Mesoscale Ordering and Charge-Transport of Crystalline Spiro

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Mesoscale Ordering and Charge-Transport of Crystalline Spiro-OMeTAD Organic Semiconductors Ilhan Yavuz, and Kendall N. Houk J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08624 • Publication Date (Web): 15 Dec 2016 Downloaded from http://pubs.acs.org on December 16, 2016

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The Journal of Physical Chemistry

Mesoscale Ordering and Charge-Transport of Crystalline SpiroOMeTAD Organic Semiconductors Ilhan Yavuz1* and K. N. Houk2** 1 2

Department of Physics, Marmara University, 34722, Ziverbey, Istanbul, Turkey. Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States.

Supporting Information Placeholder ABSTRACT: The mesoscale ordering and charge-transport of crystalline spiro-OMeTAD, a hole-transporting material extensively used in perosvkite and dye-sensitized solar-cell applications, were explored using molecular dynamics and hole mobility calculations. Morphologies were evaluated through conformational changes, nematic order and paracrystallinity at various temperatures. Charge transport is predicted with electronic structure methods employing a hopping mechanism. Our calculations show that along with strong fluorene backbone packing, phenylenes in the methoxyphenyl-amine substituents of spiro-OMeTAD are an integral part of the material performance. Backbone and substituent paracrystallinity predictions showed highly ordered crystalline phase. The methoxyphenyl substituents have multiple conformations in the unit-cell scale, but interphenylene electronic-coupling remain nearly constant. A thermal increase in positional disorder results in a systematic increase in energetic disorder and a decrease in hole mobility. The predicted crystalline hole mobility is approximately two-orders of magnitude higher than the experimental thin-film measurements, indicating that the performance of spiro-OMeTADs can be improved significantly by exploiting crystallinity.

1. INTRODUCTION Hole transport materials (HTMs) are one of the crucial components of photovoltaic devices with perovskitesensitized or dye-sensitized active layers. HTMs are used to transport photogenerated holes in the active layer to the electrodes and to prevent mechanical active-layer/electrode contacts. To achieve high power conversion efficiencies and long-term device stabilities, novel HTM with a proper energy level offset, high crystallinity and high hole mobility must be 1-9 utilized. However, Belisle et al. have recently shown that 10 level offset has little influence on performance. Tremendous numbers of HTMs have been developed over the years.6,11,12 Among them, spiro-OMeTAD (2,2′,7,7′tetrakis(N,N-di-p-methoxyphenyl-amine) 9,9′spirobifluorene), consisting of two perpendicular fluorene rings with methoxyphenyl-amine substituents (see Scheme 1) is one of the most recognized organic HTMs. It has, undoubtedly, contributed to the rapid rise in the performances of perovskite solar-cell and dye-sensitized 1-9 solar-cells. Amorphous and thin-film features of spiro-

OMeTAD have been known for years, but the crystalline transport characteristics have remained unclear due to structural disorder in the films. Recently, the crystal structure of spiro-OMeTAD has been reported by Ganesan et 13 14 al. , and Shi et al. . They reported the solvent-free crystal structure of spiro-OMeTAD and elucidated the hole transport mechanism with the help of electronic structure 14 methods. The crystal structure of spiro-OMeTAD reveals π-π stacking between fluorenes and random substituent confounded ordering, that is, random alignments with respect to the fluorene backbone (see Scheme 1.). Spiral shapes of the fluorene backbones and π−π stacking between adjacent molecular pairs result in a spiral packing motif along this direction (see Scheme 2). The thin-film hole mobility of -5 -6 2 spiro-OMeTAD is reportedly ~10 -10 cm /Vs by various 14,15 Shi et al. also measured the experimental techniques. -3 single-crystal hole mobility and found a value of 1.3x10 2 cm /Vs, which is two orders of magnitude higher than the 14 best thin-film measurement. The moderately low thin-film mobility can be attributed to the sensitivity of chargetransport to defects. This is also supported by the fact that time-of-flight measurements on the amorphous phase of -4 2 spiro-OMeTAD yielded a mobility of ~10 cm /Vs, which is 16-20 higher than the thin-film mobilities measured this far. These findings suggest that the performance of the crystalline spiro-OMeTAD HTMs could be improved by further device optimizations. Shi et al. performed ωB97X-D/6-31G(d,p) computations to understand the hole mobility of spiro-OMeTAD crystal. They calculated the reorganization energy and electroniccoupling; the two most critical parameters influencing 19,20 charge-transport and mobility. They found a value of 145 meV for the reorganization energy, which approaches that of high-performance rubrene (~160 meV) and higher than that of pentacene (~100 meV). To calculate electronic coupling, they only considered the two types of inter-fluorene packing (labeled as A1 and A2, see Scheme 2) in the spiro-OMeTAD crystal and found that the electronic couplings are on the order of 40 meV for both cases. This value is promising, although it is 2-3 fold less than those of rubrene and 21 pentacene. These findings support the significant enhancement in the crystal hole mobility of spiro-OMeTAD 14 over its disordered thin-film hole mobility.

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Molecular dynamics simulations were performed to understand the relation between the mesoscale morphology and charge-transport of spiro-OMeTADs. Simulations were carried out at various temperatures in order to introduce different levels of disorder. We explored temperatureinduced properties such as conformational changes and nematic ordering of the components of the methoxyphenylamine substituent and paracrystallinity of the backbone and phenylenes. The charge-transport parameters; reorganization energy, electronic coupling and temperature-dependent energetic disorder were evaluated. Hole-mobility of chargetransport was calculated based on kinetic Monte Carlo 21,22 methods employing Marcus theory of charge hopping. We observed strong inter-fluorene backbone packing and phenylenes in the methoxyphenyl-amine substituents substantially influence the morphology of spiro-OMeTADs. The thermal increase in structural disorder broadens electronic-coupling and site-energy distributions, resulting in a systematic increase in trap states and energetic disorder. We predict crystalline hole mobilities assuming perfect structural order, and compare to simulations where we predict crystalline hole mobilities in the presence positional and energetic disorder. We find that predictions of singlecrystal mobility for spiro-OMeTAD is close to the experimental value, but the thin-film mobility prediction is two-orders of magnitude higher than the highest reported experimental thin-film spiro-OMeTAD mobility. Last year we demonstrated a computational multi-scale methodology to compute hole mobilities of both singlecrystal and thin-film organic semiconductors. Our hole mobility predictions were within one order of magnitude of 17 the experimental single-crystal or thin-film hole mobilities. A similar methodology has recently been introduced by Friederich et al. with similar accuracies in mobility 23 predictions. We anticipate that there is still place to improve the performance of the crystalline spiro-OMeTAD, through further morphological optimizations.

2. RESULTS and DISCUSSIONS 2. 1. Packing and morphology Scheme 1 shows the supercell, constructed from the experimental unit-cell, and a representative MD snapshot of spiro-OMeTAD for T=300K. All-atom MD simulations were performed by increasing the temperature of the simulation from 0 to T for 2ns, followed by equilibration for 4ns at an NPT ensemble. A final 20ns production run was performed at constant T temperature. The details of the MD simulations are in the Methods section. As shown in Scheme 1., although there are slight differences, the global order of the packing arrangement is maintained in the supercell. In order to quantify the positional order, we first calculated the temperature-dependence of distributions of the conformational changes in the methoxy groups between 250450K, as presented in Figure 1 (a). The results are shown for the dihedral angle between the C-C-O- C atoms. At low 0 temperatures, the methoxy groups are largely populated at 0 0 with slight populations at ±60 . Comparing with the experimental X-ray crystal structure and the gas phase B3LYP/6-311G(d,p) optimization of the spiro-OMeTAD

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molecule, we see that ~0 conformation in the methoxy group is intrinsically preferred in both cases. As the temperature increases populations are shifted to the more planar conformations due to increasing substituent mobility. To predict the orientational order in spiro-OMeTAD morphologies, we evaluated the temperature dependence of the nematic order tensor, Q, of the fluorene backbones and the phenylene groups; resolved for each particular phenylene of the molecule. Nematic order tensor is defined as,

,

(1)

where N is the total number of molecules, α,β=x,y,z and is th a unit vector normal to the plane of i fluorene backbone or 24 phenylene group. Q=1 and 0 corresponds to perfectly and randomly aligned unit vectors, respectively. We first calculate all the elements of the Q tensor for each system and diagonalize. We report the highest eigenvalues of a Q tensor. We first calculated the nematic order of the backbones at different temperature between the 250-450K range and found almost perfect alignment; since even the lowest Q value is ~0.98 . However, as shown in Figure 1 (b), phenylene groups are well-ordered at all temperatures, since Q values are between 0.92 and 0.98. Nematic order systematically decreases with increasing temperature. Since the relative alignment of the phenylene groups are anisotropic in the crystal, for a certain temperature Q values depend on the relative positions of the phenylene groups, due to restraining effects. For instance, relatively lower Q values at 1,2 and 8th positions correspond to the phenylene rings located at the large gaps within the crystal (see SI). Next, we calculated the distances between the centroids of neighboring molecules, as another measure of the positional disorder. Although being structurally similar, there are two strong and unique π−stacking arrangements in a close neighborhood, labeled as A1 and A2, in Figure 2. Among all others, we also considered another unique packing arrangement of spiro-OMeTAD labeled as Ap, corresponding to a slipped π−π stack between neighboring phenylene units, as shown in Figure 2. As we will show later, Ap exhibits a strong electronic coupling. We first evaluated the average intermolecular distances of A1, A2, and Ap packing and found that the results are very close (i.e., 1-2%) to the experimental crystal structure at low temperatures. The difference between the experimental and simulated values increase with increasing temperature due to supercell expansion. We then calculated paracrystalline order parameter, g, along these directions, defined as g=s/, where s is the standard deviation of an ensemble of 25-27 d distances and stands for the ensemble average. Studies have shown that, g~0-1% corresponds to a nearly 25 perfect order, 1-10% to crystalline order. Temperaturedependent g results for spiro-OMeTAD are shown in Figure 2. At room temperature, g values of A1, A2 and Ap are 1.55%, 1.96% and 0.85%, respectively, indicating a highly ordered crystalline phase. Increasing temperature results in nearly linear increase in g, which correlates with the thermal expansion of the unit-cell (see inset in Figure 2). g1 is higher than g2 at low temperatures, but the difference becomes smaller as the temperature increases. gp is the lowest in the


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250-450 K range; Ap packing is relatively well-ordered. Also, Ap is less sensitivee against temperature-induced disorder, indicated by the gradual increase in gp with increasing temperature.

2. 2. Charge-transport and hole mobility We first evaluated the hole reorganization energy, λ, of the charge-transfer reaction of spiro-OMeTAD, using the fourpoint rule with B3LYP/6-311G(d,p) calculations and found a value of 153 meV. We used this result to evaluate Marcus rates. The λ value we found for spiro-OMeTAD is comparable 28,29 with the λ=160 meV of the high-performance rubrene. Electronic coupling between molecular pairs can define the propensity and efficiency of charge-transport. In Figure 3 (a)(c) we present temperature-dependence of ZINDO electronic-coupling, J, distributions of three strong packing arrangements: A1, A2 and Ap (see Figure 2). The distributions are Poisson-like featuring weak electronic coupling tails. Weak electronic-coupling may lead to trap states thwarting charge-transport rates. We found that the number of trap states (calculated from the number of electronic couplings smaller than 0.1 meV, relative to the total number of Js) is less than 0.5% for A1 and around 1-2% for A2 within the 250450K temperature range. A2 has more trap states comparing with A1, which correlates with the higher paracrystallinity of A2 relative to A1. Although the number of trap states appears to be small in both cases, it 15,2619,30 may lead to significant decrease in transport efficiency. The distributions of A1 and A2 at 300K show peaks at ~40 meV and 10 meV. These values are on the same order of the DFT-predicted J values by Shi et al. for the ideal crystal of 14 spiro-OMeTAD. Although the peak J of A1 is relatively high, and weak-J tail is short, overall charge-transport along the direction of A1 may still be critically affected by the distribution of A2 because of the alternating packing of A1 and A2 (see the spiral packing motif in Scheme 2). Apart from strong π−π stacking of A1 and A2, J distributions of Ap is on the same order (~10 meV). Moreover, the distributions of Ap are narrow relative to A1 and A2 and trap states are ~0%. This distribution and vanishing trap states correspond to very small paracrystallinity of Ap. We can clearly see the influence of temperature on the J-distributions of Ap. The peak position of the J-distribution systematically shifts to weaker electronic coupling and widens with increasing temperature. Local thermal fluctuations in atomic positions result in broadening in the site-energy distributions leading to a marked increase in energetic-disorder, which limits the 19 transport efficiency. We calculated the energetic-disorder, σ, of spiro-OMeTAD from the site-energy difference distributions. As shown in Figure 3 (d), at lower temperatures σ is roughly 85 meV and increases up to 105 meV with increasing temperature. The temperature variation of energetic disorder correlates with the temperature variation in the positional disorder, either can be quantified by nematic order and paracrystallinity. A value of σ=88 meV at 300K is consistent with the typical energetic disorder 21 observed for small organic semiconductors.

Charge-carrier dynamics of spiro-OMeTAD were performed using kinetic Monte Carlo simulations (for details see Methods). All hole mobilities of charge transport were predicted at 300K. We first calculated the ideal crystal µ (i.e. for g→0 and σ→0) of spiro-OMeTAD from the initial -2 2 supercell and found a value of 2.8x10 cm /Vs. The experimental single crystal µ was measured to be 1.3x10 3 2 cm /Vs, which is almost an order of magnitude lower than 14 our prediction. We then calculate room temperature µ of spiro-OMeTAD for crystalline morphologies equilibrated at different annealing temperatures (without re-equilibrating at T=300K) and the results are presented in Figure 3 (e). From 250K to 450K we observed an order of magnitude drop in µ -2 2 from 10 cm /Vs with increasing T. Although the decrease in µ correlates with the increase in energetic disorder, it is obvious that µ is weakly sensitive to energetic-disorder. This could be attributed to the multi-dimensional transport network of crystalline spiro-OMeTAD, making it less 33 vulnerable to charge trapping. The crystalline mobility at -3 2 300K is predicted to be 6.5x10 cm /Vs, which is roughly twoorders of magnitude higher than the experimental thin-film 14,15 hole mobility. The mobility ratio between the predicted -2 2 -2 2 ideal-crystal (2.8x10 cm /Vs) and crystalline (6.5x10 cm /Vs) mobility is 4.3, while the experimetal mobility ratio is 1001000 fold between single-crystal and thin-film. The difference between the theoretical and experimental could be attributed to the highly disordered solution-processed morphology. We then investigated the effect of cooling/heating on charge-transport. For this, we took the final structures of the runs at T (except 300K) and cooled down (or heated up from 250K) to 300 K for 2 ns followed by a production for 8 ns at 300K. As shown in Figure 3 (d), high energetic disorder at high temperatures drops and approaches to σ of 300K, demonstrating the healing of positional and energetic disorder of spiro-OMeTAD. This healing was also reflected from the hole mobility results for the re-equilibrated morphologies. Namely, hole mobilities varied in a small hole -3 2 mobility range of (5-8)x10 cm /Vs, as opposed to an order of magnitude variation in the former case (see Figure 3 (e)), -3 approaching to the hole mobility at 300K, which is 6.5x10 2 cm /Vs. We assess the relationship between inter-phenylene packing and transport performance of spiro-OMeTAD, by performing a series of calculations by systematically exploring main transport pathways. The calculations were performed for an MD snapshot equilibrated at 300K. We first isolated the transport pathways along the spiral network (A1 and A2) and set the rest of the transport rates to zero. We found a value -4 2 of 2.2x10 cm /Vs, which is 30 times lower than the hole mobility of all-included transport. We then added the transport rates between Ap packing and the hole mobility -3 2 became 6.498x10 cm /Vs. Thus, transport pathways along the A1, A2 and Ap packings cover 99.97% of the entire transport and proves the significance of a strong interphenylene π- π stacking.



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2. 3. Dispersive to non-dispersive mobility

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One of the challenges in crystalline organic materials is to understand the influence of local short range order on charge-transport. Thin-films are typically in a polycrystalline phase, therefore the size of crystalline domains, i.e. degrees of short range order, are the crucial factors in 19,34 To address this, we investigated the sizetransport. dependence of energetic disorder and hole mobility of crystalline spiro-OMeTAD. For relatively small scales, mobility is generally sizedependent due to the so-called dispersive transport, and for larger scales size-dependence vanishes (non-dispersive 35,36 transport). Fig, 4 shows the size-dependence, L, of charge-transport for the 300K equilibrated MD snapshot. We only considered size-dependence along the spiral packing direction and maintained lateral packing at a sufficient size to impose non-dispersive transport along these directions. -4 2 For small L, mobility is ~2x10 cm /Vs and increases up to 10 2 2 cm /Vs with increasing L. There is a point (L ~ 6 nm) at which dispersive transport transitions to non-dispersive transport and becomes independent of L. The variation of hole-mobility with L correlates with the variation in energetic disorder, as shown in Figure 4. These results suggest that hole mobility depends on the range of order in the dispersive region. We expect that dispersive crystalline domains in polycrystallines limit charge-transport; this could be one of the origins of low thin-film mobilities measured for spiroOMeTAD.

3. SUMMARY and CONCLUSIONS Mesoscale morphologies and charge-transport of spiroOMeTAD have been studied. Through MD and chargecarrier dynamics simulations we predicted the conformational preferences, nematic order and paracrystallinity at various levels of disorder. We established a relationship between the temperature-induced positional disorder and charge-transport parameters; electroniccoupling distributions, energetic disorder and hole mobility. Due to the spiral shape of the spiro-OMeTAD molecule and strong alternating π-stacking between backbone fluorenes, the packing motifs along the main transport direction is spiral. We found that along with this inter-fluorene packing, a particular inter-phenylene packing is strongly assisting the transport. Positional disorder caused broadening in the electronic-coupling and site-energy distributions, resulting trap states and energetic disorder. Single-crystal and thinfilm hole mobilities are predicted to be higher than the experimental measurements. Finally, dispersive holemobility predictions suggest that transport of spiroOMeTAD is sensitive to the crystalline domain size, which could explain the low large difference between the singlecrystal and thin-film mobility. We anticipate that our study on spiro-OMeTAD not only offers further insight into crystallinity and device performances, but also will inspire further rational holetransporting materials design.

4. METHODS All-atom MD simulations were performed to study the atomistic morphologies of spiro-OMeTAD. An initial supercell containing 1024 molecules was constructed, as presented in Scheme 1. MD simulations in an NPT ensemble were performed for constant temperatures between 250 and 37 450K, using the GPU version of Amber12. Molecular mechanics parameters were prepared using GAFF force-field 38,39 following a procedure described elsewhere. Partial charges of ground-states were generated via Merz-Singh40,41 Kollman scheme , using HF/6-31G(d) method based on B3LYP/6-311G(d,p) optimized geometries, as implemented in 42 Gaussian09 . Periodic boundary conditions (PBC) were employed. The packing geometry was first energy minimized in 1000 MD steps restraining all heavy atom coordinates to their initial values. Each system was then heated for 2ns and then equilibrated for another 2 ns at T, while regulating heat 43 bath temperature at T using Langevin thermostat with a −1 weak collision parameter (5.0 ps ). Additional 2 ns relaxation 43 was carried out with Berensden barostat turned on to relax the system at 1 atm. The final production runs lasted for 20 ns while maintaining heat bath temperature at T and time averaged pressure at 1 atm. We take MD snapshots to simulate atomistic morphologies. A representative MD snapshot for 300K is shown in Scheme 2. Once the MD equilibrated morphologies are at hand, we perform chargecarrier dynamics simulations to calculate charge-transport. For this, we employed the Marcus rate, based on the assumption that charges are localized on each molecule and a non-adiabatic charge transfer reaction occurs in a hoppinglike manner. The high-temperature limit of the Marcus charge-transfer rate is defined as;

,

(2)

where T is the temperature, J is the electronic coupling, λ is the reorganization energy and ∆Eij is the free-energy (or siteenergy) difference. The electronic coupling elements, Jij, of the charge-transfer are calculated for each molecular pair 15,44,45 using the semi-empirical ZINDO method. A pair of molecules of whose centroid distance is below 0.8nm is added to the neighbor list. λ is calculated by the four-point rule using the density-functional theory with B3LYP/6311G(d,p) methodology. Site-energies are calculated selfconsistently using the Thole Model, including contributions from electrostatic interactions with polarization and from external electric field (for details see ref. [22]). Partial charges of the neutral and charged states are generated using the same methodology described above. Isotropic atomic polarizabilities of the neutral and charged states are reparameterized for each species as to reproduce the molecular polarizaibilities obtained from B3LYP/6-311G(d,p) method. In the context of the Gaussian Disorder Model (GDM), the histogram of site-energy differences, ∆Eij, are fitted to a Gaussian distribution function and related to energetic 19,35 disorder, σ. Charge-transport is predicted by kineticMonte Carlo methods for a single charge-carrier in an applied electric field. We found that the hole mobility of


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spiro-OmeTAD is insensitive to charge-carrier 31,32 concentration. Field-effect hole mobilities are evaluated using velocity-averaging, µ=/F, where F is the field 46 strength. All charge-transport simulations were performed 22 using VOTCA. ASSOCIATED CONTENT

Supporting Information DFT optimized geometry, partial charges, MD snapshots at different crystallographic directions. This material is available free of charge via the Internet at_____ . AUTHOR INFORMATION

Corresponding Authors *[email protected] **[email protected]

+90-216-414-0545 +1-310-206-0515

Notes The authors declare no competing financial interests. ACKNOWLEDGMENT We would like to thank Dr. Steven A. Lopez for helpful discussions and critical reading of the manuscript. Simulations were performed at Hoffman2 at UCLA mainly and the Simulation Research Laboratory, Department of Physics, MU under the research project FEN-C-DRP-1206130273 supported by the MU, Scientific Research Commission (BAPKO).

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ToC Graphic

spiro-OMeTAD



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SCHEMES and FIGURES

Scheme 1. Molecular and crystal structure of spiro-OMeTAD.

A2 A1

Spiro-OMeTAD Spiral packing motif (R=subs.)

a

c b

Unit-cell

Supercell

Equilibrated at 300K

Scheme 2. Molecular structure, spiral packing motif, unit-cell, supercell and the snapshot of the MD simulation at 300K of spiroOMeTAD. Crystallographic coordinates are indicated.


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(a)

(b)

Figure 1. (a) Temperature dependent distributions of C-C-O-C dihedral angles of the methoxy groups. (b) Temperature dependence of the nematic order parameter, Q, of each phenylene group.



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A1

A2

Ap

Figure 2. (top) Three strong packing arrangements of spiroOMeTAD, (bottom) temperature dependence of the paracrystalline order parameter, g. (inset) temperature dependence of the percentage expansion along a crystallographic direction relative to the initial supercell.


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A1

(a)

Ap

A2

(b)

(d)

(c)

(e)

Figure 3. (top) Temperature (T) dependent, direction-resolved electronic coupling element distributions of (a) A1, (b) A2 and (c) Ap packing arrangements (see Figure 2). (d) T-dependent energetic disorder for a virtually casted atomistic morphology at T (red squares) and for the morphology brought to 300K from that T and re-equilibrated (purple triangles). (e) Similar to bottom-left but for hole mobilities. Each hole mobility result is calculated for T=300K (see text for details).

a

c b

L

Figure 4. (left) Variation of hole-mobility, µ, and (inset) energetic-disorder, σ, with size L for the equilibrated morphology at 300K. (right) Representative MD snapshot showing that L.


Mesoscale Ordering and Charge-Transport of Crystalline Spiro

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