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# Impact of molecular quadrupole moments on the energy levels at organic heterojunctions

## Abstract

The functionality of organic semiconductor devices crucially depends on molecular energies, namely the ionisation energy and the electron affinity. Ionisation energy and electron affinity values of thin films are, however, sensitive to film morphology and composition, making their prediction challenging. In a combined experimental and simulation study on zinc-phthalocyanine and its fluorinated derivatives, we show that changes in ionisation energy as a function of molecular orientation in neat films or mixing ratio in blends are proportional to the molecular quadrupole component along the π-π-stacking direction. We apply these findings to organic solar cells and demonstrate how the electrostatic interactions can be tuned to optimise the energy of the charge-transfer state at the donor−acceptor interface and the dissociation barrier for free charge carrier generation. The confirmation of the correlation between interfacial energies and quadrupole moments for other materials indicates its relevance for small molecules and polymers.

## Introduction

Organic semiconductors gained much attention because of their attractive application in low-cost, large area, and flexible electronic devices1,2,3,4. While organic light-emitting diodes (OLEDs) already entered the market in thin film displays, several other promising applications such as solar cells, transistors, photodetectors, or lasers still require improvements in performance. In contrast to their inorganic counterparts, organic semiconductors typically consist of weakly bound molecules, where charge carriers occupy rather localised states. Associated to these states are the ionisation energy (IE) and electron affinity (EA) of organic molecules, which are related to the transport energies of holes and electrons and, consequently, determine the functionality of electronic devices5,6.

In organic solar cells (OSCs), fundamental processes determining the device performance are the dissociation of charge-transfer (CT) states at the donor−acceptor interface into free charges and their non-geminate recombination via CT states back to the ground state7,8,9. Therefore, the CT state energy (ECT) determines the open-circuit voltage (Voc) of OSCs10, while its difference to the energy of separated charges (ECS) influences the generation efficiency of free charge carriers and, thus, crucially affects both the short-circuit current density (jsc) and the fill-factor (FF)11,12. Both ECT and ECS are linked to IE of the donor and EA of the acceptor.

IE and EA of molecules in organic films significantly depend on molecular orientation and mixing ratio in blends13,14,15. In particular, charge−quadrupole interaction can induce large electrostatic shifts of the electronic levels in crystalline films16,17,18,19, which, for example, allows in blends with molecular intermixing, a continuous tuning of IE and EA by adjusting the ratio of two different molecular species20,21. Furthermore, simulations indicated that these interactions can assist the dissociation of CT states at planar donor−acceptor interfaces22,23. However, it remains an open question to which extent such findings for these model systems are general and, particularly, how they are applicable to donor:acceptor blends without long-range order which are usually employed in efficient OSCs.

In this study, we demonstrate the tunability of the solid-state IE by charge−quadrupole interactions and their relevance in systems with long-range and short-range order, being, thus, relevant for most organic devices. As a model system, we choose zinc-phthalocyanine (ZnPc) because of the possibility to gradually change its quadrupole moment (QPM) by stepwise fluorination (FnZnPc)20. In order to establish the role of the quadrupole component perpendicular to the molecular plane (Qπ), we measure for FnZnPc the change in IE with molecular orientation, film thickness, and mixing ratio in blends. The ultraviolet photoelectron spectroscopy (UPS) analysis reveals a linear change of IE with Qπ in all cases. Moreover, when applying these findings to OSCs, we demonstrate how QPMs influence ECT at planar and bulk heterojunctions between donor and acceptor. Time-delayed collection field (TDCF) measurements further show that electrostatic gradients induced by QPMs can assist free charge carrier generation in these solar cells. Finally, we extend the study to other material systems, indicating the relevance of the findings for a large variety of organic semiconductors.

## Results

### Dependence of thin flm energies on the component Qπ

IE and EA of molecules in thin films deviate from their gas-phase values, IE0 and EA0, due to polarisation effects24,25,26. In weakly bound solids with localised states, the electrostatic corrections (Δ+ and Δ) to the gas-phase values consist of an induced and a permanent contribution. While the first term decreases the distance between IE and EA, the latter originates from the interaction of excess charges with static charge distributions and shifts IE and EA equally17,18,19,20. We concentrate on the permanent contribution in this study, which is often dominated by the charge−quadrupole term in the multipole expansion because molecules with dipole moments often stack with alternating molecular orientations in ordered organic solids16,18. In this case, the permanent contribution can be approximated by a sum over the interaction energies of a charged molecule, described by its atomic excess charges qj at positions rj, with the quadrupole tensors Qi of all surrounding molecules at sites ri27:

$$E_{\mathrm{Q}} = {\mathop {\sum}\limits_{i,j}} \frac{q_{j}}{8 \pi \epsilon_{0}\epsilon_{\mathrm{r}}} \cdot \frac{\left({\mathbf{r}}_{i} - {\mathbf{r}}_{j} \right) \cdot {\mathbf{Q}}_{i} \cdot \left( {\mathbf{r}}_{i} - {\mathbf{r}}_{j} \right)}{\left| {\mathbf{r}}_{i} - {\mathbf{r}}_{j} \right|^5},$$
(1)

where we use the dielectric permittivity εr as a macroscopic constant. We describe the charged molecule by its actual distribution of atomic charges to have an appropriate description at distances in the range or below the spatial extent of molecules.

Due to the strong dependence of EQ on distance, EQ changes with the chemical and crystal structure of the compound. Like many other planar molecules, FnZnPc typically arranges in a π−π-stacking geometry28,29, where the intermolecular distance along the stacking direction (approximately 3.8 Å 28) is significantly smaller than along the other two directions (13−14.5 Å 30). Therefore, we first investigate if the quadrupole component perpendicular to the molecular plane (Qπ) dominates EQ (see Fig. 1 for Qπ values) by analysing for FnZnPc layers (20 nm) the difference in IE between face-on and edge-on orientation of the molecules (Fig. 2a, see Supplementary Figs. 13 and Supplementary Note 1 for X-ray scattering results). The representative UPS spectra in Fig. 2b show that IE of a ZnPc film in edge-on orientation is 0.22 eV smaller as compared to the film in face-on orientation, in agreement with previous results13. In contrast, F8ZnPc exhibits an IE value in edge-on orientation that is 0.37 eV larger than the IE value in face-on orientation. To connect this behaviour to molecular properties, we calculate Qπ by density functional theory (DFT) for ZnPc and its fluorinated derivatives (results in Supplementary Table 1). As displayed in Fig. 2c, the difference in IE between edge-on and face-on orientation increases with Qπ from ZnPc to F16ZnPc.

To prove that Qπ dominates in EQ (see Eq. 1), we calculate EQ for a single charged molecule at the film surface for both orientations (see Methods and Supplementary Fig. 4). The difference in EQ between both orientations exhibits the same correlation with Qπ as observed for the IE difference in experiment (Fig. 2c). Interestingly, the simulations reveal that the relevant range of charge−quadrupole interactions is different between both molecular orientations (Supplementary Fig. 5). For edge-on orientation, EQ is dominated by interactions between the next few neighbours along the π−π-stacking geometry. For face-on orientation, EQ is also dominated by interactions with Qπ components at small integration limits, which however is compensated by the interaction with other components when the integration limit in the lateral direction becomes larger than 100 nm. Previous investigations indicate that the interaction with other components than Qπ can be even more dominant in face-on orientation for molecules with a different symmetry than FnZnPc such as pentacene, having two molecular short axes19,31. In the absence of long-range order, such as in donor:acceptor blends with crystal sizes much smaller than 100 nm, the interaction of charges with Qπ components should dominate32,33,34.

To further verify the dominance of charge−quadrupole interactions along the π−π-stacking direction for edge-on orientation, we measure IE of FnZnPc for coverages below the monolayer thickness and evaporate the material stepwise onto p-doped BPAPF, leading to an edge-on orientation in thin films (Supplementary Figure 6). IE at very small coverages, denoted as IEs, deviates strongly from the value of thick layers (see dotted lines in Fig. 2d). Notably, for all ZnPc derivatives, IEs is reduced by 0.6 eV compared to their respective gas-phase ionisation energies IE0, indicating minor influence of charge−quadrupole interactions on IE at low coverages. With increasing layer thickness, IE strongly changes and approaches the value of a thick edge-on oriented film when the monolayer thickness (13−14.5 Å 30) is reached. The strong IE shift can be explained by the formation of an ordered monolayer in edge-on orientation, leading to an increase of the magnitude of EQ due to charge−quadrupole interactions along the π−π-stacking direction. In good agreement, the change of IE scales with the Qπ value of the respective ZnPc derivative (Supplementary Fig. 6c). Note that the change in IE until the first edge-on monolayer is formed can occur for different growth modes, such as island growth or transition of molecular orientation from face-on to edge-on.

After having demonstrated the strong effect of Qπ on the energy levels in model systems based on ZnPc derivatives, we further analyse its impact in donor:acceptor blends which are typically used in OSCs. Such blended structures usually exhibit significant structural disorder and phase separation that both can change with mixing ratio13,32,35,36. Previous studies found changes of energy levels with donor:acceptor mixing ratio, which were assigned to changes in crystal size and to electrostatic changes13,15,37. We trace back these energetic changes to the influence of the molecular tuning parameter Qπ.

We measure the energy levels of F8ZnPc:C60 blends at different mixing ratios (see UPS spectra in Supplementary Fig. 7). As shown in Fig. 3a, IE of F8ZnPc decreases by more than 300 meV with increasing C60 content. IE of C60 shows a similar change, which suggests that a large amount of donor and acceptor molecules interact electrostatically with the other species despite the phase separation in these blends. The larger IE change of F8ZnPc at higher C60 contents indicates that F8ZnPc molecules which are closer to C60 molecules experience a larger electrostatic shift.

To validate that the electrostatic changes originate from charge−quadrupole interactions, we compare the behaviour of F8ZnPc:C60 blends to previously reported ZnPc:C60 blends13, as ZnPc and F8ZnPc exhibit a similar magnitude but a different sign of Qπ. Figure 3b shows the electrostatic correction Δ+ of IE for ZnPc and F8ZnPc blended with C60. While Δ+ differs strongly between ZnPc and F8ZnPc in pure layers, this difference reduces continuously with increasing C60 concentration, and Δ+ finally approaches −0.6 eV. This value is also observed for very small coverages of (F8)ZnPc, indicating that the charge−quadrupole interaction energy EQ approaches 0 for high C60 contents (see Fig. 2d for comparison). Therefore, we attribute the decrease (increase) of IE of F8ZnPc (ZnPc) with increasing C60 content to the interaction of charges with a reduced number of Qπ components of the donor.

The dominance of charge−quadrupole interactions along the π−π-stacking direction is attributed to the shorter intermolecular distance in this direction for the ZnPc derivatives. To verify whether this simple model is also valid for other materials, we extend our investigation to other molecules that show a strong dependence of IE on molecular orientation in neat films13,14,38,39,40,41 or on mixing ratio in donor:acceptor blends15,37 (see Fig. 1 for chemical structures). We calculate their QPMs and observe that for both cases the change in IE scales linearly with the respective Qπ (Supplementary Fig. 8). Notably, the slope is surprisingly similar to the one observed for intermixed blends of different ZnPc derivatives20 (Supplementary Fig. 9). Charge−quadrupole interactions are also relevant for polymers. Similar to sexithiophene (alpha-6T), poly-3-hexylthiophene (P3HT) shows a smaller IE for end-on orientation with the polymer chain perpendicular to the substrate plane42. This analysis indicates that the impact of Qπ on thin film energy levels is relevant for many organic materials including varying molecular structures and different morphologies of their (blend) films.

### Impact of Qπ at donor−acceptor interfaces in solar cells

The functionality of OSCs is linked to the formation of charge-transfer (CT) states of a donor cation and an acceptor anion at their interface (Fig. 4a), mediating charge carrier dissociation and recombination in OSCs7,8. In the following, we demonstrate how molecular quadrupole moments can influence the CT state energy (ECT) as well as its difference to the energy of separated charges (ECS). For this purpose, we analyse ZnPc:F4ZnPc:C60 solar cells based on bulk heterojunctions (BHJ) with two electron donating molecules (ZnPc and F4ZnPc) and one acceptor (C60) with a fixed volume content of the acceptor (60%). Different mixing ratios between ZnPc and F4ZnPc are used to selectively change the average of the molecular parameters in the donor phase.

For analysing ECT, we obtain the relevant gas-phase energy levels of donor and acceptor molecules (IE0,D and EA0,A) as well as the intramolecular relaxation energies of their ions by DFT. We further calculate for ZnPc/C60 and F4ZnPc/C60 the Coulomb binding energies of the energetically relaxed ion pairs and find that they differ up to several 10 meV between ZnPc and F4ZnPc because of their different charge distributions43 (see Methods section and Supplementary Fig. 10a). We calculate from these parameters the expected variation of ECT from ZnPc:C60 to F4ZnPc:C60 (dashed line in Fig. 4b and Supplementary Fig. 10b). Experimental values of ECT obtained from Gaussian fits to sensitively measured external quantum efficiency (see Supplementary Fig. 11) and electroluminescence spectra44. In good agreement with the calculations, the experimental values increase with F4ZnPc content (purple squares in Fig. 4b). However, the measured shift of ECT is 0.1 eV larger than expected from the variation of molecular parameters, which can be partly attributed to the larger static energetic disorder at high ZnPc contents, reducing ECT (Supplementary Fig. 12). In addition to energetic disorder, charge−quadrupole interactions lower the effective IE of the donor and further reduce ECT at large amounts of ZnPc.

To verify the impact of charge−quadrupole interactions on ECT, we additionally fabricate solar cells with a planar heterojunction (PHJ) between a ZnPc:F4ZnPc blend layer with varying mixing ratio and a neat C60 layer. The ZnPc:F4ZnPc layer is grown on p-doped BPAPF to ensure edge-on orientation of the donor molecules, causing a large change of IE induced by charge−quadrupole interactions (see Fig. 2b and Supplementary Fig. 9). At high ZnPc contents, the planar devices exhibit a significantly lower ECT (green circles in Fig. 4b) than the ternary BHJ devices. This can be explained by extended long-range order, which increases the charge−quadrupole interaction energy and reduces IE of the donor for large ZnPc contents. The change of ECT with donor mixing ratio directly influences Voc because charge carriers recombine via CT states at open-circuit9. Therefore, the different shifts of ECT in BHJ and PHJ devices upon changing the donor content is reflected in a similar difference in Voc shift, demonstrating the relevance of charge−quadrupole interactions for important device parameters (Fig. 4c).

The generation efficiency of photocurrent depends on the dissociation barrier of CT excitons (ΔEdiss), which depends on the difference between ECS and ECT11. We next discuss how quadrupole moments can induce electrostatic gradients at the donor−acceptor interface that lead to a lower ΔEdiss. In the case of a negative quadrupole component Qπ,D of the donor, charge−quadrupole interactions along the π−π-stacking direction reduce IED and EAD of donor molecules within the donor phase (green arrows in Fig. 5a). This shift is smaller at the interface with C60 due to the interaction with its neutral Qπ,A components. The negative Qπ,D influences the energies of acceptor molecules (IEA and EAA) close to the interface, as indicated by the UPS measurements on donor−acceptor blends in Fig. 3. Therefore, the negative Qπ,D induces an electrostatic potential gradient from the donor to the acceptor phase, which directly reduces ΔEdiss.

To analyse ΔEdiss in ZnPc:F4ZnPc:C60 solar cells, we obtain the difference between IED and EAA in ternary blends with UPS and take this as an estimate for ECS45. The results in Fig. 5b show that ECS increases more strongly with Qπ,D as compared to ECT, indicating a rise of ΔEdiss from high ZnPc to high F4ZnPc contents and verifying our considerations that charge−quadrupole interactions can reduce ΔEdiss. For PHJs, we observe a similar increase of ΔEdiss for higher F4ZnPc contents (Supplementary Fig. 13). We perform TDCF measurements11 on ternary solar cells to investigate how the increase of ΔEdiss affects the generation efficiency of free charge carriers. In this method, donor molecules are excited by a short laser pulse. After a delay of 8 ns, when all geminate recombination has taken place46,47 (Supplementary Fig. 14), the charges are extracted by applying a large negative bias voltage. As shown in Fig. 5c, the amount of collected charges follows the current-density/voltage characteristics of the solar cells, revealing that the reduced photocurrent at high F4ZnPc contents is predominantly due to a field-dependent free charge carrier generation11. We attribute the increased field-dependence to the increased ΔEdiss. The increase of ΔEdiss with Qπ,D causes a significant reduction of the device parameters FF and jsc once Qπ,D is larger than −30 ea02 (Fig. 5d). This finding explains the observation in previous studies where the use of F4*ZnPc (a variant of F4ZnPc, see Fig. 1 for the chemical structure) as donor in combination with C60 yields well-performing solar cells48. In contrast to F4ZnPc, F4*ZnPc has a more negative Qπ,D of −41.6 ea02, being sufficiently low to ensure efficient CT exciton separation.

The correlation of FF and jsc with Qπ is not restricted to this particular system. We further calculate Qπ,D and Qπ,A values for three donors (SubNc, ZnPc, F4*ZnPc) each combined with one non-fullerene acceptor (Cl4SubPc or Cl6SubPc). In PHJ devices49, FF and jsc increase for all donors when the acceptor Cl4SubPc is substituted by Cl6SubPc, which can be explained by the increased difference between Qπ,D and Qπ,A (Supplementary Fig. 15). These results indicate that a precise adjustment of Qπ,A being larger than Qπ,D should be considered when designing efficient non-fullerene acceptor molecules. For example, Qπ,A can be increased by adding electron withdrawing side groups to the acceptor. In literature, there are already examples of efficient acceptors having such side groups50,51, where a larger degree of fluorination resulted in an improved charge extraction52. Furthermore, the results of a recent study indicate that quadrupole moments also affect polymer solar cells. Here, an improved charge generation in P3HT/PCBM bilayer solar cells was observed when P3HT was oriented end-on42, which can be explained by the reduced relevance of the positive quadrupole component along the polymer chain (see quadrupole components of alpha-6T in Supplementary Table 1 for comparison). Therefore, quadrupole moments and molecular orientation should be taken more into account for the design of future photovoltaic materials such as small molecules, oligomers and polymers.

## Discussion

In conclusion, we show that charge−quadrupole interactions along the π-π-stacking direction can induce large electrostatic energy shifts to the electronic levels of molecular films, depending on molecular orientation and blend composition. Due to the sensitivity of the interaction energy to the local morphology, the electronic levels of blends strongly depend on the mixing ratio. Utilising the example of OSCs, we show the dependency of the charge-transfer state energy at donor-acceptor interfaces on the quadrupole component in π−π-stacking direction. Moreover, we present a strategy to tune the driving force for free-charge-carrier generation by adjusting the respective quadrupole components, which can be used to optimise non-fullerene acceptor molecules. A similar correlation is found for other materials than ZnPc derivatives, suggesting that our findings can be applied to a large variety of small molecules and polymers. These results highlight the necessity to consider the quadrupole moment as an important molecular parameter in future material design for high-performing organic semiconductor devices.

## Methods

### Ultraviolet photoelectron spectroscopy

The spectra are acquired by a PHOIBOS 100 analyser system (Specs, Berlin, Germany) at a base pressure of 10−11 mbar using He I excitation lines (21.22 eV) and an energy resolution of around 150 meV. By repeating the sample production under the same experimental conditions, the experimental error for the position of the obtained energetic states is estimated to be 50 meV. The Fermi level positions of all spectra are calibrated to the Fermi edges of the gold or silver substrates. All samples are thermally (co-)evaporated at rates of 0.1–0.2 Å s−1 in UHV at a base pressure of 10−8 mbar using individual quartz crystal monitors for each material. As substrates, sputter-cleaned gold foils are used for face-on orientation and silver foils covered by 5 nm of an amorphous layer of p-doped BPAPF (3 wt%, doped with NDP9) for edge-on orientation29. NDP9 is a commercial p-dopant supplied by Novaled GmbH, Germany. The layer thickness of the organic layers under investigation is always 20 nm. IE values are obtained from the sum of the work function and the maximum position of the HOMO peak. The work function is extracted from the onset of the high binding energy cut-off.

### X-ray scattering

The experiments are performed at the ESRF, France (beamline ID03), with a photon energy of E = 22.0 keV. The reciprocal space maps (RSM) are measured under grazing incidence geometry with an angle of incidence of αi = 0.07°. Each RSM is assembled from 16 single images recorded with a PILATUS 300k area detector. All measurements are performed in air. The samples are thermally (co-)evaporated at rates of 0.1−0.2 Å s−1 in UHV at a base pressure of 10−8 mbar using individual quartz crystal monitors for each material. As substrates, glass substrates covered by 1 nm of chromium and 30 nm of gold are used for face-on orientation and glass substrates covered by 5 nm of an amorphous BPAPF are used for edge-on orientation29. The layer thickness of the FnZnPc layers is 20 nm.

### Solar cell device preparation

The solar cells are thermally evaporated at ultrahigh vacuum (base pressure < 10−7 mbar) on a glass substrate with a pre-structured indium tin oxide (ITO) contact (Thin Film Devices, USA). The layer stacks of the ternary bulk heterojunction solar cells are: Glass/ITO/BPAPF:NDP9 (40 nm, 5 wt%)/ZnPc:F4ZnPc (5 nm, varying ratio)/ZnPc:F4ZnPc:C60 (38 nm, varying ZnPc:F4ZnPc ratio, 60 vol% of C60)/C60 (15 nm)/C60:W2(hpp)4 (8 nm, 3 wt%)/Al (100 nm). The layer stacks for planar heterojunctions are: Glass/ ITO/ BPAPF:NDP9 (20 nm, 10 wt%)/ZnPc:F4ZnPc (10 nm, varying ratio)/C60 (40 nm)/BPhen (8 nm)/Al (100 nm). NDP9 is a commercial p-dopant supplied by Novaled GmbH, Germany. All the organic materials were purified 2−3 times by sublimation. The device area of 6.44 mm2 is defined by the geometrical overlap of the bottom and the top contact, verified with a profilometer. To avoid exposure to ambient conditions, the organic part of the device is covered by a small glass substrate which is glued on top. The relative content of donor and acceptor phases in ternary blends is estimated to have a precision of better than ±5 wt%.

### Current−voltage characteristics

The current−voltage characteristics in dark and under solar illumination are measured with a source measure unit (Keithley 2400, USA) at room temperature. For the latter condition, the solar cells are illuminated with a spectrally mismatch-corrected intensity of 100 mW cm−2 (AM1.5G) provided by a sun simulator (16 S-150 V.3 Solar Light Co., USA) and masked to avoid edge effects and to precisely define the area. The intensity is monitored with a calibrated Hamamatsu S1337 silicon photodiode.

### Sensitive external quantum efficiency (sEQE)

The light of a quartz halogen lamp (50 W) is chopped at 141 Hz and coupled into a monochromator (Newport Cornerstone 260 1/4m, USA). The resulting monochromatic light is focused onto the solar cell, of which the short-circuit current is fed to a current pre-amplifier before it is analysed with a lock-in amplifier (Signal Recovery 7280 DSP, USA). The time constant of the lock-in amplifier was chosen to be 0.5 s or 1.0 s and the amplification of the pre-amplifier was increased to resolve low photocurrents. The EQE is determined by dividing the photocurrent of the OSC by the flux of incoming photons, which was measured using a calibrated Si and InGaAs photodiode. The measurements are performed at room temperature.

### Electroluminescence (EL)

EL measurements were obtained at room temperature with an Andor SR393i-B spectrometer equipped with a cooled Si and cooled InGaAs CCD detector array (DU420A-BR-DD and DU491A-1.7, UK). The spectral response of the setup was calibrated with a reference lamp (Oriel 63355). The emission spectrum of the OSCs was recorded at different injection currents with respect to voltages, which were lower than or at least similar to the Voc of the device at 1 sun illumination.

### Time-delayed collection field

In TDCF measurements, the device is excited while held at a varying pre-bias and after a delay time of 8 ns a collection bias of 2.5 V is applied. The excitation was generated with a diode-pumped, Q-switched Nd:YAG laser (NT242, EKSPLA, 500 Hz rep-rate, 5.2 ns pulse duration, 590 nm wavelength). Also, to compensate for the internal latency of the pulse generator, the laser pulse was delayed and homogeneously scattered in an 85 m long silica fibre (LEONI). An Agilent 81150A pulse generator was employed to apply the pre-bias and collection bias to a homebuilt amplifier directly connected to the sample. The current through the device was measured via a grounded 10 Ω resistor in series with the sample and recorded with an Agilent DSO9104H oscilloscope.

### Density functional theory

The simulations are performed to calculate the molecular quadrupole moments, the ionisation energy, and the intramolecular relaxation energy in gas-phase of the relevant molecules. The quadrupole tensor components Qij are obtained from following definition:

$$Q_{ij} = {\int} p ( {\mathbf{r}} ) \cdot \left( 3r_{i} r_{j} - |{\mathbf{r}}|^2 \delta_{ij} \right) \cdot {\mathbf{d}}^3 {\mathbf{r}}.$$
(2)

The ionisation energy was determined as the difference of the total energy of the positively charged molecule and the neutral molecule in the relaxed geometry of the neutral molecule. The intramolecular relaxation energy is determined as the difference in total energy between the negatively (positively) charged molecule in its optimised geometry and its energy in the geometry of the neutral molecule. We used the M06-2x exchange-correlation functional53 and the correlation-consistent basis set cc-pVTZ54 as implemented in the computational chemistry package NWChem55.

The energy is calculated for a given molecule at site rj as a discrete sum including all other molecules (at sites ri) in the considered geometry, according to

$$E_{\mathrm{Q}}\left( {\mathbf{r}}_{j} \right) = {\mathop{\sum }\limits_{i,k}} \frac{q_{j,k}}{8\pi \epsilon_{0} \epsilon_{\mathrm{r}}} \frac{\left( {\mathbf{r}}_{i} - {\mathbf{r}}_{j} - {\mathbf{\tau}}_{k} \right) \cdot {\mathbf{Q}}_{i} \cdot \left({\mathbf{r}}_{i} - {\mathbf{r}}_{j} - {\mathbf{\tau}}_{k} \right)}{\left| {\mathbf{r}}_{i} - {\mathbf{r}}_{j} - {\mathbf{\tau}}_{k} \right|^5}$$
(3)

with the quadrupole tensor Qi of molecule i and the relative dielectric permittivity (assuming εr = 2.856 for all FnZnPcs). Hereby, qj,k is the fractional excess charge at atom k of the molecule j and rj + τk is its position. The quadrupole tensor and the fractional excess charges are obtained in gas phase for all molecules in their respective relaxed structures. The charge distributions and the resulting quadrupole moments might slightly differ in the film phase due to the surrounding polarisable medium. The film structure was generated according to the crystal structure of CuPc57 (see Supplementary Figs. 14). We assume a simplified orthorhombic lattice and take the intermolecular distances (approximately constant 3.8 Å and 13.5 Å) from literature28,30. For face-on geometry, a film thickness of 20 nm implies that we take into account 53 layers along the surface normal. We restrict the summation in lateral directions to a large area of 400 nm × 400 nm, which is sufficient for convergence. For edge-on geometry, we have 15 layers in the direction of the surface normal for a 20 nm film, while the lateral dimension of the integration region is equally big. To investigate the relevant range for the interaction energy, we vary the summation in lateral direction between 10 and 200 nm (Supplementary Fig. 5). In addition, we reduced the thickness of the film in edge-on orientation from 20 to 3 nm and observe an increase of the interaction energy by 10% for ZnPc, in good agreement to the change of IE observed in experiment (Fig. 2d).

### Energy change of CT states due to molecular parameters

We estimate the variation of the CT state energy (ECT) from the change of molecular parameters when replacing ZnPc with F4ZnPc using following expression:

$$E_{\mathrm{CT}} = {\mathrm{IE}}_{\mathrm{0,D}} - {\mathrm{EA}}_{\mathrm{0,A}} - E_{\mathrm{coul,CT}} - \lambda_{\mathrm{D}} - \lambda _{\mathrm{A}},$$
(4)

where IE0,D is the gas-phase ionisation energy of the donor (ZnPc/F4ZnPc) and EA0,A is the gas-phase electron affinity of the acceptor (C60). Ecoul,CT is the Coulomb binding energy between the donor cation and the acceptor anion, which is screened by a mean dielectric constant of εr = 3.6, obtained from εr = 2.8 for ZnPc and εr = 2.8 for C6056. For a detailed description how Ecoul,CT is obtained, we refer the reader to a our previous publication43. λD is the intramolecular relaxation energy of the donor cation and λA is the intramolecular relaxation energy of the acceptor anion. All values are obtained from DFT simulations. To compare with the experimental data in Fig. 4b, we additionally subtract a polarisation energy of 2.1 eV.

## Data availability

All the data supporting the findings of this study are available within the article, its Supplementary Information files, or from the corresponding authors upon reasonable request.

## Code availability

The code used for the calculation of the charge−quadrupole interaction energy is available from the corresponding authors upon reasonable request.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Journal peer review information: Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## References

1. 1.

Forrest, S. R. The path to ubiquitous and low-cost organic electronic appliances on plastic. Nature 428, 911–918 (2004).

2. 2.

Someya, T. et al. A large-area, flexible pressure sensor matrix with organic field-effect transistors for artificial skin applications. Proc. Natl Acad. Sci. USA 101, 9966–9970 (2004).

3. 3.

Mannsfeld, S. C. B. et al. Highly sensitive flexible pressure sensors with microstructured rubber dielectric layers. Nat. Mater. 9, 859–864 (2010).

4. 4.

Søndergaard, R. R., Hösel, M. & Krebs, F. C. Roll-to-roll fabrication of large area functional organic materials. J. Polym. Sci. Part B Polym. Phys. 51, 16–34 (2013).

5. 5.

Zahn, D. R. T., Gavrila, G. N. & Gorgoi, M. The transport gap of organic semiconductors studied using the combination of direct and inverse photoemission. Chem. Phys. 325, 99–112 (2006).

6. 6.

Krause, S., Casu, M. B., Schöll, A. & Umbach, E. Determination of transport levels of organic semiconductors by UPS and IPS. New J. Phys. 10, 085001 (2008).

7. 7.

Vandewal, K. et al. Efficient charge generation by relaxed charge-transfer states at organic interfaces. Nat. Mater. 13, 63–68 (2014).

8. 8.

Sini, G. et al. On the molecular origin of charge separation at the donor−acceptor interface. Adv. Energy Mater. 8, 1702232 (2018).

9. 9.

Benduhn, J. et al. Impact of triplet excited states on the open-circuit voltage of organic solar cells. Adv. Energy Mater. 8, 1800451 (2018).

10. 10.

Vandewal, K., Tvingstedt, K., Gadisa, A., Inganäs, O. & Manca, J. V. On the origin of the open-circuit voltage of polymer–fullerene solar cells. Nat. Mater. 8, 904–909 (2009).

11. 11.

Albrecht, S. et al. On the efficiency of charge transfer state splitting in polymer:fullerene solar cells. Adv. Mater. 26, 2533–2539 (2014).

12. 12.

Bartesaghi, D. et al. Competition between recombination and extraction of free charges determines the fill factor of organic solar cells. Nat. Commun. 6, 7083 (2015).

13. 13.

Tietze, M. L. et al. Correlation of open-circuit voltage and energy levels in zinc-phthalocyanine: C60 bulk heterojunction solar cells with varied mixing ratio. Phys. Rev. B 88, 085119 (2013).

14. 14.

Duhm, S. et al. Orientation-dependent ionization energies and interface dipoles in ordered molecular assemblies. Nat. Mater. 7, 326–332 (2008).

15. 15.

Graham, K. R. et al. The roles of structural order and intermolecular interactions in determining ionization energies and charge-transfer state energies in organic semiconductors. Adv. Energy Mater. 6, 1601211 (2016).

16. 16.

Poelking, C. et al. Impact of mesoscale order on open-circuit voltage in organic solar cells. Nat. Mater. 14, 434–439 (2015).

17. 17.

Poelking, C. & Andrienko, D. Long-range embedding of molecular ions and excitations in a polarizable molecular environment. J. Chem. Theory Comput. 12, 4516–4523 (2016).

18. 18.

D’Avino, G. et al. Electrostatic phenomena in organic semiconductors: fundamentals and implications for photovoltaics. J. Phys. Condens. Matter 28, 433002 (2016).

19. 19.

Yoshida, H., Yamada, K., Tsutsumi, J. & Sato, N. Complete description of ionization energy and electron affinity in organic solids: determining contributions from electronic polarization, energy band dispersion, and molecular orientation. Phys. Rev. B 92, 075145 (2015).

20. 20.

Schwarze, M. et al. Band structure engineering in organic semiconductors. Science 352, 1446–1449 (2016).

21. 21.

Ueno, N. Tuning organic band structures with Coulomb interactions. Science 352, 1395–1396 (2016).

22. 22.

Poelking, C. & Andrienko, D. Design rules for organic donor−acceptor heterojunctions: pathway for charge splitting and detrapping. J. Am. Chem. Soc. 137, 6320–6326 (2015).

23. 23.

Verlaak, S. et al. Electronic structure and geminate pair energetics at organic−organic interfaces: the case of Pentacene/C60 heterojunctions. Adv. Funct. Mater. 19, 3809–3814 (2009).

24. 24.

Sato, N., Seki, K. & Inokuchi, H. Polarization energies of organic solids determined by ultraviolet photoelectron spectroscopy. J. Chem. Soc. Faraday Trans. 2, 1621 (1981).

25. 25.

Schlettwein, D. et al. Electronic energy levels in individual molecules, thin films, and organic heterojunctions of substituted phthalocyanines. J. Phys. Chem. B 105, 4791–4800 (2001).

26. 26.

Tsiper, E. V. & Soos, Z. G. Charge redistribution and polarization energy of organic molecular crystals. Phys. Rev. B 64, 195124 (2001).

27. 27.

Jackson, J. D. Classical Electrodynamics (Wiley, New York, 1998).

28. 28.

Schünemann, C. et al. Zinc phthalocyanine—influence of substrate temperature, film thickness, and kind of substrate on the morphology. Thin Solid Films 519, 3939–3945 (2011).

29. 29.

Schünemann, C. et al. Evaluation and control of the orientation of small molecules for strongly absorbing organic thin films. J. Phys. Chem. C 117, 11600–11609 (2013).

30. 30.

Brendel, M. et al. The effect of gradual fluorination on the properties of FnZnPc thin films and FnZnPc/C60 bilayer photovoltaic cells. Adv. Funct. Mater. 25, 1565–1573 (2015).

31. 31.

Yamada, K. et al. Impact of the molecular quadrupole moment on ionization energy and electron affinity of organic thin films: experimental determination of electrostatic potential and electronic polarization energies. Phys. Rev. B 97, 245206 (2018).

32. 32.

Banerjee, R. et al. Evidence for knetically limited thickness dependent phase separation in organic thin film blends. Phys. Rev. Lett. 110, 185506 (2013).

33. 33.

Moench, T. et al. Influence of meso and nanoscale structure on the properties of highly efficient small molecule solar cells. Adv. Energy Mater. 6, 1501280 (2016).

34. 34.

Mönch, T. et al. Experimental and theoretical study of phase separation in ZnPc:C60 blends. Org. Electron. 27, 183–191 (2015).

35. 35.

Schünemann, C. et al. Phase separation analysis of bulk heterojunctions in small-molecule organic solar cells using zinc-phthalocyanine and C60. Phys. Rev. B 85, 245314 (2012).

36. 36.

Lorch, C. et al. Controlling length-scales of the phase separation to optimize organic semiconductor blends. Appl. Phys. Lett. 107, 201903 (2015).

37. 37.

Abtahi, A. et al. Effect of halogenation on the energetics of pure and mixed phases in model organic semiconductors composed of anthradithiophene derivatives and C60. J. Phys. Chem. C 122, 4757–4767 (2018).

38. 38.

Chen, W. et al. Molecular orientation dependent energy level alignment at organic−organic heterojunction interfaces. J. Phys. Chem. C 113, 12832–12839 (2009).

39. 39.

Zhong, J. Q. et al. Effect of gap states on the orientation-dependent energy level alignment at the DIP/F16CuPc donor−acceptor heterojunction interfaces. J. Phys. Chem. C 115, 23922–23928 (2011).

40. 40.

Bussolotti, F., Kera, S., Kudo, K., Kahn, A. & Ueno, N. Gap states in pentacene thin film induced by inert gas exposure. Phys. Rev. Lett. 110, 267602 (2013).

41. 41.

Han, W., Yoshida, H., Ueno, N. & Kera, S. Electron affinity of pentacene thin film studied by radiation-damage free inverse photoemission spectroscopy. Appl. Phys. Lett. 103, 123303 (2013).

42. 42.

Wang, F. et al. Effects of end-on oriented polymer chains at the donor/acceptor interface in organic solar cells. J. Mater. Chem. A 6, 22889–22898 (2018).

43. 43.

Schwarze, M. et al. Molecular parameters responsible for thermally activated transport in doped organic semiconductors. Nat. Mater. 18, 242–248 (2019).

44. 44.

Vandewal, K., Tvingstedt, K., Gadisa, A., Inganäs, O. & Manca, J. V. Relating the open-circuit voltage to interface molecular properties of donor:acceptor bulk heterojunction solar cells. Phys. Rev. B 81, 125204 (2010).

45. 45.

Widmer, J., Tietze, M., Leo, K. & Riede, M. Open-circuit voltage and effective gap of organic solar cells. Adv. Funct. Mater. 23, 5814–5821 (2013).

46. 46.

Armin, A., Durrant, J. R. & Shoaee, S. Interplay between triplet-, singlet-charge transfer states and free charge carriers defining bimolecular recombination rate constant of organic solar cells. J. Phys. Chem. C 121, 13969–13976 (2017).

47. 47.

Collado-Fregoso, E. et al. Energy-gap law for photocurrent generation in fullerene-based organic solar cells: the case of low-donor-content blends. J. Am. Chem. Soc. 141, 2329–2341 (2019).

48. 48.

Meiss, J. et al. Fluorinated zinc phthalocyanine as donor for efficient vacuum-deposited organic solar cells. Adv. Funct. Mater. 22, 405–414 (2012).

49. 49.

Cnops, K. et al. Energy level tuning of non-fullerene acceptors in organic solar cells. J. Am. Chem. Soc. 137, 8991–8997 (2015).

50. 50.

Hou, J., Inganäs, O., Friend, R. H. & Gao, F. Organic solar cells based on non-fullerene acceptors. Nat. Mater. 17, 119–128 (2018).

51. 51.

Che, X., Li, Y., Qu, Y. & Forrest, S. R. High fabrication yield organic tandem photovoltaics combining vacuum- and solution-processed subcells with 15% efficiency. Nat. Energy 3, 422–427 (2018).

52. 52.

Fan, B. et al. Fine-tuning of the chemical structure of photoactive materials for highly efficient organic photovoltaics. Nat. Energy 3, 1051–1058 (2018).

53. 53.

Zhao, Y. & Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other function. Theor. Chem. Acc. 120, 215–241 (2008).

54. 54.

Dunning, T. H. Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90, 1007 (1989).

55. 55.

Valiev, M. et al. NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun. 181, 1477–1489 (2010).

56. 56.

Scholz, R. et al. Quantifying charge transfer energies at donor−acceptor interfaces in small-molecule solar cells with constrained DFTB and spectroscopic methods. J. Phys. Condens. Matter 25, 473201 (2013).

57. 57.

Hoshino, A., Takenaka, Y. & Miyaji, H. Redetermination of the crystal structure of α-copper phthalocyanine grown on KCl. Acta Crystallogr. B59, 393–403 (2003).

58. 58.

Vandewal, K. et al. Increased open-circuit voltage of organic solar cells by reduced donor−acceptor interface area. Adv. Mater. 26, 3839–3843 (2014).

59. 59.

Yoshida, H. & Sato, N. A precise analysis of the core-level energy difference between the surface and bulk region of organic semiconductor thin films. J. Phys. Chem. C 116, 10033–10038 (2012).

60. 60.

Gaul, C. et al. Insight into doping efficiency of organic semiconductors from the analysis of the density of states in n-doped C60 and ZnPc. Nat. Mater. 17, 439–444 (2018).

## Acknowledgements

We thank Beatrice Beyer for providing F4ZnPc and F16ZnPc. M.S. acknowledges financial support by the German Research Foundation (DFG) through the project MatWorldNet LE-747/44-1. F.O. would like to thank the DFG for financial support (project OR-349/1). The TDCF setup in Potsdam was partially financed by the DFG through INST 336/94-1 FUGG. This work was supported by the German Federal Ministry for Education and Research (BMBF) grant InterPhase (FKZ 13N13661) and through the InnoProfile project “Organische p-i-n Bauelemente 2.2” (03IPT602X). Moreover, the project received funding from the NMP-20-2014—“Widening materials models” programme under Grant Agreement No. 646259 (MOSTOPHOS). K.L. is a fellow of the Canadian Institute for Advanced Research (CIFAR). We gratefully acknowledge grants for computing time from the Zentrum für Informationsdienste und Hochleistungsrechnen Dresden (ZIH). The X-ray scattering experiments were performed on beamline ID3 at the European Synchrotron Radiation Facility (ESRF), Grenoble, France. We are grateful to Maciej Jankowski for providing assistance at beamline ID3. We acknowledge support by the Open Access Publication Funds of the SLUB/TU Dresden.

## Author information

M.S. designed the study and acquired most of the UPS data. K.S.S., C.G. and R.S. performed DFT simulations. K.O. acquired further UPS data. F.O. calculated charge−quadrupole interaction energies. A.H. performed X-ray scattering experiments. J.B., M.S. and K.V. designed the solar cell devices and J.B. did the characterisation. J.B. and J.K. performed sensitive EQE measurements, whereas J.B. evaluated the data. L.P.T. performed TDCF and EL measurements on ternary BHJ solar cells. S.R. performed EL measurements on PHJ solar cells. M.L. synthesised F8ZnPc. K.L., F.O., K.V., G.C., F.S. and D.N. supervised different parts of the study. D.A. and C.P. valuably contributed to the physical understanding of the underlying electrostatic interactions. M.S., F.O. and K.L. wrote the manuscript and all authors contributed to discussions and finalising the manuscript.

### Competing interests

The authors declare no competing interests.

Correspondence to Martin Schwarze or Frank Ortmann or Karl Leo.