Ambipolar charge transport in a non-fullerene acceptor

Non-fullerene acceptor (NFA) materials revolutionized the field of organic photovoltaics, making their commercialization tangible.^1–4 Most successful of them are fused-ring electron acceptors with an electron-pushing backbone and electron-pulling end-capping units.^5,6 Solar cells with NFAs based on this molecular design⁷ have power-conversion efficiencies (PCEs) of up to 20%.^6,8–11 Despite the progress in the PCE, only limited research has been performed on charge transport in NFAs. Charge transport directly impacts the performance of solar cells,¹² while the electron and hole transport may also be relevant to exciton diffusion.¹³ The electron transport in several NFAs has so far been characterized by means of space-charge-limited current (SCLC), time-of-flight (TOF), and field-effect transistor (FET) measurements.^14–18 A general issue with TOF measurements is that the transients are often dispersive, giving rise to a time-dependent mobility. Indeed, a recent study on the electron transport in two NFAs¹⁵ shows a highly dispersive transport, possibly due to energetic disorder. Such dispersive transport may not necessarily reflect the (time-averaged) steady-state transport relevant to solar cells.¹⁹ 

Field-effect transistor measurements may also not reflect the bulk transport relevant to solar cells, as in an FET, the transport in a horizontal plane adjacent to the gate dielectric is probed. In addition, charge-carrier densities are substantially higher in FETs, compared to solar cells.²⁰ SCLC measurements, on the other hand, are ideally suited to probe the steady-state transport in the bulk. However, the SCLC measurements of NFAs published to date provide little detail on the charge-transport characteristics.^16,21 In addition, for SCLC measurements to be reliable, they have to be performed on devices without charge-injection barriers at the contacts, which is difficult to achieve.

Apart from the electron transport, little is known about the hole transport in NFAs. Organic semiconductors are generally capable of transporting both electrons and holes, depending on their energy levels with respect to an energetic window in which charge transport is trap-free.²² Efficient NFAs seem to have energy levels within or close to this energetic window. While the benefit of trap-free electron transport is obvious for solar cells, efficient hole transport might be key for long-range exciton diffusion, which is one of the reasons for the efficient operation of NFA-based solar cells.

In a recent study, it was found that the non-fullerene acceptor IT-4F has an exciton diffusion length of up to 45 nm, the longest among a series of NFAs.¹³ In addition, FET measurements demonstrate ambipolar characteristics.¹³ IT-4F has been among the best-performing acceptors in the first generation of NFAs,¹⁶ guiding the development of recent NFAs.^23,24 In a binary blend with the donor polymer PM6, a record-breaking PCE value of 13.5% was reported,²⁵ while IT-4F scores among the compounds with the highest spectrally averaged internal quantum efficiency values.²⁶ The good performance of IT-4F in terms of internal quantum efficiency, exciton diffusion length, and its molecular structure as a predecessor for high-performance NFAs makes it an ideal model compound for a detailed study on its charge-transport characteristics.

Here, we investigate the electron and hole transport in pristine films of the non-fullerene acceptor IT-4F. Temperature-dependent space-charge-limited current measurements are analyzed with drift-diffusion simulations, revealing that the electron and hole transport is fairly balanced, differing by about an order of magnitude. These experimental observations are corroborated by computer simulations, which further reveal that the balanced charge transport is a result of molecular ordering.

IT-4F was purchased from Ossila Ltd. and used as received. All other materials were purchased from Sigma-Aldrich.

The device fabrication and characterization were performed under nitrogen atmosphere (O₂ < 0.1 ppm; H₂O < 0.1 ppm). Electron-only devices were fabricated in a glass/Al(30 nm)/IT-4F(200 nm)/TPBi(4 nm)/Ba(5 nm)/Al(100 nm) structure, where the interlayer of TPBi (1,3,5-tris(N-phenylbenzimidazol-2-yl)benzene) enables injection via electron tunneling,²⁷ enhancing the current density by 1.5 orders of magnitude at an applied bias of 4 V. The layer stack of the hole-only devices is glass/Au(30 nm)/PEDOT:PSS(40 nm)/IT-4F(200 nm)/MoO₃(10 nm)/Al(100 nm), where PEDOT:PSS denotes poly(3,4-ethylenedioxythiophene)–poly(styrenesulfonate). Introducing an additional fullerene (C60) tunneling interlayer²⁷ between IT-4F and MoO₃ did not improve the hole injection, indicating that the MoO₃ contact is already Ohmic. The device area amounted to 1 mm² for all devices. A small device area was used to keep the current through the device low, ensuring a negligible voltage drop due to the series resistance of the electrodes in the measured current range.

The metals and metal oxides were evaporated at a base pressure of around 3 × 10⁻⁷ mbar and TPBi was evaporated at around 2 × 10⁻⁶ mbar, whereas PEDOT:PSS and IT-4F were solution processed. PEDOT:PSS was deposited using spin coating, and the layer was subsequently annealed for 10 min at 140 °C. IT-4F was spin coated from a chlorobenzene solution (23 mg/ml, stirred overnight at 60 °C) at a speed of 1000 rpm for 70 s. Annealing for 10 min at 140 °C had no influence on the electrical properties. PM6 was spin coated from chlorobenzene solution (15 mg/ml, stirred overnight at 60 °C) at a speed of 2000 rpm for 60 s. Layer thicknesses were measured with a DektakXT^® stylus profilometer.

Electrical characterization was performed with a Keithley 2400 source meter. The devices were not exposed to ambient air until after device characterization.

To characterize the charge transport, numerical 1D drift-diffusion simulations²⁸ were fitted to the experimentally obtained, temperature-dependent J–V characteristics. Temperature-, field-, and density-dependent mobilities in the framework of the extended Gaussian disorder model (EGDM) were used to describe the experimental data (see the supplementary material for further information on the drift-diffusion solver).²⁹ 

The fitting procedure first involves estimating the charge-carrier mobility parameters, whereas trapping parameters are included in the second step. The mobility can be fitted in the high-voltage regime, where all traps are filled. In the EGDM, there are three fit parameters: a mobility prefactor μ_∞, the width of the DOS distribution σ, and the lattice constant a. Here, σ mainly controls the temperature dependence, whereas a predominantly affects the field dependence and μ_∞ controls the magnitude of the mobility. Trapping is added subsequently by using a Gaussian distribution of trap states. The trap density influences the voltage at which trap filling is completed, i.e., the trap-filled limit, whereas the trap depth influences the magnitude of the current below the trap-filled limit.³⁰ 

All bonded parameters were taken from the empirical OPLS-AA force field^31,32 and our previous work.³³ The non-bonded parameters, atomic partial charges, and Lennard-Jones parameters were derived following the protocol proposed by Cole et al.³⁴ In short, the overlapping atomic electron densities were obtained via the density-derived electrostatic and chemical (DDEC6) electron density partitioning scheme.³⁵ On the one hand, the atomic partial charges can then be obtained by integrating the corresponding atomic electron densities over the whole space. On the other hand, the two parameters, A and B, in the Lennard-Jones potential were derived using the Tkatchenko–Scheffler (TS) scheme³⁶ and the radius of the free atom in a vacuum was taken from Ref. 34. The electron density was obtained by using Gaussian16³⁷ at ωB97X-D/6-311G(d,p) level, and the DDEC6 computations were performed using Chargemol of version 09_26_2017.³⁸ All molecules considered in this work were partitioned into several rigid fragments following the same procedure as our previous work.³³ After non-bonded parameters were set, the dihedral potentials that connect these rigid fragments were parameterized using the constrained optimization scanning performed at ωB97X-D/6-311G(d,p) level using Gaussian16. For more details on the parameterization of dihedral potentials, please refer to Ref. 38.

To construct the amorphous morphology, 2000 IT-4F molecules were initially randomly placed in a simulation box with a low target density of around 100 kg/m³ using Packmol.³⁹ The whole system was then compressed and heated up to 800 K with an NPT barostat followed by a 10 ns equilibration at 800 K. Finally, the system underwent a linear cooling procedure from 800 to 300 K at a 500 K/ns cooling rate, followed by a further equilibration at 300 K for 9 ns. The second-rank orientational order parameter⁴⁰ $P̄2$ of the final snapshot of the trajectory is calculated to be 0.04.

As for the smectic phase, 2000 IT-4F molecules were placed on the simple cubic lattice sites without relative rotation. The whole system was then compressed and heated up to 500 K with an NPT barostat, followed by a 10 ns equilibration at 500 K. Finally, the system underwent a linear cooling procedure from 500 to 300 K at a 500 K/ns cooling rate followed by a further equilibration at 300 K for 9 ns. The $P̄2$ of the final snapshot of the trajectory is calculated to be 0.65.

For the crystalline phase, we created a supercell with 2000 molecules from an experimental crystal structure.⁷ The whole system was then equilibrated at 300 K for 10 ns. The $P̄2$ of the final snapshot of the trajectory is calculated to be around 1.0.

All classical MD simulations were performed using GROMACS version 2020.3.^41,42 For the long-range electrostatic interactions, the particle mesh Ewald (PME) method was employed with a 0.12 nm Fourier spacing. A cutoff of 13 Å was applied to all non-bonded interactions. The temperature and pressure control was accomplished using velocity rescaling with a stochastic term (τ_T = 0.5 ps) and an isotropic coupling for the pressure from a Berendsen barostat (P₀ = 1 bar, χ = 4.5 × 10⁻⁵ bar⁻¹, and τ_P = 0.5 ps).

The ionization energy (IE) and electron affinity (EA) in the bulk were computed using a perturbative way, with the solid-state charge stabilization computed using atomic multipoles and the Thole model.⁴³ 

For the gas-phase computations, the geometry of the neutral IT-4F was optimized using the ωB97X-D* functional and 6-311G(d,p) basis set. The optimal ω was obtained following the same ω-tuning procedure we used in our previous work.³³ The electronic total energy of cationic and anionic IT-4F was evaluated using the neutral optimized geometry and the same level of theory. This is used to calculate the gas-phase IE and EA shown in Fig. 2; IE_gas = E_nN − E_cN and EA_gas = E_aN − E_nN, where E_nN, E_aN, and E_cN are the electronic total energy of neutral, anionic, and cationic IT-4F molecules evaluated at the optimized neutral geometry.

The atomic multipoles for all states (n, c, a) and geometries (N, C, A) were derived using the DDEC6 method. The atomic polarizabilities of all states were obtained by linearly scaling the isotropic atomic polarizabilities of the AMOEBA force field. The scaling factor is the value at which the effective molecular polarizable volumes of the QM computations and this method match. These two properties were evaluated using B3LYP/6-311G(d,p). All computations mentioned above were performed using Gaussian16.³⁷ 

The atomic multipoles and polarizabilities were then mapped onto the simulated morphology obtained via MD simulations. The solid-state stabilization for each molecule (site) in the solid was then computed using the long-range embedding approach⁴⁴ implemented in VOTCA.⁴³ 

The transfer integrals were evaluated for all molecular pairs (dimers) within the 7 Å nearest-atomic-distance cutoff in the molecular solids. We utilize the cost-efficient MOO-ZINDO method⁴⁵ to calculate the transfer integrals, which has shown to give reasonable results.⁴⁶ 

The gas-phase reorganization energy is computed using the four-point method,⁴⁷ $λh=EcN−EcC+EnC−EnN$ and $λe=EaN−EaA+EnA−EnN$⁠, where λ_h and λ_e are the reorganization energy for hole and electron transfers, respectively. E_nN, E_aN, and E_cN follow the same definition as before. E_aA and E_cC are the electronic total energy of the optimized anionic and cationic IT-4F, respectively. These energies were evaluated using the B3LYP/6-311G(d,p) method.

The mobilities were extracted from the trajectory of charge dynamics evolved using kinetic Monte Carlo (kMC) simulations (F = 10⁵ V/cm; simulation time 10⁻³ s). The hopping rates between any two molecules (sites) were evaluated using the Marcus theory,⁴⁸ $ωij=Jij2ℏπλkBTexp−ΔEij−λ24λkBT$⁠, where T is the temperature, J_ij is the transfer integral between the i and j site, ΔE_ij is the site energy difference E_i − E_j, and λ is the reorganization energy. The computational details of these parameters are discussed in the subsections titled Site energy computation, Transfer integrals, and Reorganization energy.

The direct extraction of mobility from kMC simulations at 300 K suffers from the finite-size effect, which belongs to the dispersive transport regime. Therefore, we utilized the extrapolation scheme where the nondispersive mobility at 300 K could be extrapolated from the nondispersive (high-T) regime using an empirical T–μ relation.^49,50 All charge transport calculations were performed using the VOTCA package.⁴³ 

Please note that while the EGDM, which is based on Miller–Abrahams hopping, is used to evaluate the experimental characteristics, this does not influence the experimentally obtained value of the mobility. However, there may be minor differences in the evaluated energetic disorder when comparing Miller–Abrahams hopping to Marcus hopping. In the investigated field and temperature regime, however, these differences are fairly small.⁵¹ 

To characterize the electron and hole transport in IT-4F, electron- and hole-only devices were fabricated. To ensure efficient electron injection in the electron-only device, a top electrode consisting of TPBi(4 nm)/Ba(5 nm)/Al(100 nm) was used. The thin TPBi layer functions as a tunneling interlayer to form an Ohmic electron contact, which cannot be achieved with a barium layer alone, despite its low work function. The temperature-dependent electron currents are displayed in Fig. 1. The near-quadratic dependence of the current on the voltage is indicative of a space-charge-limited current that is almost trap-free. To analyze the electron currents in more detail, the J–V characteristics were fitted with a numerical drift-diffusion model. In these simulations, the mobility is considered to be dependent of temperature, charge-carrier density, and electric field according to the extended Gaussian disorder model.

The obtained room temperature electron mobility in IT-4F is relatively high, amounting to 2.9 × 10⁻⁴ cm² V⁻¹ s⁻¹, when extrapolated to zero electric field and zero charge-carrier density. The mobility at nonzero charge-carrier density and electric field is slightly higher, as shown in Fig. S1, which would be more representative of a solar cell under illumination. The high electron mobility is a result of the low energetic disorder of the unoccupied molecular orbitals, which can be derived from the temperature dependence of the J–V characteristics, where the width of the Gaussian distribution was observed to amount to 0.085 ± 0.010 eV. The narrow energetic disorder implies a significant degree of molecular ordering.

Despite the electron affinity of IT-4F (4.14 eV)¹⁶ being situated in the trap-free window for organic semiconductors,²² a low density of electron trap states of 8.0 × 10²¹ m⁻³ with a depth of 0.4 eV was identified. This low density of trap states (in the 0.01% range relative to the density of states) might originate from chemical impurities. Because the charge concentration in operating solar cells is in the 10²²–10²³ m⁻³ range, these traps are easily filled and, thus, most photogenerated electrons will be free and unaffected by these traps in a solar cell (see Fig. S2 for the effect of the trap density on the J–V characteristics for the electron and hole transport).

When comparing the electron mobility of IT-4F to other non-fullerene acceptors, such as Y6, the mobilities seem to be quite similar. For Y6, the mobilities estimated from SCLC measurements are reported to be 1.8 × 10⁻⁴,⁵² 2.15 ± 0.87 × 10⁻⁴,⁵³ and 2.35 × 10⁻⁴ cm² V^-1 s^-1.⁵⁴ 

To characterize the hole transport and to compare it to the electron transport, hole-only devices were fabricated and analyzed in the same manner as the electron-only devices. It was found that a MoO₃/Al hole contact could provide an Ohmic hole injection into IT-4F, having an ionization energy of 6.0 eV.²⁷ 

The temperature-dependent J–V characteristics are displayed in Fig. 1(b). Despite IT-4F being known as an electron-accepting and electron-transporting material, a considerable hole current could be injected. From the fits with the drift-diffusion simulation, the hole mobility at room temperature and zero field and density was observed to be approximately one order of magnitude lower than the electron mobility, amounting to 2.0 × 10⁻⁵ cm² V⁻¹ s⁻¹. From the temperature dependence of the hole current, the extracted energetic disorder for holes amounts to 0.110 ± 0.006 eV. This value for energetic disorder is higher than for electron transport, which is a possible reason for the somewhat lower hole mobility. The amount of hole traps is also higher than the amount of electron traps, where a concentration of 1.65 × 10²² m⁻³ was observed. This is, however, still a low concentration of traps, which is in line with the ionization energy being inside the window for a trap-free charge transport. Note that outside the trap-free window, charge-trap concentrations surpassing 10²³ m⁻³ are typically observed, which severely hampers charge transport, as the trap density exceeds the concentration of charge carriers in organic devices.

To put the hole transport of IT-4F into perspective, the hole current in IT-4F is compared to the hole current in the donor polymer PM6 (see the supplementary material for the J–V characteristics). Interestingly, the observed hole currents are quite similar. The fitted hole mobility of PM6 with 5.7 × 10⁻⁵ cm² V⁻¹ s⁻¹ is only slightly higher than that of IT-4F (2.0 × 10⁻⁵ cm² V⁻¹ s⁻¹), showing that IT-4F has decent hole transport capabilities with respect to well performing donor materials. The energetic disorder of PM6 is identified to be similar to IT-4F with 0.100 eV, as is the amount of the Gaussianly distributed hole traps in PM6 with a density of 1.5 × 10²² m⁻³. The fact that the hole transport in IT-4F compares quite well with a state-of-the-art donor material highlights the good hole transport in IT-4F, although the hole transport in IT-4F is still inferior to the electron transport.

The mobilities found for the pristine donor and acceptor materials, although decent, appear rather low in light of the high power-conversion efficiency of 13.5% obtained for a PM6:IT-4F blend solar cell.²⁵ Therefore, we assess whether there are substantial differences between the pristine-film mobilities and the mobilities obtained for a PM6:IT-4F blend. The reported mobilities for the PM6:IT-4F blend⁵⁵ (obtained by the SCLC method) are 2.11 × 10⁻⁴ and 1.95 × 10⁻⁴ cm² V⁻¹ s⁻¹ for electrons and holes, respectively. We obtain an electron mobility for pristine IT-4F of 2.9 × 10⁻⁴ cm² V⁻¹ s⁻¹, which is slightly higher than for the blend.⁵⁵ The reported hole mobility for the blend is about a factor of 3 higher than the hole mobility we obtain for PM6, which is, however, the value extrapolated to zero density and zero field. As shown in Figure S1, this amounts to a mobility in the 10⁻⁴ cm² V⁻¹ s⁻¹ range for pristine PM6 at a nonzero charge density, comparable to the value for the PM6:IT-4F blend. The minor differences between the mobility in the pristine materials are likely due to different molecular ordering in the blend. In view of the relatively low mobilities, the high power-conversion in PM6:IT-4F solar cells may rather originate from low bimolecular recombination rates, which allows for efficient charge extraction prior to recombination.

To support and further investigate the experimental observations, we simulated material morphologies using molecular dynamics simulations of 2000 IT-4F molecules and the charge transport process using kinetic Monte Carlo simulations, as described in the section titled Methods. We studied three types of molecular ordering: the crystalline, the smectic (layered), and the amorphous phase as displayed in Fig. 2. The crystalline mesophase had the highest order parameter of S ≈ 1 and the smallest energetic disorder of σ_e = 0.04 eV. The smectic mesophase with S ∼ 0.6 and σ_e ≈ 0.12 eV was in between the crystalline and amorphous phases, for which S = 0.02 and σ_e ≈ 0.15 eV were calculated. The experimental value of σ_e = 0.080 eV indicates that the spin-coated IT-4F film is mostly orientationally ordered and has a partially more crystalline and partially rather smectic molecular alignment. This picture of the local morphology in IT-4F thin films is in line with a study quantifying the number of face-on interactions in dimers extracted from MD simulations⁵⁶ and can be put into context with studies on molecular packing of IT-4F.²¹ Experimental 2D GIWAXS and AFM studies on IT-4F also support the existence of 10–20 nm crystalline grains in IT-4F upon annealing or treatment with an additive.^17,21,57

For hole transport, the measured value of energetic disorder lies in between simulated σ_h = 0.04 eV (crystalline) and σ_h = 0.13 eV (smectic) mesophases. The simulated directional average hole mobility in the smectic phase of 1.4 × 10⁻⁴ cm² V⁻¹ s⁻¹ deviates by one order of magnitude from the experimental value of 2.0 × 10⁻⁵ cm² V⁻¹ s⁻¹ (Table I).

As shown in Table I, the simulated electron mobility is consistently higher (on average, 4.8 × 10⁻⁴ cm² V⁻¹ s⁻¹) than the hole mobility in all phases and transport directions. The small anisotropy of the mobility in the smectic phase may seem surprising: While considering the layered structure, the transport in the direction along the layers is expected to be favorable. However, two effects need to be considered here: the hopping distance is larger along the molecular axis, but the electronic coupling elements are smaller. These two effects seem to compensate each other, leading to an efficient three-dimensional ambipolar charge transport network.

Both the simulation and the experimental data provide evidence for a higher electron than hole mobility. The experimental measurements, however, yield a larger difference for both the mobility and the energetic disorder. In the multiscale simulations, the disorder values are similar for the hole and the electron transport.

Nonetheless, the higher electron mobility in all simulated phases can be explained in the framework of the hopping transport model. In this model, the low reorganization energy, high transfer integrals, and low energetic disorder are key to the high charge carrier mobility. The reorganization energies for the hole and electron of IT-4F are very similar (0.24 vs 0.25 eV), which could not explain the difference in their mobility. Instead, the transfer integral J plays a role in this case. The analysis of the size of the largest percolating cluster (Fig. 2), based on the transfer integrals between neighboring molecules, shows that in all simulated phases, the electron reaches the percolation threshold with a larger value of J as compared to the hole carrier. This result confirms the anticipated effect of the design of an acceptor–donor–acceptor molecular architecture on the favorable electron transfer. At the same time, the experimentally determined lattice constant for both types of charge transport amounts to ∼2.3 ± 0.3 nm, indicating comparable hopping lengths.

The electron and hole transport in the non-fullerene acceptor IT-4F was studied by combining space-charge-limited current measurements with drift-diffusion modeling. Electron mobilities in the order of 10⁻⁴ cm² V⁻¹ were obtained, which were found to be one order of magnitude higher than hole mobilities. Low trap densities were observed for both the electron and hole transport. Values for the energetic disorder inferred from the experimental measurements amounted to 0.085 eV for electrons and 0.110 eV for holes. The ambipolar charge-transport characteristics of IT-4F were further confirmed with molecular multiscale simulations, demonstrating orientational molecular ordering and a better charge percolating network for electrons.

See the supplementary material for drift-diffusion simulations, experimental device characteristics, and simulated mobilities.

The authors have no conflicts to disclose.

Franziska H. Hasenburg: Data curation (equal); Formal analysis (equal); Visualization (equal); Writing – original draft (equal). Kun-Han Lin: Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Bas van der Zee: Formal analysis (equal). Paul W. M. Blom: Supervision (equal). Denis Andrienko: Conceptualization (equal); Supervision (equal); Writing – review & editing (equal). Gert-Jan A. H. Wetzelaer: Conceptualization (lead); Formal analysis (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.