Benduhn, J.

Czyrska-Filemonowicz, A.

Friederich, P.

Holzmueller, F.

Koerner, C.

Leo, K.

Moench, T.

Rutkowski, B.

Strunk, T.

Vandewal, K.

Wenzel, W.

English

KITopen

as donor and the fullerene C 60 as acceptor (see  Figure   1  ). [ 11,14–19 ] With this material system, calibrated PCEs of 8.3% were recently achieved. [ 20 ]  To analyze the various BHJ absorber layer morphologies created by different substrate temperatures during mate-rial deposition, we utilized a scanning transmission electron microscope (STEM) equipped with a high-angle annular dark fi eld (HAADF) and energy dispersive X-ray (EDX) detector. [ 21 ] Hence, we are able to study the phase separation by means of chemical contrast at relevant nanoscopic length scales. [ 22,23 ] To compare changes in the effective interface area upon substrate heating, we used sensitive external quantum effi ciency (sEQE) measurements. [ 24 ]  Subsequently, the experimental fi ndings from the STEM-EDX images are used in microscopic and mesoscopic models to obtain 3D morphologies of the donor–acceptor blend, allowing for a straightforward interpretation of the current–voltage ( j–V) curves in terms of microscopic parameters such as exciton migration, percolation paths, etc. We show that energetic disorder is the limiting parameter, determining the effi ciency of organic solar cells instead of donor and acceptor domain sizes.  2.  Results  2.1.  Device Characterization  Three OSCs were prepared with the layer sequence shown in Figure  1 . For device A, the DCV5T-Me:C 60 absorber layer was deposited at room temperature (RT). The absorber layers of devices B and C at  T sub = 80 °C and  T sub = 140 °C, respectively. The  j – V characteristics of the respective OSCs were recorded with a mismatch corrected illumination to achieve AM1.5 equivalent conditions. The recorded  j – V curves are presented in  Figure   2  a and the extracted solar cell parameters in  Table  1  .  The  j – V characteristics reveal that moderate substrate heating improves the device performance. The fi ll factor (FF) increases from 43% to 57%, which is a clear indication for an enhanced charge carrier extraction. The short-circuit current  Figure 1.  Layer sequence of the investigated OSCs and the corresponding molecular structures of its compounds. DCV5T-Me and C 60 constitute the absorber layer. For this study, they have been deposited at various substrate temperatures  T sub . The absorber layer is sandwiched between an electron conducting C 60 layer and a hole conducting BPAPF layer. To place the absorber layer in the optical fi eld maximum, optically transparent, highly conduc-tive n-doped (C 60 :W 2 (hpp) 4 ) and p-doped (BPAPF:NDP9 and BF-DPB:NDP9) layers are attached.respective electrodes and suffi cient donor–acceptor-interface for exciton dissociation.  Increasing the substrate temperature during absorber layer deposition to  T sub = 140 °C results in a decreased solar cell PCE. The STEM-HAADF image ( Figure   5  a) indicates large thickness fl uctuations. A large surface roughness of the absorber layers is disadvantageous for a solar cell because it induces increased shunting of the device. Furthermore, the induced light scat-tering complicates the optical optimization of the device by means of transfer-matrix methods, possibly placing the absorber layer outside the optical fi eld maximum. Moreover, the STEM-EDX images (Figure  5 b,c) indicate a disadvantageous, large-area  Figure 3.  STEM images of a DCV5T-Me:C 60 blend layer deposited at  T sub = RT. The STEM-HAADF image a) shows small thickness variations of the DCV5T-Me:C 60 sample, whereas the STEM-EDX images b) and c) show the quantitative elemental distribution of carbon and sulfur indicating C 60 and DCV5T-Me-rich areas. Figure 4.  STEM images of DCV5T-Me:C 60 deposited at  T sub = 80 °C. The STEM-HAADF image a) is indicating an overall homogeneous sample thick-ness. The STEM-EDX images depicted in b) and c) show small C 60 rich domains in a well-connected DCV5T-Me enriched network. Figure 5.  STEM images of DCV5T-Me:C 60 deposited at  T sub = 140 °C. The STEM-HAADF image a) indicates strong thickness variations. The STEM-EDX images b) and c) show dark spots of 0 wt% material content, indicating an incomplete substrate coverage as well as disadvantageous phase separation of the constituents. Note the larger scale bar as compared to Figure  4 .connectivity of material domains, but also facilitate charge carrier recombination, hereby counterbalancing an increased internal quantum effi ciency by a worsened charge carrier col-lection effi ciency.  In order to quantify the interplay between domain size and island formation, we generate 3D morphologies based on the STEM-EDX data for the RT and the  T sub = 80 °C samples and estimate the exciton and charge mobility in both samples. We do not consider the  T sub = 140 °C sample in the simulations as the layer is not entirely closed.  2.3.1.  Mesoscale Monte Carlo Simulations  To generate 3D morphologies, we applied a Monte Carlo (MC) simulated annealing method (see the Experimental section) based on 2D STEM-EDX data. [ 28 ] We utilized a heuristic model using the sulfur-sensitive images shown in Figures  3 c and  4 c, to extract the relative amount of DCV5T-Me in the layer below every pixel of the STEM-EDX image. Afterwards, we generated 3D morphologies that have an identical out-of-plane-projection of the DCV5T-Me content as the STEM-EDX data. Representa-tive illustrations of the morphologies with realistic domain sizes and interconnectivity in all 3 dimensions are shown in  Figure   7  .  Based on these morphologies, we compute the fraction of voxels in each material that are connected to their respective electrode. In agreement with visual inspection, we fi nd the 80 °C sample to consist of essentially two interpenetrating, singly connected C 60 and DCV5T-Me domains that percolate through the entire sample. Surprisingly, the connectivity of the RT sample is equally good, despite its apparent bulk-interface roughness of the domains in the volume. At both substrate tem-peratures, >99% of the voxels in both domains are connected to the electrodes. This is in agreement with percolation theory, as the volume fraction of the two material components is larger than the percolation threshold of 0.10–0.31, depending on the degree of connectivity. [ 29,30 ] The consequence of this fi nding is depicted in the side views shown in Figure  7 c,d, where the color represents the connectivity of material domains. It is visible that almost all domains are interconnected with each other and build up a complete percolation network (marked in blue). This result explains the observation of similar currents at high nega-tive voltages in Figure  2 a. Under these conditions, almost all charge carriers with a connection to the electrodes are extracted with negligible recombination losses and thus, only exciton  Figure 7.  a,b) Top and side views on the 3D DCV-5T-Me (colored):C 60 (transparent) microstructure generated by the described MC simulated annealing scheme based on STEM images (Figures  3 c and  4 c). Part a) shows the simulated morphology of the RT sample and b) of the 80 °C sample. Parts c) and d) show representative vertical slices of the morphologies viewed from the arrow direction for the RT and the 80 °C morphology, respectively.Connected domains are drawn in the same color.relatively pure domains in the 80 °C sample and strongly mixed domains in the RT sample. The width of this distri-bution is closely related to the local density of states and is calculated using the Quantum Patch method. [ 38 ] We fi nd that the width of electrostatic energetic disorder in the pristine C 60 system is 8 meV for electrons and 3 meV for holes, respec-tively. Combined with thermal fl uctuations of ≈25 meV, we obtain values of ≈26 meV which is commensurate with lit-erature data for crystalline organic semiconductors. [ 39 ] In the mixed morphology shown in Figure  8 b, the energy disorder of C 60 molecules (see Figure  8 d) is drastically increased to 158 meV for electrons and 164 meV for holes. This order-of-magnitude increase is caused by the random orientation distribution of DCV5T-Me molecules with respect to the C 60 molecules. The intrinsic electrostatic dipole moment of the DCV5T-Me (1.0 Debye) generates a very different electro-static environment for each C 60 mole cule, which shifts their respective energy levels. As a result, we obtain a two to three orders of magnitude increase in charge carrier mobility in pure domains of the 80 °C, compared to the mixed RT sample domains (see the Supporting Information for details). As the exciton diffusion coeffi cient and the exciton diffusion length are exponentially dependent on the energy disorder, we expect a similar effect for excitons, which would largely over-compensate for the increased domain size at the  T sub = 80 °C sample. [ 35 ] Note that the size of the dipole moment will barely affect the exciton mobility in pristine DCV5T-Me domains as in the 80 °C sample, as these are expected to be highly ordered and, thus, have an energy disorder similar to the low values computed for C 60 above. [ 36 ]  3.  Discussion  We are able to explain the origins for the improved perfor-mance of the 80 °C sample, combining the experimental fi nd-ings from OSC and morphology characterization with the computational results. Starting from exciton generation, we fi nd a decreased direct absorption into the CT state due to a declined interfacial area in the 80 °C sample compared to the RT sample. Nonetheless, this effect plays only a minor role as most of the absorbed photons generate bound Frenkel type excitons in the absorber.  These excitons have to reach a material interface within their lifetime. Our microstructural analysis yields an increased domain size in the 80 °C sample resulting in two to three times larger average distances (≈10 nm) to the nearest donor–acceptor interface compared to the RT sample. This is still within the limits of typical exciton diffusion lengths of 5–40 nm and matches the value for DCV-6T ( ±9 3  nm). [ 31,40–42 ] Therefore, we expect that the fraction of excitons reaching a material interface and being dissociated into electron-hole pairs is not reduced for the sample prepared at 80 °C.  The high current density compared to the RT sample in the  j–V curve for negative voltages confi rms this experimentally. As the external electric fi eld does not infl uence the diffusion pro-cess of a neutral exciton, this current density refl ects the total amount of electrons and holes being generated in the sample and extracted due to the high fi eld strength. separation and material connectivity play a role. An experi-mentally accessible parameter related to the domain size is the interface area, which we estimated above using sEQE measure-ments. From the simulated 3D morphology, we derive an inter-face area per volume in the 80 °C sample which is around 70% smaller than the interface area per volume in the RT sample. This decrease in interface area is in agreement with the sEQE measurement, although the experimental DCV5T-Me:C 60 bulk-interface roughness cannot be resolved with the fi nite voxel size in the simulations.  Based on the simulated 3D morphologies, we compute the mean distance an exciton has to travel to reach an interface. The distribution of distances to the interface (see Figure S4 in the Supporting Information) results in an average equivalent sphere radius of  R RT = 3.1 nm and 2.8 nm for C 60 and DCV5T-Me domains, respectively. For the device prepared at  T sub = 80 °C, we obtain  R 80°C = 10.6 nm and 9.8 nm for C 60 and DCV5T-Me, respectively. These average equivalent sphere radii are in good agreement with the 2D images in Figures  3 cand Figure  4 c. Even though the equivalent sphere radius in the 80 °C sample is ≈10 nm, 83% of the excitons generated are within 4 nm from a donor–acceptor interface. Those values demonstrate that the phase separation at this substrate temperature is just favorably to avoid losses due to exciton recombination, as it is still in the range of estimated values of the exciton diffusion length for this material class ( ±9 3 nm for the DCV6T derivative). [ 31 ]  2.3.2.  Microscopic Simulations  In order to understand why the RT sample has a smaller EQE than the 80 °C sample, we next consider the infl uence of the microscopic material composition on the charge car-rier mobility. It is well known that the most signifi cant factor affecting the zero-fi eld mobility of charge carriers in disor-dered organic semiconductors is the width of the distribution of site energies  σ in the system. [ 32–35 ] In principle, there are two sources for energy differences of charge carriers on dif-ferent sites: (1) differences of the molecular geometry and (2) polarization effects. As both C 60 and DCV5T-Me are relatively rigid, the energy disorder mainly arises from electrostatic inter actions between the molecules at different sites and their environment. [ 36 ] In order to estimate the energetic disorder as a function of the local material composition, we investigate the strength of polarization effects and their infl uence on the local energy levels in mixed and pristine material domains. The mixed material domains represent highly disordered material regions in close proximity to the heterointerface which are mainly found in the RT sample. To account for this interface-disorder effect, we generate atomically resolved models for pure C 60 and mixed DCV5T-Me:C 60 morphologies, representa-tive for the small domains in the RT sample, using a force-fi eld based MC simulated annealing protocol. [ 37 ] The morpholo-gies contain 700 molecules each nd are periodically extended in  x - and  y -direction in order to obtain an electrostatic bulk embedding.  Figure   8  shows the on-site energetic disorder distribution of pure C 60 (Figure  8 c) and mixed DCV5T-Me:C 60 domains (Figure  8 d), which correspond to the limiting cases of large,  We furthermore fi nd in the analysis of the 3D domain struc-ture that the connectivity of the percolation network is equally good in the 80 °C sample and in the RT sample. The inter-penetrating domain network comprises more than 99% of the molecules in the bulk-heterojunction, providing well connected transport paths for the majority of charge carriers towards their respective transport layers.  This fi nding depends only on the volume fraction of the two materials. 3D percolation theory for different connectivity models predicts infi nite percolation paths without signifi cant island formation for material fractions larger than 12%–30% of the material volume. [ 29,30 ] For most BHJs used in OSC, both materials have a signifi cantly larger fraction than these values. Therefore, this result can be generalized: Carrier trapping due to the formation of small isolated islands will only play a role for extreme volume ratios and is usually independent of the domain sizes in the BHJ. Note that despite an island-free perco-lation network, dead-end formation of material domains in fi eld direction may lead to charge traps.  Due to the independence of the percolation network on the domain sizes, we emphasize another parameter playing an important role for charge transport, namely the energetic disorder. Mixed material domains in close proximity to a dis-ordered material interface and other deviations from relatively ordered pure material domains lead to a strong decrease of the charge carrier mobility. This is particularly crucial in the case of material combinations where at least one material has an intrinsic dipole moment, such as DCV5T-Me, leading to energetic disorder contributions from polarization effects. Improved exciton mobility in the more pristine domains of the 80 °C sample increases the exciton diffusion lengths and over-compensates the increased distances to the next material inter-face. At the same time, enhanced charge transport properties lead to a faster charge extraction and to a lower series resistance yielding an improved fi ll factor.  These fi ndings are well supported by both theory and experi-ment and conclusively explain the improved performance of the 80 °C sample. Simultaneously, they give design rules for the development of more effi cient organic solar cells. One impor-tant factor determining the device effi ciency is the formation of pristine and, in the case of materials which have an intrinsic dipole moment, ordered material domains. As shown in this study, this can be achieved e.g., by tuning the substrate tem-perature during deposition of the bulk-heterojunction.  4.  Summary  We characterized the absorber layer morphology of the highly effi cient donor–acceptor couple DCV5T-Me:C 60 on various  Figure 8.  Atomistic morphologies of a) pure C 60 and b) mixed DCV5T-Me:C 60 morphologies. Parts c) and d) show the C 60 on-site energy differences around the HOMO/LUMO (red/green bars and lines) of C 60 for the morphologies shown in (a) and (b). The solid lines represent Gaussian fi ts. The width of these distributions is the energetic disorder and determines the electron and hole mobilities.

Influence of Meso and Nanoscale Structure on the Properties of Highly Efficient Small Molecule Solar Cells

https://publikationen.bibliothek.kit.edu/1000053884/150116549

Influence of Meso and Nanoscale Structure on the Properties of Highly Efficient Small Molecule Solar Cells

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