Special Section on Solution-Processable Organic Solar Cells

Modeling approach to derive the anisotropic complex refractive index of polymer:fullerene blends for organic solar cells utilizing spectroscopic ellipsometry

[+] Author Affiliations
Michael F. G. Klein, Gustavo Q. Glasner de Medeiros, Panagiota Kapetana, Uli Lemmer, Alexander Colsmann

Karlsruhe Institute of Technology (KIT), Light Technology Institute (LTI), Engesserstrasse 13, Karlsruhe, 76131, Germany

J. Photon. Energy. 5(1), 057204 (Jan 06, 2015). doi:10.1117/1.JPE.5.057204
History: Received August 18, 2014; Accepted November 10, 2014
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Open Access Open Access

Abstract.  The knowledge of the complex refractive indices of all thin layers in organic solar cells (OSCs) is a prerequisite for comprehensive optical device simulations that are particularly important for sophisticated device architectures, such as tandem OSCs. Therefore, refractive indices are often determined via spectroscopic ellipsometry and subsequent time-consuming modeling. Here, we investigate a modeling approach that allows for the determination of complex refractive indices of bulk-heterojunctions by superimposing the optical models of the respective fullerenes and polymers. The optical constants of neat [6,6]-phenyl C71-butyric acid methyl ester (PC71BM), poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT) and poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole) (PCPDTBT) are determined, covering the OSC relevant spectral region from 250 to 1,000 nm. Then the blends PSBTBT:PC71BM and PCPDTBT:PC71BM are described within an effective medium approximation. From this approximation, the mass density ratio of polymer and fullerene can be derived. This approach furthermore allows for a uniaxial anisotropic optical description of the polymers and provides insight into thin-film morphology. In contrast to x-ray diffraction experiments, this method also allows for probing amorphous materials. Spectroscopic ellipsometry can be a valuable tool for the investigation of bulk-heterojunction morphologies of the latest high-performance OSC materials that exhibit a low degree of crystallinity.

Figures in this Article

Organic solar cells (OSCs) combine the advantages of low-cost and large-area fabrication with the use of nonhazardous and environmentally friendly materials. Over the last few years, power conversion efficiencies improved continuously, now exceeding 10% in single-junction solar cells.1 Improvements often originated from the synthesis of new absorber materials that allowed for an enhanced spectral coverage of the solar spectrum or enabled higher internal quantum efficiencies.27 In the lab, screening and optimization of new materials and cell architectures often follow a trial and error approach, although only very little amounts of material are available. An alternative and material saving route to optimized OSCs is a comprehensive optoelectronic device simulation that reduces the experimental parameter space. This becomes particularly important for sophisticated device architectures, such as tandem solar cells.8 However, in order to carry out meaningful optical simulations, a profound knowledge of the refractive indices is mandatory.5,912

Unfortunately, optical constants from the literature often cannot be used to describe certain experiments since the optical properties strongly depend on the substrate, the underlying interface, the intrinsic polymer properties (molecular weight, polydispersity), the polymer:fullerene ratio, and the process conditions, such as the solvent system, the drying kinetics, and the postprocessing treatments.1324 Therefore, an urgent need for flexible optical descriptions of bulk-heterojunctions emerged, which use parametric descriptions and allow for individual adjustments.

If carried out purposefully, the optical model further reveals information about anisotropy within the bulk-heterojunction.25 Such models were recently utilized to determine the vertical gradient in the active layer of OSCs13,25 and to investigate the shape of [6,6]-phenyl C61-butyric acid methyl ester (PC61BM) inclusions in poly(3-hexylthiophene-2,5-diyl) (P3HT) solar cells.26

In this work, we present a modeling approach for spectroscopic ellipsometry (SE) data analysis, which facilitates the determination of the complex refractive indices of various polymer:fullerene blends. Therefore, in a first step, the relative dielectric functions of the fullerene [6,6]-phenyl C71-butyric acid methyl ester (PC71BM) and the polymers poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT) and poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b’’]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT) are described by the superposition of Gaussian oscillators. In a second step, the relative dielectric functions of the polymer:fullerene blends are determined by superimposing the optical models of both constituents. PSBTBT and PCPDTBT are well-known donor-acceptor copolymers with good power conversion efficiencies when blended with PC71BM.2731 Their similar structures allow a direct comparison. For the active layer deposition and blend ratios, we follow literature-known process protocols, which are optimized for high-performance solar cells.2729 Optical data are presented in the spectral region from 250 to 1,000 nm.

We further compare isotropic and anisotropic optical models of neat polymers. The results of this comparison serve as input parameters for anisotropic optical descriptions of the blends, which are then analyzed with respect to the predominant polymer orientation and the degree of aggregation.

SE is a contactless and nondestructive measurement technique that allows for deriving the complex refractive indices of thin-films and their thicknesses simultaneously. The complex refractive index n˜, given by Display Formula

n˜=nik=εr˜=εr,1iεr,2(1)
comprises the refractive index n (real part) and the extinction coefficient k (imaginary part) and is directly related to the complex relative dielectric function εr˜, assuming a relative permeability μr˜=1.

The basic ellipsometry working principle relies on measuring the change of the light beam polarization state after interacting with the sample. This change is described by the two ellipsometric values Ψ and Δ, which represent the amplitude ratio and phase difference between p- and s-polarization.32 In this study, various wavelengths and angles of incidence were investigated. In addition, transmission spectra were recorded at normal incidence on the very same spot and incorporated into the analysis.

We use vendor-supplied software (WVASE32®, J. A. Woollam) to analyze the datasets. First, a multilayer model is constructed, where each individual layer describes a certain subset of physical properties of the sample, e.g., the level of interface intermixing, surface roughness, and the relative dielectric function of the material. In the following, “layer” will refer to a layer in the optical model and not necessarily to a physical layer.

The relative dielectric functions are defined by oscillator models, i.e., the description of each optical transition by an appropriate oscillator. Then the relative dielectric function εr˜ of a material can be described by the sum of these oscillators. To describe the transitions within the measurement range, we choose an oscillator type generating a Gaussian line shape in εr,2, Eq. (2), with a Kramers-Kronig consistent counterpart in εr,1, Eq. (3). Display Formula

εr,2,n(E)=Ane[2ln(2)(EEn)Brn]2Ane[2ln(2)(E+En)Brn]2,(2)
Display Formula
εr,1,n(E)=2πP0ξε2,n(ξ)ξ2E2dξ,(3)
where An is the amplitude, En is the center energy, Brn is the width, and P is the principal value.33 Higher-energy transitions outside the measurement range are summarized in a high-energy pole function, i.e., an oscillator with zero-width. Further, a real constant εr, is added to εr,1.

Based on this parameterized model, the optical response of the sample is calculated and compared to the measured Ψ and Δ data and the transmission. The parameters for the individual layers (thickness, oscillator parameters, etc.) are fitted in order to achieve a good match between model-generated and measured values. The difference between these values is quantified by the mean squared error (MSE).34 MSE is used by the analysis software as weighted test function during the fitting procedure to further reduce the deviation between the three values by making use of the Marquardt-Levenberg algorithm.35,36

We verify the results of the fit and ensure physical significance of the calculated optical constants by, first, measuring the thicknesses of thin-films deposited on glass substrates in a transparent energy band by applying the Cauchy dispersion relation and by comparing them to profilometry results. (We note that the Cauchy model does not fulfill the Kramers-Kronig relation but is a valid approximation for transparent spectral regions.) Second, we perform a multisample analysis: several samples with varying thin-film thicknesses are characterized. All respective datasets are described with the same optical model, hence enabling a general and robust optical description and reducing parameter correlation.37,38 In the end, the oscillator model will guarantee full Kramers-Kronig consistency.

Further, we include a wide range of angles of incidence in the analysis, typically ±25deg around the Brewster angle (step width: 5 deg). To perform the multisample analysis, the datasets are measured on several samples with different layer thicknesses. All SE investigations cover the spectral region from 250 to 1,700 nm (1,000 nm for PC71BM) and layer thicknesses are determined in the transparent (k=0) wavelength regime from 1,000 to 1,700 nm.

For reasons of clarity, we will show a reduced dataset in the following figures. In particular, we skip data in the infrared region beyond 1,000 nm, restrict to some representative angles of incidence, and only show typical data for one sample of the multisample analysis.

Spectroscopic Ellipsometry

Ψ and Δ were measured with a variable angle spectroscopic ellipsometer (VASE®, J.A. Woollam Co., Inc.), equipped with a rotating analyzer and two detectors. A rotating retarder plate (MgF2 Berek waveplate) in the beam path behind the fixed polarizer allows for a precise determination of Δ.39 Datasets were recorded between 250 and 1,700 nm (1,000 nm for PC71BM). Transmission data of the samples were collected at normal incidence and by moving the VASE detector arm into the optical path behind the sample. Thus, the transmission spectra were determined on the very same spot as the ellipsometric data, allowing for their incorporation into the analysis. The datasets were analyzed with the software WVASE32® (J. A. Woollam, version 3.774).

Transmission Spectroscopy

Transmission spectra of diluted solutions and of solid films spin cast onto quartz-glass substrates were recorded with a spectrophotometer (Lambda 1050, Perkin Elmer), enabling a lower noise level than the measurements carried out with the ellipsometer.

Materials and Sample Preparation

Soda-lime glass substrates were cleaned with acetone and isopropyl alcohol and then dried in a nitrogen stream. All materials were used as received and were deposited under inert conditions in a nitrogen glovebox (O2 and H2O<1ppm).

PC71BM (Solenne, >99%) was dissolved in DCB (anhydrous, 99%, Sigma-Aldrich®) at a concentration of 60mg/mL, stirred overnight at 80°C, and spin cast on substrates at room temperature with different spin coater settings to achieve thicknesses between 85 and 120 nm.

PSBTBT and PCPDTBT were both dissolved in DCB with a concentration of 13mg/mL, stirred overnight at 70 or 90°C, respectively, and were deposited from hot solution on hot soda-lime glass substrates. Different spin coater settings allowed for tuning the layer thicknesses between 40 and 60 nm for PSBTBT or 15 and 30 nm for PCPDTBT.

The blends PSBTBT:PC71BM (12, layer thicknesses between 90 and 115 nm) and PCPDTBT:PC71BM (13.4, layer thicknesses between 90 and 130 nm) with a polymer concentration of 13mg/mL in DCB were spin coated following the same conditions used for neat films. The blend ratios were chosen according to optimized process protocols.27,29

SE data of the neat polymer films and the blend films were recorded between 250 and 1,700 nm at different angles of incidence α between 30 and 80 deg in 5 deg steps. Datasets were analyzed over the entire spectral range. For reasons of clarity, we only show a reduced dataset in the figures, i.e., we skip data in the infrared beyond 1,000 nm, restrict to some representative angles of incidence, and only show data for one sample of the multisample analysis.

Thin-film thicknesses were cross-checked with a stylus profiler (DektakXT, Bruker AXS GmbH) and compared with ellipsometry results.

Glass Substrate

Soda-lime glass is used as substrate for all thin-films.37 Therefore, we first set up an optical model for the glass substrate. As the substrate is 1mm thick, unwanted backside reflections are expected. They can either be suppressed by roughening the substrate’s backside or be accounted for in the analysis software. Here we use the latter approach as this allows measuring the transmission spectra on the very same spot after the ellipsometry characterization.

The glass substrate is described with a Cauchy dispersion relation40 with an Urbach-tail41 and a surface roughness layer of 1.3nm.

The derived complex refractive indices (n,k) of the soda-lime glass substrates are depicted in Fig. 1 versus wavelength. In the following, we keep the parameters of the model constant and treat the surface roughness layer as an intermixed layer of the subsequently applied thin-film and the glass substrate.

Graphic Jump LocationF1 :

Optical constants n and k of the soda-lime glass, which is used as substrate for all thin-films discussed in this study. The optical model includes a surface roughness layer of 1.3nm.

PC71BM

Solar cells based on the polymers PCPDTBT and PSBTBT in combination with the electron acceptor PC71BM exhibit enhanced power conversion efficiencies. We first analyze PC71BM. Therefore, the fullerene is dissolved in 1,2-dichlorobenzene (DCB) and then spin cast on the glass substrates as described in Sec. 3.3. A multisample SE analysis is performed on six samples with varying thicknesses. Figures 2(a) and 2(b) show the experimental data of a typical sample. Transmission spectra of PC71BM in DCB solution and of a solid PC71BM thin-film are recorded with a spectrophotometer, Fig. 2(c). From the absorption features present in all spectra, the starting values En,input for the center energies of the Gaussian oscillators are derived, Table 1. Based on this estimation of En, an optical model is set up comprising nine Gaussian oscillators Gaun, a pole taking into account higher-energy transitions, and a real constant εr,. A stepwise fit (MSE=11.14), starting from the infrared and progressing toward higher energies, results in the oscillator parameters given in Table 1. The fitted center energies En differ slightly from their respective starting values En,input. In this multisample analysis, all measured datasets are taken into account. If the fit is restricted to a single sample, lower MSEs can be achieved. As the multisample analysis only differs slightly from the results of the single-sample analysis and as we aim, here and in the following, at finding a widely applicable optical model, we utilize the multisample approach. The model-generated data Ψmod, Δmod, and the optical constants are depicted in Figs. 2(a), 2(b), and 2(d), respectively. The good agreement with the optical constants in 42, supporting information, verifies the chosen approach. The good match between simulated and experimental transmission, which was measured on the same spot as the ellipsometry data, proves the fit quality, Fig. 3(a).

Graphic Jump LocationF2 :

(a) and (b) Spectroscopic ellipsometry data of an 87 nm [6,6]-phenyl C71-butyric acid methyl ester (PC71BM) thin-film spin cast on a glass substrate for five angles of incidence. The colored solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data. (c) Transmission spectra of PC71BM in diluted dichlorobenzene (DCB) solutions and of a solid film on fused silica measured with a spectrophotometer. The gray shaded area indicates the absorption of the cuvettes. The center energies of the absorption features Gau1 to Gau9 are used as starting values for the Gaussian oscillator center energies in the optical model. (d) Optical constants n and k are derived from a multisample analysis.

Table Grahic Jump Location
Table 1From the transmission spectra in Fig. 1(c), the starting values En,input for the fit of the Gaussian oscillators’ center energies are derived. The optical model of [6,6]-phenyl C71-butyric acid methyl ester (PC71BM) comprises nine Gaussian oscillators (Gaun with center energy En, amplitude An, and width Brn,33 a pole, and the real constant εr,=2.00eV.
Graphic Jump LocationF3 :

Measured (red lines) and simulated transmission (black dashed lines) of (a) PC71BM, (b) poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT), (c) poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT), (d) PSBTBT:PC71BM, and (e) PCPDTBT:PC71BM. The measured transmission spectra were determined at the same spot as the ellipsometry data by rotating the ellipsometer’s detector straight behind the sample. The noise levels are higher than in the spectrophotometer measurements that were described in Sec. 3.2 and that are depicted in Figs. 2(c), 5(c), and 7(c). The simulated data in Figs. 3(b)3(e) rely on anisotropic models.

All thin-film thicknesses tStylus as determined by profilometry are well within the 90% confidence limit of the thickness tSE as determined by SE.

Polymers

Both polymers, PCPDTBT and PSBTBT, exhibit strong structural similarities. They differ only in the 5-position, where PCPDTBT comprises a carbon atom, whereas PSBTBT features a silicon atom, Fig. 4(a). It was shown that the silicon substitution in PSBTBT reduces the steric hindrance from the bulky alkyl groups and improves molecular packing.43 The main absorption features of both polymers are still comparable though.

Graphic Jump LocationF4 :

(a) Chemical structure of PSBTBT and PCPDTBT and definition of the polymer-chain reference frame (a, b, and c). The c axis is oriented along the polymer backbone. (b) The optical constants nxy and kxy describe light-polymer interaction for polymers with their c axes being aligned parallel to the substrate surface, while the z-component describes vertically oriented polymers. (x, y, and z) is the substrate reference frame. Schemes of the morphology of (c) neat PSBTBT, (d) neat PCPDTBT, (e) PSBTBT:PC71BM, and (f) PCPDTBT:PC71BM showing different degrees of aggregate alignment relative to the surface. Black dots represent PC71BM.

The measured datasets Ψ and Δ for a PSBTBT thin-film spin cast on a glass substrate are shown in Figs. 5(a) and 5(b), respectively. The isotropic optical model is constructed in analogy to the procedure described for PC71BM. The transmission spectra of PSBTBT in DCB solution and of a solid PSBTBT thin-film are recorded, Fig. 5(c). The analysis of the absorption features leads to the starting values En,input for the center energies En of the Gaussian oscillators. Then, all oscillator parameters, a pole for the high-energy transitions and εr, are fitted. The respective values are summarized in Table 2. Based on this model, the isotropic optical constants are derived, Fig. 6(a).

Graphic Jump LocationF5 :

(a) and (b) Spectroscopic ellipsometry data Ψ and Δ of a typical neat PSBTBT thin-film spin cast on a glass substrate. The colored solid lines correspond to the measured data; the dashed black lines correspond to data generated from a uniaxial optical model. (c) Transmission spectra of PSBTBT in diluted DCB solutions and of a solid film on fused silica. The starting values for the Gaussian oscillator center energies En,input are derived from the center energies of the absorption features, Table 2. (d) The optical constants comprise an in-plane (index xy) and out-of-plane component (index z) and are derived from a multisample analysis with an overall mean squared error (MSE)=6.37.

Table Grahic Jump Location
Table 2Isotropic, parameterized description of poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT). The starting values En,input are derived from the transmission spectra in Fig. 5(c). The center energies En change only slightly upon performing the fit. The parameters An and Brn are determined defining the Gaussian oscillators Gaun. The offset was found to be εr,=2.46eV.
Graphic Jump LocationF6 :

Optical constants of (a) PSBTBT and (b) PCPDTBT within an isotropic description. We note the different scaling of the y axes.

PCPDTBT is investigated accordingly. The respective isotropic datasets are shown in Fig. 7, Table 3, and Fig. 6(b). The spectral shape of the complex indices of refraction is comparable with the isotropic data presented by Guerrero et al.42 As they used PCPDTBT from a different supplier, the amplitudes are different though.

Graphic Jump LocationF7 :

(a) and (b) Spectroscopic ellipsometry data Ψ and Δ of a typical neat PCPDTBT thin-film spin cast on a glass substrate. The solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data within a uniaxial description. (c) Transmission spectra of PCPDTBT in dilute DCB solutions and of a film on fused silica. The center energies En,input of the absorption features Gaun are given in Table 3. (d) Anisotropic optical constants derived from a multisample analysis with an overall MSE=7.51.

Table Grahic Jump Location
Table 3Poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole] (PCPDTBT). Starting values En,input as derived from Fig. 4(c). The parameters En, An, and Brn determine the optical model. εr,=2.28eV. Gau7 is outside the ellipsometer’s measurement range; the pole function covers its contribution.

Both polymer models are derived independently. However, the derived optical models utilize very similar sets of Gaussian oscillators, which reflect their strong structural similarity. A comparison of the isotropic optical constants further shows that the overall optical density of PSBTBT is somewhat higher than the optical density of PCPDTBT. This can be either attributed to a higher intrinsic absorption or to a denser packing of the polymer chains.43

For both polymers, we assign the transitions Gau1 and Gau2 to the 0–0 and 0–1 absorption peaks, while Gau3 comprises higher vibronic progressions and an amorphous background. The nature of Gau4 remains unclear, but may be attributed to transitions involving more localized states.44

A more detailed model has to take into account the anisotropy of the films. OSC polymers often exhibit elongated structures and, hence, form mostly flat two-dimensional molecules.4548 Therefore, we probe the thin-films for anisotropy, assuming no preferential order in the in-plane direction as indicated by the invariance of Ψ under in-plane sample rotation.32,49,50 This assumption allows us to utilize a uniaxial optical description, only distinguishing between the xy- and the z-contribution. [The xy-component is sometimes referred to as (in-plane) and z as (out-of-plane).] For this orientation, the off-diagonal elements of the Jones matrix vanish.32

In the uniaxial configuration, the optical constants nxy and kxy are determined by the xy-layer, and the z-component by the z-layer. The xy-optical constants describe light-matter interaction for light under normal incidence with its electrical field vector E parallel to the sample surface. For light impinging at grazing incidence, E is almost normal to the sample surface and the interaction with the polymer is described with nz and kz.

For the anisotropic model, the isotropic oscillator parameters serve as input parameters for both the xy- and z-layer, consequently doubling the number of fit parameters. Since doubling of the fit parameters does hamper finding a unique solution, we simplify our model by assuming that the same optical transitions will be observed in both directions (xy and z), changing their relative amplitude only. Accordingly, the oscillator amplitudes An,xy and An,z are defined as fit parameters.

The fitted datasets Ψ and Δ for PSBTBT are shown in Figs. 5(a) and 5(b) and the derived anisotropic optical constants in Fig. 5(d). The MSE improves from 7.23 to 6.37 upon utilizing an anisotropic model. The respective datasets for PCPDTBT are shown in Fig. 7. For PCPDTBT, the MSE improves from 7.77 to 7.51. Evidence of the fit quality is provided in Figs. 3(b) and 3(c), where we compare the experimental transmission data that were measured on the same spot as the ellipsometry data, with the simulated transmission based on the ellipsometric model. Both neat polymers exhibit pronounced uniaxial anisotropy. Since the polymer ππ* transitions, here modeled with Gau1Gau3, are excited by an electrical field that is polarized parallel to the polymer backbone, i.e., the polymer c axis as defined in Fig. 4(a), a detailed analysis of the anisotropic optical constants can further reveal morphological details.51,52,53 The optical constants nxy and kxy describe light-polymer interaction for polymers with their c axes aligned parallel to the substrate surface, while the z-component describes upright polymers with their c axes oriented in z-direction, Fig. 4(b).

The extinction coefficient of PSBTBT splits up in an xy- and a z-component between 540 and 800 nm, Fig. 5(d). Toward lower wavelengths, no splitting is observed, indicating a different nature of the involved transitions. According to similar observations in the literature, we attribute the shoulder around 761 nm (Gau1) to polymer aggregation.43 As the contribution of the xy-component is more pronounced than the contribution of the z-component, we conclude that aggregates of polymers with a c axis aligned in-plane prevail, Fig. 4(c).

For PCPDTBT, the xy- and z-extinction coefficients also split up and show anisotropic behavior in the low-wavelength regime, Fig. 7(d). The low-energy shoulder, which is visible in the kxy data, does not appear in the kz data. In analogy to PSBTBT, the shoulder in kxy can be attributed to aggregates of polymers with c axes aligned parallel to the xy-plane, whereas the interpretation of kz leads to ambiguous results. This can either be attributed to nonaggregated standing polymers or an isotropic amorphous background, Fig. 4(d).

Blends

The measured spectroscopic ellipsometry data Ψ and Δ of a PSBTBT:PC71BM and a PCPDTBT:PC71BM thin-film are depicted in Figs. 8(a) and 8(c) and in Figs. 8(b) and 8(d), respectively. The optical properties of the polymer:fullerene blends are modeled within an effective medium approximation (EMA). Therefore, the optical constants of polymer and fullerene constituents are superimposed. As the analysis of neat polymers in Sec. 4.3 revealed a preferred orientation of the PSBTBT and PCPDTBT c axes parallel to the substrate, we choose uniaxial models for the blends as well. The oscillator parameters in Tables 1, 2, and 3 are used as starting parameters.

Graphic Jump LocationF8 :

Spectroscopic ellipsometry data Ψ and Δ of [(a) and (c)] a typical PSBTBT:PC71BM (12) thin-film and [(b) and (d)] a typical PCPDTBT:PC71BM (13.4) thin-film. The solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data within a uniaxial description. Anisotropic optical constants of (e) PSBTBT:PC71BM and (f) PCPDTBT:PC71BM are derived from a multisample analysis with an overall MSE=3.90 and MSE=4.64, respectively.

After determining the layer thicknesses in the transparent spectral regime, the volume ratio of polymer to PC71BM is fitted. The resulting ratios are listed in Table 4 showing excellent agreement with volume ratios being calculated on the basis of material density as determined by helium pycnometry in the literature.54,55 This result shows that SE can be an alternative and contactless metrology approach to determine material density ratios in blend films. If the material density of one component is already known, the absolute material density of the other component can be determined.

Table Grahic Jump Location
Table 4The normalized volume ratios in the blends as derived from ellipsometry fittings show excellent agreement with the volume ratio calculated from the material densities. ρPC71BM=1.52g/cm3, ρPSBTBT=1.17g/cm3, and ρPCPDTBT=1.10g/cm3 as determined by helium pycnometry in the group of Dadmun et al.54,55

In the next step, we investigate whether the polymer’s anisotropy is preserved upon blending with PC71BM. Therefore, the polymer oscillator amplitudes are fitted leading to the anisotropic optical constants shown in Fig. 8(e) for PSBTBT:PC71BM and in Fig. 8(f) for PCPDTBT:PC71BM. As indicated in Figs. 8(a) and 8(c) and in Figs. 8(b) and 8(d), both multisample fits describe the experimental data very well (MSE=3.90 and 4.64). Again, the comparison of the simulated and the experimental transmission in Figs. 3(d) and 3(e) confirms the good fit quality. Further, the anisotropic optical constants of PSBTBT:PC71BM match the shape of the isotropic optical constants known in the literature.56 When performing the fits, only the amplitudes of the oscillators Gau1 to Gau3 change considerably. In analogy to the analysis of the neat polymers, those oscillators are an indicator for the degree of polymer aggregation.

For PSBTBT:PC71BM, a pronounced uniaxial anisotropy becomes visible in the optical constants, Fig. 8(e). Similar to neat PSBTBT, both the in-plane and the out-of-plane extinction coefficients exhibit shoulders around 760 nm, where the xy-contribution dominates the z-contribution. The dominance of the xy-contribution can be attributed to polymer aggregates with their c axes aligned in-plane as illustrated in Fig. 4(e). This interpretation of the polymer orientation from SE experiments fits well to the time-resolved x-ray analysis that we published earlier, where we found that PSBTBT nucleation takes place in defined orientation at an interface, while randomly oriented aggregates form in the bulk during solvent evaporation.29 As the degree of PSBTBT:PC71BM anisotropy is similar to the anisotropy of neat PSBTBT, the polymer orientation remains mostly unaffected upon blending with PC71BM.

For PCPDTBT:PC71BM, the optical constants in xy- and in z-directions differ slightly, Fig. 8(f). The PCPDTBT low-energy shoulder appears in both directions. This can be attributed to randomly oriented PCPDTBT aggregates as depicted in Fig. 4(f). In the blend model, the low-energy shoulder is more pronounced than in the model for neat PCPDTBT, indicating a higher degree of aggregation in the blend.

The higher degree of the c axis in-plane alignment within the PSBTBT:PC71BM blend as compared to the PCPDTBT:PC71BM blend, probably induced by the substrate surface, may be explained by the lower PC71BM volume fraction, Table 4.

Limitations

The EMA approach requires negligible cross-coupling of optical transitions between the blend’s components. For example, charge transfer (CT) absorption could cause such a new excitation channel. Since CT absorption in state-of-the-art OSCs is some magnitudes lower than the ππ* transition,57 we disregard CT absorption.

Both polymers that are investigated in this study exhibit a lower degree of crystallinity than other semicrystalline materials, such as P3HT.58 Upon blending more crystalline materials, the degree of crystallinity may be reduced significantly. Therefore, in order to generate a suitable model for highly crystalline materials, care should be taken that the degree of crystallinity between the neat material and the blend is comparable. For example, for neat P3HT, we suggest deposition from a low-boiling point solvent, such as chloroform, thus accelerating the film drying time and, thereby, effectively suppressing crystallization of the neat polymer.

The determination of the anisotropic blend models benefits from the weak spectral overlap of the polymer and fullerene extinction coefficients, which allows separating both components and performing a precise fit. Fortunately, this applies to the vast majority of polymer:fullerene blends. Even more stable fit results can be achieved by taking into account advanced photophysical descriptions.59 So far, such a detailed description has been elaborated for P3HT only.60,61 A description of the complex absorption spectra of the low-band gap polymers is still lacking. Therefore, we suggest utilizing the phenomenological derived values of the oscillator center energies and robust multisample fits as discussed in this work.

In conclusion, we present a modeling approach for the analysis of ellipsometry data, which facilitates the precise determination of the optical constants of various polymer:fullerene blends. The optical constants of the neat constituents PC71BM, PSBTBT, and PCPDTBT are determined, first, by parameterizing the constituents’ relative dielectric functions, where each optical excitation is described by a Gaussian oscillator. The center energies of the oscillators are derived phenomenologically from their respective transmission spectra.

Based on this set of optical constants, the blends PSBTBT:PC71BM and PCPDTBT:PC71BM are described within an EMA. An initial fit on the polymer-to-fullerene ratio allows to derive the volume density ratio of both constituents.

Our approach further allows for considering a uniaxial anisotropic optical description of the neat polymers and their blends. The detailed analysis of the anisotropy provides deep insight into the PSBTBT, PCPDTBT, and blend morphology. Since many of the latest high-performance materials exhibit a lower degree of crystallinity than the vastly studied P3HT,62 we propose SE as a nondestructive bulk-heterojunction probing technique for future polymer:fullerene bulk-heterojunction investigations.

The authors acknowledge funding by the Federal Ministry of Education and Research (BMBF) within the project Taurus, contract 03EK3504, the Deutsche Forschungsgemeinschaft (DFG) priority program 1355 “Elementary Processes of Organic Photovoltaics,” and the State of Baden-Württemberg through the DFG Center for Functional Nanostructures (CFN). Poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] and poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} were supplied from Konarka. The authors thank Professor M. Dadmun, Professor G. Bazan, Dr. H. Chen, Dr. J. Peet, Dr. S. Hu, and Dr. J. Azoulay for the communication of their results54,55 prior to publication, Dr. B. Schmidt-Hansberg (Karlsruhe Institute of Technology) for fruitful discussions, and Dr. T. Wagner (LOT-QuantumDesign) for technical support. M.F.G.K. was supported by the Karlsruhe School of Optics and Photonics (KSOP).

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Biographies of the authors are not available.

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Citation

Michael F. G. Klein ; Gustavo Q. Glasner de Medeiros ; Panagiota Kapetana ; Uli Lemmer and Alexander Colsmann
"Modeling approach to derive the anisotropic complex refractive index of polymer:fullerene blends for organic solar cells utilizing spectroscopic ellipsometry", J. Photon. Energy. 5(1), 057204 (Jan 06, 2015). ; http://dx.doi.org/10.1117/1.JPE.5.057204


Figures

Graphic Jump LocationF6 :

Optical constants of (a) PSBTBT and (b) PCPDTBT within an isotropic description. We note the different scaling of the y axes.

Graphic Jump LocationF1 :

Optical constants n and k of the soda-lime glass, which is used as substrate for all thin-films discussed in this study. The optical model includes a surface roughness layer of 1.3nm.

Graphic Jump LocationF2 :

(a) and (b) Spectroscopic ellipsometry data of an 87 nm [6,6]-phenyl C71-butyric acid methyl ester (PC71BM) thin-film spin cast on a glass substrate for five angles of incidence. The colored solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data. (c) Transmission spectra of PC71BM in diluted dichlorobenzene (DCB) solutions and of a solid film on fused silica measured with a spectrophotometer. The gray shaded area indicates the absorption of the cuvettes. The center energies of the absorption features Gau1 to Gau9 are used as starting values for the Gaussian oscillator center energies in the optical model. (d) Optical constants n and k are derived from a multisample analysis.

Graphic Jump LocationF3 :

Measured (red lines) and simulated transmission (black dashed lines) of (a) PC71BM, (b) poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT), (c) poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole)] (PCPDTBT), (d) PSBTBT:PC71BM, and (e) PCPDTBT:PC71BM. The measured transmission spectra were determined at the same spot as the ellipsometry data by rotating the ellipsometer’s detector straight behind the sample. The noise levels are higher than in the spectrophotometer measurements that were described in Sec. 3.2 and that are depicted in Figs. 2(c), 5(c), and 7(c). The simulated data in Figs. 3(b)3(e) rely on anisotropic models.

Graphic Jump LocationF4 :

(a) Chemical structure of PSBTBT and PCPDTBT and definition of the polymer-chain reference frame (a, b, and c). The c axis is oriented along the polymer backbone. (b) The optical constants nxy and kxy describe light-polymer interaction for polymers with their c axes being aligned parallel to the substrate surface, while the z-component describes vertically oriented polymers. (x, y, and z) is the substrate reference frame. Schemes of the morphology of (c) neat PSBTBT, (d) neat PCPDTBT, (e) PSBTBT:PC71BM, and (f) PCPDTBT:PC71BM showing different degrees of aggregate alignment relative to the surface. Black dots represent PC71BM.

Graphic Jump LocationF5 :

(a) and (b) Spectroscopic ellipsometry data Ψ and Δ of a typical neat PSBTBT thin-film spin cast on a glass substrate. The colored solid lines correspond to the measured data; the dashed black lines correspond to data generated from a uniaxial optical model. (c) Transmission spectra of PSBTBT in diluted DCB solutions and of a solid film on fused silica. The starting values for the Gaussian oscillator center energies En,input are derived from the center energies of the absorption features, Table 2. (d) The optical constants comprise an in-plane (index xy) and out-of-plane component (index z) and are derived from a multisample analysis with an overall mean squared error (MSE)=6.37.

Graphic Jump LocationF7 :

(a) and (b) Spectroscopic ellipsometry data Ψ and Δ of a typical neat PCPDTBT thin-film spin cast on a glass substrate. The solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data within a uniaxial description. (c) Transmission spectra of PCPDTBT in dilute DCB solutions and of a film on fused silica. The center energies En,input of the absorption features Gaun are given in Table 3. (d) Anisotropic optical constants derived from a multisample analysis with an overall MSE=7.51.

Graphic Jump LocationF8 :

Spectroscopic ellipsometry data Ψ and Δ of [(a) and (c)] a typical PSBTBT:PC71BM (12) thin-film and [(b) and (d)] a typical PCPDTBT:PC71BM (13.4) thin-film. The solid lines correspond to the measured data; the dashed black lines correspond to the model-generated data within a uniaxial description. Anisotropic optical constants of (e) PSBTBT:PC71BM and (f) PCPDTBT:PC71BM are derived from a multisample analysis with an overall MSE=3.90 and MSE=4.64, respectively.

Tables

Table Grahic Jump Location
Table 2Isotropic, parameterized description of poly{[4,4’-bis(2-ethylhexyl)dithieno(3,2-b;2’,3’-d)silole]-2,6-diyl-alt-(2,1,3-benzothidiazole)-4,7-diyl} (PSBTBT). The starting values En,input are derived from the transmission spectra in Fig. 5(c). The center energies En change only slightly upon performing the fit. The parameters An and Brn are determined defining the Gaussian oscillators Gaun. The offset was found to be εr,=2.46eV.
Table Grahic Jump Location
Table 1From the transmission spectra in Fig. 1(c), the starting values En,input for the fit of the Gaussian oscillators’ center energies are derived. The optical model of [6,6]-phenyl C71-butyric acid methyl ester (PC71BM) comprises nine Gaussian oscillators (Gaun with center energy En, amplitude An, and width Brn,33 a pole, and the real constant εr,=2.00eV.
Table Grahic Jump Location
Table 3Poly[2,6-(4,4-bis(2-ethylhexyl)-4H-cyclopenta[2,1-b;3,4-b′′]dithiophene)-alt-4,7-(2,1,3-benzothiadiazole] (PCPDTBT). Starting values En,input as derived from Fig. 4(c). The parameters En, An, and Brn determine the optical model. εr,=2.28eV. Gau7 is outside the ellipsometer’s measurement range; the pole function covers its contribution.
Table Grahic Jump Location
Table 4The normalized volume ratios in the blends as derived from ellipsometry fittings show excellent agreement with the volume ratio calculated from the material densities. ρPC71BM=1.52g/cm3, ρPSBTBT=1.17g/cm3, and ρPCPDTBT=1.10g/cm3 as determined by helium pycnometry in the group of Dadmun et al.54,55

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Liang  Y. et al., “For the bright future—bulk heterojunction polymer solar cells with power conversion efficiency of 7.4%,” Adv. Mater.. 22, , E135 –E138 (2010). 0935-9648 CrossRef
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Puetz  A. et al., “Solution processable, precursor based zinc oxide buffer layers for 4.5% efficient organic tandem solar cells,” Org. Electron.. 13, , 2696 –2701 (2012). 1566-1199 CrossRef
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Hoppe  H. et al., “Modeling of optical absorption in conjugated polymer/fullerene bulk-heterojunction plastic solar cells,” Thin Solid Films. 451–452, , 589 –592 (2004). 0040-6090 CrossRef
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Klein  M. F. G. et al., “Poly(3-hexylselenophene) solar cells: correlating the optoelectronic device performance and nanomorphology imaged by low-energy scanning transmission electron microscopy,” J. Polym. Sci., Part B: Polym. Phys.. 50, , 198 –206 (2012). 0887-6266 CrossRef
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Klein  M. F. G. et al., “Carbazole-phenylbenzotriazole copolymers as absorber material in organic solar cells,” Macromolecules. 46, , 3870 –3878 (2013). 0024-9297 CrossRef
Sun  K. et al., “The role of solvent vapor annealing in highly efficient air-processed small molecule solar cells,” J. Mater. Chem. A. 2, , 9048 –9054 (2014). 0959-9428 CrossRef
DeLongchamp  D. M. et al., “Molecular characterization of organic electronic films,” Adv. Mater.. 23, , 319 –337 (2011). 0935-9648 CrossRef
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