Accurate Determination of the Index of Refraction of Polymer Blend

Aug 13, 2010 - Tel: +852 2859 7946 Fax: +852 2559 9152 E-mail: [email protected]., †. Department of Physics, The University of Hong Kong. , ‡...
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Accurate Determination of the Index of Refraction of Polymer Blend Films by Spectroscopic Ellipsometry Annie Ng,† Chi Ho Li,‡ Man Kin Fung,† Aleksandra B. Djurisˇic´,*,† J. A. Zapien,§ Wai Kin Chan,‡ Kai Yin Cheung,| and Wai-Yeung Wong| Department of Physics, Department of Chemistry, The UniVersity of Hong Kong, Pokfulam Road, Hong Kong, Department of Physics and Materials Science, City UniVersity of Hong Kong, Tat Chee AVenue, Kowloon Tong, Hong Kong, and Department of Chemistry and Centre for AdVanced Luminescence Materials, Hong Kong Baptist UniVersity, Waterloo Road, Kowloon Tong, Hong Kong ReceiVed: September 27, 2009; ReVised Manuscript ReceiVed: July 21, 2010

To model the performance of a bulk-heterojunction solar cell, it is necessary to obtain information about the index of refraction of the blend layer, which is typically determined by spectroscopic ellipsometry measurements. The optical functions of poly(3-hexylthiophene)-[6,6]-phenyl C61-butyric acid methyl ester (P3HT-PCBM) blend films have been extensively studied. However, there is a large variation of the reported optical functions in the literature. Because of this fact, as well as the widespread use of P3HT-PCBM films in organic photovoltaics, we have selected this material system as an example and performed a detailed analysis of spectroscopic ellipsometry data. We illustrate the occurrence of multiple solutions and the importance of a dedicated methodology to reach a satisfactory unique solution. The proposed methodology involves the following steps: (1) multisample analysis; (2) independent thickness and surface characterization; (3) use of the adequate optical description of substrate; (4) thickness estimation from transparent range using Cauchy model; (5) fitting n and k in the entire range with fixed thickness; verify result is physically meaningful; (6) optimization of the parameters to be fitted; (7) repeating steps 5 and 6 with and without EMA layer to account for the surface roughness; (8) finally, and only if no satisfactory fit could be obtained from previous steps, attempts to introduce anisotropy, graded layers, or other nonideal models should follow. 1. Introduction Organic solar cells have been attracting increasing interest in recent years and consequently exhibited improved performance, which brings them closer to practical applications. As the efficiencies of these devices continue to improve, it becomes increasingly important to accurately characterize their performance, and a comprehensive article on accurate measurement of organic solar cell performance has been recently published.1,2 However, for continuing advance of the field of organic photovoltaics, it is necessary not only to be able to accurately measure the cell performance, but also to model the performance as a function of material parameters. Optical simulations of organic solar cells3 require knowledge of the material optical properties, in particular the complex index of refraction N ) n - ik of the polymer blend. However, the extraction of the extinction coefficient k and the refractive index n of the material from spectroscopic ellipsometry (SE) often results in multiple solutions, especially if optical functions and the film thickness are being determined simultaneously.4 The problem with multiple solutions is that while they all provide a good fit for one particular thickness of the film, they do not necessarily adequately describe the properties of the material and cannot be used to model a film with different thickness. We have previously shown that multiple solutions for the refractive index and extinction coefficient of polymer blend can be obtained for * To whom correspondence should be addressed. Tel: +852 2859 7946Fax: +852 2559 9152 E-mail: [email protected]. † Department of Physics, The University of Hong Kong. ‡ Department of Chemistry, The University of Hong Kong. § City University of Hong Kong. | Hong Kong Baptist University.

different substrates used and differences in taking into account surface roughness of the samples.5 Therefore, we present a comprehensive analysis of spectroscopic ellipsometry data of poly(3-hexylthiophene)-[6,6]phenyl C61-butyric acid methyl ester (P3HT-PCBM, 1:1) blend films. P3HT-PCBM blend has been chosen as a model system since this material combination can yield solar cells with efficiencies equal to or exceeding 5%,6-8 and there are available data on this material combination in the literature.5,9-24 Also, a very wide range of refractive index and extinction coefficient values has been reported in the literature for P3HT-PCBM blends. Thus, it is necessary to not only establish which n and k values are correct, but also to identify difficulties in determining the correct values and suggest a method to overcome those difficulties. Commonly, absorption coefficient R of the films is given9-16 instead of the n and k values.5,17,18,21,22 Extinction coefficient can be calculated from the given absorption coefficient, since R ) 4πk/λ.25 From the published data, we can find that maximum k values for P3HT-PCBM (1:1) blends calculated from the absorption coefficient range from ∼0.1211 to ∼0.38.14 For reported ellipsometry data, even higher k values (with a maximum of ∼0.5717 or ∼0.422) are obtained. Published data on n and k of P3HT-PCBM blends even include data sets with high values of k at 900 nm for some blend compositions (different from 1:1).18 Furthermore, both isotropic5,17,18 and anisotropic12,15,16,22 models have been used to describe P3HT-PCBM blends. In general, out-of-plane anisotropy has been observed in a range of polymer films,12,15,16,26-31 and it is expected to occur due to different orientation of the polymer chains with respect to the substrate, since the transition dipole moment for π-π* transition

10.1021/jp104398f  2010 American Chemical Society Published on Web 08/13/2010

Index of Refraction of Polymer Blend Films is along the chain axis of the polymer.30 Any preferential molecular orientation in thin films would thus result in uniaxial anisotropy.26,30 For P3HT-PCBM, absorption coefficient calculated from the parallel component of the dielectric function had a maximum in the visible spectral range of ∼5-6 × 106 m-1, corresponding to a value of kmax of ∼0.19-0.23.12,15 On the other hand, extinction coefficients for parallel and perpendicular polarization obtained from ellipsometry data for P3HT-PCBM blends (without annealing) exhibited small differences with both maximum values of ∼0.4.22 In other words, anisotropy was very small without annealing, but it increased with annealing and it was dependent on the regioregularity of the polymer.22 In addition, for a different polymer it has been shown that the degree of anisotropy is dependent on the molecular weight.32 Thus, molecular weight could also possibly affect the observation of anisotropy for P3HT. It has also been shown on the example of poly(vinylcarbazole) that polymer films exhibiting anisotropy determined by one technique, exhibit similar properties when characterized by other optical techniques.33 However, no such comparative study has been performed for P3HT-PCBM blend films. In addition to anisotropy, optical functions of P3HT-PCBM have also been modeled by employing graded layer with different ratios of P3HT-PCBM at the substrate and the surface of the film with PCBM located at the surface and being the main contributor to the surface roughness.24 However, other studies found preferential segregation of P3HT at the top surface without annealing, while after annealing PCBM was the dominant component.23 Preferential segregation of PCBM at the substrate rather than the top surface was also confirmed by neutron reflectivity.34 Thus, due to a wide range of models used to describe P3HT-PCBM blends, as well as a wide range of published values for k, it is necessary first to establish which value is correct and second and more importantly how to reliably obtain n and k values of polymer blend films. Commonly, studies reported in the literature do not provide the details on how the fitting of the ellipsometry data is performed and multiple sample analysis is rarely used. Also, the variation in obtained values of n and k due to multiple solutions falls within the range of variation in the optical properties attributed to the effects of annealing,21 so that developing a procedure for accurate determination of n and k is essential for reliable and reproducible studies of the effect of processing conditions on the optical properties of P3HT-PCBM and other polymer blend films. It should also be noted that some of the variations in the reported values could occur due to differences in processing conditions of the films. While it can be expected that the films prepared by spin-coating, without annealing, and on the same substrate should have similar values of n and k, it is essential to report all relevant details on sample preparation, measurement and fitting procedures for a meaningful comparison of the data. Because of the importance of accurate determination of n and k for modeling the solar cell performance, we have performed detailed analysis of the spectroscopic ellipsometry data obtained from P3HT-PCBM blend films with different thicknesses and on different substrates to establish the best method for obtaining a reliable estimate of n and k from the measured data. 2. Experimental Section Sample Preparation. P3HT and PCBM were obtained from American Dyes. For P3HT, the properties are in the range Mw ) 20 000-70 000, polydispersity is in the range 1.4-5.0, and RR ) 95-98%, depending on the lot number. For the lot

J. Phys. Chem. C, Vol. 114, No. 35, 2010 15095 number used in this work, the P3HT properties were Mw ) 23 000, Mn ) 11 500, and RR g 95%. Substrates (microscope slide glass with rough back surface, thick glass or Si (001)) were cleaned by sonication in toluene, acetone, ethanol, and deionized water. Then the cleaned substrates were dried in a vacuum oven at 100 °C and exposed to UV ozone for 300 s before spin-coating. P3HT/PCBM solution was prepared in chlorobenzene and stirred overnight in N2 at 40 °C.35 A 20 mg/ mL chlorobenzene solution of P3HT-PCBM was then spincoated (at 600, 1000, or 1500 rpm). The substrates were dried at room temperature in low vacuum (vacuum oven) for 1 h, and then stored in high vacuum (10-5 to 10-6 Torr) overnight. To test the optical functions of realistic devices, commercial ITO substrates (obtained from Varitronix Ltd.) were used, and the back side of the substrates was roughened before use. The optical functions of the bare glass substrate in this case were determined after the ITO was etched by HCl and the ellipsometry measurements were performed on a bare substrate. PEDOT-PSS was spin coated on cleaned ITO substrates from an aqueous solution (passed through the 0.45 µm filter) on ITO substrates at 5000 rpm for 3 min. The substrates were then baked in a vacuum oven at 120 °C for 20 min. Then, P3HT-PCBM layer was spin-coated with a spinning speed of 1000 rpm. Sample Characterization. SE measurements (on bare substrates and substrates with films) were performed with a J. A. Woollam VVASE spectroscopic ellipsometer with autoretarder (rotating analyzer ellipsometer with a computer-controlled Berck waveplate, which removes the errors in ∆ encountered near 0 and 180°) and J. A. Woollam M2000 ellipsometer (rotating compensator ellipsometer). Data were taken from 350 to 900 nm with 5 nm step and at incident angles of 60, 65°, 70, 75, and 80°. For each sample, a second set of measurements were taken at different sample orientation to verify the in-plane isotropy of the film and the samples were confirmed to be isotropic in X-Y plane. Reflectance measurements (for s and p polarizations, at the incident angle of 75°) were also performed using J. A. Woollam VVASE spectroscopic ellipsometer. Transmission measurements were performed on bare substrates first, and then on substrates with film using J. A. Woollam VVASE and J. A. Woollam M-2000 spectroscopic ellipsometers, and Cary 50 Bio UV-vis spectrophotometer (which was also used for absorption measurements). For multilayer structure, optical characterization was performed after addition of each layer to enable fitting of each layer separately. The substrate area was typically 1.9 cm × 3.5 cm, and the light spot size (centered at the center of the substrate) was 0.4 cm × 2.4 cm (RAE) and 0.45 cm × 2.8 cm (RCE) at 80° incident angle. Surface morphologies of the samples were characterized by atomic force microscopy (AFM) using a Digital Instruments Nanoscope IV in semicontact mode (with a silicon tip coated with highly reflective Al, force constant of 40 N/m and resonant frequency of 300 kHz) and Asylum Research MFP 3D (with a silicon tip coated with highly reflective Al, force constant of 2 N/m and resonant frequency of 70 kHz). Initial estimate of the film thickness was obtained using a step-profiler. Ellipsometry Fitting. For fitting of the data, J. A. Woollam WVASE32 Software was used. The spectroscopic ellipsometry data of the bare substrate were fitted first, and then the substrate parameters were fixed and the data for film on the substrate were fitted. Si(100) substrates could be described using builtin dielectric function of Si and SiO2 (native oxide, fitted thickness 22.4 Å, MSE ) 2.19), while for glass substrates, Cauchy model or generalized oscillator model (GOM) were used for fitting (MSE ) 1.16 for GOM). Glass substrate with the

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rough back side was ∼1 mm thick, while thick glass substrate was 1 cm thick. For the polymer blend film, a generalized oscillator model (3-5 oscillators, Lorentzian,36 Gaussian, or Tauc-Lorentz) was used and effective medium approximation (EMA)37 was employed to include the effect of surface roughness. For multilayer structures r-glass/ITO/PEDOT-PSS/ P3HT-PCBM, ITO was described by a generalized oscillator model, PEDOT-PSS was described by a Cauchy model, GOM, and both isotropic and anisotropic models were considered. The roughness (another EMA layer) between all layers was also included. In GOM model, other types of oscillators in addition to Lorentzian oscillators were considered, since the use of Lorentzian oscillators only may result in the overestimation of k at longer wavelengths due to extended absorption tail inherent to Lorentzian line shape. In all cases, fitting of n and k by direct inversion of the ellipsometric equations (that is without assuming a particular model for the optical functions) was also attempted. After obtaining n and k by direct inversion, the use of a parametric model was attempted again by fitting the obtained n and k as a reference material to obtain a good initial guess (as well as verify Kramers-Kronig (KK) consistency of the direct inversion, since oscillator model is inherently KK consistent). During the fitting, reasonable boundaries were set for model parameters to restrict them to physically meaningful values. Fitting in the range of 700-900 nm was performed first using a Cauchy model and the thickness value determined by a stepprofiler as the initial guess to obtain a good estimate of film thickness. Then, the n and k (or model parameters if a model was used) were fitted in the entire range of interest with the thickness fixed. Finally, both thickness and optical functions were allowed to vary in the last fitting run to verify that a reasonable solution has been obtained. In some cases, uncertainties for some parameters, such as material fraction in EMA, thickness of the EMA layer in samples used for transmission, and so forth, were high. In general, the addition of EMA layer increases the number of multiple solutions, although it can improve the fit quality. This problem was handled by fixing the percentage of volume fraction in EMA to a reasonable value (i.e., 50%), and by coupling the thickness of EMA layer in samples used for ellipsometry and transmission that were prepared at the same spinning speed. For fitting the data with an anisotropic model (uniaxial), procedure similar to that previously described for different polymer films27,31 was used. The use of surface roughness corrections containing the P3HT-PCBM blend or PCBM only24 was also investigated. 3. Results and Discussion To investigate the influence of the substrate, we considered Si, glass with roughened back surface, and thick glass substrate (to eliminate contribution from the incoherent reflection from the back side of the substrate, which can be done either analytically38 or by modifying the back surface, either by roughening or even Blue-tack39). P3HT-PCBM films on both types of substrates (glass and Si) had similar morphology (see Supporting Information, Figure S1). Commonly used oscillator model22,36 was used to fit the optical functions of the polymer blend films. Initial guesses for the oscillator energy were obtained from the absorption spectrum of the polymer film, shown in Figure 1a. Other models used in the literature include standard critical points model.24 As expected, multiple solutions can be obtained for all substrates if only one thickness is fitted at a time (see Supporting Information, Figures S2-S4); this occurs even if multiple incident angles are fitted at the same time and a good estimate of the thickness is available (e.g., from

Figure 1. (a) Absorption spectra; (b,c) phase and topography AFM images (1 µm × 1 µm) of P3HT-PCBM blend film on glass.

step-profiler measurements). While some of the multiple solutions can be discarded as unphysical based on simple observations such as, for example, discontinuous dielectric functions and/or high absorption at longer wavelengths; a multisample analysis is a preferred method in the search for a physically sound solution.4,27,31,40 If we adopt the multiple sample fitting approach,4 that is, assuming that n and k data for samples with different thickness are the same and allow only film thickness and samples to vary, the number of multiple solutions can be significantly reduced. The use of multiple sample analysis reduced the number of multiple solutions, but different values of n and k were obtained for glass substrates and Si substrate (see Supporting Information, Figure S5) in agreement with our previous results.5 Consistently lower values of k obtained on Si substrates also indicate that some of the data reported in the literature for polymer blends on Si substrate may be underestimated.41,42 A possible reason

Index of Refraction of Polymer Blend Films for this behavior is that the optical functions are indeed different on different substrates, and that anisotropy may need to be considered for samples on Si. It has been reported that an indication that an anisotropic model is necessary is that either fitting with isotropic model is not possible or that a good fit for one sample cannot recreate the data for other samples.27 Thus, if the samples can be fitted with isotropic model, the use of anisotropic models should be avoided to increase the reliability of the fitting results. However, fitting with isotropic model may no longer be valid if the sample preparation method is changed or if a different substrate is used. Possible differences in preferential orientation of polymer chains could possibly account for significantly different values of n and k obtained on Si substrates. In addition to possible differences in P3HT-PCBM properties on different substrates, depolarization for the data for polymer films on Si substrates was higher (see Supporting Information, Figure S6). Therefore, we concentrated on the films prepared on glass substrates (with rough back surface) to determine the accurate optical functions of P3HT-PCBM. Since the substrates were transparent (without back surface roughening), transmission instead of reflectance (since Si is not transparent) could be used to provide additional information to obtain more reliable optical functions of the polymer blend film (it is known that the inclusion of normal incidence transmission data into experimental data set for fitting can improve the reliability of the determined solution30,40). The first difficulty encountered in the fitting was that the agreement of the model with the transmission data was significantly worse than the agreement with the ellipsometry data. This can partly occur due to higher sensitivity of the MSE value to the agreement between experimental and calculated (Ψ, ∆) as compared to T, and/or due to inadequate description of the optical properties of the substrate. Therefore, we have examined the optical functions of the glass more closely and have performed simultaneous fitting of the transmission and ellipsometry data for the substrate. We found that the commonly used Cauchy model (since the substrate is transparent) does not adequately describe the substrate transmission, while good fit can be obtained using a generalized oscillator model to account for the fact that there is a very small absorption in the substrate resulting in a significant fit improvement (MSE ) 1.16) (see Supporting Information, Figure S7). This effect may be partly responsible for the previously observed overestimation of k in low refractive index films on transparent substrates.43 While typically ellipsometry is not sensitive to k values below ∼0.01 for the thin films usually dealt with, a transmission measurement could reflect even lower values of extinction coefficients since the thickness of the substrate is large and results in significant absorbance. As an illustration consider a 1 mm thick substrate with k as low as 3 × 10-6 for λ ) 900 nm. The absorbance A, given by A ) Rl ) 4πkl/λ, where l is the thickness, R is the absorption coefficient, λ is the free-space wavelength, is thus A ) 4.19 × 10-2. Should this value be wrongly assigned to a 40 nm film it would result in an incorrectly calculated k ≈ 0.06. It is noted that the default MSE function in WVASE software appears to have a relatively low sensitivity to the transmission. In fact, changing the fitting function to “ε2 only” results in higher sensitivity to k and consequently transmission (but the fit for Ψ and ∆ worsens). Once a good fit to the transmission has been found, reverting to the default fitting function typically results in good fit for transmission, as well as Ψ and ∆. However, in some cases lower MSE value is obtained when fit to Ψ and ∆ is slightly improved, even though fit to T worsens. In that case, the fit quality should be judged not only by the

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Figure 2. Schematic model of the sample.

MSE value but also agreement between experimental and calculated Ψ, ∆, and T. In general, the fit quality could be improved by introducing parameter constraints to force the solution to obtain equally good fit to all three quantities. The second difficulty encountered was the fact that the model used did not provide sufficiently good description of the optical functions. While it is known that Lorentz oscillator model results in the extended absorption tail,26,36 which can be improved by using a mixture of Gaussian and Lorentzian oscillators, for number of oscillators kept at 5 or lower, relatively high MSE values were obtained. An increase in the number of oscillators resulted in increased parameter uncertainties, as expected,40 which makes this approach unsuitable to obtain reliable fitting parameters. Therefore, we decided to fit the n and k by direct inversion without assuming any model. This approach can result in excellent agreement with the experimental data,27,36,40 but it can also result in n and k values which are not Kramers-Kronig (KK) consistent (KK consistency is automatically satisfied for Lorentz oscillator model40). Thus, if such an approach is attempted, fitting over a wide spectral range should be performed, and KK consistency should be verified. Also, careful fitting methods can be employed to ensure smooth curves and control numerical instabilities.27 It should also be noted that once direct inversion data have been obtained, the resulting optical functions can be imported into GOM as “reference material” and initial guess for GOM model can be obtained which typically results in a good fit and also confirms KK consistency of the direct inversion (see Supporting Information, Figure S8 and Table 1). It should also be noted that multisample analysis is also needed in the case of direct inversion. While for direct inversion of a single sample some incorrect solutions can be more easily discarded as unphysical compared to oscillator model (i.e., presence of very sharp features in the spectra), fitting the single thickness may not in every case result in a solution which provides good fit for all the thickness values (see Supporting Information, Figure S9). Thus, we have performed multisample analysis using direct inversion for P3HT-PCBM blend films on glass. We performed the fitting without the surface roughness layer because the films on glass substrates were relatively smooth (with rms roughness below 1 nm, and peak-to-peak roughness of ∼3 nm), as shown in Figure 1c. The obtained MSE value was 6.91, and the obtained agreement with the experimental data was good (see Supporting Information, Figure S10). To further improve the fit quality, surface roughness was introduced. The volume fraction was at first kept fixed, and then it was allowed to vary. Since it was proposed that there is surface segregation of PCBM in P3HT-PCBM blend films (and that blend composition is depth dependent),24 we have considered both rough layer containing P3HT-PCBM blend, and the rough layer containing PCBM only. The schematic sample model is shown in Figure 2. Before considering the EMA roughness layer

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Figure 3. (a-f) Spectroscopic ellipsometry and (g) transmission data (comparison of model and experiment) and (h) obtained n and k values for RAE data with EMA (P3HT-PCBM blend, 37.8%). Obtained layer thickness (d indicates film dEMA indicates roughness layer) values are 600 rpm, d ) 61.9 ( 1.0, dEMA ) 7.3 ( 1.6 nm; 1000 rpm, d ) 49.2 ( 0.9, dEMA ) 5.9 ( 1.5 nm; 1500 rpm, d ) 44.5 ( 0.9, dEMA ) 3.8 ( 1.5 nm for ellipsometry samples and 600 rpm, d ) 54.0 ( 6.4, 1000 rpm, d ) 42.5 ( 5.2, 1500 rpm, d ) 36.7 ( 3.7 for transmission samples (thickness values of EMA layer have been coupled).

containing only PCBM, optical functions of PCBM have been determined using multisample analysis with ellipsometry and transmission (see Supporting Information, Figure S11). Similar values of MSE were obtained (MSE ) 6.56 for P3HT-PCBM EMA; MSE ) 6.49 for PCBM EMA), and the obtained optical functions are shown in Figure 3 for the P3HT-PCBM blend EMA (for PCBM EMA, obtained results are shown in the Supporting Information, Figure S12). However, for PCBM only, there was large uncertainty for the composition of the EMA layer. Combined with the fact that no protruding PCBM islands are evident in the AFM phase contrast image (Figure 1b), and the fact that preferential PCBM segregation on the surface of P3HT-PCBM films without annealing has not been found by other studies,23,34 we have decided to use P3HT-PCBM EMA roughness layer as a more reliable description of the sample. Consequently, graded model24 of the P3HT-PCBM layer was not investigated. To test the reliability of the obtained results, measurements were repeated using rotating compensator ellipsometer and the obtained results are shown in Figure 4. Good agreement with the data obtained from RAE ellipsometer has been obtained, as shown in Figure 5. The uncertainties of the obtained n and k are also shown. It should be noted that fit of the transmission

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Figure 4. (a-f) Spectroscopic ellipsometry and (g) transmission data (comparison of model and experiment) and (h) obtained n and k values for RCE data with EMA (P3HT-PCBM blend, 37.8%).

data obtained with RCE instrument results in additional ∼2% error in the transmission with respect to the quality of fit using VVASE, the latter being closer to the value obtained using a UV-vis spectrometer. The overall MSE value from M-2000 is higher (MSE ) 25.96), however the differences between the measured and generated data show similar values, as shown in Figure 6. The larger values of MSE are thus a reflection of the smaller uncertainties in the determination of ∆ and Ψ using a rotating compensator ellipsometry (see Supporting Information, Figure S13) and reflect the possibility to retrieve additional information from a more complete optical model. In general, the obtained MSE values in all cases of multisample analysis are higher than those obtained for fitting individual samples one by one. This is because multisample analysis results in an average set of values of n and k which result in the best fit for all the data, so that any small variations in n and k for samples with different thickness may result in worsening of the fit.40 Previous ellipsometry studies in the literature report maximum extinction coefficient values that range from as low as (∼0.25)21 to as high as (∼0.5-0.6).17,18 The results obtained here are between the reported extremes in the literature and they are in good agreement with previously reported values for P3HT-PCBM films without annealing.22 While differences in sample preparation and properties cannot be discarded, large spread in the optical functions could also result from insufficiently comprehensive optical characterization and rigorous fitting procedures. This is clearly shown in the simplified data analysis performed

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Figure 5. Comparison between (a) transmission data (model and experimental) for RAE and RCE. Transmission measured using UV-vis spectrometer is included. The transmission data for different spinning speeds are given in separate panels to improve figure clarity. (b) Obtained n and k values using RAE and RCE. Error bars for the RAE data are also indicated.

Figure 7. (a,b) Spectroscopic ellipsometry and (c) transmission data (comparison of model and experiment) obtained for RAE data for glass/ ITO/PEDOT-PSS/P3HT-PCBM multilayer device using P3HT-PCBM n and k data shown in Figure 3.

Figure 6. The difference between experimental and calculated data for (a) RCE, T; (b) RAE, T; (c) RCE, Ψ; and (d) RAE, Ψ.

by fitting each sample individually (Supporting Information, Figures S4 and S9), which also results in a range of maximum extinction coefficient values. These difficulties are largely avoided with the use of multisample analysis at the expense of a required extra effort needed to find a suitable dielectric function that can describe all samples simultaneously. As a final test of the obtained fitting result, glass/ITO/ PEDOT-PSS/P3HT-PCBM structure was also fitted with previously obtained n and k values for P3HT-PCBM. GOM model was used for ITO (without the assumption of a graded

layer)44 while for PEDOT-PSS, uniaxial anisotropy was assumed45 and oscillator model was used for both ordinary and extraordinary refractive index (see Supporting Information, Figures S14 and S15). Obtained MSE is 19.7 and the results are shown in Figure 7. Good agreement between experimental and calculated data can be observed. Even though reasonably good fit (for a multisample analysis) could be obtained with isotropic model, the use of anisotropic model was also investigated for the sake of completeness. It should be noted that while some degree of anisotropy is expected for polymer thin films, dependence of the degree of anisotropy on thickness and preparation method (drop-casting, spin-coating)28,29 could create problems when using multiple samples for the fitting, although multiple sample use has been demonstrated.27 Also, it has been proposed that variable angle spectroscopic ellipsometry does not have sufficient sensitivity for accurate determination of both in-plane and out-of-plane optical functions, which leads to high correlation of fitting parameters and low reliability of the outof-plane refractive index.26 This issue could be improved by combination of measurement techniques, or adequate choice of

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substrate.26 Thus, introduction of anisotropy may result in additional difficulties in extracting unique and reliable solution for n and k of a polymer blend. For P3HT-PCBM films in our work, introduction of anisotropy did not result in significant improvement of the fit. Therefore, we found that the isotropic model provides adequate description of the P3HT-PCBM films without annealing, in agreement with other works.22 Lower MSE values could probably be obtained by considering more complex models (graded layer, anisotropy), but they would also lead to increased uncertainties of fitting parameters and thus cannot be considered justified if reasonably good fit is obtained with an isotropic model. Thus, for reliable fitting of the ellipsometry data of polymer thin films we propose that the following procedures should be done. (1) Multisample analysis: prepare the films with different thickness and perform ellipsometry and transmission (or reflectance for nontransparent substrates) measurements. (2) Perform independent thickness measurement (for example step-profiler or AFM) and surface characterization (AFM). (3) Use adequate optical description of substrate; perform the same measurements for the substrate. It is essential to adequately describe the substrate using a suitable model to describe both ellipsometry and T (R). (4) Obtain thickness estimate from transparent range; fit the data for the polymer film in the range where polymer is transparent using Cauchy model to obtain thickness estimate. (5) Fix the thickness, and fit n and k in the entire range. If a model is used, ensure that values are physically meaningful; if no model is used, ensure that smooth, KK consistent curves are obtained. (6) Optimize the parameters to be fitted. (i) If necessary, restrict the range or number of parameters to be fitted or the sensitivity of fitting function to a certain parameter (by choosing to different fitting functions) until satisfactory fit is obtained over the entire range of interest; (ii) it should be noticed that a low MSE value could be symptomatic of excessive number of parameters and not necessarily reflect a good fitting or validates a model; (iii) repeat the fitting while allowing all the parameters to vary within reasonable boundaries; if some parameters exhibit large uncertainties, consider obtaining additional measurements, fixing them to a reasonable value (i.e., volume fraction in EMA to 50%, etc.) or coupling related parameters in different layers (i.e., EMA thickness for the same spinning speed). (7) Repeat steps 5 and 6 with and without EMA layer to account for the surface roughness (if roughness is small, improvement with EMA is also small, and parameter uncertainties may be large). (8) Finally, and only if no satisfactory fit could be obtained from steps 1-9 above, attempt to introduce anisotropy, graded layers or other nonideal models. Some limitations of the proposed approach should be recognized. If the optical functions are not the same for samples with different thickness, whether due to anisotropy or composition variations, multisample analysis cannot be used. In this case, additional information could be obtained by insertion of additional layers between the film and the substrate and the inclusion of transmission or reflectance.40 In addition to the possibility that optical functions may be thickness dependent, another important issue that should be considered is the validity of EMA approximation37,46 for blend films exhibiting phase separation and roughness. If the lateral size of the islands is of the same order of magnitude as the wavelength, EMA approximation is not valid, and different treatment of scattering needs to be used.46 In all those cases, the most appropriate approach is to fit the layers in the solar cell device structure one by one directly, rather than rely on estimates obtained for other thicknesses and on other substrates.

Ng et al. 4. Conclusions We have performed comprehensive study of spectroscopic ellipsometry data of P3HT-PCBM blends on different substrates, using different ellipsometers, and different combinations of experimental data fitting. We have clearly demonstrated the need to perform multisample analysis, include transmission data, and adequately take into account the glass substrate. For a suitable selection of model parameters, measurements performed on two different instruments result in similar values of n and k. While the range of maximum k values reported in the literature for P3HT-PCBM blend is from ∼0.12 to ∼0.6, we obtain a value of ∼0.35. Acknowledgment. This work was supported by the Strategic Research Theme, University Development Fund, and Small Project Grant and Outstanding Young Researcher Award (administrated by The University of Hong Kong) are also acknowledged. W.-Y.W. thanks the Hong Kong Research Grants Council for a GRF Grant (HKBU202607), the Hong Kong Baptist University for a Faculty Research Grant (FRG/06-07/ II-63) and the Croucher Foundation for a Croucher Senior Research Fellowship. J.A.Z. thanks support from CityU Strategic Research Grants (7002442). The authors thank the Department of EEE, The University of Hong Kong for the use of spectroscopic ellipsometer, as well as Professor C. Surya and Dr. H. F. Lui from the Department of EIE, Hong Kong Polytechnic University for the use of atomic force microscopy (AFM). The authors would also like to thank Dr. Tom Tiwald from J. A. Woollam company for useful discussions concerning the fitting and help in fitting the optical functions of glass substrate. Supporting Information Available: AFM images of P3HT-PCBM films on different substrates, comparisons between experimental and calculated data for different fitting approaches, substrate fitting results, depolarization data for different substrates, GOM fitting parameters, and experimental uncertainties for different ellipsometers. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Shrotriya, V.; Li, G.; Yao, Y.; Moriarty, T.; Emery, K.; Yang, Y. AdV. Funct. Mater. 2006, 16, 2016. (2) Riede, M. K.; Sylvester-Hvid, K. O.; Glatthaar, M.; Keegan, N.; Ziegler, T.; Zimmermann, B.; Niggemann, M.; Liehr, A. W.; Willeke, G.; Gombert, A. Prog. PhotoVolt: Res. Appl. 2008, 16, 561. (3) Persson, N.-K.; Ingana¨s, O. Simulations of optical processes in organic photovoltaic devices. In Organic PhotoVoltaics: Mechanisms, Materials, and DeVices; Sun, S. S., Sariciftci, N. S., Eds.; CRC Press: Boca Raton, FL, 2005; pp 107-138. (4) Ja¨rrendahl, K.; Arwin, H. Thin Solid Films 1998, 313-314, 114. (5) Ng, A. M. C.; Cheung, K. Y.; Fung, M. K.; Djurisˇic´, A. B.; Chan, W. K. Thin Solid Films 2008, 517, 1047. (6) Kim, J. Y.; Kim, S. H.; Lee, H. H.; Lee, K.; Ma, W.; Gong, X.; Heeger, A. J. AdV. Mater. 2006, 18, 572. (7) Reyes-Reyes, M.; Kim, K.; Carroll, D. L. Appl. Phys. Lett. 2005, 87, 083506. (8) Kim, K.; Liu, J.; Namboothiry, M. A. G.; Carroll, D. L. Appl. Phys. Lett. 2007, 90, 163511. (9) Zhao, Y.; Xie, Z. Y.; Qu, Y.; Geng, Y. H.; Wang, L. X. Appl. Phys. Lett. 2007, 90, 043504. (10) Erb, T.; Zhokhavets, U.; Gobsch, G.; Raleva, S.; Stu¨hn, B.; Schilinsky, P.; Waldauf, C.; Brabec, C. J. AdV. Funct. Mater. 2005, 15, 1193. (11) Mihailetchi, V. D.; Xie, H. X.; de Boer, B.; Koster, L. J. A.; Blom, P. W. M. AdV. Funct. Mater. 2006, 16, 699. (12) Zhokhavets, U.; Erb, T.; Gobsch, G.; Al-Ibrahim, M.; Ambacher, O. Chem. Phys. Lett. 2006, 418, 347. (13) Ai, X.; Beard, M. C.; Knutsen, K. P.; Shaheen, S. E.; Rumbles, G.; Ellingson, R. J. J. Phys. Chem. B 2006, 110, 25462.

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