Charge transport in oligo phenylene and phenylene–thiophene nanofibers

7
Charge transport in oligo phenylene and phenylene–thiophene nanofibers Jakob Kjelstrup-Hansen a, * , Joseph E. Norton b , Demetrio A. da Silva Filho b , Jean-Luc Brédas b , Horst-Günter Rubahn a a NanoSYD, Mads Clausen Institute, University of Southern Denmark, Alsion 2, DK-6400 Sønderborg, Denmark b School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, GA 30332-0400, USA article info Article history: Received 12 March 2009 Received in revised form 17 June 2009 Accepted 25 June 2009 Available online 28 June 2009 PACS: 72.80 Le 73.40 Sx Keywords: Organic nanofibers Mobility Space-charge limited current Marcus theory abstract Charge carrier mobilities have been measured in elongated crystalline aggregates with nanoscale cross-sectional dimensions. These molecular crystals are grown via dedicated epitaxial surface growth. They consist of well-ordered phenylene–thiophene (co-) oligo- mers that have been systematically tailored to study mobility of oligomers containing six rings and a variable number of thiophene rings. These organic nanoscale one-dimen- sional systems demonstrate charge mobilities as high as 1 cm 2 V 1 s 1 . Density functional theory calculations have been performed in order to correlate the experimentally observed trends in mobility with molecular charge transport properties. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Considerable attention has been given to molecular or- ganic semiconductors from both fundamental research and industrial application standpoints. This has been triggered by a rich theoretical framework based on the interplay be- tween geometric and electronic structure [1], and by the potential technological applications of organic semicon- ductors in (opto)electronic devices such as light-emitting diodes (LEDs) [2], solar cells [3], and field-effect transistors (FETs) [4]. The charge mobility is an important parameter describing the charge transport properties for such (opto)electronic applications, while for transistor applica- tions the carrier mobility determines the achievable switching speed. In the case of LEDs, the process of gener- ating light requires electrons and holes to be transported to the recombination zone from the cathode and anode, respectively. In solar cells, charge carriers need to be trans- ported to and collected at the electrodes upon dissociation of photon-generated electron–hole pairs. Thus, the ability of organic electronic devices to perform sufficiently well for practical applications is highly influenced by the charge carrier mobility. The charge carrier mobility in organic semiconductors is, in general, several orders of magnitude lower than the mobility found in inorganic semiconductors such as Si and Ge [5]. Consequently, such materials are not useful in applications requiring high switching speeds. However, organic semiconductors do possess significant advantages. Organic synthetic techniques can provide materials that are tailor-made for a given application, thereby providing much higher flexibility than what can be obtained with their inorganic counterparts. In addition, organic materials can be processed at low temperatures, over large areas, and at low costs. For novel micro- or nanoscale applications, phenylene- based oligomers constitute a particularly appealing class 1566-1199/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.orgel.2009.06.015 * Corresponding author. Tel.: +45 65 50 16 85; fax: +45 65 50 16 54 E-mail address: [email protected] (J. Kjelstrup-Hansen). Organic Electronics 10 (2009) 1228–1234 Contents lists available at ScienceDirect Organic Electronics journal homepage: www.elsevier.com/locate/orgel

Transcript of Charge transport in oligo phenylene and phenylene–thiophene nanofibers

Organic Electronics 10 (2009) 1228–1234

Contents lists available at ScienceDirect

Organic Electronics

journal homepage: www.elsevier .com/locate /orgel

Charge transport in oligo phenylene and phenylene–thiophene nanofibers

Jakob Kjelstrup-Hansen a,*, Joseph E. Norton b, Demetrio A. da Silva Filho b, Jean-Luc Brédas b,Horst-Günter Rubahn a

a NanoSYD, Mads Clausen Institute, University of Southern Denmark, Alsion 2, DK-6400 Sønderborg, Denmarkb School of Chemistry and Biochemistry and Center for Organic Photonics and Electronics, Georgia Institute of Technology, Atlanta, GA 30332-0400, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 12 March 2009Received in revised form 17 June 2009Accepted 25 June 2009Available online 28 June 2009

PACS:72.80 Le73.40 Sx

Keywords:Organic nanofibersMobilitySpace-charge limited currentMarcus theory

1566-1199/$ - see front matter � 2009 Elsevier B.Vdoi:10.1016/j.orgel.2009.06.015

* Corresponding author. Tel.: +45 65 50 16 85; faE-mail address: [email protected] (J. Kjelstrup-Han

Charge carrier mobilities have been measured in elongated crystalline aggregates withnanoscale cross-sectional dimensions. These molecular crystals are grown via dedicatedepitaxial surface growth. They consist of well-ordered phenylene–thiophene (co-) oligo-mers that have been systematically tailored to study mobility of oligomers containingsix rings and a variable number of thiophene rings. These organic nanoscale one-dimen-sional systems demonstrate charge mobilities as high as 1 cm2 V�1 s�1. Density functionaltheory calculations have been performed in order to correlate the experimentally observedtrends in mobility with molecular charge transport properties.

� 2009 Elsevier B.V. All rights reserved.

1. Introduction

Considerable attention has been given to molecular or-ganic semiconductors from both fundamental research andindustrial application standpoints. This has been triggeredby a rich theoretical framework based on the interplay be-tween geometric and electronic structure [1], and by thepotential technological applications of organic semicon-ductors in (opto)electronic devices such as light-emittingdiodes (LEDs) [2], solar cells [3], and field-effect transistors(FETs) [4]. The charge mobility is an important parameterdescribing the charge transport properties for such(opto)electronic applications, while for transistor applica-tions the carrier mobility determines the achievableswitching speed. In the case of LEDs, the process of gener-ating light requires electrons and holes to be transported tothe recombination zone from the cathode and anode,

. All rights reserved.

x: +45 65 50 16 54sen).

respectively. In solar cells, charge carriers need to be trans-ported to and collected at the electrodes upon dissociationof photon-generated electron–hole pairs. Thus, the abilityof organic electronic devices to perform sufficiently wellfor practical applications is highly influenced by the chargecarrier mobility.

The charge carrier mobility in organic semiconductorsis, in general, several orders of magnitude lower than themobility found in inorganic semiconductors such as Siand Ge [5]. Consequently, such materials are not usefulin applications requiring high switching speeds. However,organic semiconductors do possess significant advantages.Organic synthetic techniques can provide materials thatare tailor-made for a given application, thereby providingmuch higher flexibility than what can be obtained withtheir inorganic counterparts. In addition, organic materialscan be processed at low temperatures, over large areas, andat low costs.

For novel micro- or nanoscale applications, phenylene-based oligomers constitute a particularly appealing class

J. Kjelstrup-Hansen et al. / Organic Electronics 10 (2009) 1228–1234 1229

of molecules due to their ability to self-assemble intomicroscopic elongated crystalline aggregates, or ‘nanofi-bers’ [6]. In addition to their polarized and highly aniso-tropic photoluminescence output [7] and their waveguiding [8] and lasing [9] properties, chemical functionali-zation of these molecular building blocks opens the wayfor the specific tailoring of nanofiber properties at themolecular level [10]. Electrical interfacing to individualnanofibers allows the electrical properties to be studied[11] and could enable the fabrication of nanoscale LEDs(as electroluminescence has been observed from oligo-phenylene thin films [12]) with configurable properties.

We have previously conducted experimental investiga-tions of charge transport in a large number of individualnanofibers made from para-hexaphenylene (p6P) mole-cules and have found their hole mobility to be above0.3 cm2 V�1 s�1 [13]. In this work, we present a similarinvestigation of two other types of nanofibers made from5,50-di-4-biphenylyl-2,20-bithiophene (PPTTPP) [14,15]and 4–40-di-2,20-dithienyl-biphenyl (TTPPTT) [15], respec-tively, and compare the results here with those from thep6P nanofibers. The molecular structures, crystal latticegeometries, and fluorescence microscopy images of allthree materials are shown in Fig. 1.

To complement the experimental studies, we have alsoused quantum–mechanical calculations to study thecharge transport properties. There are two main régimesof charge transport in organic molecular crystals, theband-like régime, similar to ‘conventional’ charge trans-

Fig. 1. Molecular and crystal structures of (a) p6P, (b) PPTTPP, and (c) TTPPTrespectively. The arrows indicate the crystal lattice directions used in the denmicroscopy images of nanofibers made from the above molecules (p6P nano130 lm � 74 lm).

port in inorganic single crystals, or the hopping régime,where the carrier is localized on one molecule throughthe formation of a self-trapped state (a polaron) and trans-port occurs through a thermally activated hopping mecha-nism [19]. The band-like régime is generally observed onlyat low temperatures in highly ordered samples [20], so thatthe hopping mechanism is usually in effect at tempera-tures relevant for practical technological applications. Inthe hopping régime, the carrier mobility is proportionalto the intersite electron transfer rate kij, which, in thesemi-classical approximation, can be evaluated by theMarcus equation [19,21],

kij ¼ t2ij

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip

�h2kBTkij

sexp �ðDEij � kijÞ2

4kijkBT

!; ð1Þ

where tij is the transfer integral, kij is the reorganization en-ergy, DEij is the energy difference between the initial andfinal states, T is the temperature, and kB and ⁄ are the Boltz-mann and Planck constants, respectively. Since the energydifference between initial and final states in a crystal is of-ten vanishingly small [22], the two parameters governingthe transfer rate at a particular temperature are the reorga-nization energy and transfer integral. Here, we have useddensity functional theory (DFT) to evaluate differences inreorganization energies and transfer integrals of the threetypes of molecular crystals and have related these calcu-lated charge transfer parameters to experimentally deter-mined charge carrier mobilities.

T. The geometric data of the crystal structures are from Refs. [16–18],sity functional theory calculations. The bottom part shows fluorescencefibers, 112 lm � 63 lm; PPTTPP nanofibers, 223 lm � 125 lm; TTPPTT,

1230 J. Kjelstrup-Hansen et al. / Organic Electronics 10 (2009) 1228–1234

2. Methods

2.1. Experimental details

The nanofibers are fabricated by physical vapor deposi-tion of the molecules from a Knudsen cell onto a heatedmuscovite mica substrate under high vacuum conditions[6]. Through interaction with the electrical surface dipolesof the mica substrate, the molecules align and self-assem-ble into nanofiber aggregates with typical cross-sectionaldimensions of a few hundred nanometers (width) by tensof nanometers (height) and a length of tens of microme-ters. The fluorescence micrographs in Fig. 1 show the threetypes of as-grown nanofibers on mica substrates. Upongrowth, a few nanofibers are transferred from the micasubstrate to a prefabricated device substrate consisting ofan elevated silicon dioxide platform on a silicon chip. Thenanofiber transfer is accomplished by gently pressing themica substrate against the device substrate under condi-tions of high humidity, which releases the nanofibers fromthe mica substrate. By inspection with a fluorescencemicroscope, a suitable nanofiber is identified and a set ofelectrodes is made using a silicon nanowire as a local sha-dow mask during metal deposition to form the two goldtop contacts on the nanofiber [11]. Gold has a relativelyhigh work function and, consequently, the use of gold con-tacts leads to hole conduction [13]. After metal deposition,the nanowire shadow mask is removed by mechanicalmanipulation, and the sample is wire bonded for electricalcharacterization. The electrical measurements are carriedout using a home built setup consisting of a Labview-con-trolled NI PCI-6229 DAQ device and Stanford ResearchSR570 current pre-amplifier. The transport properties arestudied by two-point measurements in which current ismeasured as the applied voltage is increased from 0 V.The sample dimensions, in particular the uncoated lengthof the nanofiber (distance between electrodes) and itscross-sectional dimensions, have been determined fromSEM and AFM (tapping mode) measurements.

2.2. Theoretical details

To determine the charge transfer rate, kij, using Eq. (1),the transfer integral and the reorganization energy must becalculated. The transfer integral is determined mainly bythe intermolecular overlap of the frontier molecular orbi-tals of the involved molecules – HOMO (highest occupiedmolecular orbital) for hole transfer and LUMO (lowestunoccupied molecular orbital) for electron transfer. There-fore, its value depends on molecular packing structure. Re-cently, Valeev et al. [22] described a transfer integralcalculation method that includes the influence from siteenergy differences that can arise from geometric differ-ences and polarization effects between inequivalent mole-cules in the crystal unit cell. By defining one-electrondimer states from localized monomer orbitals (wi) andassuming that the dimer HOMO and HOMO�1 (LUMO+1and LUMO) originate only from the interaction of themonomer HOMOs (LUMOs), the site energies ei and trans-fer integrals tij are obtained from

ei ¼ wih jHjwii ð2Þ

tij ¼ wih jHjwj

�; ð3Þ

where H is the Hamiltonian. Since Eq. (1) assumes anorthogonal basis and the monomer orbitals are, in fact,not strictly orthogonal, the transfer integral as determinedby Eq. (3) cannot be applied directly. First, an orthonormalbasis set is required and is obtained using Löwdin’s sym-metric transformation [22] to give

teff12 ¼

t12 � 12 ðe1 � e2ÞS12

1� s212

; ð4Þ

where S12 is the overlap integral. Here, density functionaltheory (DFT) is used together with Eqs. (2)–(4) for calcula-tion of transfer integrals.

The reorganization energy comprises both inter- andintramolecular contributions [1]. The intermolecular partis due to the polarization and relaxation of the surroundingmedium. The intramolecular part is due to the changes inequilibrium geometries of both the donor and acceptormolecules upon charge transfer and, therefore, consists oftwo terms related to each of the molecules involved: (1)the relaxation of the donor molecule upon going fromthe charged-state geometry to the neutral-state geometry(k0) and (2) the relaxation of the acceptor molecule upongoing from the neutral-state geometry to the charged-stategeometry (k1), respectively. The intramolecular reorganiza-tion energy is determined from the adiabatic potential sur-faces ask 0 ¼ E0=1 � E0=0 ð5Þ

k1 ¼ E1=0 � E1=1; ð6Þwhere E0/0 and E1/1 are the ground state energies of theneutral and charged molecule, respectively, E1/0 is the en-ergy of the charged state at the optimal geometry of theneutral state, and E0/1 is the energy of the neutral state atthe geometry of the charged molecule. The intramolecularreorganization energy is determined by calculating theenergies at the various optimized geometries of a singlemolecule in the gas phase. In the gas phase, all three mol-ecules considered here will exhibit significant inter-ringtorsional angles that are not observed in the solid-stategeometry where the molecules exhibit more coplanargeometries. To be consistent with the geometries observedin the crystal structure, intramolecular reorganizationenergies have been obtained by constraining the moleculesto planar geometries during the optimization process.

The transfer integral calculations have been performedusing the Amsterdam Density Functional [23] and Gauss-ian 98 [24] software packages, while the calculation ofthe intramolecular reorganization energies was done usingGaussian 98 [24]. For the transfer integral calculations, thePW91 functional was used with a DZP basis set. This func-tional was found by Huang and Kertesz to provide resultsin closest agreement with experimental values [25]. Inthe calculation of reorganization energies, hybrid function-als that include a fraction of Hartree–Fock exchange pro-vide higher estimates of reorganization energies thanpure DFT methods. By comparison with experimental re-

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sults from photoelectron spectroscopy studies on oligoac-enes [26] and oligothiophenes [27], recent reports foundthe B3LYP functional to yield values closest to experi-ments. Therefore, the B3LYP functional is used in the calcu-lations of intramolecular reorganization energies.

3. Results and discussion

3.1. Experiment

Fig. 2a shows a typical current–voltage data set from anindividual nanofiber (a TTPPTT oligomer type) contacted

Fig. 2. (a) Typical result of a current versus voltage measurement on asingle nanofiber (here made from TTPPTT molecules) contacted with twogold electrodes. The arrow indicates the point used in the calculation ofthe mobility as described in the text. (b) Scanning electron microscopyimage of a nanofiber supported on silicon dioxide and contacted with twogold electrodes. (c) Charge carrier mobility estimates from individual p6P,PPTTPP and TTPPTT nanofibers based on the Mott–Gurney formalism asdescribed in the text.

with gold electrodes. We use the Mott–Gurney formalismto analyze the data, as has been done in previous studies[13]. This allows the charge carrier mobility l to be esti-mated from

lmin ¼8IL3

9ere0AV2 ; ð7Þ

where I is the current, L is the device length, ere0 is thedielectric permittivity, A is the cross-sectional area, and Vis the applied voltage. The use of Eq. (7) implicitly assumescharge transport in the space-charge limited (SCL) regimeand does not account for additional current-limiting fac-tors such as interface barriers or charge traps. These factorseffectively reduce the current from its theoretical maxi-mum. The resulting mobility estimated from Eq. (7)should, therefore, be interpreted as a lower bound to theaccurate value of the mobility.

A TTPPTT nanofiber with gold electrodes is seen in theSEM image in Fig. 2b, from which the uncoated length(321 nm) and width (428 nm) are obtained. The height(35 nm) is determined from AFM data (not shown), and Ais found as the product of the width and height. We esti-mate the uncertainty on the length and width data to be±5% and on the height data to be ±10%. The uncertaintyon the mobility is considered to be affected primarily bythe uncertainty on the SEM and AFM data. This leads to aworst-case uncertainty on lmin of +35%/�26%. Ten sampleswere prepared for each of the PPTTPP and TTPPTT nanofi-bers. From those samples, seven PPTTPP and nine TTPPTTsamples exhibited current–voltage characteristics thatindicate current flow through the nanofibers. The remain-ing samples displayed much lower resistances, which uponcloser inspection were found to originate from short cir-cuits caused by metal residues from the contacting pro-cess. Fig. 2c shows these 16 mobility values versusnanofiber length together with the data from 24 p6P nano-fiber samples from Ref. [13].

Since charge carrier mobility is an intrinsic materialparameter, no length dependence is expected. The mobilitydata presented in Fig. 2c seems to indicate that the longerthe nanofiber, the higher the estimated mobility. This im-plies that for the shorter nanofibers, the estimate providedby Eq. (7) is significantly below the true mobility, mostlikely due to contact effects that reduce the current. Thisis not unexpected, as contact effects are more severe forshort samples where the bulk nanofiber resistance is com-parably small. For longer nanofibers, however, the contri-bution from the nanofiber bulk to the resistance ishigher, and Eq. (7) is expected to provide a better estimate.Therefore, we expect that the long nanofibers provide thebest estimate of the true mobility. The largest estimatedcarrier mobility is found for PPTTPP and is 1 cm2 V�1 s�1.Both p6P and TTPPTT exhibit carrier mobilities approxi-mately an order of magnitude below that.

3.2. Theory

The transport properties and hence charge mobility inmolecular crystals exhibit a directional anisotropy. Byselecting different combinations of molecules, the effective

Table 2B3LYP/6-31G(d) intramolecular reorganization energies (k) for p6P, PPTTPP,and TTPPTT, in comparison to the hexathiophene and pentacene values.

khole (meV) kelectron (meV)

p6P 162 192PPTTPP 225 236TTPPTT 195 185a-6Ta 255Pentaceneb 97 132

a Ref. [27].b Ref. [31].

Fig. 3. Hole and electron transfer rates in the d direction of the p6Pcrystal as a function of varying the amount of intermolecular reorgani-zation energy.

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transfer integrals along various crystal directions indicatedin Fig. 1 can be found and are listed in Table 1. Pentacene isoften regarded as a benchmark for evaluating electroniccoupling strengths and hole mobilities, with typical mobil-ity values of more than 1 cm2 V�1 s�1 at room temperature[28] and with values up to 35 cm2 V�1 s�1 having been re-ported [29]. For comparison, the transfer integrals forpentacene are larger than those calculated for the systemsthat are investigated here. In pentacene, the effective holetransfer integral (along the d1 diagonal direction) is85 meV [30]. The intramolecular reorganization energiesrelevant for both hole and electron transfer in p6P, PPTTPP,and TTPPTT molecules were calculated and are listed in Ta-ble 2. Reorganization energies for pentacene and hexathi-ophene (a-6T) are provided for comparison.

In order to obtain an estimate of the charge transferrate, the charge transfer parameters we have calculatedcan be injected into Eq. (1). The contribution of the inter-molecular part to the total reorganization energy is usuallyassumed to be smaller than or of same order of magnitudeas the intramolecular contribution [1,32]; exact values aredifficult to estimate since they require to take account ofthe lattice phonons. Here, since we are mainly interestedin trends, we have chosen to take into account the poten-tial contributions of the intermolecular reorganization en-ergy to the entire reorganization energy in an effectiveway: we have simply calculated the hole and electrontransfer rates along the diagonal direction in the p6P crys-tal for different amounts of external reorganization energy,shown in Fig. 3. If an intermolecular reorganization energyof 0.1 eV is used, transfer rates of 3 � 1012 s�1 and3 � 1010 s�1 for electron and hole transfer are obtained,respectively. Fig. 3 illustrates that when similar valuesfor the external reorganization energies are used for bothelectron and hole transfer, the hopping rate for electronsis �102 larger than for holes in this crystal direction.

The intermolecular contribution to the reorganizationenergy is generally less dependent on the chemical struc-ture than the intramolecular part [1]. Thus, as a first step,we assumed that the external contributions were similarin all the systems considered here and evaluated thecharge carrier transfer rates relative to that in pentacene.Due to its superior transport properties, the latter can beconsidered as a benchmark system and its transfer ratehas been found by inserting the previously quoted transferintegral and reorganization energy into Eq. (1). The chargetransport parameters for oligophenylene and oligophenyl-ene–thiophene crystals have been calculated to describecharge transport in nanofiber structures. In order to make

Table 1Absolute values of the effective transfer integrals (teff) along different crystal dire

teff,a (meV) teff,b

p6P hole (HOMO) 0 16p6P electron (LUMO) 1 71PPTTPP hole (HOMO) 0 7PPTTPP electron (LUMO) 1 77TTPPTT hole (HOMO) 0 8TTPPTT electron (LUMO) 1 62

a Cofacial dimer configuration with a separation distance of 3.6 Å.

this correlation, we consider the transfer integrals corre-sponding to charge transfer along the long direction ofthe nanofiber, which approximately corresponds to thedirection of the applied electric field in the experimentalgeometry shown in Fig. 2. For p6P, this would correspondto the charge transfer occurring in the d direction of thecrystal (see Fig. 1). Since the contact face between thegrowth substrate and the PPTTPP or TTPPTT crystals is cur-rently not known experimentally, the direction of the ap-plied electric field relative to the crystal structure is alsounknown. Therefore, a charge hopping direction similarto that observed in p6P is assumed, i.e. along the diagonal.For hole transfer, we find that the transfer rates in p6P andPPTTPP are similar and approximately three orders of mag-nitude smaller than in pentacene. The large hole transferintegral along the d direction in TTPPTT (see Table 1) re-

ctions in p6P, PPTTPP, and TTPPTT.

(meV) teff,d (meV) teff,cofaciala (meV)

4 24744 2975 25237 30824 25556 308

J. Kjelstrup-Hansen et al. / Organic Electronics 10 (2009) 1228–1234 1233

sults in a hopping rate (using a planar geometry to calcu-lated the intramolecular reorganization energy) �10�2

times that of pentacene.

3.3. Discussion

The experimentally found carrier mobilities are up to1 cm2 V�1 s�1 for PPTTPP and roughly an order of magni-tude smaller for both p6P and TTPPTT. The value of1 cm2 V�1 s�1 for PPTTPP is one of the largest observedmobilities for such nanoscale organic crystals. These re-sults can be compared with the mobility found in penta-cene of up to 35 cm2 V�1 s�1. However, it should benoted that pentacene molecules cannot to our knowledgeself-assemble into nanofibers and are, therefore, less suitedfor applications that require structuring at the nanoscale.Based on the transfer rate calculations, crude estimates ofthe mobility can be made from the Einstein relationl = eD/kBT, in which e is the electronic charge and D thediffusion coefficient [33]. D can be estimated fromD = L2kij/2, where L is the effective length of charge transferthat can be approximated by the center of mass distance[33]. By neglecting the intermolecular reorganization en-ergy, this leads to mobility estimates of 10�2 cm2 V�1 s�1

for p6P and PPTTPP, while TTPPTT is predicted to have amobility of 10�1 cm2 V�1 s�1. For comparison, this type ofcalculation provides an estimate of the mobility in penta-cene of 101 cm2 V�1 s�1. We again emphasize that theapproximations made here render these mobility esti-mates rather crude.

The theoretical evaluations of the transfer rates (andthus mobilities) for all three systems considered here re-sult in values that are two to three orders of magnitudelower than that found in pentacene, in reasonable agree-ment with the experimental findings. However, whilePPTTPP is found experimentally to exhibit the highestmobility, theory estimates TTPPTT to be the better conduc-tor. The likely explanation resides in the assumption wemade of equal intermolecular contributions to the reorga-nization energy of all systems; we come back to this pointbelow.

In general, the LUMO transfer integral is larger than thecorresponding HOMO transfer integral. The magnitude ofthe transfer integrals along different directions can berationalized by considering the molecular structures inFig. 1. The distance between molecules in a pair has astrong influence on the degree of electronic interaction[19]. As seen in Table 1, the electronic coupling strengthis large in the cofacial geometry. Since the dimers takenout of the crystal structure in the a and b directions areessentially displaced cofacial dimers, and since the mole-cules oriented along the b direction are significantly closerto one another than the molecules along the a direction,the transfer integrals are found to be larger along the bdirection.

The reorganization energies in the oligophenylene andoligophenylene–thiophene molecules are larger than thecorresponding values determined for pentacene. This isconsistent with the observed lower charge mobilities.The molecular backbone of these structures is less rigidthan in pentacene, which has very low reorganization en-

ergy on the order of 0.1 eV [34]. The reorganization energyfor hexathiophene is also included in Table 2, since hexa-thiophene would be the next molecular structure in thesequence of p6P, PPTTPP, and TTPPTT. An increase in reor-ganization energy is observed upon the presence of thio-phene rings with TTPPTT having a lower reorganizationenergy than PPTTPP. We recall that the reorganizationenergies have been calculated while constraining the mol-ecules to planar geometries, which is reasonable in thecase of p6P and PPTTPP for which on average approxi-mately coplanar geometries are observed in the crystalstructure [17,35]. In contrast, TTPPTT exhibits a wavyoscillation in the geometry along the long axis of the mol-ecule [18] (seen clearly looking down the long axis of themolecule shown in Fig. 1). We speculate that the wavystructure in the crystal phase could give rise to moresignificant intermolecular contributions to the reorganiza-tion energy; this might be the origin of the discrepancyin the trends between the calculated transfer ratesand the measured carrier mobilities in our series ofcompounds.

4. Conclusions and outlook

The charge transport properties for three molecular sys-tems: p6P, PPTTPP, and TTPPTT, all of which can self-assemble into nanofiber structures, have been investigatedboth experimentally and theoretically. The experimentalstudy was made by electrical two-point measurementson individual nanofibers. The analysis of the electricalmeasurements is based on the Mott–Gurney formalism,which describes charge transport in the space-charge lim-ited régime. Therefore, it provides estimates of the lowerbound of the carrier mobility. Experimentally, all threetypes of nanofibers were found to exhibit carrier mobilityranging from 0.1 to 1 cm2 V�1 s�1 with PPTTPP nanofibershaving the highest mobility.

In such molecular crystals, charge transport occurs viaincoherent hopping between neighboring molecules. Weanalyzed the transport parameters on the basis of thesemi-classical Marcus theory, which relates the rate ofcharge transfer to the transfer integral between the twomolecules involved in the transfer process and to the reor-ganization energies accompanying the charge relocation.The transfer integrals in various crystal directions andthe intramolecular reorganization energies were estimatedfor the three systems by density functional theory calcula-tions. In the crystal direction corresponding to the chargetransport direction in the experimentally realized geome-try, the theoretical estimates of the magnitude of the car-rier mobilities in p6P, PPTTPP, and TTPPTT with respectto that for pentacene were found to be in good agreementwith experiment.

Further experimental effort is now focused on investi-gating the charge transport properties in a field-effect tran-sistor configuration to enable the determination of thefield-effect mobility. Furthermore, other types of nanofi-bers can be formed from other phenylene-based mole-cules, which could exhibit improved electricalcharacteristics. The next step will be to include theoretical

1234 J. Kjelstrup-Hansen et al. / Organic Electronics 10 (2009) 1228–1234

modeling of these systems to determine the most promis-ing candidates for experiments.

Acknowledgements

We thank Dr. Manuela Schiek for providing the nanofi-ber samples incl. the synthesis of the PPTTPP and TTPPTTmolecules. The VILLUM KANN RAMUSSEN FONDEN andthe Danish research councils FTP and FNU are acknowl-edged for financial support. This work has been partly sup-ported by the MRSEC Program of the National ScienceFoundation under Award DMR-0212302.

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