Microscopic observation of efficient charge transport processes across domain boundaries in donor-acceptor-type conjugated polymers

Backbone rigidity of conjugated polymers is suggested to play an essential role in realizing high-mobility transistors through the efficient interconnection of crystalline domains by tie molecules as discussed for the recently-developed donor-acceptor (DA)-type copolymers. However, no studies have directly observed interdomain hopping in these DA copolymers. Here, highly-efficient interdomain charge transport is observed in two typical high-mobility DA copolymers from the microscopic observation of charge carriers using field-induced electron spin resonance (ESR) spectroscopy. The in-plane ESR signal exhibits a clear motional narrowing effect associated with the carrier motion across the boundaries. The activation energy of the interdomain charge motion is as low as that of intradomain motion (~10 meV), both of which are clearly lower than those observed in the conventional semicrystalline polymer. The structural origin of this efficient interdomain electrical connection is the rigid, nearly torsion-free backbone conformation of the tie molecule, as demonstrated from density functional theory calculations. Donor-acceptor-type conjugated polymers are expected to be a promising candidate for high mobility materials in flexible electronic devices such as thin film transistors. Using field-induced electron spin resonance spectroscopy and density functional calculations, the authors investigate the highly-efficient interdomain charge transport in two typical high-mobility donor-acceptor copolymers.

C onjugated polymers have been extensively investigated as materials for low-cost, light-weight, and flexible electronic devices, such as thin-film transistors (TFTs). In general, charge transport in polymer thin films is highly susceptible to structural/energetic disorders, which are inevitably introduced into the films and/or device interfaces [1][2][3][4][5][6][7] . Thus, suppression of these disorders has been a major subject for improving the mobility of polymeric TFTs. From a materials perspective, the use of semicrystalline-conjugated polymers, such as poly(3-hexylthiophene) (P3HT) and poly(2,5-bis(3-alkylthiophene-2-yl) thieno [3,2-b]thiophene) (PBTTT, Fig. 1a), has been a major approach for this purpose [8][9][10][11] . In these materials, large crystalline domains with edge-on molecular orientations are formed within the film, as schematically illustrated in Fig. 1b. Nearly twodimensional charge delocalization is expected within these crystallites through the π−π stacking network, resulting in high TFT mobilities up to 1 cm 2 V −1 s −1 (refs. 10,12 ). However, even in these semicrystalline materials, positional disorders of the molecules within the crystallite are still non-negligible, producing charge trapping sites 13,14 . Furthermore, domain boundaries between adjacent crystallites, as well as amorphous regions surrounding the crystallites, can also be a major source of charge trapping, although the presence of tie molecules improves the electrical connectivity of the domains with different chain alignments within the film [15][16][17][18][19][20] .
In recent years, the emergence of another design principle of high-mobility materials has attracted considerable research interest [21][22][23] . Several groups of conjugated copolymers with donor-acceptor (DA)-type alternating backbones have exhibited surprisingly high mobilities exceeding 1 cm 2 V −1 s −1 without forming long-range ordered crystalline domains [24][25][26][27][28][29][30][31][32][33][34][35] . Even some of these polymers take face-on orientations and/or mixed edge-on and face-on orientations to the substrate, which are apparently disadvantageous for efficient charge transport through the transistor channel according to the above design principle for semicrystalline polymers. Through various structure-property studies, some key characteristics that enable charge transport that is resilient against structural disorders have been revealed for these DA copolymers. Among these characteristics, a rigid and nearly torsion-free backbone structure plays a crucial role in high mobilities; a long, highly planar polymer backbone without folding enables both nearly trap-free charge transport along the chain [36][37][38] and efficient interchain charge transfer through the strong π-π interaction between adjacent D-A subunits 23,24,36 , thus improving the intrinsic charge transport within the ordered domains. In addition, this structural feature seems to be advantageous for interdomain transport through the efficient electrical connection of the domains by rigid tie molecules 39 . However, the above discussion is mostly based on the structural characterization or modeling of the polymer backbones and films [21][22][23][36][37][38]40,41 , and almost no direct observations of intradomain and interdomain charge transports have been reported in DA copolymers. To clarify the detailed charge transport mechanism and the complex structure-property relationship in DA copolymers, it is indispensable to understand the relationship between the microscopic structure and the carrier dynamics in these materials.
Field-induced electron spin resonance (FI-ESR) spectroscopy is a particularly suitable method for this purpose because it can sensitively detect charge carriers injected into the TFT devices, providing a variety of microscopic information which is crucial to understand the charge transport process at the insulator interface [42][43][44][45][46][47][48][49] . For example, local molecular orientation at the interface can be determined from the angular dependence of the g value. Furthermore, thermal carrier motion in thin films is directly reflected on the temperature dependence of the ESR linewidth and the line shape through the motional narrowing effect, providing a key to clarify the microscopic transport properties. Matsui et al. 50 have demonstrated that two types of motional narrowing effects are observed in polycrystalline thin films of PBTTT depending on the applied magnetic field directions, i.e., the narrowing due to the intradomain and interdomain carrier motions. In the case of uniaxially oriented molecules along the substrate normal, such as PBTTT in thin films, the former narrowing case is observed when the magnetic field (H) is perpendicular to the substrate (H ⊥ configuration), whereas the latter case is observed when H is applied parallel to the substrate (H // configuration). In the case of PBTTT, the interdomain carrier hopping gives the same activation energy as that of the mobility, strongly indicating that the macroscopic charge transport is limited by domain boundaries in this system. Similar boundarylimited charge transport has also been reported for the TFTs of polycrystalline small molecules 50,51 . The direct evaluation of interdomain carrier motion similar to that described above can be a powerful method to confirm the interconnectivity of the domains in recently developed high-mobility DA copolymers.
In the present study, we demonstrate that diketopyrrolo-pyrrole (DPP)-based DA copolymers shown in Fig. 1a, with a thiophenevinylene-thiophene (TVT) donor unit (DPP-TVT) 32,34,35 and with thiophene (T)-thieno[3,2-b]thiophene (TT) donor units (DPPT-TT) 28-31 , indeed exhibit highly efficient charge carrier motions, as indicated by observing the temperature dependence of the FI-ESR linewidths. The former polymer takes a highly ordered lamellar structure, as in the case of semicrystalline polymers 32 , whereas the latter polymer takes less crystalline structures if the film is treated below 150°C 28-31 . We observed a clear motional narrowing effect associated with the intradomain carrier motion down to 4 K in the H ⊥ configuration. For the H // configuration, the linewidth analyses based on the density functional theory (DFT) calculation of the g values show a clear signature of signal averaging associated with the interdomain carrier motion occurring down to at least 70 K. This efficient interdomain electrical connection should be realized by the rigid, nearly torsion-free backbone conformation, as demonstrated by the structural modeling with the DFT calculation.

Results
Device performance. Figure 2 shows the results of transistor characteristics of the present DPP-based copolymers. Here, we adopt a top-gate device geometry with parylene gate insulators, as schematically illustrated in Fig. 2a, to avoid any operational instabilities, such as the gate-bias-stress effect 52,53 . We adopt an long rectangular substrate with dimensions of 3 mm × 30 mm, by which simultaneous measurements of the transistor characteristics and the FI-ESR measurements can be performed within the ESR sample tube 42,47 . In order to avoid the deterioration of the Q-factor of the ESR cavity, the thickness of the gate/source/drain electrodes was designed less than the skin depth of the microwave and the contacts and wirings were made at an end of the substrate, which is out of the sensitive part of the ESR cavity. The insulator film was formed on top of the polymer film using a chemical vapor deposition (CVD) method. This process does not affect the crystalline molecular order of the DPP-TVT film, as confirmed by the grazing-incidence X-ray diffraction (GIXD) pattern taken before and after the parylene deposition, as shown in Supplementary Fig. 1 and Supplementary Note 1. By using the above device structures, both polymer TFTs exhibit standard transfer and output characteristics as shown in Fig. 2b and c, respectively, for the DPP-TVT device and Fig. 2d, e, respectively, for the DPPT-TT device. The linear mobilities extracted from the transfer characteristics are μ~0.1 cm 2 V −1 s −1 for both as-grown DPP-TVT and DPPT-TT devices, whereas higher mobilities of0 .2 cm 2 V −1 s −1 are reproducibly obtained in the DPP-TVT device annealed at 200°C, which is consistent with the improved crystallinity 32 , as confirmed in the present study ( Supplementary  Fig. 1b).
FI-ESR measurements. Figure 3a, b shows the FI-ESR signals obtained for the PBTTT and DPP-TVT TFTs under the negative gate voltage (V g ) of −100 V at 150 K. The background signals observed in the off state (V g = +30 V) are subtracted from the signals in the on state. We observe clear FI-ESR signals of positive charge carriers (polarons) accumulated at the polymer/insulator interface. These signals exhibit clear anisotropies with respect to the applied magnetic field direction. In the case of PBTTT, a single ESR signal is observed in the H ⊥ configuration, whereas a doubly split signal is observed in the H // configuration. This feature is typical of the edge-on-oriented molecules with an orthorhombic g anisotropy; 50 the doubly split signal in the H // configuration comes from the difference in the resonance magnetic field H 0 (H 0 = hν/gμ B ; h: Plank's constant, ν: microwave frequency, and μ B : Bohr magneton) due to the g anisotropy of g z and g y , whereas the single ESR signal in the H ⊥ configuration comes from the g x component, where x, y, and z directions correspond to the molecular short axis, long axis, and the pπ-orbital direction, respectively [10][11][12]50 . In addition, clear line splitting in the H // configuration indicates the minor contribution of the interdomain carrier hopping at 150 K. If the interdomain charge hopping is efficient, then the g anisotropy is averaged out, and a Lorentzian-shaped single ESR signal is expected in the H // configuration. Based on the conventional ESR theory 54,55 , signal averaging occurs under the condition of τ inter −1 > |g y − g z |μ B H/h, where τ inter represents the interdomain hopping time, which has been observed in PBTTT TFTs at high temperatures above~200 K 50,56 .
In contrast to the case of PBTTT, the FI-ESR spectrum obtained for the DPP-TVT device exhibits no line splitting in the H // configuration, as shown in Fig. 3b. The absence of line splitting in the H // configuration clearly demonstrates the efficient interdomain motion of charge carriers in the polycrystalline DPP-TVT film based on the following discussion.  . Unfortunately, no direct information exists on the principal g values, which are essential to determine the molecular orientation 42,46,51‚57-60 , for DPP-based copolymers. Thus, we adopted a computational method to obtain the principal g values based on DFT calculations. DFT calculations of the g tensor were performed for oligomer models of DPPT-TVT and DPPT-TT. Figure 3c, d shows the optimized structure and spin density distribution, respectively, calculated by DFT method for a DPP-TVT oligomer with repeating unit number n = 2, and Table 1 summarizes the calculated principal g values for DPP-TVT, together with those of DPPT-TT. As in the case of PBTTT, the principal axes (x, y, z) of the g tensor are along the molecular short axis, long axis, and the pπ orbital direction, respectively, as shown in Fig. 3c. The maximum g value is obtained along the x-axis, showing a fairly good agreement with the g ⊥ value observed for DPP-TVT. This result indicates the edge-on orientation of the polymer backbone at the insulator interface, which is consistent with the previous Xray structural analyses for the bulk film 32 and the GIXD patterns shown in Supplementary Fig. 1.
In the case of a uniaxial edge-on molecular orientation, we expect the ESR line splitting in the H // configuration when the interdomain carrier motion is negligible, as in the case of PBTTT. We confirm that no line splitting signature is observed in the H // and H ⊥ configurations down to 4 K, as shown in Fig. 4a. In general, there are two possible explanations for the absence of the line splitting in the in-plane signal: (i) an intrinsically small g anisotropy of |g y −g z | gives only a small line splitting, which is masked by the natural linewidth in the target material, and (ii) the interdomain charge hopping averages out the split signals into a single line. For the former possibility, the DFT calculation of the g values provides crucial information; the g anisotropy of |g yg z | shown in Table 1 indicates the in-plane line splitting of 0.67 G for n = 2 and 1.1 G for n = 3 of DPP-TVT at the X-band microwave frequency (9.6 GHz), which are sufficiently larger than the peakto-peak linewidth (ΔH pp ) observed for these polymers at 150 K (ΔH pp = 0.3 G for DPP-TVT). In this case, if the interdomain charge hopping is negligible, then a clear line splitting should be observed in the in-plane ESR signal. Therefore, the absence of this line splitting is clear evidence of efficient interdomain charge hopping at 150 K, in contrast to the case of PBTTT.
Analyses of microscopic transport processes. In this section, we provide a more detailed insight into the microscopic charge transport mechanism in DPP-TVT, for both intradomain and interdomain transport, based on the temperature dependence of the FI-ESR signal. Figure 4b, c shows the temperature dependence of the spin concentration N spin and ΔH pp , respectively, obtained from the FI-ESR signals of the DPP-TVT device shown in Fig. 4a. The Arrhenius plot of the normalized ΔH pp is also shown in Fig. 4d. Here, N spin is calculated from the spin susceptibility χ by considering the Curie law (χ = N spin g 2 μ B 2 S(S + 1)/3k B T; k B : Boltzmann constant, and S = 1/2), and it agrees well with the charge concentration (N charge ) calculated from the insulator capacitance down to 4 K, as shown by the dashed line in Fig. 4b. This result indicates that the charge carriers are isolated polarons that have both spin and charge 61 . In this case, the hyperfine (hf) magnetic field originating from the proton and nitrogen nuclei on the polymer backbone causes a finite ESR line broadening. If the charge carriers are static, then the random distribution of the hf field produces a Gaussian-shaped ESR spectrum, whereas if the carriers are mobile, then the hf field is averaged out, and a Lorentzian-shaped narrow signal is produced 54,55 . This effect is known as motional narrowing, which can be used to probe the microscopic motion of charge carriers. In the case of edge-on oriented molecules, the ESR linewidth in the H ⊥ configuration is not affected by the g anisotropy and only the hf field contributes to the linewidth; thus, the motional narrowing in this configuration reflects the information of the intradomain carrier motion within the ordered domains, even for the case in which the domain boundaries limit the macroscopic transport by the poor interdomain connectivity 50 . As shown in Fig. 4c, ΔH pp in the H ⊥ configuration exhibits a clear narrowing below 150 K as the temperature is increased, indicating intradomain motional narrowing. Above 150 K, a line broadening is observed contrary to the motional narrowing, resulting in the minimum of the linewidth at 150 K. This line broadening is due to the shortening of the spin-lattice relaxation time through the spin-phonon interaction, which is beyond the scope of the present analyses 46,49,51 . In the extreme narrowing condition of γ (ΔH d )τ c « 1, the motionally narrowed ESR linewidth is described in Eq. (1): where ΔH d is the half-width at half-maximum of the static linewidth without narrowing, τ c is the spin correlation time, and γ is the gyromagnetic ratio of the electron 55 . Considering the trapand-release processes of charge carriers, τ c can be identified with the trapping time (τ tr ) of the carrier, 48,57 which becomes shorter for higher temperatures. The observed ΔH pp in the H ⊥ configuration displays an activation behavior in the temperature range of 100 K < T < 150 K, as shown in Fig. 4d, with an activation energy (E a intra ) of 10.6 meV. This value is smaller than those observed in the semicrystalline polymer PBTTT (E a intra = 21 meV for the TFT with an SiO 2 insulator 50 and E a intra = 17 meV for the device using a parylene insulator 56 ). Although the microscopic motion of the carriers depends strongly on the insulator material, as demonstrated in Supplementary Fig. 3 and Supplementary Note 3 using the Al 2 O 3 insulator, the smaller E a intra value in the present DPP-TVT device than that in the semicrystalline PBTTT device using the parylene insulator indicates the highly mobile nature of charge carriers within the ordered domains with small trap energies in DPP-TVT. This result is also supported by the fact that we observe a signature of motional narrowing even at approximately 4 K, as shown in Fig. 4c, although the detailed origin of the trap energy, which should be related to the defects or disorders within the crystalline domains, is still unclear at present. In fact, we observe an FI-ESR signal that is close to the Lorentzian signal at 4 K, as shown in Supplementary Fig. 3, for the device using a parylene insulator, which is characteristic of the motionally narrowed ESR signal.
In contrast to the FI-ESR signal in the H ⊥ configuration, the linewidth in the H // configuration contains the contribution from the g anisotropy of |g yg z | in addition to the hf interaction, as already mentioned, which is not averaged out by the intradomain carrier motion but by the interdomain carrier motion among the randomly aligned domains 50,51 . As in the case of the H ⊥ configuration, the motionally narrowed in-plane ESR linewidth is described by Eq. (1). When the hyperfine interaction is sufficiently averaged by the intradomain charge motion, ΔΗ d in Eq. (1) is dominated by the difference in the resonance magnetic field due to the g anisotropy of g y and g z (hereafter defined as Δg width) and τ c in this case is identified as τ inter 55 . In the low-temperature region, the observed linewidth is larger than the Δg width expected from the g anisotropy in Table 1, as shown by the dashed lines in Fig. 4c. In this case, ΔH d in Eq. (1) is dominated by the hf interaction and the motional narrowing reflects the intradomain carrier motion even in the H // configuration. On the other hand, the observed in-plane linewidth shown in Fig. 4c becomes narrower than the Δg widths above~70 K. In this temperature region, the Δg width is even larger than the hf-determined linewidth observed in the H ⊥ configuration due to the prominent averaging effect of the hf interaction by the intradomain carrier motion. In this case, if the interdomain carrier motion is negligible, clear line splitting by the Δg width should be expected as already mentioned, whereas no such splitting is observed in Fig. 4a. This clearly indicates the occurrence of the interdomain carrier hopping, which averages out the Δg width, at least above~70 K.
Next, we compare the intradomain and interdomain charge transport processes based on the activation energies of these processes. Interestingly, the temperature dependences of ΔH pp for the H ⊥ and H // configurations are almost identical, as shown in Fig. 4c, d, for DPP-TVT. The extracted activation energy E a inter of the interdomain charge transport is 10.3 meV, which is almost the same value as that of E a intra obtained for the same device, as summarized in Table 2 together with those of DPPT-TT and those reported for the PBTTT TFTs 50 . This agreement is surprising considering the fact that the boundary of the differently aligned domains is usually the major limiting factor of the macroscopic charge transport, which is clearly demonstrated for the PBTTT devices by the FI-ESR results 50 . In the case of PBTTT, E a inter is much larger than E a intra , and it is close to the mobility activation energy (E a μ ), as shown in Table 2, giving clear evidence of boundary-limited charge transport. In contrast to the case of the PBTTT device, the present results indicate that the interdomain charge transport is as efficient as intradomain charge transport. In other words, no excess energy is necessary for the charge transport across the domain boundaries from a microscopic viewpoint. Thus, this result clearly demonstrates the superior connectivity of the domains through the tie molecules in DPP-TVT, which is schematically illustrated in Fig. 4e.
Structural modeling by DFT calculations. Here, we discuss the structural origin of the efficient intradomain and interdomain charge transport processes realized in the present DPP-TVT device based on the DFT calculation. Figure 5 summarizes the structural optimization of a single DPP-TVT unit. The DPP-TVT backbone exhibits a highly planar conformation with fairly small torsion angles (shown in Fig. 5a) between the subunits, the torsion potential of which are given in Fig. 5b. In the lowest-energy conformation, the torsion of each subunit is almost negligible. Although the DPP-based copolymers still show some energetic disorders presumably arising from the finite backbone torsion in the actual film 38,62 , this structural feature is in contrast to the case of PBTTT, where a finite torsion angle between the thienothiophene and thiophene units is expected from the similar structural optimization 38 . The nearly torsion-free molecular conformation of DPP-TVT results in a rather delocalized nature of the carrier wave function within the chain, as reflected in the spin density distribution of the cationic state shown in Fig. 3d. The delocalized nature of the carrier wave function is advantageous for the onchain carrier motion, which might be reflected in the small activation energy of the microscopic charge motions in DPP-TVT.
In addition, face-to-face packing of the coplanar backbone can promote interchain charge transfer, which is essential for largescale charge transport because of the finite chain length of the actual polymers. Although the interchain hopping of the carriers cannot be observed directly from the present FI-ESR measurements, the efficient interchain charge delocalization is demonstrated by our DFT calculation of the spin density distribution considering face-to-face-packed, two oligomer chains, as shown in Supplementary Fig. 4 and Supplementary Note 4. In this calculation, we clearly observe a delocalization of the carrier wave function of the positive polaron (P + ) to the adjacent polymer chain. It is also noteworthy that the principal g values calculated based on this delocalized state between two chains are g x = 2.0037, g y = 2.0017, and g z = 2.0021, where the g x value is closer to the experimental g ⊥ value than that calculated by considering only a single chain (g x = 2.0042), whereas the other two components are unchanged. This result supports the concept that the carriers are delocalized to the adjacent chains within the ordered domains in the actual DPP-TVT film.
In addition to the above discussion, the highest impact of the torsion-free backbone on the charge transport lies in the electrical connection of the adjacent domains as a tie molecule. In general, torsion of the backbone prevents the π-π interaction, especially in the amorphous regions, which limits the interdomain electrical connectivity 39 . However, the domain boundaries are not the limiting factor of the interdomain charge transport in DPP-TVT TFTs. Since the high backbone planarity is also expected in the amorphous region because the present structural optimization is performed for the single isolated chain, it is natural to consider that this high planarity of the present polymer is also responsible for the high electrical domain connectivity, in addition to the strong interchain interaction generally expected between the donor and acceptor units in the DA copolymers 23,24,36 . In contrast, the backbone planarity of the PBTTT in the amorphous region is low, which limits the mobility as demonstrated by the molecular dynamics simulation 63 , resulting an inferior domain connectivity in the case of PBTTT.
The charge transport processes mentioned above are also summarized in Fig. 4e, i.e., the charges can be delocalized within the domains through the strong intermolecular π−π interactions and can be transported to adjacent domains by the high on-chain mobility of the highly planar tie molecules. The planar backbone can also promote the face-to-face packing of the backbones, even in the amorphous region, thus improving the domain connectivity. In contrast, the finite backbone torsion of PBTTT prevents the efficient connection of the domains, thus limiting the macroscopic charge transport. However, the intradomain charge transport is not severely affected by the backbone torsion, which was demonstrated by our previous FI-ESR measurement revealing that the intradomain carrier motion is not frozen, even at 4 K, in the PBTTT TFTs on the parylene insulator 56 . Therefore, the backbone torsion more severely affects the interdomain transport than the intradomain charge transport by limiting the on-chain carrier motion of the tie molecules.
The above discussion is also applicable to DPPT-TT. Figure 6 shows the FI-ESR results of DPPT-TT devices with the parylene insulator. We observed an anisotropic ESR signal with the extremal g values of g ⊥ = 2.0040 and g // = 2.0024. Based on the DFT calculation shown in Table 1, the observed g ⊥ agrees well with the g x value, strongly indicating that the carriers accumulate in the region with the edge-on molecular orientation, as in the DPP-TVT device, even though the bulk film tends to show structural disorders in this polymer [28][29][30] . In addition, no line splitting is observed down to 4 K both in the H ⊥ and H // configurations, as shown in Fig. 6a. Since the ESR linewidth in the H // configuration in Fig. 6b becomes narrower than the line splitting expected from the g anisotropy in Table 1 (0.94 G at the X-band, as shown by the dashed line in Fig. 6b), an efficient interdomain charge transport is again demonstrated down to~70 K in the DPPT-TT devices. Furthermore, the activation energies of the intradomain and interdomain carrier motion, which are obtained from the Arrhenius plot of the normalized linewidth in the H ⊥ and H // configurations in Fig. 6c, respectively, agree well with each other, as shown in Table 2. Therefore, efficient intradomain carrier motion is extended to adjacent domains with different chain alignments through rigid tie molecules in DPPT-TT devices. The planar backbone conformation of DPPT-TT has also been reported 64 , which is consistent with the above observations.

Discussion
Here, we compare the microscopic carrier dynamics clarified by the FI-ESR measurements to the macroscopic charge transport observed in the same devices. We measured the activation energy of the mobility from the temperature dependence of the transfer characteristics shown in Supplementary Fig. 5 and Supplementary Note 5 for both polymer TFTs. The results are also shown in Table 2. Here, the observed activation energies are E a μ = 74 and 68 meV for the DPP-TVT and DPPT-TT devices, respectively.
Although these values are similar to those usually observed for the semicrystalline polymers and the high-mobility DA copolymers 14 , they are much larger than those of the intradomain and interdomain charge transport processes obtained by the present FI-ESR measurements. In other words, the microscopic charge transport process is still different from the macroscopic process in the present DPP-based devices, even though the interdomain transport is highly efficient. This result indicates the presence of another limiting factor of macroscopic charge transport.
Although the detailed origin of this limiting factor is unclear, relatively large-scale domain or grain structures of the film should be responsible. For example, the surface of the DPP-TVT film exhibits a granular structure with the typical grain size on the order of~100 nm, as shown in Supplementary Fig. 6 and Supplementary Note 6. This rough film surface can be a limiting factor of macroscopic charge transport, especially in the case of top-gate devices, as in the present study. This phenomenon is also consistent with the fact that the FI-ESR signal of DPP-TVT exhibits almost no change before and after annealing at 200°C, as shown in Supplementary Fig. 7 and Supplementary Note 7, even though both the crystallinity and the room temperature mobility are improved by annealing. This result indicates that the microscopic properties or dynamics of charge carriers, as well as the local molecular orientation around them, are almost unchanged, whereas large-scale structural changes, which are reflected in the GIXD profiles in Supplementary Fig. 1, affect the mobility. However, we emphasize that the microscopic transport properties obtained by the present FI-ESR measurements indicate that the charge transport ability in the present DPP-based copolymers is potentially quite high, meaning that they can be suitably applied to high-mobility organic electronic devices if adequate optimizations of the film morphology are carried out. In summary, we performed FI-ESR measurements on the TFT devices of DA-type DPP-based conjugated polymers, DPP-TVT and DPPT-TT, to clarify the microscopic charge transport properties. Even though the macroscopic charge transport should be limited by the large-scale grain structure of the films, information of the highly mobile charge carriers realized within the crystalline domains was extracted by the FI-ESR measurements. The carrier motion within the domains was observed down to 4 K, where the macroscopic TFT operation was not observed. The activation energy of the intradomain carrier motion was as low as~10 meV, which is lower than those in conventional semicrystalline polymers. Such small trapping energy is reasonably ascribed to the highly planar molecular structures theoretically expected from DFT calculations. Furthermore, the high molecular planarity also results the efficient electrical connection between the crystalline domains. The activation energy of the interdomain carrier motion, obtained by the motional narrowing effect of the in-plane ESR linewidth, was almost the same as that of the intradomain motion. The same activation energy between the intradomain and interdomain carrier motion indicates that these processes are essentially identical with each other, i.e., the on-chain carrier motion within and across the domains is observed as the dominant contributions to the motional narrowing effect. The present FI-ESR method is therefore a powerful tool to probe the intrinsic transport properties which cannot be accessed by the macroscopic transport measurements.

Methods
Sample preparation. Samples of PBTTT with hexadecyl side chains (M w = 73,700-82,800) were purchased from Merck Co. Ltd. Samples of DPP-TVT (M w = 50,000, PDI = 2.4) were purchased from 1-Materials Co. Ltd. DPPT-TT (M n = 70,000, PDI = 3.13) was synthesized in house, and details of this procedure are described in a previous paper 65 . The TFTs with the top-gate device geometry shown in Fig. 2a were fabricated on a 3 mm × 30 mm quartz substrate as follows. The substrate was first cleaned by sonicating in deionized water, acetone, and 2propernol for 5 min each. In the case of PBTTT, the polymer layer was fabricated by drop casting the 4 mg/ml o-dichlorobenzene solution followed by annealing (180°C, 15 min) on the substrate patterned by 30-nm-thick Au source/drain electrodes. In the case of DPP-TVT, the drop cast film was fabricated using a 3 mg/ml chlorobenzene solution. We prepared both the as-grown film without annealing and the annealed film (200°C, 2 h) to modify the crystallinity. For the DPPT-TT film, a 10 mg/ml dichlorobenzene solution was spin coated on the substrate at 1500 r.p.m., followed by annealing (120°C, 1 h) to remove the solvent. Then, a thin-film of parylene-C with a thickness less than 1 μm was fabricated on these polymer films as a gate insulator by CVD. The insulator capacitance was 2.8 nF cm −2 for the PBTTT device, 3.8 nF cm −2 for the DPP-TVT device, and 4.4 nF cm −2 for the DPPT-TT device. Finally, an Al gate (G) electrode was vapor deposited. In the case of DPP-TVT, a bottom gate, topcontact device was also prepared using a 300-nm-thick Al 2 O 3 insulator with an Al gate electrode. The channel length (L) and width (W) were L = 1.4 mm and W = 19 mm for the PBTTT and DPPT-TT devices and L = 1.4 mm and W = 15 mm for the DPP-TVT device. The fabricated device was inserted into the ESR sample tube and sealed with 100 Torr He gas for thermal exchange.
Device characterization. The GIXD measurements were performed using a Rigaku FR-E Micro-focus High Intensity X-ray Generator system with a CuKa X-ray source (λ = 1.5418 Å) at the High Intensity X-ray Diffraction Laboratory (HIX) at Nagoya University. The in-plane and out-of-plane diffractions were detected by an imaging plate. TFT characteristics were measured using a Keithley 2612A source measuring unit. ESR measurements were performed using a Bruker E-500 X-band spectrometer equipped with an Oxford ESR 900 gas-flow-type cryostat. The gate voltage was applied by using a Keithley 2612A source measuring unit. For the angular-dependence measurements, the ESR sample tube with the TFT device was rotated with respect to the applied magnetic field direction inside the ESR cavity equipped with a home-made protractor, which is schematically illustrated in Fig. 2a. For the low-temperature FI-ESR measurements, the gate voltage was applied at room temperature with the source and drain electrodes being short circuited, and then the system was cooled down during the application of the gate voltage.
DFT calculation. DFT calculations of the g tensor for a DPP-TVT oligomer with repeat unit number n = 2 (see Fig. 3c) were performed with the UB3LYP functional and 6-31 G(d) basis set. To reduce finite chain-length effects, we also carried out calculations for longer oligomers with n = 3 at the UB3LYP/6-311++G(d,p)// UB3LYP/6-31G(d) level for DPP-TVT as well as DPPT-TT. The alkyl side chains on the DPP units were replaced with methyl groups. The calculations were carried out using the Gaussian 09 and Gaussian 16 software packages 66 . Data availability