Crossover from band-like to thermally activatedcharge transport in organic transistors due tostrain-induced trapsYaochuan Meia, Peter J. Diemera, Muhammad R. Niazib,c, Rawad K. Hallanid, Karol Jarolimekd, Cynthia S. Daye,Chad Riskod, John E. Anthonyd, Aram Amassianb,c, and Oana D. Jurchescua,1

aDepartment of Physics, Wake Forest University, Winston-Salem, NC 27109; bDivision of Physical Science and Engineering, King Abdullah University ofScience and Technology, Thuwal 23955-6900, Saudi Arabia; cKAUST Solar Center, King Abdullah University of Science and Technology, Thuwal 23955-6900,Saudi Arabia; dDepartment of Chemistry and Center for Applied Energy Research, University of Kentucky, Lexington, KY 40506; and eDepartment ofChemistry, Wake Forest University, Winston-Salem, NC 27109

Edited by Alberto Salleo, Stanford University, Stanford, CA, and accepted by Editorial Board Member Tobin J. Marks July 5, 2017 (received for review March30, 2017)

The temperature dependence of the charge-carrier mobility providesessential insight into the charge transport mechanisms in organicsemiconductors. Such knowledge imparts critical understanding ofthe electrical properties of these materials, leading to better designof high-performance materials for consumer applications. Here, wepresent experimental results that suggest that the inhomogeneousstrain induced in organic semiconductor layers by the mismatchbetween the coefficients of thermal expansion (CTE) of the consec-utive device layers of field-effect transistors generates trappingstates that localize charge carriers. We observe a universal scalingbetween the activation energy of the transistors and the interfacialthermal expansion mismatch, in which band-like transport is ob-served for similar CTEs, and activated transport otherwise. Ourresults provide evidence that a high-quality semiconductor layer isnecessary, but not sufficient, to obtain efficient charge-carriertransport in devices, and underline the importance of holistic devicedesign to achieve the intrinsic performance limits of a given organicsemiconductor. We go on to show that insertion of an ultrathin CTEbuffer layer mitigates this problem and can help achieve band-liketransport on a wide range of substrate platforms.

organic semiconductors | organic field-effect transistors | charge-carriermobility | electronic traps | organic devices

The exceptional chemical versatility of π-conjugated organicmaterials, coupled with their facile processing and mallea-bility to any substrate shape, size, and type, make them excellentcandidates for a broad range of (opto)electronic applicationsaddressing the fields of energy, environment, health, information,communication, robotics, and sensing. Despite the vast improve-ments recorded for emerging organic electronic materials, theseorganic-based active layers often demonstrate insufficient perfor-mance for implementation in many technologies. The modestperformance of organic devices, however, is not necessarily anintrinsic property of the organic semiconductor layer, as theselimitations may originate from extrinsic effects, such as the pres-ence of impurities, variations in thin-film microstructure, traps atthe organic semiconductor–dielectric interface, or contact effects.The weak van der Waals interactions between organic moleculesresult in narrow electronic bandwidths (compared with inorganicsemiconductors), strong interactions between the charge carriersand the lattice, and high susceptibility to defect formation (1, 2).These effects diminish the electrical performance, and preventaccess to the intrinsic properties of these materials. As a conse-quence, many groups have focused their efforts on determiningthe charge carrier transport characteristics of single crystals, whichoffer an experimental platform to investigate organic semicon-ductors in a nearly perfect form, with minimal defects.Variable-temperature mobility (μ) measurements are typically

carried out to evaluate the mechanism of charge carrier transport

in organic semiconductors. An increase in mobility with decreasingtemperature that obeys a power-law relation, μ α T-n, with 0.5 ≤n ≤ 3, typically suggests a band-like transport (3–5). Although theband-like transport proposed for high-mobility organic semicon-ductors has many common features with the classical bandtransport found in many inorganic semiconductors, it is funda-mentally different due to the fact that, in organic crystals, thecharge carriers are delocalized only over a few molecules (unitcells). The transient localization (dynamic disorder) model, whichrelates charge localization with the lattice vibrations, captures amore accurate picture of charge transport in high-mobility organiccrystals (6). A thermally activated mobility, described by anArrhenius-like relation, μ ≈ exp[-EA/kBT], where EA stands for theactivation energy and kB is the Boltzmann constant, is generally asignature of disorder, and is described in terms of the multipletrapping and release model (7, 8) or variable range hopping (9,10). These models agree well with measurements carried out onpolymeric and polycrystalline small-molecule devices, where chargesare localized and higher temperatures provide energy to overcomethese barriers. Band-like transport is expected for high-qualitysingle-crystal devices; indeed, band-like transport was reported inseveral different materials from time-of-flight (11–13), time-resolvedterahertz pulse spectroscopy (14, 15), and space-charge-limitedcurrent measurements (16). In an organic field-effect transistor(OFET) configuration, however, this type of behavior was observedin a very limited number of samples and only with specific dielectrics(17–23). The differences arise from the fact that, while the first

Significance

The operation of organic field-effect transistors is governed bythe processes taking place at the device interfaces. Themismatchin the coefficients of thermal expansion of the consecutive layerscan induce inhomogeneous strain in the organic semiconductorlayer and reduce performance by increasing the electronic trapdensity. We show that a high-quality organic semiconductorlayer is necessary, but not sufficient, to obtain efficient charge-carrier transport, and we propose a device design strategy thatallows us to achieve the intrinsic performance limits of a givenorganic semiconductor regardless of the relative thermal ex-pansions of the constituent layers.

Author contributions: Y.M., C.R., J.E.A., A.A., and O.D.J. designed research; Y.M., P.J.D.,M.R.N., R.K.H., K.J., C.S.D., C.R., J.E.A., A.A., and O.D.J. performed research; Y.M., C.R.,A.A., and O.D.J. analyzed data; and Y.M., K.J., C.R., J.E.A., A.A., and O.D.J. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. A.S. is a guest editor invited by the EditorialBoard.1To whom correspondence should be addressed. Email: jurchescu@wfu.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1705164114/-/DCSupplemental.

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techniques probe the bulk properties of the organic semiconductor,in OFETs, the charges accumulate at the functional interface ofthe device, i.e., between the organic semiconductor and the gatedielectric. Here charge motion is not only related to the intrinsicproperties of the semiconductor layer but also to processes takingplace at the organic–dielectric interface. For example, Fröhlichpolarons form in devices fabricated on high-k inorganic dielectrics(strong coupling regime) (19, 24), and broadening of the densityof states occurs due to static dipolar disorder in devices withpolymeric dielectrics (weak coupling) (25, 26). As a consequence,the charges become localized, their mobility is reduced, and, insome cases, depending on the strength of the coupling, the trans-port becomes thermally activated. The conformation of the organicsemiconductor molecule was also shown to affect the chargetransport via the coupling of the charge carriers to the polar-izability of the organic semiconductor (21). For systems inwhich two or more molecular conformers can coexist, orienta-tional disorder was recognized to yield tunneling transportwhen the interconversion is prohibited and a thermodynamicnonequilibrium occurs (27).In this article, we show that the inhomogeneous strain induced

in the semiconductor film by virtue of a mismatch in the coeffi-cients of thermal expansion (CTE) between the consecutive layersin a device increases the interfacial trap density, lowers the ef-fective device mobility, and can induce a crossover from band-liketo activated transport irrespective of the nature and quality of theorganic semiconductor. A signature of new phenomena arisingfrom strain effects was recently recognized by Frisbie and co-workers (28), who discovered a change in the work function of theorganic semiconductor rubrene as a result of compressive andtensile strains. Takeya’s group (29) reported on an increase incharge-carrier mobility upon the application of compressive strain,which they assigned to the reduction in the dynamic disorder as aresult of minimizing molecular vibrations. Nickel and coworkers(30) found that pentacene crystals transition between two poly-morphs to reduce the mechanical strain created in the lattice dueto differences in contraction/expansion behavior of the film andthe substrate. Nanoscale confinement effects during solution pro-cessing have also been shown to tune the polymorphism by alteringthe lattice constants of 6,13-b(triisopropylsilylethynyl)pentacene(TIPS) pentacene films (31). In other studies, the crystals in contactwith different surfaces were reported to crack upon cooling, due tostrain formation, an effect that was greatly reduced or eliminatedwith slow cooling (32–34). In the present work, we focus exclusivelyon devices for which the cooling/heating is performed sufficientlyslowly that no irreversible change (i.e., cracking) is induced. Thiswas confirmed by the recovery of the electrical properties upon aheat/cool cycle. We tune the thin-film morphology and structure byvarying processing parameters and use these films in combinationwith different dielectrics, including “vacuum gap” and SiO2, as wellas SiO2 modified with an ultrathin layer of polystyrene. In doing so,we assess ratios between the CTEs of the organic semiconductorand the gate dielectric varying between 1 and 30. By combining ourresults with data extracted from the literature, we discover a uni-versal dependence between the activation energies of chargetransport in OFETs and the relative thermal expansion of the or-ganic semiconductor and dielectric layer. Our analysis indicatesthat observations of band-like transport in OFETs are only possibleif the thermal expansions of the dielectric and semiconductor layersare similar, and that a transition to an activated transport occurswhen CTE ratio is greater than ∼3, irrespective of materials used.We hypothesize that this transition is a result of the electronic trapsinduced by the strain arising in the organic semiconductor film. Wepropose that thermal expansion mismatch, a widely overlookedparameter despite its ubiquitous presence in layered devices, maybe the key missing link to help achieve consistently high per-formance and band-like transport across a wide range of organicsemiconductors.

Results and DiscussionTemperature Dependence of the Electrical Properties at ModelDielectric Interfaces. All devices included in this study are bottom-gate, bottom-contact OFETs; see the schematic structure includedin Fig. 1A. We first focused on two model dielectrics, namely thevacuum gap and thermally grown SiO2, to evaluate the effect of a“free” interface with that of the most commonly used inorganicdielectric. For this comparison, we used the small-molecule or-ganic semiconductor 2,8-difluoro-5,11-bis(triethylgermyl-ethynyl)anthradithiophene (diF-TEG ADT), a material that exhibitscharge carrier mobilities greater than 5 cm2·V−1·s−1 and is com-patible with large-area spray deposition (35). We first focused oncrystals obtained by slow evaporation of the solvent using thesolvent-assisted crystallization (SAC) technique (36). Typical trans-fer and transport characteristics are presented in Fig. 1 B and C,respectively. Fig. 1D shows, in black squares, the evolution of mo-bility with temperature for a vacuum-gap OFET. The monotonicincrease in mobility with lowering temperature is a signature ofband-like transport at the diF-TEG ADT–vacuum interface, similarto results obtained in other molecular crystals (20, 37, 38). In con-trast, OFETs fabricated with the same material, but on SiO2 di-electric, exhibit an activated behavior with a small activation energyEA = 19.7 ± 6.6 meV (Fig. 1D, blue circles). The activated thermalbehavior is generally assigned to electronic states present in thesemiconductor band gap, i.e., traps. To understand the effect of thetraps on the temperature dependence of mobility, we estimatedthe interfacial trap density NT as a function of temperature T fromthe subthreshold swing S, using the following expression (39):

NT =Cie2

�eS

ln10 · kBT− 1

�. [1]

Here, Ci denotes the capacitance per unit area across gate dielec-tric, and e is the elementary charge. More details on the evolutionof the current–voltage characteristics with temperature are in-cluded in SI Appendix, Fig. S1 and Tables S1–S3. In the vacuum-gap device, NT increases only slightly upon cooling (ΔNT < 20%),and this is simply the result of the fact that trap occupancy in-creases with decreasing temperature, following Fermi–Dirac sta-tistics (2) (Fig. 1E, black squares). A much more drastic change inNT (ΔNT ≈ 160%) is observed at the organic semiconductor–SiO2interface (Fig. 1E, blue circles). These results are also supported bythe observed shifts in the threshold voltage, which became morenegative in both cases, with a larger increase being recorded forthe device on SiO2 dielectric (ΔVt = 11 V) compared with the air-gap dielectric (ΔVt = 6 V). As the values of room-temperature NTare similar for the vacuum-gap (2 × 1016 m−2·eV−1) and SiO2devices (3 × 1016 m−2·eV−1, slightly higher for the latter due todielectric polarizability), we argue that the additional trappingstates are extrinsic in nature and introduced during cooling ofthe sample through the strain arising in the organic film due toCTE mismatch between the semiconductor and SiO2 layers. Thiseffect is absent in vacuum–dielectric devices, where the free-standing surface of the crystal is not affected by the cooling cycle.

Evaluation of the CTE Mismatch at the Semiconductor–DielectricInterface. To quantify the effects of strain in organic semicon-ductors, we investigated the CTE quantitatively. CTE, α, is de-fined as the change in the dimensions (L) of a material as afunction of temperature (T),

α=1L

dLdT

. [2]

As organic semiconductors tend to be highly anisotropic, CTEmust be evaluated for each crystallographic direction. To do so,

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we performed variable temperature powder X-ray diffractionmeasurements.Fig. 2A, Top shows the diffraction patterns at 153 K (blue) and

233 K (red), respectively, for a diF-TEG ADT film deposited bySAC, then delaminated from the substrate, cut using a laboratoryblade, and dispersed on a rotating cryoloop with paratone oil tominimize the preferential orientation. As previously shown, thismaterial adopts a triclinic structure, with a 2D π-stacking motif(35). The film obtained by this method exhibits a strong (001)lamellar stacking texture and molecules oriented edge-on withrespect to the substrate plane, which is parallel to the ab plane ofthe unit cell (Fig. 2B) (35). The monotonic shift in the peakpositions with increasing temperature can be ascribed to thermalexpansion, with no significant change in the diffraction patternindicating that the crystals do not undergo a phase change withinthe temperature window investigated. We analyzed the unit cellparameters and obtained thermal expansions typical for organicmolecular crystals: Δa = 0.23%, Δb = 0.29%, and Δc = 1.0%.

The estimated in-plane CTE is therefore αSAC = 32 ppm/K bytaking the average of the expansions along the a and b axes (seeSI Appendix, Methods 1 for details on calculations). We nowdefine the interfacial thermal expansion mismatch (ITEM) simplyas the ratio between the in-plane CTE of the organic semi-conductor film and that of the dielectric layer (ITEM = αOS/αD),and we will use this parameter as the figure of merit for a quan-titative evaluation of the CTE mismatch. With an αD = αSiO2 =4.1 ppm/K characteristic to SiO2 (40), the ITEM corresponding tothe devices on SiO2 dielectric presented in Fig. 1 is 7.9. Such amismatch is not present at the interface between the crystal andvacuum/air, and thus the equivalent ITEM for the vacuum gap canbe approximated to be unity.

Temperature-Dependent Transport Properties in Systems ExhibitingTunable CTE. The coexistence of several polymorphs or textures isa common occurrence in small-molecule organic semiconduc-tors; hence the expectation that associated polycrystalline films

Fig. 1. (A) Schematic illustration of the OFET structure used in this study. (B and C) The electrical properties of OFET with vacuum-gap dielectric. (D) Charge-carrier mobility and (E) interfacial trap density as a function of temperature in OFETs with vacuum-gap (black squares) and SiO2 (blue circles) dielectrics.

Fig. 2. (A) X-ray diffraction powder pattern of (Top) SAC (solvent-assisted crystallized), (Middle) LG, and (Bottom) SG diF-TEG ADT spin-coated films at 153 K(blue) and 233 K (red). (B) The (001) preferred orientation characteristic to SAC and LG films. (C) Mix of (001) and (111) molecular orientations present inSG films.

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should exhibit different in-plane CTEs is well founded. Thechemical and crystal structures of diF-TEG ADT further allowus to tune the CTE, and therefore the ITEM value, by thin-filmprocessing. We have shown recently that the microstructure ofsuch molecules can be controlled via the manipulation of inter-actions at chemically tailored interfaces (41, 42). Large grains(LG) of molecules preferentially oriented along the (001) crys-tallographic direction form on surfaces treated with fluorinatedself-assembled monolayers (SAMs) as a result of noncovalentinteractions between the SAM and the organic semiconductor(Fig. 2B). In contrast, the regions where this interaction is absentor prohibited consist of small grains (SG) comprising a mixtureof (001) and (111) textured crystals (Fig. 2C) (43–46). In Fig. 2A,Middle, we show the X-ray diffraction spectra at 153 K (blue) and233 K (red), for the LG films obtained by spin-coating the so-lution over pentafluororobenzene thiol (PFBT) treated Au, re-moved from the substrate, and dispersed similarly to the SACsample. We estimated αLG = 39 ppm/K for this film using thesame algorithm described earlier for the SAC films. A similarprocedure was adopted for the SG films (Fig. 2A, Bottom),considering 50% content of each of the two molecular orienta-tions (43) and averaging over the (001) and (111) planes, re-spectively (see SI Appendix,Methods 1). The resulting CTE valuewas estimated as αSG = 115 ppm/K. We can thus vary the CTE offilms of the same organic semiconductor by more than a factor of3, from 32 ppm/K to 115 ppm/K, by modifying the depositionprocedure and substrate chemistry.We fabricated organic thin-film transistors of diF-TEG ADT

with mixed texture by spin-coating the semiconductor over asubstrate with SiO2 dielectric and Ti/Au source and drain elec-trodes treated with PFBT. The film exhibited LG microstructureon and near the contacts and SG away from the contacts, mainlyin the middle of the channel. By varying the transistor channellength, L, we thus monotonously varied the fractions of LG andSG textures in the channel and therefore their contribution tothe overall device performance. Fig. 3A depicts the evolution ofthe mobility versus L for such devices. This figure was obtainedby averaging the results over five devices for each channel length.At short channel lengths, the mobility is high (μ = 3.0 ±

1.0 cm2·V−1·s−1 at L = 5 μm), and its value decreases as the channellength increases. This behavior, as well as the mechanism re-sponsible for the microstructure formation, was described in detailin our earlier work (45). The high mobility is a result of the factthat, in these narrow channel-length devices, the LG that form onthe treated contacts bridge the channel and connect source–drain

electrodes to provide an effective path for the charge carriertransport (Fig. 3B). Similar film microstructure was also ob-served by Kymissis and coworkers (47) for the same material. Asthe channel length increases, the presence of the fine-grain re-gions of mixed molecular orientations in the middle of thechannel diminishes the charge transport (Fig. 3C). This micro-structure change is captured as a change in slope in the mobilityversus channel length plot at the transition point (L = 25 μm),followed by a more abrupt decrease in mobility values as afunction of channel length after this point, reaching μ = (6.7 ±1.1)·10−4 cm2·V−1·s−1 at L = 100 μm. At channel lengths ex-ceeding 25 μm, the film consists of high-mobility LG of (001)textured crystals in the vicinity of the contacts and low-mobilitymixed texture of (001) and (111) SG crystals in the middle of thechannel. The relative fraction of the SG in the channel increaseswith channel length (45). We therefore estimated the averageCTE of films consisting of both LG and SG microstructures by aweighted sum including the contribution of the CTEs of the twomicrostructure types.The ability to tune their relative areal fraction as a function of

channel length provides us with access to films of different globalCTE on the same dielectric. To relate this parameter to theelectrical properties, we measured the evolution of mobility withtemperature for devices of various channel lengths, for which theresults are shown in Fig. 4A. The transport is activated for allsamples, and the activation energy, EA, is proportional to thechannel length (Fig. 4B). For high-mobility devices, consisting ofLG (5 μm < L < 25 μm), EA is constant and small (EA = 22.4 ±2.9 meV). The increase in SG content for longer L is accompaniedby a gradual decrease in μ and increase in EA, which becomesEA = 76.6 ± 7.3 meV for the largest channel investigated in thisstudy (L = 100 μm). This relation between EA, μ, and L resultsfrom the fact that, with increasing L, there are more grainboundaries and possibly more disorder in the texturing of the film,as suggested by Fig. 3A, and in agreement with other reports (48,49). Our results strongly indicate now that, in addition to micro-structure effects, there is a second reason for increased trappingwith increasing channel length, and that is the introduction ofinhomogeneous thermal strain during heating and cooling cycles.To test this idea, we evaluated the change in the interfacial trapdensity NT as a function of channel length and temperature in Fig.5A. It can be observed that, at 300 K, a low NT accompanies thehigh mobility recorded in short channel length devices. NT in-creases gradually as the channel length increases and mobilitydecreases. Although this would suggest that the interfacial trap

Fig. 3. Spin-coated diF-TEG ADT transistors. (A) Evolution of the mobility with channel length. (B) Optical micrograph of a short channel device (L = 20 μm)completely covered with large grains. (C) Optical micrograph of a long channel device (L = 80 μm) showing the differential microstructure.

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density determines the mobility value, note that the estimation ofNT from S does not allow access to the energy distribution of thesetraps, as we have shown in our earlier work using other methods(50–52), and it is likely that traps located at different energy levelswill impact the mobility and its temperature dependence in adistinct way (53). Devices with channel lengths between 5 μm and25 μm, consisting entirely of LG, showed similar changes in NTwithin the accuracy of our measurements. The increase in NT withcooling ranges from ΔNT = 20% for devices with L = 10 μm toΔNT = 110% for L = 100 μm; therefore, the additional contri-bution to the trap generation, due to the inhomogeneous thermalstrain, should be considered. The dependence of ΔNT on channellength (Fig. 5B, black, left) mirrors the changes in CTE (Fig. 5B,blue, right), where the CTE was calculated as a weighted sum ofthe values corresponding to the LG and SG, respectively, by takinginto account both the crystal lattice constant and the texture in-formation (see SI Appendix,Methods 1). This observation supportsour hypothesis that the additional traps are of extrinsic origin andresult from the local strain induced during device cooling dueto the CTE mismatch between the organic semiconductor anddielectric layer.

Mechanism of Trap Formation Due to Thermal Strain: Modeling andSimulations. The total trap density NT in Fig. 5A originates fromthe intrinsic trap densities present in the film before cooling (NT,iÞand the extrinsic traps generated due to thermal strain (NT,thÞ,such that NT =NT,i +NT,th. The first term coincides with thetrap densities estimated at room temperature, namely NT val-ues estimated using Eq. 1, which result from the energetic andstructural disorder at the semiconductor–dielectric interface(18, 50, 52, 54); we obtain NT,i ≅ 3× 1016m−2 · eV−1 for SACdevices, NT,i ≅ 2× 1016m−2 · eV−1 for devices consisting entirely ofLG, and NT,i ≅ 20× 1016m−2 · eV−1 for SG devices. The thermaltrap density is proportional to the thermal strain, NT,th ∝ «th,which, in turn, is proportional to the CTE mismatch, «th ≈ ITEM.Thus, a large increase in NT is expected for large CTE mismatch,i.e., large ITEMs. We further modeled the experimental points inFig. 5A with the following expression:

NT =NT,i + x ·CLGNT,i · ðITEMLG ·ΔTÞn+ ð1− xÞ ·CSGNT,i · ðITEMSG ·ΔTÞn, [3]

where x represents the areal fraction of LG, and CLG and CSGdenote constants reflecting the effect of strain normalized perareal unit within the LG and SG, respectively. ITEMLG = αLG/αSiO2 = 9.5, and ITEMSG = αSG/αSiO2 = 28 reflect the mismatchin CTE for films consisting of entirely LG or SG on SiO2, and ΔTis the temperature interval over which the measurements weretaken. Indeed, we were able to model the data in all four differ-ent measurements in Fig. 5A simply by varying the content of LGand SG (i.e., the value of x corresponding to the values extractedfrom the optical micrographs). We obtained CLG = 6.7 · 10−6 andCSG = 7.6 · 10−6, and n varied between 1.51 and 1.54. The lines inthis graph resulted from our modeling, and a good agreementwith the experimental points can be observed. The dependenceof the interfacial trap density on ITEM (SI Appendix, Fig. S2),as well as the dependence of the trap densities and activationenergies on CTE of the thin films (Fig. 5C), denote clear corre-lations, thus further supporting our assumption that the inhomo-geneous strains generated upon varying the temperature of thedevice induce additional trapping sites due to the thermalexpansion mismatch.To probe the physical basis of interface trap formation as a

function of tensile strain, we make use of periodic densityfunctional theory (DFT) calculations that model the materialsinterface. Specifically, the diF-TEG ADT crystal models consistof 1 × 4 × 1 supercells, each with eight molecules stacked alongthe b axis (Fig. 6A), oriented such that the a and b axes lie on thesubstrate surface; we note that the substrate is not explicitly in-cluded in the model, as we want to understand the impact oftensile strain in a general way (see SI Appendix for full modeldetails). At 300 K, the diF-TEG ADT layer in both the vacuum-gap and SiO2 dielectric devices are considered to be identical,

Fig. 4. (A) Charge-carrier mobility as a function of temperature for OFETs ofdifferent channel lengths. (B) Activation energy as a function of channellength for the same devices. (Inset) The molecular structure of diF-TEG ADT.

Fig. 5. (A) Points show interfacial trap density measured at different tem-peratures. Lines show fitting from trap generation model. (B) The increase ininterfacial trap density between 210 K and 300 K as a function of channellength (black). The coefficient of thermal expansion, CTE, of the same films(blue) shows a similar trend. (C) The increase in interfacial trap densities withrespect to 300 K value as a function of the coefficient of thermal expansionof thin films (black). In red is the dependence of the activation energy on thecoefficient of thermal expansion of thin films.

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i.e., perfect crystals with no defects. Evaluating the valence bandcharge density, for the unit cell parameters determined from thepowder X-ray studies at 300 K, leads to the expected result thatthe charge density is completely delocalized (Fig. 6B) within thesupercell. At 210 K, the crystal structure of the vacuum-gap deviceis compressed in all three directions to the unit cell parametersobtained from the powder X-ray measurements, as crystal re-laxation is considered not to be impeded by contact with the Auelectrodes. Here, the charge density also remains delocalized (Fig.6B), as the intermolecular spacing is constant (although decreasedcompared with the structure at 300 K). We note that the evalu-ation of the electronic characteristics of each crystal structureobtained from the temperature-dependent powder X-ray studiesshows very similar electronic band structures across the series,with the bands narrowing with increasing temperature. The resultof the consistent band narrowing with increasing temperature is abulk feature, and highlights the fact that there is more going on atthe interface than a simple full contraction of the lattice. Hence,there is a need to explicitly account for tensile strain. To accountfor tensile strain in the SiO2 device at 210 K, the supercell isderived from the cell parameters and molecular positions used forthe vacuum-gap device at 210 K, with the b axis elongated to thevalue experimentally determined at 300 K. This process leadsto an increased molecular spacing (by 0.16 Å) for those mol-ecules close to the supercell boundary. This positional rear-rangement arising from the thermal expansion-induced tensilestrain localizes the valence band charge density to areas wherethe molecular density is greatest, i.e., where there appears ahole trap. These variations in the valence band charge density,along with the variations in the band structures reported in SIAppendix, provide the physical understanding of how the sub-strate interactions, and in particular the CTE mismatch, caninduce charge carrier traps.

Toward a Universal Model.Our experimental and theoretical resultssuggest that inhomogeneous strain, which arises from CTE mis-match between the dielectric and organic semiconductor, yieldslocal distortions in the positions of the organic semiconductor

molecules that lead to deviations from the molecular equilibriumpositions found in the bulk crystal, which in turn induce variationsin the charge density distributions and distinct modifications to theband structures at the dielectric–organic semiconductor interface.These effects represent a form of cumulative lattice disorder,which results in the formation of trap states of depth and densitycorrelating with the structural imperfections (55, 56). Indeed, wefind that, in the temperature range investigated here, the trapdensity at the interface between the diF-TEG ADT films and SiO2dielectric increases by 22% for the LG devices, and by 5 timesmore for the SG devices, where the difference in thermal behavioris significantly larger. In the vacuum-gap devices, on the otherhand, the «th → 0, and therefore the total number of traps is givenonly by the quality of the crystal before cooling, in agreement withthe results shown in Fig. 1E.In Fig. 7, we summarize the results obtained in this work (red

stars), and we also review results on 23 other types of OFETs,consisting of different dielectrics and/or organic semiconductors.In Table 1, we outline the values obtained from literature, alongwith the corresponding references. We plot the activation energyEA as a function of the ratio between the coefficient of thermalexpansion of the organic semiconductor and dielectric, which welabeled ITEM. The measurements where band-like transport wasobserved are included as EA = 0 meV. We find a crossover fromband-like to activated transport when ITEM ≈ 3, followed by anincrease in EA with increasing the thermal expansion mismatch,ITEM. The spread in the data may originate from several fac-tors. First, the CTE values were estimated based on existingreports on the structures at different temperatures, and, in mostcases, they correspond to a free-standing crystal. It was shown,however, that the CTE itself can vary depending on the substrateover which the crystal is placed during the cooling/heating cycle(28). Rubrene, for example, exhibits a CTE of 28 ppm/K whenfree standing (57), 46 ppm/K on PDMS (polydimethylsiloxane),and 17 ppm/K on Si (28). Second, in addition to the thermalstrain, there is also a mechanical strain induced simply by themismatch of the lattice constants between the dielectric andsemiconductor. Third, the dielectrics summarized here (vacuum,Cytop, PEO [poly(ethylene oxide)], parylene, Al2O3, SiO2, Si3N4,and Ta2O5) have different dielectric constants, which impliesthat the Fröhlich polaron landscape is different. Note that thedielectric constant of the gate dielectric, «r, also correlates pos-itively with EA: High dielectric constant dielectrics tend to po-larize and thus trap slow-moving charges, a phenomena referredto as the Fröhlich polaron effect (19). A plot of the activationenergy as a function of the dielectric constant of the gate dielectric

Fig. 6. (A) Representation of the 1 × 4 × 1 supercell of the diF-TEG ADT crystal.(B) Valence band charge density evaluated at the X point at 210 and 300 K.

Fig. 7. Activation energy (EA) versus the ITEM coefficient, defined as theratio between the coefficient of thermal expansion of the organic semi-conductor and that of the dielectric. The red stars represent data obtained inthis study, and the black squares are data taken from literature.

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(SI Appendix, Fig. S7) indicates no correlation between the twoparameters when different sets of organic semiconductors anddielectrics are probed, suggesting that the polaronic effectsalone are not responsible for the experimental observations.Although these effects are important, our results suggest thatthere is another important mechanism by which the dielectriccan influence trapping and transport activation energies,namely the introduction of inhomogeneous microstrains uponvarying the temperature of the device due to the CTE mismatchdescribed above.Fig. 7 suggests that band-like transport can be obtained in

OFET measurements only if there is a minimal mismatch betweenthe thermal expansion of the organic semiconductor and dielectriclayers. This affirmation assumes that the intrinsic trap density, NT,iin Eq. 3, is low. A low intrinsic defect density, however, althoughnecessary, is not sufficient for attaining band-like transport. In diF-TES ADT single-crystal transistors on SiO2 dielectric, for example(point 13), an activated transport was measured (58) despite a verylow interfacial trap density obtained in these devices (59).We further tested our hypothesis by inserting an ultrathin layer

(∼10 nm) of polystyrene between the organic semiconductor filmand the SiO2 dielectric by blending the semiconductor with poly-styrene, which can spontaneously stratify into bilayer structuresduring solution processing with the polystyrene layer buried be-tween the semiconductor and SiO2 (46, 60, 61). The polystyrenelayer has a CTE of 72 ppm/K (62), which is very similar to theCTE of the organic semiconductor incorporated in these devices(diF-TES ADT, CTE =162 ppm/K), yielding an ITEM of 2.3. Thislayer contributes to the overall dielectric capacitance, as was dis-cussed in detail elsewhere (46); it improves the morphology of theorganic semiconductor film; and it forms a “buffer layer” pro-tecting the semiconductor from the thermally induced strain fromthe SiO2 surface.In Fig. 8 A and B, we show transfer and transport curves, re-

spectively, for an OFET of this structure, with channel length L =80 μm and width W = 1,000 μm. The room temperature mobil-ity for this device was 1.85 cm2/V·s, and the average mobility

determined on 5 devices was 1.57 cm2/V·s. The high mobility andgood consistency in the electrical properties are a result of theenhanced film morphology achieved at the surface of the poly-styrene layer, as we have shown in our earlier work (46). In Fig.8C, we plot the evolution of the interfacial trap density as afunction of temperature; this value is roughly constant, asexpected, because, in this case, the thermal strain is negligible.Consequently, the inverse dependence of mobility with temper-ature is observed (Fig. 8D). This last example demonstrates that,although technological applications might require transistors tobe fabricated on substrates with significant CTE mismatch withthe organic semiconductor, insertion of ultrathin dielectric layersexhibiting lower CTE mismatch can mitigate this problem, en-suring band-like transport is operant on a wide range of sub-strates, an important technological implication of this work.

ConclusionsThe development of organic electronic devices relying on efficientcharge transport will require materials whose near-intrinsic chargetransport properties can be measured in a device-relevant config-uration, such as in a transistor. To date, very few materials haveproven amenable to characterization in such a configuration. Wepresent here experimental results pointing toward a universal de-pendence of the transport activation energy on the relative mis-match of the CTE between the semiconductor and dielectric layersin OFETs, and find that band-like transport can be achieved fortransistors characterized by low intrinsic interfacial defect densityat the semiconductor–dielectric interface, and for which the twoadjacent layers exhibit similar thermal expansion. Otherwise, thestrain induced in the organic semiconductor layer results in trapgeneration and localization of the charges. The crossover from aband-like to an activated transport occurs for ITEM coefficientsaround 3. Further studies are necessary to understand the mech-anism of trap generation through the inhomogeneous strain cre-ated at device interfaces due to thermal expansion. Nevertheless,our results suggest that a high-quality organic semiconductor layeris necessary, but not sufficient, to access the intrinsic charge

Table 1. Activation energy (EA), coefficient of thermal expansion of the organic semiconductor(αOS), and that of the dielectric (αD)

Number Organic semiconductor Dielectric EA, meV (Ref.) αOS, ppm (Ref.) αD, ppm (Ref.)

1 Rubrene Parylene 0 (19) 28 (57) 69 (69)2 TIPS pentacene Cytop 0 (23) 90 (70) 120 (71)3 Rubrene Air 0 (19) 28 (57) /4 P3HT PEO 4 (72) 470 (73) 117 (74)5 Naphthalene Al2O3 8.3 (75) 55 (76, 77) 5.4 (78)6 Rubrene SiO2 10 (19) 28 (57) 4.1 (40)7 Rubrene Al2O3 25 (19) 28 (57) 5.4 (78)8 Rubrene Ta2O5 43 (19) 28 (57) 3.6 (79)9 Rubrene Si3N4 51 (19) 28 (57) 3.9 (80)10 Anthracene SiO2 40 (81) 43 (77) 4.1 (40)11 TIPS-Pentacene SiO2 30 (82) 90 (72) 4.1 (40)12 Sexithiophene SiO2 40 (83) 108 (84, 85) 4.1 (40)13 diF-TES ADT SiO2 50 (58) 162 (59, 86) 4.1 (40)14 Pentacene Al2O3 54 (87, 88) 140 (89, 90) 5.4 (78)15 Tetracene SiO2 70 (91) 72 (92) 4.1 (40)16 TIPS pentacene SiO2 60–80 (93) 90 (72) 4.1 (40)17 Pentacene Ta2O5 80 (94) 140 (89, 90) 3.6 (79)18 Pentacene SiO2 100 (94) 140 (89, 90) 4.1 (40)19 Dihexyl-ADT SiO2 79 (95) 243.7 (95) 4.1 (40)20 pBTTT-C14 SiO2 86 (96) 238 (97) 4.1 (40)21 P3HT Al2O3 90.5 (87, 88) 470 (73) 5.4 (78)22 P3HT SiO2 110 (98) 470 (73) 4.1 (40)23 F8T2 SiO2 122 (99) 400–500 (100) 4.1 (40)

Values taken from literature.

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transport properties of a material, and thus careful design of thedevice interfaces, not only in terms of roughness and chemistry, aspreviously shown, but also with respect to the thermal propertiesof consecutive layers, is critical for the construction of high-performance organic devices. Because organic semiconductors typ-ically exhibit very low thermal conductivities, the heat generatedduring device operation cannot be easily dissipated, and thus thethermal properties of the consecutive layers become important. Theinsertion of an ultrathin insulating polymer layer between highlyCTE mismatched dielectric and semiconductor layers is shown tomitigate the strain problem and lead to consistent observation ofband-like transport in organic semiconductors on any substrate.

Materials and MethodsField-Effect Transistor Fabrication. To fabricate OFETs on SiO2 dielectric, westarted with highly doped silicon wafers, with a 200-nm SiO2 layer. The sourceand drain electrodes were Ti/Au deposited by e-beam evaporation and pat-terned by photolithography and liftoff with channel lengths between 5 μmand 100 μm and channel width of 1,000 μm. Substrates were cleaned in hotacetone, isopropanol, and UV ozone before use. For contact treatment, thesubstrates were soaked in a 50-mM room-temperature PFBT (Sigma Aldrich)solution in high-purity ethanol (Sigma Aldrich) for 30 min followed by 5 min ofsonication in ethanol. The SAC samples were deposited from a 0.25% wt so-lution of organic semiconductor in chlorobenzene (Sigma Aldrich), and addi-tional solvent was placed around the substrates in a Petri dish with a closed lidto ensure a slow evaporation rate. The spin-coated samples were depositedfrom a 2% wt solution in chlorobenzene at 1,000 rpm spinning speed. Thevacuum-gap devices were fabricated by placing thick SAC-grown crystals overAu contacts of short channel length, such that the crystals bridge the contactswithout touching the underneath layer. Through atomic force microscopymeasurements, we found that the crystal was not bent, which confirmed thepresence of the vacuum gap. The polystyrene/SiO2 dielectric devices werefabricated from a diF-TES ADT/polystyrene blend, following the proceduresdescribed in ref. 60.

Field-Effect Transistor Characterization. The devices were measured in avacuum probe station, under dark. At least five samples were measured for

each type of device structure. The cooling rate was 1 K/min, and mea-surements were taken every 10 degrees, during the cooling cycle. Themobility was determined from the saturation regime, using the equation:ID = ðW=2LÞμCiðVGS −VT Þ2, where ID denotes the current from source todrain,W and L are channel width and length, μ is the field-effect mobility, Ci isthe dielectric capacitance per unit area, VGS is the voltage between gateand source, and VT is the threshold voltage.

Temperature-Dependent Structural Studies. Powder diffraction patterns wererecorded on a Bruker diffractometer (MoKα radiation; λ = 0.71073 Å) operatedat 50 kV and 30 mA. Frame data were collected using Bruker SMART softwarewhile the powder sample was bathed in a Kryoflex-controlled nitrogen streamoperated at 153 K and 233 K. Beam coordinates and detector distance werecalibrated using a corundum standard sample. Single data frames were col-lected in 240-s exposures; area integration was performed using GADDSsoftware, and data were merged using Merge software to produce the con-ventional 1D trace.

DFT Calculations. All calculations were carried out via DFT. We used the Viennaab initio simulation (VASP) package (63) with PAW (projector augmented-wave) potentials (v.52) (64, 65) and the Perdew–Burke–Ernzerhof func-tional (66). The kinetic energy cutoff was set to 400 eV. Gaussian smearingwith a width of 0.05 eV was used. van der Waals interactions were takeninto account with the DFT-D2 method of Grimme (67). Atoms were re-laxed with the conjugated gradient method until forces were smallerthan 0.01 eV/Å.

The Brillouin zone was sampled with a 2 × 2 × 1 Gamma-centered meshduring calculations on the diF-TEG ADT unit cell. We used the automaticflow software to order the unit cell vectors and to obtain a standardizedpath in the reciprocal space (68). Calculations on the benzene toy modelused a Gamma-centered 1 × 10 × 1 mesh. During calculations on the diF-TEGADT supercell, the k-point mesh was reduced to 2 × 1 × 1.

ACKNOWLEDGMENTS. J.E.A. and C.R. thank the National Science Founda-tion (DMR-1627428) for support of calculations and organic semiconductorsynthesis. The device work at Wake Forest was supported by the NationalScience Foundation under Grants ECCS-1254757 and DMR-1627925.

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