Effects of Magnetic Nanoparticles and External Magnetostatic Field on the Bulk Heterojunction Polymer Solar Cells

The price of energy to separate tightly bound electron-hole pair (or charge-transfer state) and extract freely movable charges from low-mobility materials represents fundamental losses for many low-cost photovoltaic devices. In bulk heterojunction (BHJ) polymer solar cells (PSCs), approximately 50% of the total efficiency lost among all energy loss pathways is due to the photogenerated charge carrier recombination within PSCs and low charge carrier mobility of disordered organic materials. To address these issues, we introduce magnetic nanoparticles (MNPs) and orientate these MNPS within BHJ composite by an external magnetostatic field. Over 50% enhanced efficiency was observed from BHJ PSCs incorporated with MNPs and an external magnetostatic field alignment when compared to the control BHJ PSCs. The optimization of BHJ thin film morphology, suppression of charge carrier recombination, and enhancement in charge carrier collection result in a greatly increased short-circuit current density and fill factor, as a result, enhanced power conversion efficiency.

I n recent years, bulk heterojunction (BHJ) polymer solar cells (PSCs) composed of conjugated polymers (as the electron donor, D) and fullerene derivatives (as the electron acceptor, A) with interpenetrating networks have attracted a myriad of attention for both academic and industrial sectors due to their premium features of flexibility, fabrication simplicity, low manufacturing costs, short energy payback time, and low environmental impact [1][2][3] . In the past few years, progresses have mainly focused on breaking the Shockley-Queisser limit by ameliorating device structures [4][5][6] and developing novel low bandgap conjugated polymers 7 . Power conversion efficiencies (PCEs) over 10% from singe junction cells and as high as 12% from the tandem cells have been reported 8,9 . However, the fundamental question regarding energy losses during the photophysical process still remain obscure; particularly, the mechanisms of charge carrier recombination in BHJ PSCs are far from elucidated 10 .
As shown in Fig. 1, the charge carrier collection in BHJ PSCs includes the following steps/processes: formation of photo-induced excitons in D and A, respectively (1 & 19); intra-molecular electron-hole recombination (2 & 29); the excitons diffusion and dissociation at the D/A interface (3 & 39) 1-3 ; charge-transfer (CT) states generation and then dissociation into free charge carriers (electrons and holes) with an ultrafast quasi-adiabatic charge transfer process (4 & 49); charge carriers that are transported through either D or A (5 & 59) and then being collected by the respective electrodes (6 & 69) 11 ; the separated charge carriers may recombine with each other (7, geminate recombination) before dissociation; moreover, the separated charge carriers may also being collided and recombined (8, bimolecular recombination or non-geminate recombination) before collected by the respective electrodes (6 & 69). The germinate and non-germinate recombinations are certainly responsible for the low PCEs in BHJ PSCs 2,12 .
On the other hand, the relative dielectric constant (e r ) of BHJ composite in PSCs is as low as 3, which is much smaller than that of typical inorganic counterparts (,10). The small dielectric constant results in strongly bounded Frenkel excitons with a diffusion length of ,10 nm for organic semiconductors rather than the Wannier excitons for inorganic semiconductors with a diffusion length of 10 4 , 10 5 nm 13 . Thus, in order to efficiently dissociate the photo-excited excitons in BHJ composite of PSCs, optimal phase separation with ,10 nm scale is required 1 . However, it is not easy to form a uniformly ideal ,10 nm interpenetrating phase separation in BHJ composite. As a result, most high efficiency PSCs were obtained by optimization of BHJ thin film morphology through huge processing effects. In addition, the traps and defects in BHJ composite also play a crucial role in exciton recombination 14 . Therefore, the challenge in forming uniformly ideal ,10 nm interpen-etrating A-D phase separation and traps defects therein together with the low e r of disordered organic materials induced various recombinations are responsible for approximately 50% efficiency loss among all loss pathways in BHJ PSCs 15,16 .
Studies from the transient photoconductivity, the time-delayed collection field, and the time-delayed dual pulse experiments have demonstrated that there is a competition process between the carrier sweep-out by the internal field and the loss of photogenerated carriers by recombination in BHJ PSCs 17 . Wherein the internal electric field with a value as high as 50 to 70 V/mm is required to ensure efficient charge collection at the short-circuit condition and in reverse bias in PSCs 18,19 . The asymmetrical electrode materials used in most of BHJ PSCs, however, afford a work-function difference of less than 2 eV producing an external electric field of ,20 V/mm (assuming the BHJ thickness is ,100 nm for typical device dimensions). This electric field is less efficient to sweep out photogenerated carriers and suppress charge carrier recombination in BHJ active layer 19,20 . Considering the insufficient electric field from the electrodes discussed above, a coercive electric field from magnetic nanoparticles (MNPs) show potential to strengthen the external electric field in BHJ PSCs.
In MNPs, a coercive electric field is produced among MNPs due to dipole interactions 21 . If the BHJ composite is incorporated with MNPs and then followed with an external magnetostatic field alignment, an orientated coercive electric field (E) will be created within BHJ composite (see in Fig. 2G). The E is described as: E 5 (4psf/e) [22][23][24] , where e is the dielectric permittivity, s is the surface charge density and f is the volume fraction of MNPs. For example, an additional E of 177.4 V/mm, which is at least 2 times larger than 50-70 V/mm, can be obtained by BHJ composite incorporated with 5% (by volume) of Fe 3 O 4 MNPs. The details in calculation of E are described in Supplementary Information (SI 1). This additional coer-  (1 & 19); intra-molecular electron-hole recombination (2 & 29); the excitons diffusion and dissociation at the D/A interface (3 & 39); generation of charge-transfer (CT) states and these CT states dissociate into free charge carriers (electrons and holes) with an ultrafast quasiadiabatic charge transfer process (4 & 49); charge carriers that are transported through either D or A (5 & 59) and then collected by the respective electrodes (6 & 69); the separated charge carriers may recombine with each other (7, geminate recombination) before dissociation; the separated charge carriers may also collide and be recombined (8, bimolecular recombination or non-geminate recombination) before being collected by the respective electrodes (6 & 69).  cive electric field is expected to enlarge the sweep-out rate of photogenerated carriers and suppress charge carrier recombination (both geminate and non-geminate); consequently resulting in enhanced PCEs in BHJ PSCs. In addition, these MNPs are also expected to influence the formation of thin film morphology of BHJ composite due to the motion of these MNPs under an external magnetostatic field 23 .
The e r of Fe 3 O 4 MNPs is 20, which is 5 times higher than that of BHJ composite (4) (e r of poly(3-hexylthiophene) (P3HT) is 6.5 and e r of phenyl-c61-butyric-acid-methyl ester (PC 61 BM) is 3.9, the e r of P3HT:PC 61 BM BHJ composite is assumed to be ,4) 25 . The average e r of BHJ composite incorporated with 5% (by volume) Fe 3 O 4 MNPs can be enlarged by a factor of 20% 25 . Consequently, the Coulomb potential energy E c , E c~e 2 4pe 0 e r r (where e is the charge of an electron, e r is the relative dielectric constant of the surrounding medium, e 0 is the vacuum permittivity, and r is the electron-hole separation distance) of the CT state could be reduced due to enlarged e r and optimized r (due to optimized BHJ film morphology). Moreover, the reduced E c will enlarge the total energy U of the CT state since the U is described as 26 : where E D (HOMO) and E A (LUMO) are the HOMO (highest occupied molecular orbital) energy level of D and the LUMO (lowest unoccupied molecular orbital) energy level of A; V e and V h are the electron and hole drifting velocities, respectively; m e and m h are the masses for electron and hole, respectively. In the eq. (1), the kinetic energies ( 1 2 m e V 2 e and 1 2 m h V 2 h ) of charge carriers are increased due to the introduction of Fe 3 O 4 MNPs dipole-induced coercive electric field, which is an additional electric field to drive the separated charge carriers to be transported through either D or A. As a result, decreased E C and increased kinetic energy would result in an enlarged U of the CT state. Therefore, it is unequivocal that the CT state becomes unstable which would facilitates the charge carrier dissociation 26 resulting in an enlarged short-circuit current density (J SC ) in PSCs 17,27 . Moreover, the direction of the dipolar moment produced by Fe 3 O 4 MNPs is parallel in the presence of the vertically external magnetostatic field [22][23][24] . This parallel alignment could force Fe 3 O 4 MNPs to be temporarily bound with the separated charge carriers in ''ordered'' structures, which facilitates the charge carrier to be transported to the respective electrodes (see Fig  The incident photon-to-electron conversion efficiency (IPCE) spectra for all PSCs were measured and the results are shown in Fig. 3C. The spectral responsibilities of all PSCs span from 350 to 850 nm. These observations are in good agreement with the absorption spectra observed from PTB7-F20:PC 71 BM BHJ composite thin films (SI and Fig. S3). Based on IPCE spectra, the estimated J SC for the PSCs-Fe 3 O 4 W/H, the PSCs-Fe 3 O 4 and the control PSCs are 16.10 mA/cm 2 , 14.71 mA/cm 2 and 13.39 mA/cm 2 , respectively. These estimated J SC values are consistent with those observed from J-V characteristics (Fig. 3B)   for efficient charge generation. In short, the magnetically induced film morphology rearrangement leads to an ordered and nanoscale optimized interpenetrating network, which facilitates charge carriers to be transported to the respective electrodes, simultaneously reduces the possibility of charge carrier recombination 4,10 . As a result, enhanced PCEs are observed from PSCs-Fe 3 O 4 W/H. The photo-electronic characteristics of PSCs are further investigated to confirm the effect of coercive electric field on charge carrier collection efficiency. Fig. 6A shows the photocurrent (J ph ) versus the effect voltage (V eff ) (J ph -V eff ) characteristics of PSCs under AM 1.5 G illumination. At a large reverse voltage (V eff 5 1.9 V), J ph is saturated for three different PSCs, suggesting that the photogenerated excitons are dissociated into free charge carriers and these charge carriers are collected by the electrodes without any residual non-geminate recombination [36][37][38] . As a result, the saturation current densities (J sat ) are only dependent upon the amount of absorbed incident photon flux 37 . The maximum obtainable exciton generation rates are essentially the same for all three types of PSCs because the Fe 3 O 4 MNPs contributed negligible absorption to BHJ composite (SI 4, Fig. S3). At V eff 5 V OC (V OC 5 0.65 V), the J ph /J sat are 92.2%, 91.6% and 88.8% (J sat is the reverse saturation photocurrent at V eff 5 21.9 V) for the PSCs-Fe 3 O 4 W/H, the PSCs-Fe 3 O 4 , and the control PSCs, respectively. Interestingly, in the low effective voltage range, i.e. V eff , 0.5 V, J ph -V eff characteristics of these three types PSCs show distinct differences. At the maximum power output condition at V eff 5 0.2 V, J ph /J sat are 84.6%, 83.1% for the PSCs-Fe 3 O 4 W/H and the PSCs-Fe 3 O 4 , while it is only 78.7% for the control PSCs. Since the ratio of J ph /J sat is the essential of exciton dissociation efficiency and charge carrier collection efficiency, a decreased J ph /J sat suggests either reduced exciton dissociation efficiency or decreased charge carrier collection efficiency. The decreased charge carrier collection efficiency suggests that non-geminate recombination is dominated (compete over exciton-dissociation), resulting in a low FF. The charge carrier recombination in PSCs is manifested by the deviation of the photocurrent from the square-root dependence on effective voltage, which is one of the signatures of charge carrier recombination-limited photocurrent in PSCs 38 . The superior J ph -V eff characteristics from the PSCs-Fe 3 O 4 W/H clearly demonstrate the effect of Fe 3 O 4 MNPs and external magnetostatic field alignment on reducing the geminate recombination at the low effective voltage, at which maximum power output condition of PSCs usually takes place. Such reduced geminate recombination in PSCs is probably originated from high charge carrier mobility of BHJ composite therein. Therefore, the enhancement in charge carrier diffusion and charge carrier transport are responsible for the distinctly different J ph /J sat among all PSCs.
Light intensity-dependent efficiencies (J SC and V OC ) were further studied to confirm the effect of the coercive electric field on suppression of geminate and non-geminate recombinations in PSCs. In solar cells, if the mean drift length of the electron or hole (or both) is smaller than the thickness of photoactive layer, geminate recombination becomes considerable.  In PSCs, due to the low charge carrier mobility of disordered organic materials, charge carrier recombination becomes the dominant loss mechanism as the thickness of BHJ active layer increases. Fig. 6D presents PCEs versus the thickness of BHJ active layer. It was found that as the thickness of BHJ thin films increases from 120 nm to 260 nm, the PCEs from the control PSCs are significantly decreased from 5.2% to 4.5%; however, the PCEs from the PSCs-Fe 3 O 4 decreased from 5.8% to 5.4%; while the PCEs from the PSCs-Fe 3 O 4 W/H maintained almost the same value, around 7.0%. These results demonstrate that Fe 3 O 4 MNPs and an external magnetostatic field alignment indeed can suppress the charge carrier recombination in the PSCs based on BHJ composite incorporated with Fe 3 O 4 MNPs and then followed by an external magnetostatic field alignment.
In BHJ PSCs, the built-in electric field can be canceled at the condition of applied bias voltage (V appl ) equals to V OC ; at this condition, the photogenerated charge carriers in the active layer flowing toward the electrodes can be prevented 17 . As a result, the possibility of charge recombination at the D/A interface is increased to the maximum value. The impedance spectroscopy (IS) is carried out to monitor the detailed electrical properties of BHJ composite and/or the interface between each layer that cannot be observed by direct current measurement. The details of IS measurement is described in SI 7. In all PSCs, the difference in the resistance of PSCs solely comes from the CT resistance with BHJ composite active layer. Fig. 7 shows the Nyquist plot of PSCs at V appl 5 V OC and under 100 mW/cm 2 from AM 1.5 G illumination. The plot of PSCs contains a semicircle which indicates that BHJ active layer is relatively homogeneous along the transport pathways without having discernible multiple interfacial boundaries 39 . At V appl 5 V OC , the CT resistance of the control PSCs is ,83 V and this value decreases to ,58 V and ,32 V for the PSCs-Fe 3 O 4 and the PSCs-Fe 3 O 4 W/H, respectively. A significantly decreased CT resistance demonstrates that thin film morphologies are rearranged through PTB7-F20 crystallization and/or PC 71 BM aggregation 11 , which enhances the charge carrier transport and decreases the possibility of charge carrier recombination at the D/A interface in BHJ active layer. These observations are consistent with the film morphologies presented in AFM images (SI 6,     ity of PTB7-F20 and electron mobility of PC 71 BM are observed from PTB7-F20 and PC 71 BM incorporated with Fe 3 O 4 MNPs and then followed with an external magnetostatic field alignment, respectively. Consequently, reduced charge carrier recombination and enlarged J SC and FF are observed from the PSCs-Fe 3 O 4 W/H. While the microscopic origin of enhanced mobility remains uncertain at this point, we speculate that aligned dipoles by an external magnetostatic field may facilitate charge carriers to escape shallow traps; thus, improving their mobilities 37,38 . In conclusion, we have investigated the influence of magnetic nanoparticles and an external magnetostatic field on the PCEs of PSCs. The optimization of BHJ thin film morphology, suppression of charge carrier9s recombination and enhancement in free carrier collection result in more than 50% enhanced efficiency from the PSCs fabricated by BHJ composite blended with Fe 3 O 4 magnetic nanoparticles and then followed with an external magnetostatic field alignment. Our work represents an evolution of PSCs that applications of magnetic nanoparticles and magnetostatic field alignment to BHJ composite have proven to be an extraordinarily effective way to enhance power conversion efficiency of PSCs.  (Fig. 2D). During the processing for PSCs-Fe 3 O 4 W/H, an external magnetic field is applied to align the MNPs inside the active layer. The direction of magnetostatic field is perpendicular to the ITO substrate. The magnetostatic field is generated by square magnet (C750, 3/4'' Cube, Licensed NdFeB, the intensity of the magnetostatic field is 30 , 40 Gauss, the distance to the ITO substrates is ,10 cm) (Fig. 2E). Its direction and intensity is manipulated by tuning the magnet pole direction (North and South) as well as adjusting the distance between these two square magnets, respectively. By using such specific magnet, the distance and intensity on the surface of active layer is controlled to ,10 cm and ,400 G, respectively. Finally, top electrode (Ca and Al) are sequentially deposited onto the active layer under a pressure of ca. 5 3 10 26 mbar (Fig. 2C).

Materials
Characterization and Measurement. The J-V curves characteristics are measured using a Keithley 2400 Source Measure Unit. The solar cells are characterized using a Newport Air Mass 1.5 Global (AM 1.5 G) full spectrum solar simulator with irradiation intensity of 100 mW/cm 22 . The light intensity is measured by a monosilicon detector (with KG-5 visible color filter) which is calibrated by National Renewable Energy Laboratory (NREL). Device masks were made using laser beam cutting technology and had well-defined areas of 0.16 or 0.045 cm 2 .
GISAXS experiments were done at the Advanced Photon Source at Argonne National Laboratory. And the IS is obtained using a HP 4194A Impedance/gainphase analyzer. All the devices are measured under 100 mW/cm 2 AM 1.5 G illumination, with an oscillating voltage of 10 mV and frequency of 1 Hz to 1 MHz. All PSCs are held at their respective open circuit potentials obtained from the J-V measurements, while the IS spectra are recorded.