Monte Carlo Simulation for Investigation of Morphology Dependent

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Monte Carlo Simulation for Investigation of Morphology Dependent Charge Transport in Bulk-Heterojunction Organic Solar Cells Mahyar Taherpour and Yaser Abdi*

J. Phys. Chem. C Downloaded from pubs.acs.org by REGIS UNIV on 10/19/18. For personal use only.

Nanophysics Research Laboratory, Department of Physics, University of Tehran, North Kargar Avenue, Tehran 1439955961, Iran

ABSTRACT: Morphology, the spatial distribution of traps, interdomain connectivity, and phase separation of the active layer play a critical role in the performance of the bulk heterojunction (BHJ) organic solar cells (OSCs). In this work, we utilize the hopping transport model to simulate the effect of morphological and structural parameters on the diffusion coefficient and efficiency of the polymer-fullerene BHJ solar cells. In BHJ solar cells there are two distinct phases as electron transport material (acceptor) and hole transport material (donor). Here we try to create an almost realistic network containing P3HT polymer chains and PCBM clusters for simulating the charge transport in the active layer. The blend ratio of P3HT:PCBM polymers and alignment of these bicontinuous networks of active layer are considered here as the morphological parameter affecting the cell performance. The dependency of the charge transport on such morphological parameters is obtained in this study by using Monte Carlo continues time random walk simulations.

1. INTRODUCTION Nanostructured solar cells have attracted remarkable interest as an alternative to silicon-based solar cells. Many types of nanostructured solar cells have been developed in recent years based on semiconducting nanoparticles,1 perovskites,2 and polymers.3,4 In all types of the last generation of solar cells, optimization of the morphology is critical for cell performance. Experimental investigations on the efficiency of the fabricated solar cells have shown that the cell performance strongly depends on the morphology of the transport media.5 Electrical performance of the solar cells comes from three successive steps: generation of electron−hole pairs, transferring the electron to electron transporter and hole to hole transporter, and finally charge transport in transport media. After separation of the electron−hole pairs, they need to be conducted to their respective electrodes by a successive transport. Depending on the mobility of the electrons and holes through their transport materials, the charge transport may be limited by electron transport or hole transport. Charge transport in nanostructured media seems to be occurred through the localized states by the hopping mechanism.6,7 Also, the recombination of the charge carriers is believed to be aided by impurities that act as deep traps.8 Morphology of the transport media strongly affects the charge transport, leading to affecting the cell performance.9,10 © XXXX American Chemical Society

Charge transport in the nanostructured solar cells was recently studied by continuous time random walk (CTRW) by using the Monte Carlo (MC) simulations.11 In the RW simulation of charge transport, a random movement of charge carriers in a 3dimensional network of traps is considered.11−14 Arrangement of the traps in the simplest version is carried out on an ordered lattice with the same average distance, although disordered trap configurations can be implemented. CTRW simulation of charge transport is based on diffusion of photocharge carriers through a trap contained media. The precise nature of the localized traps and their spatial location in the transport media are in doubt. Besides, Street et al.15,16 have suggested that the recombination rate through hole-traps in the polymer play an important role in the performance of BHJs. There are two main ideas about the energy distribution of the trap states. Exponentially decreasing tail of trap states below the conduction band is usually given for inorganic media.17 For example, Anta et al. have been utilized a truncated exponential distribution for trap states in dye-sensitized solar cells.18 On the other hand, Gaussian distribution is believed to be observed for localized states in disordered organic materiReceived: May 26, 2018 Revised: August 16, 2018 Published: October 9, 2018 A

DOI: 10.1021/acs.jpcc.8b04962 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. (a) P3HT crystal schematic containing lamellar stacking direction with face-on and edge-on orientations. The chains in the crystalline lamellae are drawn in black. (b) Schematic showing the shift factor and overlap parameter defined in our simulation.

als.19−22 Charge transport in disordered trap contained media as photoanode in solar cells was investigated versus the morphological parameters.23 Ansari et al. have shown by CTRW simulation in a porous TiO2 that the geometry dependency of the diffusion coefficient can be described only as a function of the porosity.24 Also, Abdi et al. have introduced equations describing the morphological dependency of electron transport in nanostructured solar cells.25 The mentioned previous reports on the morphology-dependent electron transport are applicable just for semiconductor media in which the limiting parameter for charge transport is only porosity. On the other hand, there are some reports on the simulation of charge transport in organic solar cells. For example, Koster26 and Woellner et al.27,28 have reported the investigation of the influence of morphology on the charge transport of BHJ solar cells by numerically solving the Pauli master equation. Heiber et al.29 have investigated the effect of the tortuosity of the charge-transport pathways through a bulk heterojunction film on the charge transport using kinetic Monte Carlo simulations. They have used simplified models such as the Ising-based model to generate a porous media for charge transport. Here, we have tried to create a more realistic media to simulate the BHJ active layers. According to the experimental reports, in the organic BHJ solar cells, the limiting cases are a perfect mixture of donor and acceptor.30,31 However, the perfect morphology for organic bulk heterojunction (BHJ) solar cells is unknown because of

experimental limitations. In this work, we investigate the effects of morphology on the charge transport in BHJ solar cells. We show that not only the blend ratio but also the phase separation and the interdomain connectivity can affect the charge transport in this kind of solar cells. There are two main approaches for utilizing in CTRW simulation to explain charge transport. In the first one, which is called multiple trapping (MT) model, transport is affected by trapping and detrapping events.32 In this model, the charge transport occurs by electrons in the conduction band or holes by the valence band. The second approach is hopping transport model in which, the transport can be occurred by the direct transition between the localized trap states.33−36 The hopping events are assumed to be occurred as a consequence of thermal activation and quantum mechanical tunneling.37 Here we utilized hopping transport model in CTRW Monte Carlo simulation, with a Gaussian distribution for trap energies, to describe the morphological dependency of the charge transport in BHJ solar cells.

2. FILM MORPHOLOGY SIMULATION There are some experimental reports on the study of the morphology and structure of organic semiconductors and organic photovoltaics.38−42 Grazing incidence X-ray scattering (GIXS) and scanning tunneling microscope (STM) analyses of P3HT show rectangular crystallites. According to these reports, the lamellar stacking of P3HT has a spacing of ∼1.6 nm and B


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Figure 2. (a) Realistic network including the P3HT clusters and PCBM spherical clusters obtained in the simulation with the parameters of SF = 0.7, Ov = 0.1, and average tortuosity of 1.41. (b) PCBM cluster obtained by random-cluster model and the schematic showing the P3HT cluster with the aromatic (π−π) stacking spacing of ∼0.39 nm.

the aromatic (π−π) stacking has a spacing of ∼0.39 nm. Verploegen et al.43 have investigated the effects of the thermal annealing on the orientation of P3HT rectangular crystallites relative to the substrate. Sirringhaus et al.44 showed that, in the P3HT films with high regioregularity and low molecular weight, the preferential orientation of ordered domains is with the (100)-axis normal to the substrate and that, in the films with low regioregularity and high molecular weight the preferential orientation of ordered domains is with the (010)-axis normal to the substrate. Also, scanning tunneling microscope images of P3HT clearly show an ordered polymer domain with an average size of 20 nm.45−47 Besides this, it has been shown that after annealing, this polymer chain is extended in the lateral side to create a P3HT crystal along (100) and (010).45,47−50 In order to simulate P3HT as donor species, we have used a cubic box containing flat sheets as P3HT face-on and edge-on crystallites51 with spacing of 0.4 nm between the sheets, as shown in Figure 1a. In order to generate the network for the simulation of the charge transport, the prepared clusters are randomly distributed at the surface of simulation box with the size of 150 × 150 × 150 nm at z = 0 with the overlap parameter less than a desired value. Then, the same clusters are placed randomly on top of the initial clusters in the manner that the overlap parameter (OV) and shift factor (SF) for all of the neighboring clusters be less than the specific values. Shift factor and overlap parameter are defined as SF = shift factor =

Sy Sx = Lx Ly

OV = overlap parameter = 1 −

of the clusters in the vertical direction can be achieved by a minimum value of shift factor. This process is repeated so that the structure grows up in the z-direction. In the literature, such alignment is quantified as a well-known parameter called tortuosity.29,52 Tortuosity quantitatively indicates how convoluted a transport pathway is relative to the shortest straight path. In order to obtain the average tortuosity for the networks with different shift factors, we calculated the shortest pathways through each phase from each corresponding point on the bottom of the simulation box to the top. As calculated pathway was then divided by the box height (150 nm) to achieve the tortuosity for that specific pathway. This calculation was repeated to get an average tortuosity for a specific network. In order to create PCBM clusters as acceptor species, we used a random-cluster model.53 The procedure is started by putting a sphere (as PCBM) with radius r = 1.5 nm at the void spaces between the P3HT network. Then, spheres with the same radius are being brought randomly around the initial sphere on the condition that they have to be connected to at least one other sphere. This process is repeated enough to fill the free spaces between the P3HT layered clusters. It must be mentioned that conflicted clusters with P3HT clusters were removed in this process. A realistic media produced by this algorithm is shown in (Figure 2). The values of the constants which have been chosen from the previous experimental and simulation reports are listed in Table 1. The proper references are included in the table.

(1)

Oy Ox =1− Lx Ly

Table 1. Constants Used in the Morphology Simulation (2)

parameters

where Sx (Sy) is the distance between the edges of the upper cube and initial one along the x (y) direction and Ox (Oy) is the distance between the edges of the cubes located at the same height along the x (y) direction (see Figure 1b). Decreasing the shift factor in the produced network leads to have an ordered continuous region and a maximum alignment

simulation box size cluster size (P3HT) shift factor (P3HT) overlap parameter (P3HT) sphere size (PCBM) C

value

references

Lx, Ly, Lz SF Ov

150 × 150 × 150 nm 20,12,10 nm 0.1 to 0.9 0.1 to 0.25

ref 24 ref 50 − −

r

1.5 nm

ref 54


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Figure 3. (a) Realistic 3-dimensional network of traps produced by the r3 model with Ntv = 0.3 nm−3 for the network with average tortuosity of 1.15. The picture has been visualized by the VMD software. (b) Schematic showing the localized states distributed in the volume of P3HT clusters (r3 model) and illustration of the random walk simulation employed in this work. Some of these traps are occupied by charge carriers (black circles). The possible jump to the neighboring states is selected between the unoccupied traps (open circles) located within the cutoff radius, rcut, with minimum hopping time.

Figure 4. (a) Band structure of the P3HT:PCBM heterojunction in steady-state illumination under open-circuit conditions (V = Voc). (b) Schematic showing the Gaussian energy distribution of the localized states with disorder parameter of σ around the transport level,20 E0. Arrows in the schematic show the realization of the hopping through the localized states.

3. MONTE CARLO RANDOM WALK SIMULATION

g (E , E 0 ) =

3.A. Transport Model Implementation. To simulate the charge transport through the trap states in the P3HT polymer, static traps are distributed throughout the clusters of P3HT (as shown in Figure 3). These static traps were placed on the P3HT sheets based on the well-known r3 models23 (volume diffusion), in which the traps are distributed through the material with a volume density of Ntv. We assume that the energy distribution of the localized states has an exponential form such as36,55

É ÄÅ ÅÅ (E − E )2 ÑÑÑ Ntv 0 Ñ Å ÑÑ Å expÅÅ− 2 ÑÑ ÅÅÅ 2πσn σ 2 ÑÑÖ n Ç

(3)

where Ntv is a total density per unit volume, σn is the half width of the distribution, and E0 is the transport level (Figure 4,parts a and b). The Gaussian peak of occupied states is reported to be shifted down by σ2/kT with respect to the Gaussian peak of localized state.56 Charge transport through the generated traps is simulated here by single-carrier random walk simulation. Anta et al. have shown that the single-carrier simulation can reproduce the results of multicarrier simulation.13 The random walk simulation based on hopping transport is started by jumping a hole (or an electron) to a neighboring D


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The Journal of Physical Chemistry C trap with the minimum hopping time.57 Collection efficiency in the BHJ solar cells is affected by both electron transport in acceptor species and hole transport in donor species. However, in the case that the mobilities of electron and hole in their media are different, electron or hole transport can limit the transport parameters. For example, the hole mobility in annealed P3HT:PCBM (50 wt %) is lower than the mobility of electrons.58−60 Consequently, investigation of the hole transport in such BHJ solar cells is more important than the electron transport. According to this discussion, we consider the hole transport in P3HT in this work. In order to calculate the release time (tij) of each hopping step from trap i to the neighboring trap j in a cutoff radius of rcut, we have used the Miller−Abrahams equation:36,61−65 ÄÅ É ÅÅ 2rij Ej − Ei + |Ej − Ei| ÑÑÑÑ 1 Å + tij = −ln(P) expÅÅÅ ÑÑÑ ÅÅÇ αl ÑÑÖ 2kBT υ0 (4)

To simulate the recombination process, i.e., charge transfer from the donor polymer to acceptor species, we have used the Marcus theory of charge transfer. The recombination rate Krt , using the Marcus theory can be written as ij (ΔG 0 + λ)2 yz zz K tr ∝ exp( −β ·r ) expjjj− zz j 4 λ k T B k {

(5)

The first distance depended exponential term represents the electronic coupling between the wave functions of donor and acceptor species. The exponent factor, β, is a measure of the electrical coupling between the donor and acceptor. The second exponential term represents the thermal activation over an activation barrier. ΔG0 in this term is free energy change resulting from the electron-transfer reaction, and the positive parameter of λ is called the reorganization energy, which depends on polarization and relaxation in the surrounding environment. Calculating the probability of charge-transfer at the interface, recombination rate, and carrier lifetime is difficult problem in BHJ organic solar cells.73−75 Recently, a simple and general approach was developed based on the assumption of the Marcus model to formulate the recombination rate in such solar cells.67,76−83 Using this approach, we have calculated the recombination rate Krt at each step of the simulation by the following equation:

Here Ei (Ej) is the energy of the starting (target) trap, P is a random number distributed uniformly between 0 and 1, υ0 is the attempt to jump frequency, rij is the distance between the starting and target traps, and αl is the localization radius. Simulation of the hole transport is started by the distribution of the trap states on the produced network. At the beginning of the simulation, a hole randomly selects an initial trap state of i and the hopping time for the possible jump to an empty site j among neighbor traps in the cutoff radius is calculated by the above equation. After that, the hole is jumped to a neighboring trap with the minimum hopping time (Figure 3b). Such a procedure is repeated in each step of the simulation, and the calculated hopping times are added to the total time of the simulation. 3.B. Recombination Model Implementation. Mechanism of the recombination in the disordered nanostructured materials is not well-defined yet. But, the most common mechanism for the recombination of the charge carriers in such media is the recombination via intraband localized states. This trap-assisted recombination, which is referred to the nongeminate recombination of the electron−hole pairs in the presence of a density of localized states is assumed to be the dominant mechanism for recombination in the bulk heterojunction organic solar cells.9,50,66−70 Nongeminate recombination defines the loss process of two charges which originate from different generation processes. There are some reports describing the mechanism of recombination in P3HT: PCBM solar cells. For example, MacKenzie et al.71 show that the dominant mechanism for recombination in such solar cells is the nongeminate recombination of the free carriers with trapped carriers because the number of free carriers is smaller than the trapped carriers. Also Nalwa et al.72 show that the trap-assisted recombination dominates at low light intensities and that, independent of the light intensity, the trap-assisted recombination is the dominant mechanism for the fast grown active layers in which the trap density is very high. In this model of recombination, the rate of recombination is proportional to the depth of trap states. Charge carriers in the shallow traps with small ionization energies can be released with high probabilities into delocalized states. On the other hand, charges located in deep traps, those having much higher ionization energies, are not released easily. According to this assumption, the traps can act as recombination centers in the disordered materials.

2 ji (E − En + λ) zyz zz K tr = K 0i expjjj− i j z 4λkBT k {

(6)

where Ki0 is the time constant of tunneling and assumed to be a constant with units of s−1. Ei is the energy of ith trap state in the HOMO distribution of donor polymer, and En is the most probable energy for the electrons state in LUMO distribution of acceptor polymer. For realization of the recombination in our simulation, we have calculated the recombination probability as Γ = tijK tr

(7)

We have assumed that this probability is proportional to the recombination rate of the holes and the average time that hole spends in localized states. This probability is calculated for each hopping event and as obtained probability is compared with a produced random number. When the random number is equal to or smaller than the calculated probability, the recombination occurs. If it occurs, the total time of the simulation and the distance traveled by the holes are recorded and saved. Finally, carrier lifetime and diffusion length can be computed by statistical averaging over large enough simulations. For a normal diffusion, after a long enough time t, the diffusion coefficient can be calculated by the following expression:55,84,85 Dj =

rt − 1 r0 )2 ⟩ ⟨(1 6t

(8)

Dj is the jump-diffusion coefficient and the ⟨⟩ symbol denotes a statistical average. In order to overcome the finite size effects, the periodic boundary condition is applied to the nonrecombined holes when reaching to the boundary of the simulation box. We have averaged the results over up to 1500 realizations to reduce the statistical error. In order to calculate the collection efficiency, after 1000 times realizations, the number of carriers reaching to the conducting electrode is E


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The Journal of Physical Chemistry C counted. The percentage of the collected charge is assumed to be collection efficiency (ηcoll) of the solar cell. The values of the constants have been chosen from some theoretical and experimental reports. They are listed in Table 2. The proper references are included in the table.

VD =

value ‑3

density of traps

Ntv

0.3 nm

attempt to jump frequency

υ0

2 THZ

system temperature traps characteristic temperature most probable energy in acceptor LUMO distribution quasi Fermi level center of the DOS donor HOMO energy constant rate of recombination from trap states localization radius reorganization energy

T T0 En

300 K 600 K −4.1 eV

Ef 0 E0 Ep K0

−4.75 eV −5 eV −5.4 eV 3.6 × 102 s‑1

αl λ

0.5 nm 0.7 eV

cutoff radius half-width of the distribution

Rcut σn

2.5 nm 0.08 eV

(9)

where Ntot v is the total number of traps that are distributed homogeneously in the volume of donor species. In addition, the shift factor has a direct impact on the tortuosity. In order to achieve the different tortuosities, the networks with different shift factors were created and the average tortuosity of the networks were calculated using the previously mentioned algorithm. As obtained tortuosities for the different shift factors are shown in Figure 5b. Also, the domain size which is defined as the total volume of the active layer over the interfacial area is a good indication for phase separation. Parts a and b of Figure 6 show the domain size and the normalized interface area achieved for different average tortuosity, and Figure 6c shows the normalized interface area at constant blend ratio 50%. 4.B. Effect of Morphology on Charge Transport. At the first step of the simulation, we have calculated the diffusion coefficient as a function of the blend ratio. We expect that the diffusion coefficient decreases by decreasing the blend ratio. Figure 7a shows the diffusion coefficient versus the blend ratio. Results of this figure are in agreement with the results of the previous works24,100−103 reporting that the diffusion coefficient is proportional to|P − PC|δ, where PC is the critical porosity obtained to be around 78% and the conductivity exponent of δ is around 1. Ansari et al. have defined the porosity as the volume ratio of the voids in the transport media over the total volume, where (1 − P) is a measure of the volume percentage of donor polymer. According to this definition, the blend ratio can be a good substitution for (1 − P) in the BHJ solar cells. Also, they show that the diffusion coefficient of the photoanodes in nanostructured solar cells only depends on the porosity and the effects of other morphological parameters can be interpreted in the context of porosity.24 Experimental studies of the impact of blending composition on device performance suggested that an optimum P3HT blending ratio was around 50−60% for the P3HT:PCBM system.104−107 So, in order to investigate the effects of other morphological parameters on the diffusion coefficient, we have prepared some simulation network with the same blend ratio of 50% and the different

Table 2. Constants Used in Simulation parameters

Nvtot Ntv

references refs 6 and 86−90 refs 91 and 92 room temp refs93 and 94 ref 74 − − ref 74 refs 76 and 95 ref 96 refs 74 and 76 ref 97 refs 21, 98, and 99

4. RESULTS AND DISCUSSION 4.A. Film Characterization. As mentioned previously, the blend ratio (volume percentage of P3HT) and the interfacial area (total surface area of P3HT polymer) are important morphological parameters affecting the cell performance. In order to achieve a wide range of the blend ratio, we have changed the overlap parameter and shift factor. As shown in Figure 5a, different blend ratios ranging from 25 to 60% can be obtained by changing the shift factor from 0.1 to 0.9. Also, in a constant shift factor, an increase in the overlap parameter leads to an increase in the P3HT blend ratio. Practically blend ratio can be obtained by computing the volume of donor over the total volume of the active layer. Also, the volume of donor species, VD, can be obtained by

Figure 5. (a) Blend ratio versus the shift factor for different overlap parameters. (b) Shift factor versus the average tortuosity obtained by morphological simulations. F


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Figure 6. Domain size (a) and normalized interface area (b) with overlap parameter of OV = 0.1 versus the average tortuosity. (c) Normalized interface area at constant blend ratio (50%) versus the average tortuosity (different morphologies with constant blend ratio obtained by changing the overlap parameter).

Figure 7. (a) Diffusion coefficient versus the blend ratio. The red solid line shows the fitted curves corresponding to |B − Bc|δ. The critical blend ratio, Bc, is ∼22% which is in good agreement with the critical porosity of ∼78% obtained by Ansari et al. (b) Diffusion coefficient and its components versus the average tortuosity at the constant blend ratio of 50% (SF parameter was changed from 0.1 to 0.6).

component of the diffusion coefficient, Dz, decreases by increasing the average tortuosity, but the X and Y components of the diffusion coefficient remain almost constant. Also, the total diffusion coefficient decreases by decreasing the average

average tortuosity. Results of diffusion coefficient versus the average tortuosity are presented in Figure 7b. X, Y, and Z components of the diffusion coefficient are also shown in this figure separately. As we can see, at a constant blend ratio, the Z G


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Figure 8. (a) Diffusion coefficient versus the interfacial area and (b) domain size obtained for the constant blend ratio of 50%. Domain size is defined as the volume divided by the interface area.

Figure 9. (a) Visualization of the actual path of a successive collection of a charge carrier. Each point is the indication of 100 jumps in the diffusion process. (b) Normalized collection efficiency as a function of average tortuosity at the constant blend ratio of 50% for the P3HT network with faceon (circles) and edge-on (squares) orientations.

tortuosity, as a direct consequence of decreasing the Dz. At the much smaller tortuosities, Dz and D begin to grow dramatically. Such increment in the diffusion coefficient is a direct consequence of the directional transport which can be occurred in columnar structures. Javadi and Abdi108 have shown in their previous work that the electron diffusion coefficient in a disordered material which contained localized states in a columnar structure is significantly higher than the diffusion coefficient in the conventional isotropic structure. They believe that the high diffusion coefficient in columnar structures is a consequence of confinement in x and y directions, which leads to vanish the diffusion coefficient in the confined directions and to have a directional transport in the unconfined direction. The diffusion coefficient versus the interfacial area and domain size are provided in Figure 8 to demonstrate the effects of the phase separation on the hole transport. The simulations are carried out at a constant blend ratio. According to the definition of the interfacial area and the domain size, a higher phase separation occurs at higher interfaces and lower domain

sizes. Figure 8b shows that improving the phase separation due to decreasing the domain size leads to a higher diffusion coefficient. 4.C. Effect of Morphology on Collection Efficiency. As an important electrical parameter showing the performance of a solar cell, the experimental works mostly report the efficiency of the fabricated cells. We calculated the collection efficiency of the BHJ solar cells using the calculation of the percentage of carriers reaching to the conducting electrode. The Collection efficiency of the solar cell strongly depends on the thickness of its active layer. Our simulations for calculating the collection efficiency are carried out for the constant thickness of 150 nm. A charge carrier generated in this 150 nm thickness can be collected if it reaches to the bottom electrode at z = 0. After 1000 times simulations, the percentage of carriers reaching to the bottom electrode is calculated to obtain collection efficiency. A successive collection of a carrier is visualized in Figure 9a. Figure 9b shows the collection efficiency of the cells as a function of the average tortuosity. As shown in this figure, decreasing the average tortuosity leads to a significant H


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5. CONCLUSION Charge transport in BHJ solar cells was investigated by continuous time random walk Monte Carlo simulation based on a hopping model. Morphology, spatial distribution of traps, interdomain connectivity, and phase separation of active layer were considered in the simulations. Diffusion coefficient as the main parameter in charge transport and collection efficiency as an output characteristic were calculated. The blend ratio of the donor and acceptor species as a mixing parameter was considered in the simulations. It can be concluded from the simulation results that, by decreasing the blend ratio below the 50%, the diffusion coefficient decreases. Such a decrement, which is in agreement with experimental results, is a direct consequence of decreasing the accessible space for charge carriers in P3HT:PCBM. Tortuosity of the active layer which quantitatively indicates the convolution of the transport pathway was considered as an affecting parameter in charge transport. Tortuosity is a measure of ordering the bicontinuous structure of active layer in BHJ organic solar cells. Results showed that an increment in the tortuosity leads to a decrement in the diffusion coefficient and the collection efficiency of the cell. Accordingly, it can be concluded that the directional deposition of the polymers can improve the cell performance. Results showed that by decreasing the interdomain connectivity, the collection efficiency decreases dramatically which is in agreement with the experimental results. Orientation of the P3HT clusters relative to the substrate was also considered and it was obtained that the perpendicular P3HT lamellae orientation relative to the substrate has a lower collection efficiency comparing to the parallel P3HT lamellae orientation relative to the substrate.

increment in the collection efficiency. Such increment in the collection efficiency is a direct consequence of the ordering the bicontinuous structure of active layer and realizing the directional charge transport. Figure 9b also shows the effect of the P3HT clusters orientation on the collection efficiency. As shown in this figure, the perpendicular P3HT lamellae orientation relative to the substrate (edge-on) has lower collection efficiency comparing the parallel P3HT lamellae orientation relative to the substrate (face-on). The results of Figure 9b is in agreement with the previously reported experiments. For example, Crossland et al.109 have measured anisotropic charge-transport in P3HT films using field-effect transistor channels placed within well-aligned domains of quasi-parallel lamellae. They have found that the charge mobility is three times higher in the direction parallel to the ordered π-stacks comparing the direction perpendicular to them. The same results have been reported by Wu et al.110 Their results exhibit an improvement in the performance of the field effect transistor in which the direction of most of the (π−π) overlaps was consistent with that of the charge transport from source to drain. It is worth mentioning that the collection efficiency shown in Figure 9b is not the total efficiency of the cell. The measured efficiency in the experiments is affected by not only the charge collection but also the light absorption and successive injection. On the other word, the total efficiency of a solar cell is a multiplication of the collection, injection and absorption efficiencies. In order to investigate the impact of spatial distribution of the traps and the interdomain connectivity on the performance of the BHJ solar cells, we have carried out a set of simulations, and the results are provided in Figure 10. In this regard, we

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AUTHOR INFORMATION

Corresponding Author

*(Y.A.) E-mail: [email protected]. ORCID

Yaser Abdi: 0000-0002-7583-7687 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank the Iran National Science Foundation (INSF) for partial financial support.

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REFERENCES

(1) Archer, M. D. Nanostructured and Photoelectrochemical Systems for Solar Photon Conversion; Imperial College Press: 2008; Vol. 3. (2) Snaith, H. J. Perovskites: The Emergence of a New Era for LowCost, High-Efficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623− 3630. (3) Huang, H.; Huang, J. Organic and Hybrid Solar Cells; Springer: 2014. (4) Tress, W. Organic Solar Cells. Springer Ser. Mater. Sci. 2014, 208, 67−214. (5) Liu, Y.; Zhao, J.; Li, Z.; Mu, C.; Ma, W.; Hu, H.; Jiang, K.; Lin, H.; Ade, H.; Yan, H. Aggregation and Morphology Control Enables Multiple Cases of High-Efficiency Polymer Solar Cells. Nat. Commun. 2014, 5, 5293. (6) Arkhipov, V.; Heremans, P.; Emelianova, E.; Adriaenssens, G.; Bässler, H. Weak-Field Carrier Hopping in Disordered Organic Semiconductors: The Effects of Deep Traps and Partly Filled Densityof-States Distribution. J. Phys.: Condens. Matter 2002, 14, 9899.

Figure 10. Collection efficiency as a function of the percentage of the removed clusters for the network of face-on P3HT clusters with tortuosity of 1.01 and 1.32.

have removed some of the clusters randomly, and the collection efficiency of the cells was calculated as a function of the percentage of the removed clusters. Figure 10 shows that by decreasing the interdomain connectivity (increasing the percentage of the removed clusters), the collection efficiency decreases dramatically. Low efficiencies of BHJ solar cells reported in the experiments may come from such poor connectivity in the organic polymers. I


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