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Jakob Lenz, Martin Statz, [K Watanabe](https://orcid.org/0000-0003-3701-8119), [T Taniguchi](https://orcid.org/0000-0002-1467-3105), Frank Ortmann, R Thomas Weitz

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[Charge transport in single polymer fiber transistors in the sub-100 nm regime: temperature dependence and Coulomb blockade](https://mdr.nims.go.jp/datasets/a5a498f8-4cf4-401d-8f70-c477b395a45b)

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Charge transport in single polymer fiber transistors in the sub-100 nm regime: temperature dependence and Coulomb blockadePAPER • OPEN ACCESSCharge transport in single polymer fiber transistorsin the sub-100 nm regime: temperaturedependence and Coulomb blockadeTo cite this article: Jakob Lenz et al 2023 J. Phys. Mater. 6 015001 View the article online for updates and enhancements.You may also likeThe evolution characteristics of surfacecharge on the gas–solid interface underthe long-time co-action of DC-temperaturegradientYi Zhang, Bo Qi, Xiao Yang et al.-Charge state and Energy distribution ofcarbon ions and protons emitted fromlaser-produced graphite plasmaShahab Ahmed Abbasi, Bushra Ilyas,Ashiq Dogar et al.-Chemical Defects and Impurities IntroduceCharge Traps to Silicone Rubber: aQuantum Chemistry StudyWei Duan, Guangzhi Guo, Guozhu Zhu etal.-This content was downloaded from IP address 144.213.253.16 on 24/12/2022 at 09:43https://doi.org/10.1088/2515-7639/aca82f/article/10.1088/1361-6463/aca33d/article/10.1088/1361-6463/aca33d/article/10.1088/1361-6463/aca33d/article/10.1088/1361-6463/aca33d/article/10.1088/1402-4896/acab97/article/10.1088/1402-4896/acab97/article/10.1088/1402-4896/acab97/article/10.1088/1742-6596/2404/1/012005/article/10.1088/1742-6596/2404/1/012005/article/10.1088/1742-6596/2404/1/012005https://googleads.g.doubleclick.net/pcs/click?xai=AKAOjsvqSLIhqiVtKpsIHGZ1M45AMGkBwVEfFdFQ44QpmUBkFz2akfo8wRvaYQ7WjgxlmqYnXIvhdKTlcGNd8YJhcu29zFKb1xtEiM2jJ3va8NHs-GTKuaueyiZDtp8WxyD_LE4WEaMc7yVjG_tSoRBZ72n9krQOOcm7CsTgKUCJ_9JR_LN4xhdONuGnnFjX2gY1h3pab61u7idBidslmfMbaJlr0O1mLc-cN0YFmiRBKTlu9g1fEah2y8F_eWfmVjrJhkjPxSPE9R-7t2490PUCVHEAgKuflQkYP4KKJCHcjMGETg&sai=AMfl-YS4Lj16kJ-nKv9v3b45S1sE5K8-m-MtGBawk87ZGu5qLzExmOFLN4Z0h2JBBqCOR2W02qoHxUkORLaZjRLtcg&sig=Cg0ArKJSzG0tHZWg7FcY&fbs_aeid=[gw_fbsaeid]&adurl=https://www.electrochem.org/toyota-fellowship%3Futm_source%3DIOP%26utm_medium%3Dbanner%26utm_campaign%3D2023ECSTYIFJ. Phys. Mater. 6 (2023) 015001 https://doi.org/10.1088/2515-7639/aca82fJournal of Physics: MaterialsOPEN ACCESSRECEIVED14 October 2022REVISED28 November 2022ACCEPTED FOR PUBLICATION1 December 2022PUBLISHED15 December 2022Original content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.PAPERCharge transport in single polymer fiber transistors in thesub-100 nm regime: temperature dependence and CoulombblockadeJakob Lenz1, Martin Statz2, K Watanabe3, T Taniguchi4, Frank Ortmann5 and R Thomas Weitz1,2,6,∗1 AG Physics of Nanosystems, Faculty of Physics, Ludwig-Maximilians-University Munich, Munich, Germany2 1st Institute of Physics, Faculty of Physics, Georg-August-University, Göttingen, Germany3 Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4 International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan5 School of Natural Sciences, Department of Chemistry, Technical University of Munich, 85748 Garching b. München, Germany6 International Center for Advanced Studies of Energy Conversion (ICASEC), University of Göttingen, Göttingen, Germany∗ Author to whom any correspondence should be addressed.E-mail: thomas.weitz@uni-goettingen.deKeywords: organic semiconductor, organic electronics, charge transport, Coulomb blockadeSupplementary material for this article is available onlineAbstractEven though charge transport in semiconducting polymers is of relevance for a number ofpotential applications in (opto-)electronic devices, the fundamental mechanism of how charges aretransported through organic polymers that are typically characterized by a complex nanostructureis still open. One of the challenges which we address here, is how to gain controllable experimentalaccess to charge transport at the sub-100 nm lengthscale. To this end charge transport in singlepoly(diketopyrrolopyrrole-terthiophene) fiber transistors, employing two different solid gatedielectrics, a hybrid Al2O3/self-assembled monolayer and hexagonal boron nitride, is investigatedin the sub-50 nm regime using electron-beam contact patterning. The electrical characteristicsexhibit near ideal behavior at room temperature which demonstrates the general feasibility of thenanoscale contacting approach, even though the channels are only a few nanometers in width. Atlow temperatures, we observe nonlinear behavior in the current–voltage characteristics in the formof Coulomb diamonds which can be explained by the formation of an array of multiple quantumdots at cryogenic temperatures.1. IntroductionOrganic (semi-)conducting polymers are of significant scientific and technological interest due to their usein organic solar cells, light emitting diodes, batteries, neuromorphic devices, sensors and field-effecttransistors. Despite this manifold of existing and potential applications, the fundamental question of howcharges are transported through conductive polymers requires further investigation due to the complexstructure-property relation between local morphology and charge conduction. A significant problem in thisrespect has been to locally identify the relative role of the main contributing factors towards the conductivity,namely the inter- and intrachain charge transport. Intrachain transport critically depends on the conjugationlength, which in turn depends on the chain rigidity. The interchain mobility on the other hand depends onthe π–π overlap of adjacent repeat units, and is enhanced in crystalline regions of polymer assemblies. Therelative weights of intra- and interchain transport in turn depend critically on the paracrystallinity of thepolymer film that is typically composed of nanoscale crystalline regions connected via amorphous regions,whereas in the latter the so-called tie chains are located [1]. Their importance as conductive highwaysconnecting nanocrystalline regions of the polymers has been highlighted extensively [1–3]. Recently it wasalso found that additionally, nominally non-conductive parts can support conductivity via providing© 2022 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2515-7639/aca82fhttps://crossmark.crossref.org/dialog/?doi=10.1088/2515-7639/aca82f&domain=pdf&date_stamp=2022-12-15https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0001-7791-3981https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-5884-5749https://orcid.org/0000-0001-5404-7355mailto:thomas.weitz@uni-goettingen.dehttp://doi.org/10.1088/2515-7639/aca82fJ. Phys. Mater. 6 (2023) 015001 J Lenz et altunneling pathways [4]. A summarized overview of charge transport mechanism in polymericsemiconductors at the nanoscale can be found in our recent review [5].Not only the nanoscale morphology of polymer thin films is complex, but also the interaction betweencharges travelling through the films and the molecular structure (polaron formation) and the Coulombinteraction between charges itself [6–8]. A viable route to study the structure-performance relationship hasbeen via electrostatically-gated thin-film field-effect transistors, that allow the investigation of chargetransport mechanisms as function of polymer morphology and charge carrier density, while charge transportis typically studied at the macroscale with lateral device dimensions well above 1 µm [9]. This has allowed toadvance our understanding of charge transport significantly despite the indirect nature of suchmeasurements. To allow for a more direct access to local charge transport, we have developed a contactingscheme that enables accessing the hard-to-probe sub-100 nm local transport regime.To develop the local probe scheme, we focus on a model organic semiconductor, namely thesemiconducting donor–acceptor copolymer poly{2,2′-[(2,5-bis(2-hexyldecyl)-3,6-dioxo-2,3,5,6-tetrahydropyrrolo[3,4-c]pyrrole-1,4-diyl)dithiophene]-5,5′-diyl-alt-thiophen-2,5-diyl} (PDPP,Mn = 4.1E+ 4 g mol−1) which is known to be a good hole conductor in organic solar cells [10], and hasshown excellent performance in thin film transistors [11, 12]. For example, charge-carrier densityindependent field-effect mobilities of up to 3 cm2 V−1s−1 (with quadratic (γ = 2 [13]) relation of ID toVGS–Von at lower temperatures; a clear indication of trap-free charge transport) as well as excellent stabilityunder ambient conditions was demonstrated. Furthermore, PDPP also showed performance when measuredin bulk films at the nanoscale in a vertical geometry, in which electrical transport at distances below 10 nmcould be realized. There, it was found that if thin nanoscale films are gated by an electrolyte, unexpectedlyultra-high current densities of MA cm−2 can be realized [14, 15]. However, this geometry was still relying onnanometer-thin films of the PDPP polymer or on thin films of multiple crystalline fibers. These crystallinefibers are a few nanometers in height and several hundreds of nanometers in length and are composed ofagglomerates of individual polymer chains that are aligned along the long axes of the fibers. These fibers canbe aligned e.g. by doctor blading into macroscopically aligned films [16]. In such films it was identified byoptical spectroscopy and x-ray diffraction measurements that the individual polymer chains are alignedalong the long axis of the fibers. [16] The possibility to deposit such polymer fibers provides the excitingperspective to be able to measure charge transport along individual crystallites. However, up to nowcontacting such individual fibers has not been demonstrated.2. Results and discussionTo study charge transport at the nanoscale, we employ a field-effect transistor geometry with a solid gatedielectric. This has the advantage with respect to electrolyte gating of allowing to study temperature-dependent charge transport as a function of charge carrier density for both electron and hole transport,thereby allowing to identify different charge transport mechanisms and regimes. In order to still realizewell-functioning transistors, special care had to be taken to maintain sufficient gate coupling to remainwithin the gradual channel approximation. This can be realized by decreasing the gate dielectric thicknessand by using high-k gate oxides. We investigate single fiber transistors with channel lengths below 100 nmusing two different gate/gate dielectric configurations, schematically depicted in figures 1(a) and (b). First, ahybrid 10 nm Al2O3 gate dielectric with a self-assembled monolayer (SAM) made of 1-tetradecylphosphonicacid (TDPA) (thickness dTDPA = 1.74 nm [17]) was used. The chemical modification of the oxide surfaceresults in a passivation of the gate-oxide due to the high packing density of the formed SAM [18, 19]. Theimproved electrical characteristics with a reduction of traps at the oxide– organic semiconductor (OSC)interface, reduced leakage currents and the tunability of the threshold voltage (V th) has been widelyinvestigated [20–23]. In a second approach we used hexagonal boron nitride (hBN) with high breakdownvoltages ranging from 0.8 [24] to 1.2 V nm−1 [25] as a dielectric. In the field of two-dimensional materials,using hBN both as a dielectric substrate or to completely encapsulate graphene is well established and hasshown to drastically increase the electrical characteristics in terms of increased mobility and reduced chargedisorder [26–29], which is mainly related to a reduction of surface charge traps. However, in the field ofOSCs, there are only a few reports demonstrating the potential of hBN as a dielectric to facilitate improvedcharge transport properties yet [30–32]. In order to maintain the atomical flatness of hBN, graphiteconsisting of several graphene layers was used as gate electrode and contacted with an additional gold lead.After gate electrode fabrication and solution-based single PDPP fiber deposition, individual fibers werelocated via atomic force microscopy (AFM) (see figure 1(c) for Al2O3/TDPA and supplementary figure 1 forhBN) and finally precisely contacted via electron beam lithography. Further details can be found in theexperimental section. Line traces in figure 1(d) of two different fibers reveal heights of 2 nm and 3 nm,respectively, which demonstrates that even the thinnest agglomerates that we can identify using AFM consist2J. Phys. Mater. 6 (2023) 015001 J Lenz et alFigure 1. Single PDPP fiber transistor. Schematic illustration of the device geometry with (a) a hybrid Al2O3/TDPA gate dielectricand (b) an hBN dielectric with graphite electrode configuration. (c) AFM image of PDPP fibers deposited on Al2O3/TDPA.(d) Line traces across two different fibers reveal thicknesses of 2 nm and 3 nm. (e) SEM image of the same region of an electricallycontacted fiber displays fibers that are not resolvable with AFM (indicated by red arrows).of multiple polymer chains. This is confirmed in the scanning electron microscopy (SEM) image of anelectrically contacted fiber in figure 1(e), in which also smaller fibers not resolvable via AFM become visible.Hence, the term ‘single fiber’ refers to individual fibers consisting of several well aligned parallel polymerchains, schematically illustrated in supplementary figure 2 and confirmed by [16]. Even though acomparison of the AFM image after fiber deposition and the SEM image after contact patterning indicatesthat PDPP is not affected by the electron beam lithography process (poly(methyl methacrylate) (PMMA)deposition, 120 ◦C soft bake, lift-off in acetone and isopropanol)(see experimental section), small damage or conformational changes cannot be fully excluded.Figure 2 shows the room-temperature electrical characteristics of single PDPP fiber transistors witheither Al2O3/TDPA or hBN as a dielectric. In the case of Al2O3/TDPA (figures 2(a) and (b)), despite achannel length of only 56 nm, the output curves exhibit fully saturating currents indicating the good gatecoupling. The increasing offset for VDS = 0 V is related to an increasing gate-leakage current for higher VGS.The saturation transfer characteristics reveal an on-off ratio of 6000 and a subthreshold swing of250 mV dec−1 with a threshold voltage of V th =−0.89 V. The weakly VGS and hence carrier-density-dependent hole mobility (see supplementary figure 3(a)) of µsat ≈ 0.3 cm2 V−1 s−1 (at VGS =−1 to−1.5 V)for an assumed channel width ofW = 3 nm (fiber diameter) is quite high given that wet processing of thefibers was used, but is a factor of 10 lower compared to macroscopic devices with channel lengths of 200 µm[33]. In the case of hBN as dielectric, the output curves exhibit saturating behavior for a channel length of67 nm (figure 2(c)) and even start to saturate for channel lengths of only 25 nm (figure 2(e)). It has to benoted that the saturating behavior might also be influenced by a decreasing gate current IG for increasingVDS (especially for the device in figure 2(c)). While for the single fiber in figure 2(d), a mobility ofµsat = 8× 10−3 cm2 V−1 s−1 (at VGS =−4.75 to−5.75 V) can be extracted, the mobility of the device in3J. Phys. Mater. 6 (2023) 015001 J Lenz et alFigure 2. Electrical characteristics of single PDPP fiber transistors. (a) Output and (b) transfer characteristics in the saturationregime (black) with corresponding gate current IG (red) on an Al2O3/TDPA hybrid gate dielectric (channel length Lch = 56 nm,Tset = 300 K) (c), (d) electrical characteristics on hBN with a thickness of dhBN = 8 nm (Lch = 67 nm) and (e), (f) with a thicknessof dhBN = 11 nm (Lch = 25 nm). The real sample temperature was lower due to poor thermal coupling (see experimental sectionfor further explanation). The solid lines represent the forward and the dashed lines the backwards sweep direction.figure 2(f) exhibits no VGS independent region (see supplementary figure 3(a)). Additionally, when hBN isused as gate dielectric, ambipolar transport can be observed (see also figure 3).While it is remarkable that using comparably crude e-beam patterning and solvent processing tools,nanoscale transistors consisting of individual polymer nanofibers can be fabricated, the charge carriermobility in these transistors is smaller than in thin film transistors made from the same polymer [33]. Whilewe fabricated the transistors with the hope to reach the intrachain transport regime (which should allow forsignificantly higher charge carrier mobility), the reason for the lower mobility is unclear. One potentialreason could be contact resistance that would explain the comparably very large required VDS values fortransport. Another explanation could be that in macroscopic devices charge transport is an average effect ofdifferent efficient conduction paths where always paths of highest conductance can form, compared to singlefiber transistors where transport is strongly restricted and by chance we have not contacted fibers witha-priori low energetic disorder and hence good charge transport.To understand in more depth the charge transport processes in our devices, we have reverted to analyzingthe temperature dependence of the mobility [5]. Figure 3 shows the electrical characteristics of a single PDPPfiber transistor on hBN for 300 K and 10 K. Interestingly, when using hBN as a gate dielectric, ambipolarcharge transport could be observed even at cryogenic temperatures (see also supplementary figure 4 foranother device). One of the major requirements that has to be ensured to realize ambipolar charge transportin organic field-effect transistors is a trap-free gate dielectric [34, 35]. The observation of ambipolartransport elucidates the high potential of using hBN as a gate dielectric also in the field of organic electronics.With decreasing temperature, the threshold voltage V th in the transfer characteristics shifts to more negativevalues for VGS < 0 and to more positive values for VGS > 0, can be explained by the filling of shallow anddeep trap states [36, 37]. While the mobility decreases significantly with decreasing temperature for smallerdrain-source voltages VDS (see supplementary figure 5), its temperature dependence is less pronounced forhigher positive and negative VDS (figures 3(c) and (d)). As the devices might suffer from large contactresistances it would be very helpful to be able to extract the contact resistance in a reliable manor. Sincehowever our devices only work in the saturation regime, methods that have been used to extract contactresistances like e.g. the Y-function method [38] are not applicable. Consequently, four-point probemeasurements or saturation transfer measurements that maintain the channel pinch-off at the drain contact4J. Phys. Mater. 6 (2023) 015001 J Lenz et alFigure 3. Transfer and mobility characteristics of a single PDPP fiber transistor on hBN (dhBN = 25 nm) at Tset = 300 K (black)and Tset = 10 K (red). (a), (b) Electrical measurements for VDS =−5 V and (c), (d) electrical measurements for VDS = 5 V. Thesolid lines represent the forward and the dashed lines the backwards sweep direction. The corresponding gate current IG is shownin grey for Tset = 300 K and bright red for Tset = 10 K. The mobility is only shown for |Von|≤ |VGS|, where |ID|⩾ |IG|.(VDS = VGS− V th) would be necessary to further elaborate on the temperature dependent mobility behavior[39].Here it should be emphasized that the presented results are not a macroscopic average measure. In fact,due to the individuality of each device, where e.g. small deviations in the fiber composition, different channellengths, variations in gate coupling or contact effects strongly influence the electrical characteristics, eachdevice has to be treated separately. Apart from the above weakly temperature dependent mobility fromT = 300 K to T = 10 K at high VDS, some devices also exhibited strongly thermally activated transport with atransport freeze-out at lower temperatures (see supplementary figure S6). Interestingly, for some devices thetransport starts to deviate from the behavior at elevated temperatures by the formation of plateaus in the firstplace when cooling down, as indicated in supplementary figure 5(a) for 10 K. If the system is cooled downfurther, the transport in these quasi 1D-systems starts to oscillate, which is indicative of Coulomb physics.The evolution of these Coulomb oscillations can be seen in supplementary figure 7. The I–V curves ofanother device at base temperature (T = 5.5 K) in figure 4(a) exhibit several irregularly spaced current peakswith varying amplitudes, highlighted with black arrows. Furthermore, it can clearly be seen that the gatecurrent noise (red curve) has no influence on the measured oscillations. Figures 4(b) and (c) show thecorresponding current and differential conductance ∂ID/∂VGS maps as a function of VGS and VDS. Thecurrent is blocked in the dark blue region in a range of |VDS|⪅ 0.6 V. At small VDS and sufficiently smalltemperatures, the energy needed to add an extra charge carrier to an at least in one direction restricted system(single fibers in our case), can be larger than the thermal energy. In this case, the number of charge carriers inthe system is fixed and charge transport through the system is blocked, which refers to Coulomb blockade.Upon varying VGS and VDS, the chemical potential inside the system respectively of the drain electrode canbe tuned, resulting in state configurations, where charge carries can tunnel through the system. Hence, thenumber of charge carriers can fluctuate and transport is allowed. Each of these resonances at specific VGS5J. Phys. Mater. 6 (2023) 015001 J Lenz et alFigure 4. Coulomb blockade measurements at T = 5.5 K on Al2O3/TDPA. (a) Exemplary transfer characteristics with draincurrent ID (black) and gate current IG (red) for VDS = 0.35 V. (b) Corresponding (VGS,VDS)-current map and (c) differentialconductance ∂ID/∂VGS as a function of VGS and VDS. Two Coulomb diamonds of different size are indicated by white lines.Excited states are highlighted by blue dashed lines. (d) Schematic representation of charge transport through single PDPP fibersin the picture of single isolated QDs.and VDS values causes two straight lines in the ∂ID/∂VGS maps separating regions where current is blockedand allowed, resulting in typical Coulomb diamonds. Although indications of Coulomb blockade physics hasbeen identified in polymer nanofibers [40, 41] and OSC thin film devices [42, 43], Coulomb diamonds haveonly been presented for single molecule [44–46] devices in the field of organic materials. Here we present thefirst observation of Coulomb diamonds for larger than single molecule organic devices. The clearly visibleCoulomb diamonds are irregular and exhibit different sizes and shapes, which results from a superpositionof different sized Coulomb diamonds with addition energies ranging from Eadd = 0.56 eV to 0.63 eV.In the ∂ID/∂VGS map, various excited states are visible as lines running parallel to the Coulomb diamondedge, some of them highlighted by blue dashed lines. In general, aside from addition energies, stabilitydiagrams can also be used for spectroscopic investigations to explore excited states which emerge additionallyto the ground state configuration [47]. These excited states can be electronic or vibrational in nature. A prioriwe can only speculate about the origin of the observed excited states here. Although they do not appear verysharp, excitation energies varying from Eex = 0.17 eV to 0.28 eV can be estimated. For similar polymersBarszcz et al [48] identified the C–C stretching vibration of thiophene rings at≈0.173 eV and the in-phaseC=C stretching of the DPP core at≈0.2 eV. Similar results have been presented by Adil et al [49], Franciset al [50] and Dorfner et al [51]. If we assume coupling to the phonon modes as the origin for the excitedstates, these results compare very well with the electrically measured results in this work, which proves thatexcited states can be investigated also for OSCs via charge transport measurements. To do so, further deviceoptimization as e.g. further reducing the channel length or contacting thinner fibers, would be necessary inorder to get sharper diamond edges as well as lines induced by excited states. It has to be noted that theexcited states are only visible on one side of the Coulomb diamond for positive slopes which is related toasymmetric coupling and hence different tunnel barriers for the source and drain electrode [47, 52]. Theasymmetric coupling is also evident from the sheared diamonds. The different tunnel barriers are evidentfrom supplementary figure 8. Upon exchanging the source and drain electrodes in two consecutivemeasurements, the size, shape and position of the Coulomb oscillations change.6J. Phys. Mater. 6 (2023) 015001 J Lenz et alIn all measurements the Coulomb diamonds are not closed near VDS = 0 V (see supplementary figure 9for another example). The occurring gap in addition with different sizes and shapes of the diamonds hasbeen widely investigated [53–58] and is caused by an array of single quantum dots (QDs) with multipletunnel junctions, schematically illustrated in figure 4(d) [40]. Within a single fiber, composed of severalPDPP polymer chains, when cooling down several different conduction paths between different chains withenergetic disorder-broadened polaronic states are available. In a schematic representation, one path ofhighest conductance is formed between several QDs. These different QDs with different capacitances areconnected via tunnel barriers. Transport is then dominated by the junction with the largest barrier withinthis path of highest conductance. Since individual diamonds are distinguishable in the ∂ID/∂VGS maps, thenumber of conduction paths as well as the number of QDs in the channel is very small. The size of thesmallest QDs, which dominates the electrical characteristics, can be estimated by comparing the backgatecapacitance Cbg and the geometrical capacitance Cgeom for nanowires (see supplementary information for adetailed description). For the device in figure 4(d), this leads to a QD length of LAl2O3/TDPA = 7.3 nm.Considering a small number of QDs in the channel, this value is in good agreement with a channel length of27 nm. For hBN as dielectric (see supplementary figure 10) the current is blocked in a range of |VDS|⪅ 1 V inthe dark blue region. However, the Coulomb diamonds are less regular and hence only partially visible in the∂ID/∂VGS map. The addition energies varying from Eadd = 1.1 eV to 1.8 eV as well as the gate voltage periodof the Coulomb oscillations∆VG are increased compared to the devices with Al2O3/TDPA as a dielectric.These observations coincide with the estimated QD size of LhBN = 1.4 nm for a channel length of 24 nm. Onepossible explanation could be that the different surface energies of hBN and TDPA (defined by differentcontact angles of 115◦ for TDPA [59] and 135◦ [60] for hBN) might lead to different fiber compositions withdifferent sized quantum dots. Further potential reasons for the formation of larger QDs in the PDPP fiberson the hybrid Al2O3/TDPA dielectric could be related to reduced energetic disorder [61], potentially reduceddipolar disorder [62] due to the lower dielectric constant of TDPA compared to hBN [26, 63], or a differentdegree of crystallinity, within the transport path of highest conductance [7, 8]. This explanation is inagreement with the substantially higher mobilities observed in the PDPP fibers on the hybrid dielectric. Todisentangle the influence of energetic disorder and different degrees of crystallinity on charge transport andhence QD sizes, further structural, spectroscopic and electrical transport measurements are required. Withsuch additional measurements a direct correlation between QD sizes and the polaron coherence lengthscould be established [3].The transfer characteristics at room temperatures in figures 2 and 3 exhibit a clear off-state in the regionaround VGS = 0 V, which is related to the band gap of Egap ≈ 1.8 eV of PDPP. Usually one would expect azero-current region in the current maps with N = 0 charge carriers in the QD, reflecting the semiconductinggap corresponding to the off-current VGS region of the transfer curves. This has been successfullydemonstrated for carbon nanotube QDs [64, 65]. The tendency of a full depletion with an emptied QD canbe seen to some extent in supplementary figure S11. In all other devices however this behavior was notobservable. One possible explanation could be that at elevated temperatures, charge transport is dominatedby thermally excited charge carriers. When cooling down, more and more charges are trapped in localizedstates resulting in reduced currents (see supplementary figure S7 T = 300 K to T= 100 K). One possibleexplanation for the occurring oscillations in the off-current region for high temperatures could be thatinstead of the classical Coulomb blockade regime, our devices operate in the quantum Coulomb blockaderegime [66]. Here, once entering the quantum regime, the intensity of Coulomb oscillations increases withdecreasing temperature. In other words, Coulomb oscillations might become visible in the off-region onlywhen cooling down the system. Presumably for most devices, a complete emptied fiber cannot be achieveddue to the priorly dielectric breakdown when increasing VGS. In order to investigate this in more detail andespecially to differentiate between the classical and the quantum Coulomb blockade regime, however, furthermeasurements would be beneficial.3. ConclusionIn conclusion, we fabricated single polymer fiber transistors with channel lengths below 100 nm andinvestigated charge transport dynamics from room to cryogenic temperatures. Utilizing ultrathinAl2O3/TDPA respectively hBN gate dielectrics resulted in almost ideal electrical characteristics despite suchshort channel lengths. Although the devices suffer from large contact resistances resulting in reducedmobilities compared to macroscopic devices, temperature dependent measurements indicate a weaklytemperature-dependent mobility for large VDS from T = 300 K to T = 10 K. For some devices at very lowtemperatures, the transport in these quasi-1D systems can be attributed to Coulomb blockade effects due tothe observation of Coulomb oscillations and Coulomb diamonds. It was shown that the fiber consists of anarray of multiple QDs which are separated by tunnel barriers. In addition, we demonstrated that by further7J. Phys. Mater. 6 (2023) 015001 J Lenz et aldevice optimization excited states could be investigated by charge transport measurements. Ourmeasurements show that nanoscale contacting can be a viable tool to address charge transport at thenanoscale in semiconducting polymers relevant in organic photovoltaics and field-effect transistors.4. Experimental sectionTo avoid degradation of the PDPP polymer all fabrication steps involving exposure to ambient conditionswere performed in an ozone cleaned atmosphere.4.1. Electrode fabricationAll structures were patterned by electron beam lithography (e-line system, Raith) using the followingparameters: 10 kV, 108 µC cm−2 for 10 µm, 145 µC cm−2 for 30 µm and 165 µC cm−2 for 60 µm aperture.A 4.5 wt.% solution of the positive-resist PMMA 950 k dissolved in anisole (AR-P 672.045, Allresist) was spincoated at 800 rpm for 1 s and 4000 rpm for 30 s followed by a 3 min 150 ◦C bake (5 min at 120 ◦C for topcontacts to prevent thermal damage of PDPP). The exposed structures were developed in a 1:3 solution ofmethylisobutylketon:isopropanol for 1 min 45 s. For structures smaller than 100 nm, a high-contrastdeveloper with the addition of 2% methylethylketone was used [67]. The gate electrodes were formed viaelectron-beam physical vapor deposition of 1 nm Cr (@ 0.3 Å s−1) and 30 nm Au (@ 1 Å s−1) at pressures<5× 10−7 mbar. Top contacts on PDPP were fabricated through thermal evaporation of 0.3 nm titanium(at 0.1 Å s−1) and 30 nm gold (at 1 Å s−1) at a pressure of∼5× 10−6 mbar.4.2. Al2O3/TDPA gateAfter patterning the local Au gate contacts, 10 nm of Al2O3 was deposited on the whole substrate viaradiofrequency (RF) sputtering (40 W, Ar pressure of 2× 10−2 mbar). In a next step, the TDPA SAM waslocally deposited (areas patterned by electron beam lithography) on the prefabricated gate electrodes byinitially applying a 1 min oxygen plasma (ICP-RIE, Plasmalab System 100, Oxford Instruments, RF power of200 W, IPC power of 70 W, a O2 flow of 30 sccm and a pressure of 10 mTorr) followed by immediatelyimmersing the sample in a 1 mM solution of TDPA in isopropanol for 2 h. Finally, the substrates were bakedfor 5 min at 150 ◦C.4.3. hBN gate with graphite electrodeFew-layer hBN and graphene were fabricated on pre-cleaned and hydrofluoric acid etched substrates bymechanical exfoliation from the bulk material. The detailed procedure for few-layer hBN as well as adescription of the stamp fabrication can be found in the methods section of our previous work [15].Graphene exfoliation is completely analogous with the only difference of using directly the as-receivednatural graphite bulk instead of crushed small crystals. In order to fabricate hBN gates with graphiteelectrodes a stamping method was adopted from [68, 69]. A detailed description can be found in thesupplementary information. The graphite gate contact is contacted with gold in an additional electron beamlithography step.4.4. Single PDPP fiber depositionSingle PDPP fibers on a local Al2O3/TDPA gate were deposited by immersing the sample overnight in a0.02 wt.% solution of PDPP in 1,3-meta-dichlorobenzene at room temperature. The solution was previouslystirred at least for 6 h at 80 ◦C. The sample was blow-dried with nitrogen and baked for 5 min at 80 ◦C.Single PDPP fibers on hBN were deposited in two different ways. One approach is completely analogousas above with the exception that a 0.2 wt.% solution was used. In another approach a 0.05 wt.% solution wasdrop casted on the substrate. Subsequently the droplet was slowly blown over the hBN-graphite stack withnitrogen, resulting in a very thin remaining layer of the PDPP solution. The sample was dried at roomtemperature and subsequently baked for 5 min at 80 ◦C.4.5. Electrical characterizationMeasurements were performed in a Lakeshore CRX-VF probe station under vacuum (temperature range5 K–450 K). Electrical contacting is realized via needle probes. In order to ensure sufficient thermalanchoring the substrates were glued with silver-conducting paint on the substrate holder of the probestation. However, some devices were only placed on the cooled chuck without silver-conducting paint. Here,at elevated temperatures, the real temperature of the sample is smaller than the setpoint temperature Tset dueto the contacted probes with a temperature of 10 K−15 K and a bad thermal contact of the sample to thechuck, resulting in a temperature offset of up to 50 K for a setpoint temperature of Tset = 300 K. Whilequantitative data evaluation is not possible in these cases, qualitative statements are still valid. The gate8J. Phys. Mater. 6 (2023) 015001 J Lenz et alvoltage VGS was applied with a Keithley 2450 and the gate current IG simultaneously measured. The drainvoltage VDS was applied with a Yokogawa 7651 DC source. To allow highly accurate current measurementsdown to the sub-nA regime the drain current ID was measured with a current preamplifier (1211 DLInstruments) and a HP 34401 A voltmeter.Data availability statementThe data that support the findings of this study are available upon request from the authors.AcknowledgmentsJ L and R T W acknowledge funding from the Center for Nanoscience (CeNS) and the SolarTechnologies goHybrid (SolTech) initiative. We additionally acknowledge funding by the Deutsche Forschungsgemeinschaft(DFG, German Research Foundation) under Germany’s Excellence Strategy ‘EXC 2089 /1−390776260(e-conversion)’. K W and T T acknowledge support from JSPS KAKENHI (Grant Nos. 19H05790 and20H00354).Author contributionThe experiments were conceived and designed by J L and R T W, J L prepared the samples, conducted themeasurements and data analysis. All authors discussed the results. M S helped with the data analysis. J L, M Sand R T W wrote the manuscript with the input of all authors. R T W supervised the project. K W and T Tsynthesized the hBN crystals.ORCID iDsMartin Statz https://orcid.org/0000-0001-7791-3981K Watanabe https://orcid.org/0000-0003-3701-8119Frank Ortmann https://orcid.org/0000-0002-5884-5749R Thomas Weitz https://orcid.org/0000-0001-5404-7355References[1] Noriega R, Rivnay J, Vandewal K, Koch F P V, Stingelin N, Smith P, Toney M F and Salleo A 2013 Nat. 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Introduction 2. Results and discussion 3. Conclusion 4. Experimental section 4.1. Electrode fabrication 4.2. Al2O3/TDPA gate 4.3. hBN gate with graphite electrode 4.4. Single PDPP fiber deposition 4.5. Electrical characterization References