Supporting Information

Transcription

1 Supporting Information Atomistic Approach to Simulate Processes Relevant for the Efficiencies of Organic Solar Cells as a Function of Molecular Properties II. Kinetic Aspects Charlo e Brückner, Frank Würthner, Klaus Meerholz #, Bernd Engels,* Institut für Theoretische Chemie, Universität Würzburg, Emil-Fischer-Straße 42, Würzburg, Germany Institut für Organische Chemie, Universität Würzburg, Am Hubland, Würzburg, Germany # Department Chemie, Universität zu Köln, Luxemburgerstr. 116, Köln, Germany bernd.engels@uni-wuerzburg.de, phone number: (+49) , fax number: (+49) Table of Contents: 1. Distance criterion used for selection of dimers 2. Approximate scheme for obtaining couplings between fullerene molecules 3. Intramolecular photoisomerization for HB194 and MD Effective epsilon values used for the calculation of the Coulomb attraction between geminate electron-hole pairs 5. Derivation of Gaussian disorder parameters for energetic disorder 6. Determination of number of MC steps per MC trajectory 7. Threshold values for minimal exciton diffusion and charge separation 8. Absolute radiative decay rates for all molecules 9. Extrapolation scheme for larger systems 10. Device parameters used for calculation of hole mobilities 11. Visualization of the geometrical arrangements as a function of the crystallographic orientation for the first layer of the p-type semiconductor 12. References S1

2 1. Distance criterion used for selection of dimers Couplings between neighboring molecules are only calculated if the distance between the centers of mass of the two molecules does not exceed a certain threshold value. Threshold values can be found in Table S1. Table S1: Threshold distances between molecules for calculation of couplings. Equal threshold values are used for exciton and charge transport coupling values. p-type molecule plane max. distance homodimers [Å] anthracene a-b 5.5 in-plane 11.0 out-of-plane a-c 5.5 in-plane 11.0 out-of-plane b-c 5.5 in-plane 11.0 out-of-plane diketopyrrolopyrrole a-b 10.0 in-plane 14.0 out-of-plane max. distance heterodimers [Å] max. distance fullerenes [Å] a-c b-c DIP a-b 7.0 in-plane out-of-plane a-c b-c HB194 a-b a-c b-c MD353 a-b a-c b-c rubrene a-b 11.0 in-plane out-of-plane a-c b-c 11.0 in-plane out-of-plane squaraine a-b a-c b-c a-b a-c b-c aldehyde-sub. a-b a-c b-c methoxy-sub. a-b a-c b-c Please note that in some cases, larger distances were used perpendicular to the stacking direction so that transport could also be modeled in these directions. S2

3 2. Approximate scheme for obtaining couplings between fullerene molecules Fullerene C 60 possesses a three-fold degenerate LUMO. Upon coupling to a second fullerene molecule, the degeneracy is removed (due the reduction of symmetry) and the orbitals split (due to the interaction with the other fullerene). The process is illustrated in Figure S1. Figure S1: Orbital splitting in fullerene dimers. Strictly speaking, the coupling strength cannot be calculated in the case of degenerate or neardegenerate orbitals via the adiabatic splitting method. We approximate average lower and upper orbitals in the case of the fullerene just by the middle orbital of the respective groups. For the the average of the two upper or the two lower orbitals was taken to approximate the coupling strength. S3

4 3. Intramolecular photoisomerization for HB194 1 and MD353 2 Multidimensional spectroscopic investigations conducted by Brixner et al. revealed an ultrafast photoisomerization of a merocyanine at times larger than 100 fs. 3 Although a full isomerization is sterically not feasible in amorphous solid-state systems, partial twisting is possible. We discussed previously that this could be an energy loss channel for merocyanines. 4 Therefore, for exciton transport in the merocyanines HB194 and MD353, a constant rate for torsion of 200 fs was included in every hopping step. As soon as this route is chosen, the exciton becomes trapped and decays eventually. Trapping in the DIP phase was similarly included via a constant rate leading to immobilized excitons (similar to radiative decay). S4

5 4. Effective epsilon values used for the calculation of the Coulomb attraction between geminate electron-hole pairs The effective epsilon values used to calculate are analog to our previous investigation and are displayed in Table S2. Table S2: Effective epsilon values used for the calculation of the Coulomb interaction. Molecule ε(interface, Coulomb) anthracene 2 diketopyrrolopyrrole 5 DIP 2 HB194 7 MD353 7 rubrene 2 squaraine 5 3 aldehyde-sub. 3 methoxy-sub. 3 S5

6 5. Derivation of Gaussian disorder parameters for energetic disorder The Gaussian disorder parameter σ is calculated from the standard deviation of the dimer energies (i.e., excitation energies of dimers, ionization potentials of dimers). Disorder parameters are shown in Table S3. Please note that they are rather small. 5 This suggests that the dimer calculations account for disorder in an average way. Since the site energy disorder in the fullerene phase is considerably smaller, it was neglected. Table S3: Gaussian disorder parameters used for exciton and charge transport. Molecule σ(exciton) [mev] σ(charge) [mev] anthracene diketopyrrolopyrrole DIP HB MD rubrene squaraine aldehyde-sub methoxy-sub S6

7 6. Determination of number of MC steps per MC trajectory For each system, i.e., each crystallographic plane, several different starting points (15 20, depending on the threshold values) were chosen. For each starting point, 100 trajectories were run and averaged. The number of steps per trajectory was calculated from the number of p-type molecule dimers and fullerene dimers for which couplings were computed, i.e., which were selected based on the distance criterion. This has the advantage that the size of the systems and its dimensionality, i.e., its intermixing and interpenetration, is implicitly included in the number of MC steps per trajectory # ( ). # ( )=400+2 ( + ) To investigate the influence of the number of steps within the KMC, we repeated the simulations with 1400 instead of 400 steps and a higher prefactor of 10, i.e., the number of steps increased by a factor larger than 6. The resulting changes turned out to be insignificant. S7

8 7. Threshold values for photon absorption and charge separation As described in the text, the exciton should cover a minimal distance between the points of photon absorption and the interface to include effects of exciton diffusion. For this distance, a percentaged value of the total size of the bulk phase of the p-type semiconductor is used (which are approximately equal and can be found in our previous work 6 ). As also the number of MC steps is proportional to the system size, the exciton must diffuse for longer distances in a slightly larger system, but also has more time, i.e., more MC steps. The values were chosen in order to have approximately equal amounts of starting points for the MC trajectories. The same is true for the definition of charge separation. Charges are considered as separate as soon as the charge in the positive bulk phase reaches a certain minimal percentaged distance from the interface. Values are given in Table S4. Table S4: Percentaged values used for determining grid points of photon absorption and charge separation. Molecule Exciton generation [%] of total dimension Charge separation [%] of total dimension anthracene diketopyrrolopyrrole DIP HB MD rubrene squaraine aldehyde-sub methoxy-sub To analyze the changes upon decreasing the threshold values in Table S4, additional KMC simulations were conducted using 50% for both values. Apart from increased exciton dissociation and charge separation efficiencies, no qualitative changes were observed in terms of KMC efficiencies or velocities. S8

9 8. Absolute radiative decay rates for all molecules Similar to the trapping, radiative decay is included in the exciton transport process as a loss mechanism with a constant rate. As soon as it occurs, the exciton vanishes and the MC stops. As described in the text, radiative decay rates are estimated via the Strickler-Berg relationship. They are displayed in Table S5. Table S5: Radiative decay rates employed for the molecules in the MC simulations. Molecule Radiative decay rate [ -s ] anthracene diketopyrrolopyrrole DIP HB MD rubrene squaraine aldehyde-sub methoxy-sub S9

10 9. Extrapolation scheme for larger systems We are only interested in the transport perpendicular to the interface, i.e., in transport in only one direction. Diffusion in kinetic Monte Carlo depends on the square of the displacement, ². Thus we assume that the error due to finite-size effects squares with the square of the dimensions of the system. Hence we utilize the following extrapolation scheme to extrapolate from our calculated mobilities to mobilities in a thin-film organic solar cell with a thickness of 50 nm,, assuming that mobilities and diffusion coefficients are related. = S10

11 10. Device parameters used for calculation of hole mobilities We directly extract drift velocities from the kinetic Monte Carlo simulations. Mobilities can be obtained from the drift velocities via the electric field strength, : = To calculate the electric field strength, we assume a built-in voltage of 0.5V 7,8 and a thickness of the thin-film of 50 nm, 9 corresponding to reasonable values used for the simulation. Please note that the influence of this built-in electric field on the charge transport rates was not taken into account in the KMC simulations. First of all, it is not known what shape the electric potential decrease across the organic::organic interface has (linear, etc.). Secondly, and most importantly for these simulations, the assumed homogeneous electric field across the interface due to the built-in voltage has a strength of Our model systems have average sizes of around 50A. Charge pairs are generated in these model systems. One charge feels the electric field created by the other. The field of a point charge at an (arbitrarily chosen) average distance of 25A attains sizes of It is hence at least one order of magnitude larger than the built-in electric field. Therefore, due to the limited size of our systems, which we later-on account for in the approximate extrapolation scheme, we neglect the effect of the built-in electric field on the rates although we use it to calculate the mobilities. This explains also why we use brackets to designate the charge (drift) velocities. Charge drift implies that the direction of charge transport is determined by an electric field gradient, which we did not include in the simulations and only considered in the subsequent evaluation. S11

12 11. Visualization of the geometrical arrangements as a function of the crystallographic orientation for the first layer of the p-type semiconductor The construction of the interfacial models started with the generation of the p-type semiconducting bulk phase. 6 For its first layer, we used the different crystallographic orientations of available experimental crystal structures. For the construction of the next layers, we mimicked the experimental spin-coating/coevaporation procedure as described in our previous paper. 6 The resulting model systems are named according to the crystallographic orientation of first layer. The different interfacial model systems for the DIP::fullerene system are shown in Figure S2 to Figure S4. The crystallographic orientations are taken from the crystal structure. 10 Figure S2: (a-b)-dip::fullerene system. The DIP molecules take on a tip-on orientation on top of the fullerene phase. Figure S3: (a-c)-dip::fullerene system. The DIP molecules are predominantly orientated face-on with respect to the fullerene phase. S12

13 Figure S4: (b-c)-dip::fullerene system. Somewhat edge-on orientations of DIP molecules on top of fullerenes prevail. Similarly, different rubrene::fullerene interfacial model systems are constructed from different crystallographic orientations of the rubrene phase on top of the fullerenes. The starting point was again the rubrene crystal structure. 11 The systems are shown in Figure S5 through Figure S7. Figure S5: (a-b)-rubrene::fullerene system. Stacked rubrene molecules are tilted by approximately 45 with respect to the fullerene surface. S13

14 Figure S6: (a-c)-rubrene::fullerene system. Figure S7: (b-c)-rubrene::fullerene system. For this crystallographic starting orientation, rubrene molecules are standing tipon on the fullerene phase. In contrast to DIP and rubrene, the molecular orientations of other molecules in the crystal structures are not necessarily reflected in the crystallographic orientations, i.e., no differences between different amorphous model systems can be observed via visual inspection. This is especially evident for triphenylamine-based compounds. Due to their three-dimensional structures, no orientational preferences like edge-on/face-on/tip-on can be observed. Nevertheless, the amorphous model systems differ in terms of their electronic structure. S14

15 12. References (1) Bürckstümmer, H.; Tulyakova, E. V.; Deppisch, M.; Lenze, M. R.; Kronenberg, N. M.; Gsänger, M.; Stolte, M.; Meerholz, K.; Würthner, F. Efficient Solution-Processed Bulk Heterojunction Solar Cells by Antiparallel Supramolecular Arrangement of Dipolar Donor-Acceptor Dyes. Angew. Chem. Int. Ed. 2011, 50 (49), (2) Kronenberg, N. M.; Deppisch, M.; Würthner, F.; Lademann, H. W. A.; Deing, K.; Meerholz, K. Bulk Heterojunction Organic Solar Cells Based on Merocyanine Colorants. Chem. Commun. 2008, No. 48, (3) Ruetzel, S.; Diekmann, M.; Nuernberger, P.; Walter, C.; Engels, B.; Brixner, T. Multidimensional Spectroscopy of Photoreactivity. Proc. Natl. Acad. Sci. U. S. A. 2014, 111 (13), (4) Brückner, C.; Walter, C.; Stolte, M.; Braïda, B.; Meerholz, K.; Würthner, F.; Engels, B. Structure Property Relationships for Exciton and Charge Reorganization Energies of Dipolar Organic Semiconductors: A Combined Valence Bond Self-Consistent Field and Time- Dependent Hartree-Fock and DFT Study of Merocyanine Dyes. J. Phys. Chem. C 2015, 119 (31), (5) Hertel, D.; Bässler, H. Photoconduction in Amorphous Organic Solids. ChemPhysChem 2008, 9 (5), (6) Brückner, C.; Würthner, F.; Meerholz, K.; Engels, B. Atomistic Approach to Simulate Processes Relevant for the Efficiencies of Organic Solar Cells as a Function of Molecular Properties. I. Thermodynamic Aspects. J. Phys. Chem. C 2016, DOI: /acs.jpcc.6b (7) Siebert-Henze, E.; Lyssenko, V. G.; Fischer, J.; Tietze, M.; Brueckner, R.; Schwarze, M.; Vandewal, K.; Ray, D.; Riede, M.; Leo, K. Built-in Voltage of Organic Bulk Heterojuction P-I-N Solar Cells Measured by Electroabsorption Spectroscopy. AIP Adv. 2014, 4 (4), (8) Li, C.; Credgington, D.; Ko, D.-H.; Rong, Z.; Wang, J.; Greenham, N. C. Built-in Potential Shift and Schottky-Barrier Narrowing in Organic Solar Cells with UV-Sensitive Electron Transport Layers. Phys. Chem. Chem. Phys. 2014, 16 (24), (9) Tress, W.; Leo, K.; Riede, M. Optimum Mobility, Contact Properties, and Open-Circuit Voltage of Organic Solar Cells: A Drift-Diffusion Simulation Study. Phys. Rev. B 2012, 85 (15), (10) Heinrich, M. A.; Pflaum, J.; Tripathi, A. K.; Frey, W.; Steigerwald, M. L.; Siegrist, T. Enantiotropic Polymorphism in Di-Indenoperylene. J. Phys. Chem. C 2007, 111 (51), (11) Jurchescu, O. D.; Meetsma, A.; Palstra, T. T. M. Low-Temperature Structure of Rubrene Single Crystals Grown by Vapor Transport. Acta Crystallogr. B. 2006, 62 (Pt 2), S15