Percolative charge transport in a co-evaporated organic molecular mixture

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Percolative charge transport in a co-evaporated organic molecular mixture

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Chen Li, Lian Duan ⇑, Haoyuan Li, Yong Qiu ⇑ Key Lab of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Department of Chemistry, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 3 July 2013 Received in revised form 12 September 2013 Accepted 25 September 2013 Available online xxxx Keywords: Charge mobility Time of flight Percolation threshold Molecule miscibility Charge transfer integral

a b s t r a c t Understanding the charge transport in molecular semiconductor mixtures remains challenging, largely due to the lack of a universal dependence of carrier mobility upon doping concentration. Here we demonstrate that it is feasible to use the percolation theory to explain the change of charge mobility in a model system of 4,40 -bis(carbazol-9-yl)biphenyl (CBP) and tris-(8-hydroxyquinoline) aluminum (Alq3) with various doping concentrations. As the fraction of CBP within the mixtures increases, the charge mobility initially firstly shows a reduction at low CBP fraction due to the scattering effect, and then increases well following a percolation model. Electron microscopy and atomic force microscopy analysis suggest that CBP and Alq3 are homogeneously mixed in their coevaporated amorphous films, which meets the precondition for using percolation theory. We describe the possible microcosmic percolating mechanism with a model combining bond percolation with charge transfer integral calculation. Based on this model, the percolation threshold in molecular semiconductor mixtures can be predicated. For the hole and electron transport in our system, the predicated percolation thresholds are very close to the experimental values. Ó 2013 Published by Elsevier B.V.

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1. Introduction

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Organic molecular semiconductor mixtures have enabled improved performance and novel functionalities in organic devices [1–10]. In organic light emitting diodes (OLEDs), mixing of the transporting host materials would improve charge transport balance and extend the recombination zone, thus enhancing the device efficiency and lifetime [2–5]. Donor–acceptor mixtures in the organic solar cells have created the morphology necessary for efficient photocurrent generation and charge separation, and sequentially high external quantum efficiency [6,7,9,10]. Despite the recent advances in the performance of the above mentioned devices, it remains a challenge to fully

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⇑ Corresponding authors. Tel.: +86 10 6277 9988 (L. Duan), tel.: +86 10 6277 1964; fax: +86 10 6279 5137 (Y. Qiu). E-mail addresses: [email protected] (L. Duan), qiuy@mail. tsinghua.edu.cn (Y. Qiu).

describe the optoelectronic properties of organic semiconductor mixtures. The difficulty in describing the effect of mixing on the performance of the organic optoelectronic devices illustrates the need for further exploration of the role of mixing on the charge transport within organic molecular semiconductor mixtures [11–18]. However, transporting in these materials has been found to be very complicated, and a generally accepted description for the dependence of carrier mobility upon concentration of the transporting phase has not been achieved. Considerable research has suggest that, a small amount of doping would often lead to a reduction of the mobility owing to the introduction of trapping or scattering centers [16–18], and the degree of the reduction can depend strongly on the energy level difference between the compositions [18]. While for the mixtures with various ratios, results have shown that the carrier mobility generally increases monotonically as the concentration of carrier phase increases [12–15], and consequently, the

1566-1199/$ - see front matter Ó 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.orgel.2013.09.039

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expectant ambipolar transport via mixing is only achieved in a limited and system specific range. The lack of a general and quantitative law of the charge mobility makes it a big challenge to expound the transporting mechanism in the molecular semiconductor mixtures. In the past decades, research of charge transport in organic materials has greatly benefited from the concepts and findings in their inorganic counterparts. For the inorganic semiconducting mixtures, percolation theory has successfully explained the power-law dependence of the carrier mobility upon concentration [19–22]. Since percolation theory holds true only when the transporting phase in the mixture is randomly distributed, analysis of the microscopic configuration of the compositions is needed. Recent evidences have shown that percolation theory may be feasible for carrier transport in polymer based organic mixtures [9,23,24]. Gomez et al. [9] used energy filtered transmission electron microscopy (EF-TEM) to demonstrate that amorphous poly(3-hexylthiophene)(P3HT)/phenyl-C61-butyric acid methyl ester (PCBM) mixtures were miscible when /PCBM (the fraction of PCBM) <0.58, and separated to two phases when /PCBM > 0.58 due to the formation of a pure PCBM phase. As a result, the electron mobility of the mixtures well followed the percolation theory in the miscible region. The percolative conductivity of graphene and single wall carbon nano-tubes has also been reported in their mixtures with polymers [23,24]. For molecular semiconductor mixtures, Grover et al. [12] recently reported conductivity in the tetracyanoquinodimethane (TCNQ) mixed 4,7-diphenyl-1,10-phenanthroline (Bphen) films were percolating dominated. They used atom force microscopy analysis to find a randomly distributed, separated crystalline TCNQ phase against the amorphous Bphen phase. Nevertheless, the effect of percolating on carrier mobility, a more significant parameter to evaluate charge transport in the molecular semiconducting mixtures, has not been discussed. And the transporting mechanism through percolating in molecule based semiconductors is yet to be understood. Here, we examined a model system composed of 4,40 bis(carbazol-9-yl)-biphenyl (CBP) and tris-(8-hydroxyquinoline) aluminum (Alq3) and show that it is feasible to apply percolation theory to charge mobility in this system. According to the transmission electron microscopy (TEM) and the atom force microscopy (AFM) analysis, we find co-evaporated films of these two materials at varies ratios are amorphous. Moreover, energy diffraction spectrum (EDS) analysis suggests the two constituents are homogeneously distributed in these films. By fabricating time of flight (TOF) devices, we have examined both the intrinsic hole and electron transport properties of amorphous CBP/Alq3 mixtures. At low CBP concentrations, CBP molecules are dispersed in Alq3 as scattering centers, leading a reduction in charge mobilities. When CBP fraction exceeds 10%, continuous CBP transporting areas are formed and lead to more efficient charge transport by promoting percolating pathways throughout the layer. We demonstrate that a 3-dimensional bond percolation model based on charge transfer calculation can better describe the carrier transport in this system than a 3-dimensional site percolation model that is often used in the inorganic

counterparts. And the percolation thresholds predicated based on this model fit well with the experimental values. Therefore, our results suggest that charge transport in organic molecular semiconducting mixtures can be described by percolation theory.

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2. Experimental methods

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As a model system for the amorphous molecule semiconductor mixtures, we mix CBP, which is an ambipolar material with mobilities at the level of 103 cm2/V s [25], with Alq3, of which the electron mobility is around 105 cm2/V s [26], at various ratios. Both of the two materials are widely used, and their mixtures as light emitting layers showed higher efficiencies than the control device with Alq3 as the emitting layer [27]. The TOF devices had a structure of ITO/Alq3:CBP (/CBP) (2 lm)/Mg:Ag (100 nm), where / is the volume fraction of CBP. The mixtures were created through co-evaporating inside a high vacuum evaporator at 106 torr onto ITO glass, with a coating rate of about 2 Å/s. Thicknesses of the organic layer were monitored in situ with a quartz crystal sensor. A nitrogen pulsed laser (pulse width 10 ns, wavelength 337.1 nm, beam size 3.14 mm2) was used as the excitation light source, which is directed from the ITO side to generate a thin sheet of excess carriers near the ITO/organic interface. The transient photocurrent signals were recorded by a digital storage oscilloscope with a current sensor resistor (R) of 50 X–1 kX, and then the transit time (tT) was measured from the double-logarithmic plot of the transient photocurrent [16–18,25,26]. With the applied bias V and the thickness L, the charge mobility could be calculated as L2/tTV. All the TOF experiments were done at the temperature of 298 K. AFM images of the films were tested by SPA 400 (Seiko Instruments Inc.). The AFM samples (100 nm) were also prepared by co-evaporating in the same condition with the TOF samples. High resolution TEM graphs, EDS spectra and selected area electron diffraction (SEAD) of the mixtures were tested by JEOL-JEM 2010. In order to obtain the nano-scale high contrast graphs, high angle annular dark field (HAADF) imaging was measured by FEI-Titan 2010. The X-ray diffraction (XRD) samples (200–300 nm) were evaporated on ITO substrate and the XRD patterns were measured by Rigaku D/ max-2500.

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3. Results and discussions

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Morphology measurement of the Alq3:CBP co-evaporating films indicate that the mixtures with various compositions are amorphous. The TEM images and SEAD images shown in Fig. 1(a)–(f) clearly suggest the non-crystalline structure of the pure CBP films and pure Alq3 films, as well as the mixtures. The amorphous morphologies of the films have reconfirmed by the AFM analysis (Fig. 1(g)–(j)). The images exhibit typical amorphous properties, with RMSs from 1.47 nm to 2.19 nm. XRD patterns of the mixed films also show no significant differences from that of the bare ITO substrate (Fig. 1(m)), with no peaks in the small-angle region. Hence, we could conclude that in the CBP:Alq3

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Fig. 1. (a)–(f), The TEM images and SEAD images of the CBP:Alq3 mixtures at /CBP of 0%, 20%, 35%, 50%, 80%, 100%. (g)–(j), The AFM images of the CBP:Alq3 mixing films (100 nm) at /CBP of 0%, 5%, 50%, 100%. (k), The HAADF image (Al element) of the mixtures at /CBP = 35%; the lighted area refers to the sample containing Al. (l), Al element weight fraction measured by EDS plotting with Alq3 volume fraction of the mixtures, and the linear fitting result (blue line). (m), Small-angle XRD patterns of the ITO substrate and the CBP:Alq3 mixed films (200–300 nm) with various fractions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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co-evaporating films, mixing do not change the amorphous properties of the neat films. In the TOF devices, the fractions of CBP (/CBP) are varied as 0%, 2.5%, 5%, 10%, 20%, 35%, 50%, and 100%. Fig. 2(a) and (b) depict the hole and electron TOF transients of the devices at 100 V, respectively. Both the hole and electron TOF transients at /CBP of 2.5% and 5% behavior like that of the neat Alq3, with tT at around 10 ls for electron and 100 ls for hole. However, the TOF transients at /CBP of 10–50% holds the similar behaviors with that of neat CBP, with tT at around 0.1 ls. Previous works have suggest that behaviors of the TOF transients are highly material dependent [16–18], which is mainly owing to the specific energetic disorder of the localized transporting sites and the consequently disparate diffuse width of the carriers in different material [28]. Thus, the change of the TOF transient behavior from /CBP of 5% to /CBP of 10% may indicate a conversion of the main transporting pathways from the Alq3 sites to the CBP sites. Fig. 3 summarizes the concentration dependent hole and electron mobility under various bias voltages. The hole and electron mobilities exhibit similar change trends with the CBP fraction. The mobility decreases at /CBP of 2.5% and 5% compared to that of Alq3, then it shows a sudden increase at /CBP of 10%, and eventually, it gets saturated at /CBP > 50%. The sudden

increase of mobility confirms the speculation of the formation of CBP transporting pathways at /CBP of 10%. Both the logarithmic electron and hole mobility vary linearly with the square root of the applied electric field (as depicted in the inset maps of Fig. 3, and in Supplementary material), which is in agreement with the Poole–Frenkel law [29] expressed by l = l0 exp (bE1/2), where l0 is the mobility at zero electric field and b is the Poole–Frenkel factor representing the slope of the field dependence of the mobility. For further analysis, the zero electric filed mobility (l0) of the films are extracted according to the Poole–Frenkel law and summarized in Fig. 4. The hole and electron mobilities of neat CBP are in the order of 103 cm2/V s, which is several orders of magnitudes lager than that of neat Alq3, being around 106 cm2/V s and 107 cm2/V s, respectively. The results are in agreement with that in the literature [25,26] and references therein. The negligible mobility of Alq3 compared to that of CBP also provides good convenience for discussing the effects of CBP percolating pathways on charge transport in the mixtures. Concepts from percolation theory are powerful in describing the transporting properties of composites [19– 24]. According to the classical percolation theory, the conductivity of a composite system is given by (/–/c)a near

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Fig. 2. The hole (a) and electron (b) TOF transients of CBP:Alq3 mixtures at various compositions measured at the bias voltage of 100 V. The insets show the double-logarithmic plots.

Fig. 4. The zero field hole mobility and electron mobility of the mixtures and their fitting results with the 3-D percolation theory and Gaussian disorder model. At /CBP > /c, the fitting equation is l0 = A(/–/c)a. At /CBP < /c, the fitting equation is l0 = l0,/=0 exp[4/(1/)(DE)2/9]. Right inset: log–log plots of l0 and /–/c, and the linear fitting results. Left inset: the energy level graph of Alq3 and CBP.

Fig. 3. Hole (a) and electron (b) TOF mobility of the CBP:Alq3 mixtures measured at bias voltage from 80 V to 110 V and 90 V to 120 V, respectively. The inset graphs show the logarithmic mobility plotting with the square root of the electric field. 245 246 247 248

the percolation threshold (/c), where /c is the critical volume fraction that the percolation pathways start to form and a is an exponent depends mainly on the dimensionality of the material [22]. For our experiments in this

letter, the CBP:Alq3 films are sufficiently thick, so we just have to take three dimensional (3-D) percolation into account. The sudden increase of the mobility at /CBP = 10% indicates the percolation threshold is between 5% and 10%. This percolation threshold is reasonable, noting that /c of a 3-D system can depend on the geometry of the structure unit and the intermolecular interactions within the system, and has been observed to vary between 7% and 65% in inorganic based mixtures [19] (for the graphene based composites [23] and the carbon nanotube based composites [24], /c can even be as low as 0.1%). Exact

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solution of the exponent, a, for 3-D percolation has also not been achieved, however, lots of numerical and experimental works have indicated that a might be universal, and have given the close values from 1.6 to 2.2 [19,20,22,30]. The zero field mobility in Fig. 4 well follow percolation behavior at /CBP from 10% to 50%, with /c = 9%, a = 1.61 for the hole mobility and /c = 8.3%, a = 1.62 for the electron mobility. As /CBP exceeds 50%, l no longer follows the power law (as shown in the inset map of Fig. 4). The deviation of l from the power law can be well understood considering that when /CBP is much larger than /c, the percolation pathways may become quite sufficient for the carriers to transport, so the average transporting speed of the carriers would tend to be saturated. At /CBP < /c (2.5% and 5%), the mixture exhibits similar transporting property with neat Alq3, and CBP percolating pathways have not formed, so we may expect the carriers mainly transport through the Alq3 framework. CBP can be regarded as dopant. The Gaussian Disorder Model (GDM) [28] has been widely used to investigate the charge mobility in doping system [16,17]. In our previous work, the increase of the energetic disorder via doping has been calculated to be /(1/)(DE)2, where DE is the HOMO (for hole) or LUMO (for electron) differential [18]. The HOMOs and LUMOs of Alq3 and CBP were measured by cyclic voltammeter (see Supplementary material), and are shown in Fig. 4. Then le and lh at /CBP = 2.5% and /CBP = 5% are calculated by GDM with the DEs. For le, the calculated value by GDM agrees well with the experimental one. As for the feasibility of the percolation theory, a homogeneous (more strictly, a random) distribution, i.e., good molecule miscibility of the constituents is a necessity [21,22]. In order to get the element-resolved images of the mixtures, energy-filtered transmission electron microscopy (EFTEM) [9] was used. However, the energy signal of the featured element, Al, was too weak for obtaining an EFTEM image. Instead, we measured the high angle annular dark field (HAADF) image (Fig. 1(k)). The HAADF image suggests that in the mixture at / = 35%, aggregation of Al element is not observed under the spatial resolution

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of 5 nm. Al element percentages of the CBP:Alq3 mixtures under various composition measured by the energy diffraction spectrum (EDS) are depicted in Fig. 1(l) (the EDS graphs can be found in Supplementary material). For the randomly chose testing area, the Al element percentage depends linearly on the fraction of Alq3, suggesting that Alq3 molecules and CBP molecule are well miscible in the mixtures. Thus, the results shown in Fig. 1(k) and (l) provide the structural precondition for the application of percolation theory and confirm the percolation dominating charge transport in the Alq3:CBP co-evaporating mixtures. According to our discussions above, CBP percolation pathways start to form at /c of near 8–9%, which is synchronously for the hole and electron transporting. And as the percolation threshold has been found to greatly depend on the intermolecular (or interatomic) interactions within the system, the synchronous percolating strongly points to similar hole and electron transporting properties of CBP at molecule level. In our previous work, quantum chemistry calculations have demonstrated that CBP have HOMO and LUMO located on the similar chromophore and have similar hole and electron reorganization energies, which provide necessity for ambipolar transporting [32]. We also note that bond percolation may be more applicable in organic molecule systems than site percolation, which has been always considered in inorganic systems where charge transport is controlled by strong chemical bond [19]. Because charge transport in organic semiconductors are more likely a hopping process that depends much on the strong (however, much weak compared to that in their inorganic counterpart) charge transfer integral inter molecules and a proper molecule orientation that ensuring effective transporting pathway [33,34], so bondlike charge transfer pathway, other than physical contact, enables efficient transporting. In order to apply the theory of bond percolation, we need to know the coordination number, i.e., the number of effective transporting pathways of the CBP molecule. According to our hole and electron transfer integral calculation results of CBP (see results in Ref. [31]), we conclude 13 and 11 transporting pathways, respectively, for hole and electron transport

Fig. 5. A diagram of the hole transporting through bond percolating. (a) The simulated configuration of the CBP:Alq3 mixtures. The sites are generated randomly, assuming a mixing ratio of 1:1. Blue color refers to the CBP area and red color refers to the Alq3 area. (b) Possible percolation pathways (arrows) of hole transport through CBP framework. (c) Effective transporting pathways (transfer integral > 0.2 meV) between a CBP molecule and its neighbors according to the results of hole transfer integral calculated in reference [31]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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(a diagram of the hole transporting through bond percolation are shown in Fig. 5). Using an approximation to bond percolation of the Bethe lattice (an ideal structure allowing most efficient percolation), /c can be exactly expressed by 1/(z1), where z is the coordination number [22]. /c for the hole and electron transporting are then estimated to be 8.2% and 10%. The values are quite close to our experimental ones. If we use an approximation to bond percolation of the 3-D face-centered cubic lattice with a coordination number of 12, /c would be 11.9% [30], which is also not far from our experimental values.

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In summary, we have demonstrated the interplay between charge transport and the percolation theory in a model molecular semiconductor mixture. We utilized time of flight method to analysis the intrinsic transport properties in CBP:Alq3 mixtures, and find the mobilities increases significantly when CBP volume fraction exceeds 10%, where CBP percolating pathways start to form. Due to the good miscibility of the composites, percolating governs the charge transport in a wide range of concentration. What is more, we show that concepts from bond percolation may be powerful in describing carrier transport in amorphous organic semiconductor mixtures owing to the bond-like nature of carrier transporting in these materials. Our modeling of the percolating process expounds the transporting mechanism and gives good predication of the percolation threshold in these materials. Our researches suggest that percolating can be critical in charge transport in organic semiconductor mixtures, and can provide guidance for designing multifunctional organic semiconducting materials.

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Acknowledgments

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This work made use of the resources of Beijing National Center for Electron Microscopy. And we thank the financial support by the National Natural Science Foundation of China under Grant Nos. 50990060 and 51173096 and the National Key Basic Research and Development Program of China under Grant Nos. 2009CB623604 and 2011CB808403.

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Appendix A. Supplementary material

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Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.orgel.2013.09.039.

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