Spectral aspects of cavity tuned absorption in organic photovoltaic films

Concentration of light and infrared capture are two favored approaches for increasing the power conversion efficiency (PCE) of photovoltaic devices. Using optical transfer matrix formalism, we model the absorption of organic photovoltaic films as a function of active layer thickness and incident wavelength. In our simulations we consider the absorption in the optical cavity formed by the polymer bulk heterojunction active layer (AL) between the aluminum cathode and indium tin oxide (ITO) anode. We find that optical absorption can be finely tuned by adjusting the ITO thickness within a relatively narrow range, thus eliminating the need for a separate optical spacer. We also observe distinct spectral effects due to frequency pulling which results in enhanced longwavelength absorption. Spectral sculpting can be carried out by cavity design without affecting the open circuit voltage as the spectral shifts are purely optical effects. 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Introduction
As interest in renewable energy has surged, research in organic photovoltaics (OPVs) has rapidly expanded because of their potential as an inexpensive, lightweight, flexible, and easyto-install alternative to inorganic semiconductors.OPV device performance can be significantly enhanced through facile customization of the constituent materials' electronic properties and phase behavior via rational chemical synthesis.This effort has focused, for example, on providing lower band gaps [1][2][3][4][5][6], larger open-circuit voltages [7][8][9][10][11], and improved environmental stability [12][13][14][15][16][17].Note, however, that device design also provides other opportunities for performance optimization.Although typical OPV polymers have relatively large optical oscillator strengths, device thicknesses in the hundreds of nanometer range are still necessary for complete light absorption.However, the large exciton binding energies and limited exciton lifetimes require that a donor-acceptor interface be accessible within the exciton diffusion length of the material, typically in the low 10s of nm.A common solution to bridge the gap between these length scales is to create co-continuous networks of donor and acceptor materials, the bulk-heterojunction (BHJ) [18,19], allowing donor-acceptor junctions to be accessible within the exciton diffusion length, while allowing thicker films for complete optical absorption.
In contrast to the above picture, bimolecular recombination [20][21][22] of dissociated excitons as the charges drift to their respective electrodes limits power conversion efficiency (PCE) in thicker BHJ films.The limited mobility of polymer semiconductors then suggests that a thinner film should be preferable due to the higher electric field obtained and shorter mean path to the electrodes, both of which should suppress recombination.Because of these trade-offs, significant effort has been aimed at decreasing the physical active layer thickness while enhancing light absorption.These approaches include optical multilayer designs to take advantage of interference effects [23][24][25][26][27] that optimize the distribution of optical fields and effective absorption length within thin-film photovoltaics, the use of photonic crystals [28][29][30][31] that guide and slow light, and the use of optical scattering [32][33][34][35][36][37] that also increases the effective absorption length.Indeed, analogous work in the field of organic light-emitting diodes (OLEDs) demonstrates that luminescence intensity and spectra versus emission angle can be finely tuned through cavity design [38].Novel cavity designs including optical spacer layers [39], Bragg reflectors [40,41], and tandem designs [42] occur first in the OLED literature.
While reducing the thickness of an absorbing medium generally reduces its optical absorbance, the presence of the indium tin oxide (ITO) and Al electrodes in OPVs creates an optical cavity that enhances absorption for standing waves of the optical fields.Thus, Pettersson et al. used optical modeling to calculate, and demonstrated experimentally, that an oscillatory dependence of the short circuit current density (J SC ) in BHJ OPVs arises from optical interference effects [23].In addition, consideration of interference effects has motivated the design of novel thin-film photovoltaic architectures [25][26][27].While the oscillations in the short circuit current have been correctly attributed to interference effects, the detailed mechanism is far from obvious given the broadband spectrum involved and the strong dispersion of the complex refractive index near resonance.Other researchers have modeled absorption spectra in OPVs as a function of BHJ thickness and optimized cavity effects for device performance [43,44].In the present contribution, we aim to elucidate the detailed mechanism of the interaction of the optical cavity defined by the electrodes in an OPV device with the highly dispersive spectrum of the complex refractive index in the absorptive spectral region of the photovoltaic polymers.We also provide a simple model to predict conditions for cavity enhanced absorption and use reflection spectroscopy measurements to verify modeling results.
To perform this analysis, we employ transfer matrix theory with complex index of refraction dispersion data as measured by spectroscopic ellipsometry, to simulate reflection, transmission, absorption, and electric field distributions in the device for various wavelengths, while varying the thickness of both the ITO anode and the absorbing medium.We focus on two different absorbing layers.The first is a BHJ active layer formed from a blend of the donor polymer poly-3-hexylthiophene (P3HT) and the fullerene derivative phenyl-C60butyric acid methyl ester (PCBM).The second is a neat absorbing film of thieno [3,4b]thiophene-alt-benzodithiophene copolymer (PTB7).We calculate the absorption within the active layer of the device as a function of its thickness and wavelength.We then compare our transfer matrix modeling results to experimental measurements of the optical absorption spectra derived from reflectance measurements in "half-cavity" films as semiconductors deposited between the ITO and reflecting aluminum.In determining how the spectral aspects of cavity-enhanced absorption effects result from the interaction of the cavity modes with the highly dispersive material, we find that: (1) strong thickness-dependent spectral tuning reveals features consistent with the concept of frequency-pulling [45], (2) these features include significant spectral broadening to both longer and shorter wavelengths, (3) these significant spectral changes, including the spectral broadening to longer wavelengths, result in a larger low-energy response to the solar spectrum that is independent of the BHJ HOMO and LUMO energies and thus do not affect the open circuit voltage (V OC ), but can significantly increase the PCE, and (4) the observed oscillations in the PV response directly emerge from these spectral changes.In addition, we find that varying the thickness of the ITO can affect these pronounced spectral changes, and thus, additional optical layers may be unnecessary.Measurements of optical characteristics in films of varying layer thicknesses are consistent with the modeling results.

Experimental
Device fabrication: Devices were fabricated with varying P3HT/PCBM and ITO layer thicknesses to evaluate optical and electrical behavior.Glass substrates (1mm) were cleaned by successive 15 min.sonications at 50  C in soapy water, water, isopropanol, methanol, and acetone.Indium tin oxide was deposited on glass substrates by ion-assisted deposition (IAD), which is known to produce dense, highly conductive films [46].The sheet resistance of these films was ~50 Ω/ .The ITO coated substrates were patterned with electrical tape and etched in boiling HCl acid.The residual acid was then neutralized in aqueous NaHCO 3 solution, and residual tape removed by sonication in hexanes.Patterned ITO substrates were then recleaned using the same procedure as above.Next, PEDOT:PSS (Clevios P VP AI 4083) was spin-cast at 5.0 kRPM for 30 sec., after passing through a 0.45μm PVDF filter, and then annealed for 15 min.at 150  C.
The BHJ active layer was prepared by dissolving poly-3-hexylthiophene (P3HT), purchased from Rieke Metals, and [6,6]-phenyl-C60-butyric acid methyl ester (PCBM), purchased from American Dye Source, in distilled o-dichlorobenzene under an N 2 purge.The active layer solution was then spin-cast in an N 2 filled glove box at various speeds to control the BHJ layer thickness.The resulting films were allowed to slow-dry in a petri dish for 20 min.Next, a 1.0 nm LiF layer followed by a 120 nm Al cathode were deposited by thermal evaporation at ~1x10 −6 Torr.The thickness of the two cathode materials was monitored during deposition using a quartz crystal monitor.
Devices with the PTB7 neat films were deposited on patterned 150 nm thick ITO coated glass substrates (XinYan) which were cleaned as above.PTB7 films were spin-cast from odichlorobenzene at various speeds to control the film thickness.Resulting films were slowly dried before coating with 100 nm Al cathode as above.
Specular reflectance: Normal incidence specular reflectance measurements were obtained using a UV-VIS-NIR spectrophotometer (Varian Cary 500).Devices were masked using a 1.0 mm diameter round pinhole.A highly reflective standard was used to calibrate the reflectance.

Results and discussion
Using the optical transfer matrix calculations and spectroscopic ellipsometric measurements of optical constants for ITO, PEDOT:PSS, PTB7 and P3HT:PCBM, we model the absorption in our PV devices at normal incidence (angle-dependent simulations and experiments will be the focus of a future publication [47]).For each film structure, the absorbance of the active layer was calculated as a function of the active layer thickness and wavelength.Additionally, the absorbance was multiplied by the AM1.5 solar spectrum to obtain the spectral dependence of absorbed light as a function of active layer thickness.Finally, the solar absorbance spectra are integrated to obtain the total absorbed photons as a function of active layer thickness.
In Fig. 1(a) we plot the calculated absorbance spectra of a free-standing P3HT/PCBM blend film surrounded by air as a contour of the film thickness and wavelength.As would be expected, the absorption spectra remain relatively unchanged and the absorbance increases nearly monotonically as the thickness is increased.However, even in the case of a freestanding film, small interference effects are observed due to reflection at the interfaces.Near 600 nm, for example, the absorbance decreases as the BHJ thickness is increased from 155 nm to 200 nm.As can be seen in Fig. 1(b), by surrounding the absorbing medium with more reflective materials, these interference effects are enhanced.Figure 1(c) depicts the same spectrum multiplied by the AM1.5 solar spectrum, thus depicting the spectrum of absorbed sunlight, showing long wavelength absorption enhancement near 200 and 350 nm thickness.A typical OPV device architecture consists of a thick glass substrate which can be treated incoherently [48,49] with subsequent layers of 150 nm ITO, 40 nm PEDOT:PSS, P3HT:PCBM of varying thickness, and 200 nm Al.The absorbance calculation for this device is shown in Fig. 1(b) as a contour plot.The darkened contours indicate wavelength/thickness regions where the absorption is much greater than observed in the bare P3HT/PCBM film.These regions coincide with resonance conditions for the coupled material-cavity system.The appearance of a remarkable series of diagonal contour structures indicates significant interaction between the first several cavity modes and the absorbing semiconducting materials.This interaction can be described by frequency pulling, similar to that described in lasers, and discussed further below.Interestingly, the absorption edges at both high and low energy are broadened.Here, integration over the wavelength of the absorption spectrum multiplied by the terrestrial solar irradiance spectrum versus thickness is depicted.
We next performed additional calculations for various ITO thicknesses between 50 and 200 nm.We find, generally, that the first cavity resonance (BHJ thickness below 100 nm) is strongest for ITO thicknesses of less than 140 nm.By plotting the total absorbed photons versus P3HT/PCBM thickness for a series of ITO thicknesses, we find that the cavity enhancement at the first interference peak can be significantly increased (Fig. 1(d)).In fact, the peak absorption for a P3HT/PCBM thickness of about 80 nm is very sensitive to the thickness of the ITO layer, and significant spectral changes can be effected merely by adjusting the ITO thickness from 150 nm to 110 nm with no other optical layers required .This result confirms that the thickness and optical constants of the transparent anode should be optimized during device design to control absorption in the BHJ layer.We find a particularly interesting design, its absorption contour depicted in Fig. 2(a), where the absorption is concentrated across most of the visible spectrum for a BHJ layer thicknesses around 80 nm.Based on our transfer matrix calculations, we expect that these 80 nm active layers would capture only slightly less optical energy than a 230 nm active layer thickness device.However, due to the arguments above, we would expect PCEs in these devices to be comparable or larger, due to reduced bimolecular recombination [22].As OPV devices of various thicknesses are fabricated, the morphology must be optimized in each case in order to realize the expected increase in power conversion efficiency.To understand the origin of the distinctive diagonal spectral features in Fig. 1(b), we calculate the resonant frequency of the multilayer cavity, ν, using a simple frequency pulling model, that depends on the bare cavity frequency, ν m , and the cavity bandwidth, δν c , as well as the absorber's transition frequency, ν 21 , and bandwidth, δν 21 .This model describes the frequency dependence of the observed coupled modes arising from dispersion of the material's refractive index interacting with the cavity.Using this model, we calculate the first several resonant modes of the cavity for various device thicknesses and plot them overlaid on the transfer matrix contours described above (see Fig. 2(b)).We find excellent agreement between the areas of cavity-enhanced absorbance and the calculated cavity resonances.The non-trivial modal structure is due in large part to the strong wavelength dependence of the material dispersion near resonance.To compare with experiment, we use specular reflectance spectroscopy.The peaks and troughs correspond to strong and weak absorption, respectively, for structures with varying active layer thickness.The transmittance for these structures is negligible due to the high reflectance of the aluminum cathode, so the absorbance is plotted as A = (1 -R). Figure 3(a) clearly shows features of the reflectance spectra shifting to longer wavelengths as the P3HT/PCBM thickness is increased.Additionally, for structures with P3HT/PCBM thickness between 200 and 250 nm, the absorption near the 600 nm edge is extended and enhanced, which is important for capturing the peak solar irradiance near 600 nm, hence increasing PCE.By plotting the points at which these absorbance peaks or troughs occur on top of the calculated absorbance for devices with identical architecture (see Fig. 3(b)), we find significant correlation in that areas of predicted absorption enhancement coincide with peaks in the absorption spectra and, conversely, areas predicted to have low absorbance coincide with absorption dips.As the P3HT/PCBM thickness is varied, no changes to the materials' HOMO and LUMO energies is made, and yet the cavity interference effects can shift absorption features by 50 or 100 nm (up to 400 meV).This optical method of extending the absorption spectrum of OPV active layers is an approach with no trade-off to other device parameters contributing to the PCE.In the next series of experiments, we fabricated a series of samples with PTB7 as the absorbing medium to determine the applicability of spectral design shaping of the active layer by thickness control for next generation alternating co-polymers.PTB7 is known to have a large extinction coefficient and an absorption edge extending further into the red [50,51].As a result of careful chemical design and device optimization, very large power conversion efficiencies have been reported using this material [52,53].Using a neat film rather than a mixture of two materials allows the most straightforward conclusions regarding any spectral shifts.As with the P3HT/PCBM samples, thickness dependent absorption features demonstrate a large degree of spectral control especially in tuning the low energy absorption edge.It can be seen in Fig. 3(b) that long wavelength absorption enhancements occur periodically as a function of thickness.Careful engineering of the active layer thickness and ITO thickness can be used to extend absorption, and importantly this enhancement occurs even in materials that have been carefully designed to capture low energy photons.In addition, oscillations in the absorption spectrum especially at shorter wavelengths appear as peaks and dips whose location depends strongly on thickness (see Fig. 4(a)).Comparing these measured absorption peaks and dips with simulations, we find that there is a strong match with corresponding absorption characteristics observed in the active layer with the transfer matrix formulation calculations.In particular, the strong agreement between measurement and calculation of the location of absorption resonant enhancement or suppression as well as their shift as a function of active layer thickness is seen in Fig. 4(b).
We note that in comparing the extinction coefficients in Figs.3(a) and 4(a) with their corresponding cavity absorption, that the cavity effects are considerably larger in the PTB7 samples than in the P3HT/PCBM samples.This observation is consistent with the values of the extinction coefficients and oscillator strengths indicating that the cavity tuned absorption is stronger for larger oscillator strengths due to stronger coupling between the cavity modes and the material.
In order to provide the maximum range of efficiency control by spectral shaping using this method, it is highly desirable to use active layers that are less subject to decreases in charge collection efficiency as the active layer thickness is modified.This could be achieved by developing new materials or by optimizing processing conditions during the BHJ deposition and annealing [54].One thickness dependent morphology study where processing was optimized [55] suggests that 100 nm P3HT/PCBM thickness produces a higher degree of P3HT crystallinity and nanowire formation which should lead to higher photocurrent collection.We believe that further optimization of nanoscale morphology for various active layer thickness BHJ films could yield large photocurrents in especially thin, spectrally optimized devices.Additionally, consideration of optical interference effects may serve to guide work on novel materials designed to interact favorably with the cavity to influence absorption spectra and efficiency in devices.

Conclusions
Transfer matrix theory has been utilized to model the absorption of organic photovoltaic devices as a function of active layer thickness and incident wavelength, with results consistent with experiment.In particular, we have examined the optical enhancements that arise from the design of the ITO and Al electrodes, and identified a high efficiency cavity structure not requiring additional optical spacer layers due to the high sensitivity of the design to the thickness of the ITO layer, within the thickness range of high-performance ITO.Significant spectral effects are observed, including frequency pulling which tunes the optical absorption and extends the absorption spectrum to longer wavelengths, decoupled from the open circuit voltage, hence also the HOMO/LUMO energetics.The absorption features can be shifted by as much as 0.4 eV, without the deleterious change in open-circuit voltages which accompany other approaches.This independence of the shift from the open-circuit voltage suggests the ability to adjust the absorption spectrum of photovoltaic devices independently of the material, which could have major implications as the extended spectrum leads to increased PCE.Note that these cavity pulling effects are highly dependent on the details of the absorption spectrum, such as oscillator strength, and refractive index dispersion for particular materials, so that such studies for other materials should be routinely carried out and used to select the optimum coupled material/device-design combination.Regardless, this modeling provides additional degrees of freedom in optimizing organic photovoltaics.Future work is aimed in this direction, taking into account that optimized processing is also a critical consideration.

Fig. 3 .
Fig. 3. (a) Normal incidence absorbance spectra of a series of structures with varying active layer thickness consisting of ITO (150 nm) / PEDOT:PSS (40 nm) / P3HT:PCBM (80-250 nm)/ Al (100 nm).Notable peaks and troughs are observed to shift with active layer thickness and distinct features are highlighted by symbols.For comparison, the material extinction spectrum is also shown as a dashed curve.(b) A zoomed-in view of the simulation results of Fig. 1(b) with peaks (green circles, black squares) and troughs (blue triangles) from normal incidence absorbance measurements (Fig. 3(a)) plotted on top showing agreement between calculations and experiment.

Fig. 4 .
Fig. 4. (a) Normal incidence absorbance spectra of a series of PTB7 films of various thickness consisting of ITO (150 nm) / PTB7/ Al (100 nm).The material extinction spectrum is also shown.(b) A contour plot simulated by optical transfer matrix calculations overlaid by data with blue corresponding to peaks in Fig. 4(a), and black corresponding to valleys.