Three-dimensional anisotropic density of states distribution and intrinsic-like mobility in organic single crystals

Organic Electronics 11 (2010) 10–15

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Three-dimensional anisotropic density of states distribution and intrinsic-like mobility in organic single crystals B. Fraboni a,*, A. Fraleoni-Morgera b, A. Cavallini a a b

Dipartimento di Fisica, Università di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy Sincrotrone Trieste, Strada Statale Km 163.5, 34102 Basovizza (Trieste), Italy

a r t i c l e

i n f o

Article history: Received 27 May 2009 Received in revised form 10 September 2009 Accepted 15 September 2009 Available online 19 September 2009 Keywords: Molecular electronics Anisotropic mobility Density of states distribution Organic single crystal Solution-grown crystals

a b s t r a c t Organic semiconducting molecules are receiving a large attention because of their potential applications, spanning from OLEDs to plastic photovoltaics to bio-chemical sensors. However, the electronic transport properties of these materials are still not fully understood, and organic single crystals (OSCs) may represent model materials for assessing the charge transport mechanisms, thanks to their high purity and molecular order. Here we show for the first time that solution-grown, millimiter-sized organic single crystals of 4-hydroxycyanobenzene (4HCB) possess a clear and reproducible three-dimensional anisotropy in their main transport parameters: (i) charge carrier mobility, (ii) distribution of the electronic density of states and (iii) deep traps energy and concentration, and we report intrinsic-like three-dimensional mobility values for these crystals. These findings demonstrate that the electronic spatial anisotropy of OSCs extends well beyond the carrier mobility, and open the way to the development of novel electronic device architectures based on the simultaneous exploitation of different electronic responses along the three spatial directions of the crystal. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Organic semiconductors are considered promising materials for implementing low-cost and large-scale produced electronics [1–8]. Among the most attractive prospects in this field are the possibility of tailoring functionalities by molecular design [9] and the realization of flexible devices [10–12], distinctive and unique features that open the way to the attainment of versatile and multifunctional electronic systems. However, in order to achieve this goal, a number of issues relative to the charge transport in organic materials are yet to be clarified. In particular, a clear and well defined comprehension of the electronic behaviour of these materials (including a complete description of the fundamental * Corresponding author. Address: Department of Physics, University of Bologna, viale Berti Pichat 6/2, Bologna 40127 Italy. Tel.: +39 0512095806; fax: +39 0512095113. E-mail address: [email protected] (B. Fraboni). 1566-1199/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2009.09.014

electronic states of the charge carriers) has still to be gained and related to their structural properties. In this view, organic single crystals (OSCs) offer the possibility to effectively probe the electronic behaviour of organic materials. In fact, thanks to their long-range molecular order, they limit charge carrier trapping and hopping phenomena due to grain boundaries, interfaces and structural imperfections, and provide an almost ideal work bench for the study of intrinsic electronic transport. Nonetheless, the low symmetry of organic molecules leads to anisotropically packed crystal structures, that affect their transport properties (for example, the direction of the strongest p-orbitals overlap usually coincides with the direction of the highest carrier mobility [13–19]). This asymmetry, on one hand introduces difficulties in a clear understanding of the transport behaviour of organic semiconductors, but on the other hand it offers the tool to investigate the correlation between the three-dimensional molecular stacking order of OSCs and their recently found

B. Fraboni et al. / Organic Electronics 11 (2010) 10–15

anisotropic electronic transport properties. In particular, in the last years different mobilities have been measured along the two dimensions (2D) in the main crystal plane for micro- or nanometer sized organic single crystals, either vapour deposited [13–19] or solution-grown [20–22]. These findings, associated to the intrinsic three-dimensional (3D) molecular asymmetry and packing anisotropy of OSCs, suggest that the anisotropic behaviour of the electronic transport could actually extend into the 3D realm. Indeed, we have recently showed that 4-hydroxycyanobenzene (4HCB) single crystals exhibit a three-dimensional anisotropic mobility, although this has been assessed using two different measurement techniques along the three crystallographic directions [23]. Another point to be considered when dealing with OSCs transport properties is that hardly avoidable differences in the crystal growth conditions and in the experimental method used to determine the mobility (usually based on a field effect transistor, FET) lead to significant discrepancies in the carrier mobility values reported for the same type of OSC (e.g. for rubrene single crystals: [7,13– 17,19,24–27]). In fact, the device fabrication processes and the defects at the crystal/gate dielectric interface unpredictably affect the absolute measured mobility, as well as its reproducibility [7,15,17,26,28]. The already mentioned inherent structural anisotropy of OSCs introduces additional complexity to this issue. Finally, besides carrier mobility other transport parameters are of fundamental importance in determining the electronic behaviour of a semiconductor: the density of states (DOS) distribution, the concentration of the electrically active electronic states and their energy level have to be known in order to develop a consistent charge transport model. This knowledge becomes even more fundamental if the mentioned parameters vary along the three different dimensions in space, especially if novel electronic device architectures have to be developed. For example, monocrystal-based, single gated devices capable of delivering source-drain responses where the gain depends on the spatial direction along which the electrodes are aligned, may be envisaged as useful tools for lowering the amount of components of a single chip. However, up to date, a full assessment of the 3D anisotropy of the carrier transport properties of OSCs is still lacking. In this work we show that, by means of Space ChargeLimited Current (SCLC) and photocurrent spectroscopy analyses, it is possible to carry out on solution-grown, macroscopic 4-hydroxycyanobenzene (4HCB) single crystals (Fig. 1) a complete characterization of several key electronic transport parameters. In particular, we determine (i) the majority carrier mobility, (ii) the density of states (DOS) distribution of the intrinsic electronic states, (iii) their concentration and (iv) their energy levels in the band gap. We bring to evidence that all of these properties are clearly anisotropic in the crystal three dimensions, with very good reproducibility over more than 30 different crystals. Moreover, we compare the carrier mobilities found along the two main crystal axes a and b using the SCLC method with the corresponding ones determined on 4HCB crystals by means of the air–gap FET technique [22,23]. From this comparison, the remarkable agreement

11

Fig. 1. (a) Examples of solution-grown 4HCB single crystals investigated in this work, (b) chemical structure of 4-hydroxycyanobenzene (4HCB) and (c) layout of the electrical contacts used for the electronic transport characterization.

between the two sets of values obtained with two different and independent experimental techniques points to the likely intrinsicity of the found mobility values. 2. Experimental 4HCB was purchased from FLUKA (99+%). The raw material was dissolved in pure ethylic ether (technical grade), and the solvent was allowed to slowly evaporate under a hood in standard laboratory conditions. The resulting 4HCB crystals have been washed thoroughly with warm petroleum ether. About 150 mg of so-purified 4HCB crystals were dissolved in 10 ml of ethylic ether, filtered through a 0.45 lm Teflon filter and left in a 500 ml beaker covered by a petri dish, at controlled temperature (approximately 6 °C) for about 48 h. A complete and slow evaporation of the solvent delivered beautiful and transparent crystals, left on the bottom of the beaker. Following this procedure, crystals with thickness varying from 150 lm to 600 lm may be grown. The higher the concentration of 4HCB in ether, the bigger (in size and thickness) the obtained crystals. The crystals have been gently removed from the beaker using a spatule, and used for the preparation of the devices with no further treatment. The molecular packing and orientation of the 4HCB crystals with respect to the crystal axes have been investigated by X-ray diffraction measurements, that assessed a clear

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B. Fraboni et al. / Organic Electronics 11 (2010) 10–15

3D packing anisotropy [22]. The thickness of the crystals has been measured by optical microscopy methods. All the electrical measurements reported in this paper have been done at room temperature in darkness using a Keithley Source-Meters 2400 and Electrometers 617 and 6512. Data were acquired at a slow gate voltage sweep, with different sweep rates. No significant hysteresis or time relaxation were observed. The ohmic contacts on 4HCB were fabricated using silver epoxy (Epo-Tek E415G) at a fixed distance, in order to form pairs of contact pads perpendicular to each other (Fig. 1c). As already reported in the literature [22] the performance of the air–gap FETs fabricated with these contacts assessed the p-type conductivity of the material and the good hole injecting properties of the electrical contacts. Spectral photocurrent (PC) measurements were carried out in the planar configuration with an optical flux of 1  1013 photons/cm2 at k = 450 nm. PC spectra were recorded in air at 295 K. The low-level injection conditions ensured that no alteration in the crystal electrical response was induced by the PC measurements, as assessed by comparing many consecutively acquired PC spectra. A good reproducibility of the electrical measurements has been assessed over many tested crystals. No sign of permanent ageing or degradation of the crystals was observed, neither from the I–V curves nor from PC analyses.

3. Results and discussion We have carried out current–voltage analyses using the Space Charge-Limited Current (SCLC) method [29,30] along all of the three spatial direction of 4HCB crystals. SCLC is a relatively easy-to-handle room temperature method that, if properly applied, allows to determine several relevant bulk transport parameters of OSCs, such as the carrier mobility and the concentration, the energy and density of states distribution of the dominant deep traps [31,32]. SCLC curves have a symmetric character for positive and negative biases and are characterized by a linear region (ohmic) followed by a Space Charge Limited (SCL) one and finally by the Trap-Filled-Limited (TFL) region, when a steep increase of the current occurs (Fig. 2). Such a behaviour is related to the balance between thermally generated and injected carriers, and to the occupation of the dominant deep traps in the material. At V P VTFL (the voltage at which the SCL/TFL transition occurs) the charge injected by the contacts fills all the traps and the transport enters the trap-free regime, with a sharp current increase. For a given distribution of states, the equations describing the SCL J–V characteristics can be obtained by solving simultaneously the current equation and the Poisson’s equation. In order to do so, however, the following assumptions are usually introduced: (i) to consider unipolar majority carrier transport (holes in our case [22]); (ii) to neglect the density of thermal carriers with respect to injected carriers; and (iii) to assume the diffusion term in the current equation to be small with respect to the drift term. Two different sample geometries can be used for SCLC measurements, i.e. the sandwich-like one (with electrical

Fig. 2. Typical SCLC characteristic of a 4HCB single crystal. The ohmic, SCLC and Trap-Fill-Limited Voltage (VTFL) are highlighted. The inset shows the L3 dependence of the measured current as a function of the crystal thickness, assessing the occurrence of proper bulk conduction during the SCLC analyses.

contacts on opposite sides of the crystal) and the planar gap-like one (with the two contacts on the same surface) [31–34]. In the sandwich geometry the transport is assumed to be one-dimensional and follows the Mott and Gurney model [35], that describes transport in bulk material:

J¼

9 V2 el 3 8 L

where J is the current density for the applied voltage V, L is the thickness of the organic layer (electrode separation), e is the dielectric constant of the material and l is the carrier mobility. In the planar geometry, the transport is twodimensional (2D) and has been modelled by Geurst [36] as:

J¼

2

p

el

V2 L2

ð1Þ

where L is the electrodes separation (see Fig. 1c). In this case the thickness of the organic layer, h, becomes a key parameter for the determination of the type of transport: for L/h > 200 the 2D law (Eq. (2)), will dominate the carrier transport, while bulk, 1D transport (Eq. (1)) occurs if L/h < 10 [33]. We applied these models to our data and, since the thickness of the examined 4HCB crystals varied between 150 and 600 lm, L/h was always small enough to grant 1D transport also in the planar electrode configuration. A typical curve measured in the sandwich geometry along axis c of a 350 lm thick 4HCB crystal is shown in Fig. 2, where the ohmic, SCLC and TFL regimes are highlighted. The inset of Fig. 2 reports the L3 dependence of the measured current as a function of the crystal thickness, at a constant electric field of 9  103 V/cm, and assesses the occurrence of proper bulk conduction transport during SCLC analyses [30,32]. SCLC measurements on axes a and b were carried out in the planar electrode configuration. The intrinsic-like carrier mobility lSCLC can be obtained from Eq. (1) calculated at V = VTFL. We have measured SCLC curves along axes a, b and c over 30 different (in size and thickness) crystals, finding maximum mobility values of

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B. Fraboni et al. / Organic Electronics 11 (2010) 10–15

1  101, 4  102 and 2  105 cm2/Vs, respectively (Table 1, column lSCLC-Max). The average mobility values for each axis are also reported in Table I (column lSCLC-Ave), and both the maxima and average values show clear anisotropic behaviour along the three different crystal directions. We recently reported anisotropic mobilities in similar 4HCB crystals measured with air–gap FETs (columns lFET-Max and -Ave in Table 1) [23]. Air–gap FETs offer the advantage of reducing the influence of the interface with the gate dielectric, that usually lowers the effective mobility value [7,15,17,26,28]. A comparison between the lSCLC and the FET-measured one (lFET) brings to evidence that: (i) for each axis the SCLC-measured mobility is always higher or, in the worst case, equal to the FET-determined one. These observations point to the intrinsic nature of the mobility values determined by SCLC, to the reliability of the SCLC technique as a mobility measurement tool and to the overall good electronic quality of solution-grown 4HCB crystals; (ii) both FET and SCLC measurements deliver maximum and average values that do not differ much. The limited difference between the lSCLC and the lFET values confirms that air– gap OFETs may provide a mobility measurement tool able to minimize interface effects induced by the gate dielectric [7,26,28], one of the major cause for mobility reduction in OFETs. Fig. 3 shows the mobility measured along each one of the three axes of the very same crystal for three different crystals, highlighting a marked and reproducible 3D anisotropic transport in each of the three. It is also noteworthy that each crystal has been repetitively measured along the three axes, providing reproducible results. The consistency of the measured values over several different crystals, which even had different dimensions, confirms that the measured mobilities may be actually considered as intrinsic to the crystal, and that the measurements did not affect their electronic properties, although all the tests were carried out in normal laboratory atmosphere and at room temperature. Another very important transport parameter that can be obtained from the SCLC method is an estimate of the density of electrically active traps in the material, NT, using the relation NT = eVTFL/(eL2), where e is the electron charge, with the underlying assumption that the traps are uniformly distributed in the material. We thus calculated NT for each crystallographic axis and the average trap density found along each crystallographic axis is reported in Table 1 (column NT). While along axis a and axis b the concentra-

Fig. 3. Charge carrier mobility measured by SCLC along the three different spatial directions on the same crystal for three different crystals, clearly showing the anisotropy and reproducibility of the measurements.

tion of traps is substantially comparable, the same parameter is one order of magnitude higher for axis c. These findings are in line with the higher mobilities found along axes a and b with respect to axis c, and confirm the inherently anisotropic nature of the electronic parameters of OSCs. The shape of the SCLC curve reflects the increment of the space charge with respect to the shift of the Fermi level as a function of the applied bias, and thus mirrors the energy dependence of the density of states (DOS) distribution. By analyzing the SCLC curves with a differential analysis method developed by Nespurek and Sworakowky [37,38], it is possible to extract an energy distribution of states h(EF) directly from a single current–voltage curve:

hðEF Þ ¼

x1 x2 eV

ð2Þ

2eL2 kTðm  1Þ

The position of the Fermi level, EF, can be obtained using the following equation:

EF ¼ kT ln

L J þ kT ln x1 N v e l V

ð3Þ

where is m = d(lnJ)/d(lnV), x1 = (2m  1)/m, x2 = (m  1)/m and NV is the effective density of states in the highest occupied molecular orbital (here NV = 5  1021 cm3). We have hence analyzed the SCLC curves obtained along the 3 crystal axes according to this model, and we have obtained the three DOS distributions shown in Fig. 4. One has to keep in mind that by assuming a unipolar

Table 1 Charge carrier mobility lSCLC and trap density NT, obtained from the SCLC analysis of J–V curves with the Mott–Gurney theory for the three crystal axes a, b and c. NT* is the trap density evaluated from the differential analysis of SCLC curves. lFET is the charge carrier mobility obtained from OSC FET measurements. Average values, measured over 30 crystals. Crystal axis

lFET (cm2/Vs)[23]

lSCLC (cm2/Vs)

Max.

Ave.

Max.

Ave.

a b c

8  102 9  103 –

3  102 5  103 –

1  101 2  102 2  105

5  102 6  103 5  106

NT (cm3)

NT* (cm3)

3  1011 1  1011 5  1012

9  1012 4  1012 2  1013

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B. Fraboni et al. / Organic Electronics 11 (2010) 10–15

Fig. 5. Photocurrent yield as a function of the incident photon beam energy for 4HCB single crystals, along the two planar direction of the crystals, axis a (dotted line) and axis b (solid line). The arrow highlights the peak associated to the band of states located in the band-gap corresponding to the DOS distribution found by SCLC analyses.

Fig. 4. The DOS distribution of the electrically active states obtained from SCLC measurements along the three spatial directions of 4HCB crystals, showing an anisotropic energy distribution and concentration of states.

majority carrier type conduction (holes in our case), the method of Nespurek and Sworakowski allows to reveal only the deep states that interact with the majority carrier band (the valence band in our case) This means that the peak energies in the h(EF) functions shown in Fig. 4 correspond to the dominant hole deep states. In the planar axis a the DOS is centered at an energy of (0.49 ± 0.01) eV, along axis b at an energy of (0.50 ± 0.01) eV, while along axis c the DOS is shifted at (0.45 ± 0.02) eV (the associated error is estimated from the scattering of the data within the various investigated crystals). Trap states at comparable energies have been recently reported along one of the axes of rubrene single crystals [32,39] and in pentacene [40]. Further evidence on the presence of deep electrically active states in 4HCB crystals is provided by spectral PC analyses, that we carried out along axes a and b on the same crystal. The photoconductivity yield spectrum is reported in Fig. 5, showing the HOMO–LUMO transport edge located at 4.5 eV, followed by exciton re-

lated features at energies >4.0 eV. A large band of deeper states is clearly visible at lower energies in the spectrum, starting at 4.0 eV and peaking at approx. 0.50 eV from the HOMO–LUMO gap, a value in line with the results obtained from the above reported SCLC analyses on the DOS energy distribution. In addition, from Fig. 5 it is also evident that the number of electrons excited per incident photon is larger along axis a than along axis b, again in good agreement with the DOS distributions reported in Fig. 4, where the density of states is higher along a than along b. The h(EF) distribution represents the actual density of trapped carriers NT(E) [30,32] and it is hence possible to exploit it to obtain trap density values along the three axes a, b and c, N Ta;b;c more accurate than the previously calculated ones. In fact, the density of traps NTa,b,c extracted from the VTFL method and reported in Table 1 is often underestimated, due to inhomogeneities in the trap distribution and to the occurrence of Poole–Frenkel effects at voltages close to VTFL, that hinder a complete filling of all the traps [41]. The more accurate determination of the trap densities N Ta;b;c , also reported in Table 1 for the three crystal axes, delivers again anisotropic values along the three crystal axes, and in line (although, as expected, higher in absolute values) with the corresponding NTa,b,c.

4. Conclusions In conclusion, we have grown from solution high quality, millimiter-sized organic single crystals of 4HCB that allowed us to carry out a complete 3D characterization of their electrical transport properties. By means of SCLC measurements we evidenced a clear 3D anisotropy for several main electronic transport parameters of the crystals, namely (i) the charge carrier mobility, (ii) the DOS distribution of the electrically active deep states, (iii) the concentration and (iv) the energy of dominant carrier traps. We reproducibly determined these parameters along the three different crystal axes over a large number of samples,

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using a differential analysis of SCLC curves and photocurrent spectroscopy to investigate the energy states in the a–b plane, and we showed examples of anisotropic mobilities measured in all the three dimensions of the same single 4HCB monocrystal. Moreover, the comparison between the mobility values obtained by SCLC analyses and by air–gap OFET measurements demonstrate a remarkable agreement, confirming that air–gap OFET measurements consistently reduce the effects of interface states on the mobility. Finally, the permanence of anisotropic 3D mobility even after repeated I–V measurements demonstrates the fair robustness of the 4HCB solution-grown crystals under room temperature and atmosphere conditions. These results indicate that solution-grown, macroscopic and easily obtainable 4HCB organic single crystals may be considered as model compounds for a deeper understanding of the anisotropic transport behaviour of organic semiconductors. As an outlook, the here demonstrated 3D electronic anisotropy of OSCs opens the way towards the realization of novel electronic devices, based on the exploitation and control of transport parameters that differ in the three spatial directions, for fully functional 3D device architectures.

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Acknowledgements The authors acknowledge financial support by the Italian Research Ministry, under the project PRIN 2006. References [1] [2] [3] [4] [5]

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