Ea interval is evaluated and the resulting electric field at the hole-injecting interface, Eint, is exhibited on Fig 2 (circles). Within the stated narrow Ea interval, it attains the shape of the distorted, inverted high order parabola that is analytically described by the approximation function presented in Table 1. It is noted that Eint is double-valued function of the argument Ea. The parameters of the SCLC curve well describing the data for Ea > 10 MV/m are shown in Table 2. Inserting the deduced bias-dependent Eint and the maximum hole mobility, |max back into Eq. (2.1), the newly calculated fit practically coincides (as it should) with the data throughout the remaining part of the measuring interval (the crosses over the measuring points, i.e., solid hexagons), Fig. 1.
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10000,
CM
<
E
0,1
0
2
3
4
5
6
Ea [ 107 V/m ]
Figure 1: Top curves: the comparison of the calculated trial SCLC curve (filled triangles) to the PEDOT:PSS/a-NPD(100 nm)/TCTA(5 nm)/MoO3/Al hole j - Ea data of [12] measured at T = 295 K (filled hexagons) reveals the existence of SCLC regime at values of the externally applied electric field Ea >10 MV/m. Bottom curves: the calculated trial SCLC curve (half-filled circles) to the data at T = 213 K (filled squares) of [12] exhibits the narrow SCLC regime only for Ea >41.8 MV/m. Crosses joined by the thin curve that in both examples coincide with the measurements denote
the predictions of Eq. (2.1), when incorporating the deduced and for each temperature appropriate Ea dependent electric field at the hole-injecting a-NPD(100 nm)/TCTA interface, Eint,
Viewing the T = 295 K curve (Fig. 1) the slow continuous merger of the SCLC fit to measurements that is taking place within the certain narrow range of Ea is noted. Consequently, Fig. 1 provides evidence that the quasi-ohmic contact may transit into a good ohmic one by an appropriate increase of the externally applied electric field, Ea. It is, however, unclear if this process is reversible. At this point, it should be stated that as seen in Fig. 1 the transition occurs continuously and it is not feasible that this interval could be univocally determined. For this reason such an interval is in this work replaced by a single current density point (here defined at Ea = 10.0 MV/m) at which both curves still coincide. This simplification affects the obtained results in two ways: (a) the calculated values of Eint are progressively scattered with increasing Ea, and (b) the derivative of the function Eint = Eint(Ea) with respect the argument Ea is then discontinuous at the point of merger, see Fig. 2. It should be emphasized that the magnitude of the T = 295 K resulting (bias-dependent) interfacial electric field, Eint, within the initial part of the Ea interval, i.e., within the quasi-ohmic region, 1.94 MV/m > Ea > 10 M2.V/m, considerably exceeds the one that characterizes the SCLC regime (i.e., Eint = 1.5 MV/m), see Fig. 2 (circles).
see Fig. 2.The data are redrawn from Fig. 2b of Ref. [12].
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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Ea [107 V/m]
Figure 2: The calculated electric fields at the hole-injecting electrode/a-NPD(100 nm) interface, Eint, as a function of the applied electric field, Ea, are exhibited for cases of the hole j - Ea data of
[12]. The deduced interfacial electric field at T = 295 K (circles) and T = 213 K (squares) are represented by the approximation functions given in Table 1, and are shown by thin curves in Fig. 2. The constant Eint, characterize the Ea regions of SCLC regime indicating the ohmic resistance at the hole-injecting contact.
Inserting the two parameters |max = 3.7x10-8 m2/(Vs), and Eint = 1.5 MV/m into Eq. (2), the calculated bias-dependent SCLC hole drift mobility, |d, at T = 295 K is exhibited in Fig. 3 (stars). For comparison with Eq. (2.3) the predicted fit with the exponential bias-dependent mobility, Eq. (2.4), (empty squares) is also included in Fig. 3. The parameters of the stated mobility are found to be: |0 = 3.6x10-8 m2/(Vs), and p = 0.4x10-4 (m/V)1/2. As shown in Fig. 3 the evaluated mobility, Eq. (2.4), and |d, Eq. (2.2) considerably differ within the initial part of the Ea interval. The calculated curves within SCLC region practically coincide, a behavior similar to the one reported; see Fig. 4 of [11]. However, the correct bias dependence of the hole drift mobility is obtained only when Eq. (2.2) is calculated with the bias-dependent Eint; see Fig. 2 (circles). The result is exhibited in Fig. 3 (solid points) and the strong Ea dependence of |d, at small values of the externally applied electric field, Fig. 3, within the range of disagreement between the data and the (trial) SCLC curve is evident. The calculated curve is characterized by the relatively slower increase of the hole drift mobility with Ea (solid points) occurring entirely within the quasi-ohmic region, Fig. 3. Consequently even at T = 295 K the sample of [12] was not absolutely barrier-free. Over Ea > 10 MV/m the ohmic region is attained that is characterized by the constant value of Eint = 1.5 MV/m. This is the region within which the hole drift mobility, Eq. (2.2), exhibits very weak Ea dependence as evidenced on Fig. 3. The bias-dependent exponential hole drift mobility, Eq. (2.4), is at Ea = 25.0 MV/m then equal to |d = 4.4x10-8 m2/(Vs). The stated interval represents the saturation region of the electric field at the hole-injecting electrode/organic interface. Consequently, the SCLC region is the region within which the parameter, Eint, the interfacial electric field is independent of the externally applied electric field, Ea. Then the hole drift mobility, Eq. (2.2), is itself only weakly Ea dependent and for this reason the current density, Eq. (2.1), within the saturation region is almost proportional to Ea2.
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Table 1: Approximation functions for the temperature dependent electric field at the hole injecting TCTA/a-NPD organic interface of the form Eint = a + b Ea + c Ea2 +d Ea3 + e Ea4 + f Ea5 + g Ea6 are shown. Ea denotes the externally applied electric field.
T [K]
a
[V/s]
b
c
[(V/s)1]
d
[(V/s)'2]
e
[(V/s)-3]
f
[(V/s)-4]
g
[(V/s)-5]
PEDOT:PSS/a-NPD(100 nm)/TCTA/MoOs/Ai Ref. [12]
213 -1.039x10s 1.733 r1.826x10-7 1.392x10-14 -5.750x10-22 1.172x10-29 295 -1.232x106 2.618 -9.311x10-7 2.009x10-12 -2.469x10-20 1.527x10-27
-9.450x10 -3.693x10-35
ITO/a-NPD(100 nm)/Pd	Ref. [13]
189 -1.872x107 4.287 -2.354x10-7 8.897x10-15 -1.814x10-22 1.939x10-39 -8.607x10-3 295 2.815x108 -88.586 1.136x10-5 7.349x10-13 2.564x10-20 -4.609x10-28 3.348x10-31
Table 2: The temperature dependent maximum hole mobility, ¡umax, of the electrode/a-NPD(100 nm) thick organic entity and the associated electric field at the hole-injecting interface, Eint, are presented. Both quantities, based on published measurements of Rohloff et al., [12], and van Mensfoort et al., [13], are deduced by Eq. (2.3) at the maximum value of the externally applied
electric field, Eamax.
	T [K]	|max [10-8 m2(Vs)-	1 ] Ent [107 Vm1]	Eamax [107 Vm1]	Ref.	
		PED0T:PSS/a-NPD(100 nm)/TCTA/MoO3/Al			[12]	
213		0.15	0.29	5.0		
295		3.7	0.15	2.5		
			IT0/a-NPD(100 nm)/Pd		[13]	
189		0.013	2.20	7.5		
295		0.08	1.41	3.1		
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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*
_i_i—i_i_i_i_i_i_i_i_i—i_i_i—i_i_i—i_i_i—i_i_i_i_i—i_i_i_
■5.5	1.0	13	2.0	2.5	3.0
Ea [107 V/m]
Figure 3: The Ea dependence of the room temperature hole drift mobility within the a-NPD structure of [12] is shown. Assuming the SCLC regime to exist within the entire interval of measurements then: (a) the exponential bias-dependent hole mobility, Eq. (2.3), with the parameters, [i0 = 3.6x10-8 m2/(Vs), and p= 4.0x10-5 (m/V)1/2 is described by empty squares, and (b) the hole drift mobility, [id, calculated from Eq. (2.2) with the constants Eint = 1.5 MV/m, and jumax = 3.7x10-8 m2/(Vs) is shown by stars. The /ud curve denoted by solid points represents the predictions (within the non-SCLC region) of Eq. (2.2) evaluated with bias-dependent Eint of Fig. 2 (circles). Within the SCLC interval of bias, all three curves coincide.
At this point it has to be emphasized that |max depends on the coordinate (Eamax, j(Eamax)) of the measured current-voltage end point. Consequently, |max is evidently Eamax sensitive, and so are the deduced bias-dependent Eint values. The initial, i.e., the first current density point with coordinates (Eamin, j(Eamin)) defines the initial intersection with the calculated (trial) SCLC curve and, consequently, this point is primarily related to the value of the second SCLC parameter, the bias-independent interfacial electric field, Eint. Discarding some given number of measurements within the highest range of the Ea interval (i.e. narrowing the given Ea interval) then the value of |max, the maximum hole mobility is decreased and, consequently, the set of bias-dependent interfacial fields calculated within the narrow Ea interval (relative to the narrowed SCLC curve) is also correspondingly changed. However, the bias-dependent hole drift mobility curves, Eq. (2,2), calculated for each data set separately are found to coincide (within the shorter Ea interval) and thus prove that the magnitude as well as the bias-dependence of the hole drift mobility, |d, is invariant to the width of the Ea interval. Thus, the auxiliary parameters the bias-independent |max and the bias-dependent set of evaluated Eint then via Eq. (2.2) define the bias-dependent hole drift mobility as a unique material property of the electrode/organic entity under the investigation.
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t—i—i—i—i—|—i—i—i—i—i—i—i—i—i—i—i—i—i—i—|—i—i—i—i—r
□
1 L_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_I_L.
0	1	2	3	4	5
Ea[ 107V/m]
Figure 4: The Ea dependence of the calculated hole drift mobility, [id, Eq. (2.2) incorporating the
deduced bias dependence of Eint at T = 295 K (circles) and T = 213 K (squares), within the a-NPD(100 nm) structure of [12] is shown The growing part of the curves denote the quasi-ohmic contact region that with the increasing Ea continuously evolves into the ohmic region of (almost) the constant values of /ud (compare Fig. 2).
The results of the similar analyses as above of the data measured at T = 213 K, [12], are also shown on Fig. 1 (filled squares). It is immediately evident that the initial (Eint = 2.9 MV/m and |max = 1.5x10-9 m2/Vs) SCLC fit calculated from Eq. (1) (half filled circles) exhibits within the interval (e.g. 3.0 MV/m < Ea < 41.8 MV/m) a noted disagreement to the data set. However, beyond that, i.e., within 41.8 MV/m < Ea < 50 MV/m interval the agreement between this initial (trial) SCLC curve and the measurements is evident. It is noted that the calculated SCLC curve using the above two bias-independent parameters again intersects the first and the last current-density data point. This is then a clear indication that the SCLC regime within the given structure (at the stated temperature) occurs within the highest range of the Ea interval only. Thus it is confirmed that the ohmic region of the PEDOT:PSS/a-NPD(100 nm)/TCTA(5 nm)/ MoO3/Al structure is temperature dependent and may be induced by the external bias, Ea. The ohmic region at T = 213 K has considerably narrowed in comparison to the one at T = 295 K. In addition the measuring Ea interval has substantially widened. Following the previously described steps, the bias-dependent interfacial electric field, Eint, is calculated, and together with the approximation function, Table 1, is exhibited in Fig. 2 (squares). Within the interval 41.8 MV/m > Ea > 45.0 MV/m the calculated values of Eint are considerably scattered. This occurs due to the fluctuations in reading off the (finite sized) data points that almost coincide with the SCLC fit, see Fig. 1. However, when the calculated bias-dependent Eint is inserted into Eq. (2.2), then the fit, Eq. (2.1) to the measured data is once again excellent (represented by the thin line passing through the crosses), Fig. 1. Once again it is observed that the magnitude of bias-dependent Eint considerably exceeds the corresponding (but bias-independent) value within the (narrow) SCLC region, Fig. 2. The Ea dependence of the hole drift mobility, Eq. (2.2), at T = 213 K is presented in Fig. 4, (empty squares).
Thus far, the emphasis has been on the dependence of the electric fields, Eint, at hole-injecting TCTA/a-NPD interfaces, as a function of the externally applied electric field, Ea, and an excellent agreement with the published data has been obtained. Quite similar quality fits are presented in
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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[12], and [13], but their calculations were based on the drift-diffusion hole transport using the well known models of the hole mobility characterized by hopping between the disordered energy states of the organic bulk as described by the Gaussian distribution function [18 - 20]. In particular, their results have shown that the half widths, a, of the Gaussian disordered states, depending on the particular case investigated, should be placed within the interval 0.08 eV < a < 0.14 eV. It is noted that a is independent of the applied electric field and describes an average over the organic sample.
The essential difference between the results reported in the literature and the findings presented here is the fact that at all temperatures the (temperature dependent) electric field at the hole-injecting TCTA/a-NPD interface is non-zero and definitely non-exponential. In addition, the resulting findings are obtained devoid of any phenomenological parameters. It is interesting that the data of [12], and [13], are in the present work also interpreted to an excellent approximation but seemingly on wholly unrelated basis. Consequently, it appears that the Gaussian disorder model and this work might be somehow related. The cause that different studies of hole mobility performed under similar conditions on chemically identical a-NPD organic semiconductor provide rather inconsistent results (compare for instance Figs. 4 and 8) is, in this work, attributed to unequal conditions at the hole-injecting interfaces, see Fig. 2, and Fig. 8.
In [21] the charge transfer from the electrode into the density of states within the organic bulk has been identified and it was suggested that the spread of the disordered energy states near the interface appeared to be correlated with the charge mobility. Consequently, it now remains to show that the above derived bias-dependent electric field at the hole-injecting TCTA/a-NPD interface, Eint = Eint(Ea), is related to the Gaussian energetic disorder at the organic side of the interface in conjunction with findings described in [18 - 20].
The deduced Eint, the inverted and distorted high order parabolas, are (for non-ohmic contacts) all double valued functions of the argument Ea, see Fig. 7. The calculations based on Eq. (2.7) are performed in the reverse order starting with Eint at the maximum value of the applied field, Ea, and proceed in a step-wise fashion towards its initial value. With the decreasing Ea, the corresponding value of the (bias-dependent) interfacial electric field, Eint, increases, attains its relative maximum and then decreases, as seen in Fig. 7. In the calculations the following parameters were used: p = 1.4x1027 m-3, see [13], L* = 5 nm, e = 3, EH = 5.4 eV, EF = 5.1 eV, [12]. The thickness L* = 5 nm of the hole charged interface is chosen such that the (areal number) density pL* of charged molecule is comparable with the similar value quoted in [27]. However, since this factor is just a scaling factor its exact magnitude is not crucial for the discussion that follows.
In the analyses of the lowest temperature T = 213 K data reported, [12], taking into consideration Eint shown on Fig. 2 (filled squares), the value for a was set to a = 0.11 eV (squares), (Eint = 2.9 MV/m at Eamax = 50.0 MV/m) and the energy shift was then found 9 = 0.7197 eV (crossed circles). The bias dependence of the pair (a, 9) exhibits shapes similar to the ones above and are shown in Fig 5. Despite the particular precaution taken by authors of [12] to eliminate the potential barrier at the hole-injecting TCTA/a-NPD interface, the barrier is nevertheless still present within the interval 2 MV/m < Ea < 42.0 MV/m as evidenced by the bias dependent interfacial electric field, Fig. 2.
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Figure 5: The Ea dependence of the Gaussian width, a, (left scale) calculated from Eq. (2.7) for the values of Eint that are shown on Fig. 2: T = 213 K (filled squares), and T = 295 (filled triangles) is exhibited. The Ea dependence of the energy shift, p, (right scale) of Gaussian peak is presented for T = 213 K (crossed circles) and T = 295 K (diamonds).
As seen, the interfacial electric field deduced from T = 295 data of [12] is bias-dependent within the initial interval 2 MV/m < Ea < 10 MV/m, see Fig. 2 (circles), while above it the SCLC regime prevails and Eint attains a constant value Eint = 1.5 MV/m (squares). The constant value of Eint is according to Eq. (2.7) reflected in bias-independent pair (a, p) and Eint then indicates the existence of a stationary, bias-independent, small potential barrier against the injection of holes at the respective interface.
A comment about the nature of the double valued inverted parabolas Eint with the increasing Ea is now in order. The increasing part of the Eint curve is related to the diminishing value of a keeping the constant value of p, while the decreasing part of Eint illustrates the increasing energy shift p, at the constant value of the Gaussian width, a. Consequently, in this way the meaning of the apparent double valued Eint with the increasing Ea is clarified.
In this section, a relationship of Eint with the Gaussian disorder energy states at the interface is thus established. It is well-known that the GDM model, [18], describes the charge hopping transport within the Gaussian disordered states in organics that is characterized by the constant width. It is demonstrated above that at given temperature the bias-independent interfacial electric field, Eint, is related not only to the bias-independent Gaussian width but also to the bias-independent energy shift of its peak. Such a specific case occurs only under the SCLC condition characterized by the (relative) highest attainable values of the hole drift mobility, |d, that then exhibit a weak monotonic increase with the externally applied electric field, see Fig. 3. As presented here, none of the samples investigated in [12] and [13] has been truly barrier-free within the investigated Ea interval of measurements.
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The externalbias-dependent electric field at hole-injecting ele ctrode/
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3.2 The ITO/a-NPD(100 nm)/Pd current-voltage data of Ref. [13]
Taguchi et al., [17], have investigated the room temperature IZO/a-NPD(200 nm)/Al organic structure by EFISHG method, in which IZO is the indium zinc oxide. Independently of the polarity of bias, it was determined that the electric field within the a-NPD organic is directed from anode to cathode (as expected) with the electrodes being charged accordingly. No other phenomena have been reported. This observation is here interpreted as the evidence that the so-called build-in voltage between the anode and cathode is compensated by a suitable collection of charge on the appropriate interface. The evidence that such compensation of the built-in voltage is also taking place in bilayer organic structures has been provided by Nishi et al., [16].
Van Mensfoort et al., [13] have reported the j - V results of the temperature and thickness dependent hole transport measurements in the amorphous small-molecule organic semiconductor a-NPD. The diode structures of the type ITO/a-NPD(L)/Pd, the organic thicknesses being L=100 nm and 200 nm are described in [13] in terms of the well-known charge transport models. The ITO contact was assigned as the anode.
In the previous section, it was shown that the fit to the SCLC data enables the two parameters, Eint, as well as |max of Eq. (2.2) to be simultaneously deduced. It is observed that the current density data at low Ea are weakly displaced from the SCLC curve. Using the previously determined |max, such data then enable the bias dependence of Eint to be determined from Eq. (2.1). However, in examples of strong deviation of data from the SCLC characteristics, the bias-independent parameter |max ought to be evaluated separately. This is accomplished by using the trial SCLC curve that intersects the first and the last current density point within the appropriate interval of Ea. The procedure is illustrated as follows.
The data of [13] are again tested for the SCLC regime characterized by the two bias-independent parameters: Eint, and |max. The disagreement between the data and the (trial) SCLC curve represents a measure of the contact deficiency. According to [11] and as shown above, the maximum hole mobility, |max, is determined from the fit of Eq. (2.1) through the current density point at the maximum Ea, within its respective interval while in the first approximation is Eint represented by the initial, but slightly decreased value of Ea. In the next step, Eint is refined so that the calculated, postulated SCLC current density curve also intersects the first current-density data point at the initial value of the Ea interval. The experimental data of [13] and the calculated, Ea dependent, trial SCLC current density curves intersecting the data at corresponding abscissa values Eamin and Eamax are shown in Fig. 6 for L = 100 nm sample of [13]. The SCLC parameters for the room temperature T = 295 K measurements are Eint = 14.1 MV/m, and |max = 7.5x10-10 m2/Vs determined within 14.12 MV/m < Ea < 31.4 MV/m (experiment - solid diamonds, calculations - solid triangles). At the lowest temperature T = 189 K the corresponding (trial) SCLC values obtained are Eint = 21.96 MV/m, and |max = 1.3x10-10 m2/Vs within 22.0 MV/m < Ea < 74.9 MV/m (experimental data - filled squares, calculations - tiny diamonds), see Fig. 6.
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100 ^

1 ~
0,1 ~
0,01
		#	m
	> • •		
if	•		
i	■		
w •			
/ ❖ J			
1 f	B7		
I f			
m			
Eg [ 10 V/m ]
Figure 6: The ITO/a-NPD(100 nm)/Pd hole j - Ea data measured at T = 295 K (diamonds) and at T = 189 K (squares) of [13] are compared to the calculated trial SCLC curves (triangles at T = 295 K, and tiny diamonds at T = 189 K). It is shown that by using the relevant temperature deduced bias dependent electric field, Ent, see Fig. 7, at ITO/a-NPD interface then by Eq. (2.1) calculated fits (T= 295 K, half fille- circles, and T = 189 K, stars) fully merge with measurements. The data
are redrawn from Fig. 3b of [13].
Evidently, the curves calculated under the SCLC assumption (solid triangles: T=295 K, and solid points: T = 189 K), apart for the first and the last data points, strongly deviate at both temperatures from the data of [13] (solid diamonds and solid squares), see Fig. 6. The disagreement indicates the complete absence of the SCLC regime within the ITO/a-NPD/Pd structure; consequently the contact in question is at most quasi-ohmic.
Eq. (2.1) in conjunction with the measured current density, j, [13], is then used to calculate Eint as a function of Ea, The obtained bias dependence of Eint is to a very good approximation described by the temperature-sensitive, 6-th order (inverted) distorted parabola, Table 1, see Fig. 7 (T = 295 K solid dots, and T = 189 K filled diamonds). Then, using the extracted Ea dependent interfacial electric field, Eint, see Fig. 7, together with the appropriate value of the (constant) maximum hole mobility in Eq. (2.1) the recalculated hole current density, j, at each temperature practically coincides with the measured data. This is shown in Fig. 6 exhibited by the thin curve through the calculated points that all coincide with the measurements.
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Figure 7: The calculated electric field at the hole-injecting ITO/a-NPD interface, Eint, as a function of the applied electric field, Ea, is exhibited for cases of the ITO/a-NPD(100 nm)/Pd hole j - Ea data of [13]. The approximation functions of the calculated interfacial field at T = 295 K (solid dots) and T = 189 K (diamonds) are given in Table 1, and are represented by thin curves in Fig. 7.
No traces of SCLC can be observed.
The room temperature zero-field mobility at T = 295 K of approximately |0 ~ 1x10-9 m2/Vs but for L = 200 nm sample is reported in [13]. The maximum hole mobility for the stated sample analyzed using Eq. (2.2), turns out to be |max = 7.0x10-10 m2/Vs (initial Eint = 5.6 MV/m). Consequently, |max and the zero-field prefactor, |0, of the conventional exponential mobility remain comparable, [11] even in cases of a minor deviation from the ideal SCLC condition. Consequently, the zero-field prefactor, |0, and the maximum hole mobility, |max, appear to be closely related under the SCLC occurrence. Since the latter parameter is strongly temperature-dependent and of the electrode/organic deposition method dependent quantity (as reflected in Eint, see Fig. 7) it is clear that the attempts of fitting various temperature-dependent current-density spectra by the single zero-field prefactor should be unsuccessful, [13].
In Fig. 8, the hole drift mobility for the room temperature structure of [13] is shown (solid dots). In comparison to Fig. 4, its Ea dependence evolves on considerably lower level on account of the smaller value of the maximum hole mobility, |max, due to the non-ohmic contacts. This occurs despite the fact that the bias-dependent interfacial electric field, Eint, (solid dots, Fig. 7) is about an order of magnitude above the one determined at the room temperature; compare Fig. 2.
For L = 200 nm organic at T = 192 K (the bias independent) maximum hole mobility is found to be |max = 5x10-11 m2/Vs at Eamax = 75 MV/m (the postulated SCLC curve is calculated with fixed Eint = 15.1 MV/m). As seen, the maximum hole mobility in a-NPD organic is thickness dependent in agreement with [11], but bias independent.
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Figure 8: The Ea dependence of the calculated hole drift mobility, jid, Eq. (2.2) at T = 295 K (solid dots), and T = 189 K (solid squares) within the ITO/a-NPD(100 nm)/Pd structure of [13] is
shown.
Based on the analyses above and in conjunction with [11] it is seen that the current density to be characterized as SCLC then the measurements should satisfy Eq. (2.1) where the parameter Eint, the electric field at the hole-injecting electrode/organic interface, ought to remain constant over the wide span of the applied electric field Ea. If a pair of suitably determined bias independent parameters Eint and |max cause the calculated curve, Eq. (2.1), to intersect just the first and the last data point in the j - Ea diagram this indicates: (a) that the electric field at the hole-injecting interface is bias-dependent, (b) that the operation of a given organic structure is limited to the quasi-ohmic region, and (c) that the maximum hole mobility would necessarily be smaller than the (optimal) one deduced under the SCLC conditions. This is well illustrated in Figs. 4, and 8.
As seen, compare Figs. 4, and 8, the (relatively) highest level of the Ea dependent hole drift mobility, |d, that is then accompanied by the minimal value of the interfacial electric field for a given electrode/organic structure is obtained for SCLC regime at room temperature. The above-presented examples and other similar observations point out the facts that the decrease in temperature is accompanied by the decrease of the hole drift mobility for over one order of magnitude that is simultaneously accompanied by the strong increase in the magnitude of the electric field at the hole-injecting electrode/a-NPD interface. The large electric field at the hole-injecting interface then implies the existence of a considerable hole barrier.
Consequently, on this account, it is claimed that the hole-drift mobility within a-NPD bulk at T = 295 K is |d = 4.4x10-8 m2/(Vs) (at Ea = 25.0 MV/m). It may now be claimed that the value |d = 7.0x10-10 m2/(Vs) (at Ea = 31.4 MV/m) determined from the data of [13] at similar temperature, points to the contact incapability to attain the regions of mobility saturation. Similar observations are valid for measurements obtained at other temperatures.
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The excellent agreement between the temperature and bias-dependent measurements of [13] and the predictions of Eq. (2.1), see Fig. 6 (thin curves), is a confirmation that the electric field at the hole-injecting ITO/a-NPD organic interface is at all temperatures strongly Ea dependent. The Ea dependence of electric fields at the stated interfaces, Eint, are all distinct and suitably described in terms of the different (inverted, higher order) parabola-like curves, see Table 1. No real SCLC can be detected in the data of [13] for any thickness and temperature.
At this point it should be emphasized that the data of [12], and [13] are to an excellent approximation described by Eq. (2.1) in terms of two physical clearly defined parameters Eint, and |max. The stated data are also well- interpreted in terms of the hole transport among the disordered energy states within a-NPD organic medium described in terms of the Gaussian distribution, characterized by its width a [12, 13]. Consequently, it remains to show that a relationship exists between Eq. (2.1) and the disordered energy states within the organic side of the interface at the hole-injecting electrode/organic junction. This will be accomplished on the basis of a simple model as expressed by Eq. (2.7).
Eq. (2.7) is applied to Eint deduced at T = 189 K, Fig. 6 (the starting value Eint = 23.37 MV/m at maximum Ea = 74.9 MV/m, see Fig. 7 (diamonds), with a initially set to a = 0.10 eV. This choice enables the direct comparison with results of [13] to be made. From Eq. (2.7) calculated corresponding energy shift turns out to be 9 = 0.719 eV. In the next step the higher value of Eint = 47.64 MV/m evaluated at the lower Ea = 62.5 MV/m, Fig. 7 (diamonds), is balanced by keeping a unchanged (filled squares) and allowing 9 (filled stars) to decrease, see Fig. 9. Then the new value of the (decreased) energy shift 9 = 0.697 eV is obtained in the calculation. In subsequent steps this value of the energy shift was kept constant. Namely, it appears unlikely that Gaussian peak could undergo an additional energy shift at still lower values of Ea. Consequently, in the subsequent calculations the parameter 9 is kept constant but a then decreases. The value of Eint = 21.96 MV/m corresponds to the initial Ea = 21.99 MV/m, see Fig. 7 (diamonds) for which a = 0.0915 eV is found at constant 9 = 0.697 eV. The results are presented on Fig. 9.
Starting once again with an arbitrary selected a = 0.10 eV for Gaussian width, and L* = 5 nm, then similar results are obtained in the analyses of the Eint at T = 295 K, see Fig. 7 (solid dots) that exists at ITO/a-NPD organic structure. The results of the calculations are exhibited in Fig. 9. As seen at a = 0.10 eV (diamonds) the energy shift 9 (triangles) is at T = 295 K equal to 9 = 0.763 eV and both parameters are considerably greater than the corresponding values calculated at lowest T. Both parameters are monotonically dependent on the externally applied electric field, Ea, and are single-valued functions of Ea, within the entire experimental region.
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Figure 9: The Ea dependence of the Gaussian width a, (left ordinate) calculated from Eq. (2.7) for the values of Eint that are shown on Fig. 7: T = 189 K (filled squares), and T = 295 (diamonds) is exhibited. The Ea dependence of the energy shift q> (right scale) of Gaussian peak is presented for T = 189 K (filled stars) and T = 295 K (triangles).
It is seen that the parameter a = 0.10 eV for Gaussian width that has been determined by CDM results in [13] provides through Eq. (2.7) a self-consistent description of the double-valued Eint as a function of Ea under the condition that the Gaussian width, a, and the energy shift of its peak, 9, are bias-dependent. Consequently, under the stated constraint the compatibility of Gaussian model derived parameter of [13] to the predictions of Eq. (2.7) has been demonstrated.
Their analyses have shown that the data cannot be consistently interpreted in terms of the driftdiffusion model incorporating the conventional exponential bias-dependent hole mobility. This inability was attributed to the fact that the dependence of the hole mobility on charge density is neglected in the stated model.
In this section, the hole drift transport within the disordered organic states has also been indirectly verified. It was shown that the experimentally determined interfacial electric field at the hole-injecting interface, Eint, is on the basis of a simplified model, well interpreted by the (Ea dependent) parameters of [22] that characterize Gaussian distribution of the disordered energy states within the a-NPD organic as reported [12, 13]. It was shown that such relationship exists irrespective of the current density being of SCLC type or not. Since by Eq. (2.2) the interfacial field, Eint, critically affects the hole drift mobility, |a, compare Figs. 4 and 8, the relationship between the hole drift mobility, |d, and Gaussian disordered states is revealed.
Returning to Figs. 4, and 8 the minimum value of the evaluated room temperature hole drift mobility for TCTA/a-NPD interface of [12] turns out to be |dmin = 3.8x10-8 m2/(Vs) at Eamin = 1.94 MV/m. The corresponding (minimum) value of |d determined for ITO/a-NPD interface of [13] is found to be |dmin = 1.7x10-12m2/(Vs) at Eamin = 14.12 MV/m. Evidently, the effect of the electrode/a-NPD electrical contact on the hole drift mobility is most instructive. The reason
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for almost four orders of magnitude between the two is traced to the existence of considerably different electric fields at the stated contacts as exhibited in Fig. 2, and Fig. 7.
As seen, Eq. (2.1) enables that the interfacial electric field, Eint, be determined directly from the measured current-voltage data. This implies that the hole current density, j, as a function of Ea implicitly incorporates the hole density Ea dependence and, for this reason, the stated effect on the deduced hole drift mobility is redundant. Likewise, the effect of the built-in voltage is at all times expected to be compensated by the corresponding part of the charge density induced at the interface and, consequently, it is expected not to have any specific role in the steady-state current-voltage determination of Eint as a function of bias, Ea.
4 CONCLUSIONS
In the present work, based upon the published current-voltage data, the influence of the electric field at the hole-injecting electrode/a-NPD organic structure on the hole transport has been investigated. It is shown that the (steady-state) hole drift current density within the organic structure crucially depends on two experimentally deduced parameters: the electric field at the hole-injecting electrode/organic interface, Eint, and the so-called maximum drift mobility, |max. It is empirically verified that, in a given experiment, |max, is a fixed constant, but the interfacial electric field, Eint, could be a function of the externally applied electric field, Ea. It is argued that hole drift SCLC occurs whenever the stated electric field, Eint, is over a given interval of the externally applied electric field, Ea a fixed small constant (with respect to Ea). Then, the hole drift mobility is prone to attain (weakly) bias-dependent saturation that represents an optimum for the organic structure under the investigation. If the data cannot be described by the constant Eint then its bias dependence may be calculated, and its detrimental effect on the hole drift mobility is clearly exhibited. It is revealed that merely by increasing externally applied electric field, the non-SCLC occurring due to the quasi-ohmic contact of the electrode/a-NPD interface may transcend into the ohmic one. It is shown that the different electric fields that originate at the hole-injecting electrode/a-NPD interfaces are closely related to vastly different values of the hole drift mobility within the chemically identical a-NPD organic.
On the assumption that the interface may be described in terms of an infinite thin uniformly charged sheet, then the relationship between Eint and the Gaussian distribution of the disordered energy states within the a-NPD organic interface is established. It is shown that the Gaussian width and the energy shift of its central position along the negative binding energy are Ea dependent.
Based on the described findings, it appears that the current-voltage method might serve as a useful tool for probing the electric fields at charge injecting/organic interfaces.
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