Determining the Dielectric Tensor of Microtextured Organic Thin Films by Imaging Mueller Matrix Ellipsometry

Polycrystalline textured thin films with distinct pleochroism and birefringence comprising oriented rotational domains of the orthorhombic polymorph of an anilino squaraine with isobutyl side chains (SQIB) are analyzed by imaging Mueller matrix ellipsometry to obtain the biaxial dielectric tensor. Simultaneous fitting of transmission and oblique incidence reflection Mueller matrix scans combined with the spatial resolution of an optical microscope allows to accurately determine the full biaxial dielectric tensor from a single crystallographic sample orientation. Oscillator dispersion relations model well the dielectric tensor components. Strong intermolecular interactions cause the real permittivity for all three directions to become strongly negative near the excitonic resonances, which is appealing for nanophotonic applications.


Sample Preparation and Morphology
2,4-bis [4-(N,N -diisobutylamino)-2,6-dihydroxyphenyl]squaraine (SQIB) was synthesized as described before. 1 A 6 mg/mL solution of SQIB in chloroform (Sigma-Aldrich, stabilized with amylene) was spincoated onto (15 mm × 15 mm) oat glass substrates (VWR objective slides) with the following settings (SÜSS MicroTec Delta+ 6RC): 1500 rpm (≈50 nm), ramping 5; 3000 rpm (≈50 nm), ramping 3 (≈40 nm); 4000 rpm, ramping 1 (≈30 nm). Approximate layer thicknesses are given in parentheses. This was followed by annealing on a pre-heated hotplate with surface temperature at 180°C for 2 hours. Polarized microscopy images of the samples are shown in Figure S1. They reveal, that average domain size of the SQIB platelets increase with increasing spin-speed, which correlates with decreasing layer thickness. Atomic force microscopy images (JPK NanoWizard, intermittent contact mode, Tap300 BudgetSensors cantilever) reveal a certain roughness of the platelets, Figure S2. The wavy texture with a preferred orientation within platelet domains originates from the processing procedure, in particular depend on the crystallization seeds generated by annealing and the following crystallization process. The features become smaller (while domain size increases) with increasing layer thickness / spin-speed. Sample areas have been selected to include S2 dewetted defect areas, where the underlying glass substrate is visible, to validate the layer thickness deduced from spectroscopic ellipsometry scans. Surface roughness parameters excluding the defect areas are summarized in Table S1. Yet, the surface roughness is small against the probing wavelength and was not included in the ellipsometetric data tting, see discussion below, Figure S6.  Table S1. For image processing Gwyddion has been used. 2 Table S1: Roughness from AFM Images in Figure S2 sample thickness (nm) R a (nm) R q (nm) (a) 50 ± 5 19 ± 2 23 ± 2 (b) 40 ± 5 14 ± 1 17 ± 1 (c) 30 ± 4 10 ± 1 13 ± 1 a Average roughness R a and root mean squared roughness R q extracted from AFM images excluding the defect areas in Figure S2 Figure S12 was used, assuming a SQIB layer thickness d = 32 nm, following the procedure as outlined in section Transfer Matrix Optical Calculations. Note that all single spectra cross in one point, the so called isosbestic point.

Imaging Mueller Matrix Ellipsometry
Imaging Mueller matrix ellipsometry was performed with a NanoFilm_EP4 system, Accurion GmbH, Göttingen at ambient conditions. It can be operated in principles of nulling and rotating compensator ellipsometry (RCE). The latter is required for recording the Mueller matrix.
4 In addition, ellipsometric contrast imaging allows a visualization and observation of the sample at dened states of polarization of the probing and reected light. A sketch of the experimental setup is shown in the main paper in Figure 2a. Further details about the setup and the operation principles of the imaging ellipsometer can also be found elsewhere.

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For the PCSA conguration the collimated beam of monochromatic light is elliptically polarized after passing through the linear polarizer (P) and the compensator (C), which is a rotating quarter waveplate. The elliptically polarized light reects from (or transmits through) the sample (S) and is collected by a long working distance objective (Nikon, 10×, NA 0.21). After passing the analyzer (A), another linear polarizer, the light is imaged onto a CCD camera. That way, spatially resolution is gained instead of averaging over the light beam spot on the sample. Here, the lateral resolution is 2 µm at a reference wavelength of 400 nm for the 10× objective (Nikon, NA 0.21) used for the measurements.
The applied imaging ellipsometer does not require any focusing of the probing beam to reach its spatial resolution. It actually uses almost collimated light as a probe (NA ≈ 0.018, spot diameter ≈ 1 mm), and the spatial resolution is purely generated by the microscope imaging in the instrument's detection arm. Due to the low NA of the probing beam, the AOI spread of the ellipsometric measurement could be neglected upon the data analysis. Furthermore, the applied Nikon 10× microscope objective features minimal stress-induced birefringence.
The maximum osets of the measured Mueller matrix elements caused by the objective lens were about ±0.001 for all applied wavelengths. This is one order of magnitude below the typical deviation observed between the modelled and measured MM-SQIB-spectra and hence did not need to be taken into account upon the model ts.
To obtain the nulling conditions, the positions of P and C are changed that the reected  Note that this is azimuthal rotation around the Euler φ angle. The phrase "theta" in Theta Scan should not be confused with the Euler θ angle referring to a tilting angle. S7 chromated Xenon-lamp light, bandwidth 4 nm), have been performed. These scans are recorded in reection at angles of incidence (AOIs) 50°and 60°in steps of 15°rotational angle. Figure S5 shows exemplarily measured (squares, circles) and tted (solid lines) data for ROI 0. From such datasets for all ROIs the layer thickness d, the in-plane φ orientation of the crystallographic c-axis, and the tilt angle θ of the crystallographic b-axis for the SQIB platelet sub-domains ROI 0 to 13 as indicated in Figure 2b main paper have been determined. The resulting values are summarized in Table 1 main paper. As a gure of merit, the t returns the root mean square deviation of data points and the optical model: For simultaneous tting of all ROIs: MSE = 0.0001.
The angles φ, θ and ψ refer to the Euler angles, which denote a rotation of the crystallographic axes with respect to the cartesian laboratory coordinate system x, y, z. 9 Combining the three rotation matrices gives the full transformation matrix A for the coordinate transformation: This transformation matrix is applied to the dielectric function tensorε, which is a secondrank tensor, to give a rotated dielectric tensorε as follows: where A T denotes the transpose (inverse) of the transformation matrix A. Coordinate rotation is counter-clockwise. However, due to the denition of the z-axis ( Interestingly, there appears a signicant but poorly tted signal in the m14 element (upper right corner) of the normal incidence transmission scans, Figure S7. These signals are no measurement artifacts and also do not originate from circular dichroism.

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As a rst step of the determination of the spectroscopic SQIB dielectric tensor elements from the Mueller matrix data, cubic-spline functions were employed to obtain a best match of the single-layer model to the experimental data without enforcing Kramers-Kronig consistency.
The latter means that ε 1 and ε 2 were tted independently for each of the three tensor elements. Supporting points, however, were equidistant and the same for the corresponding sets of ε 1 and ε 2 . The layer thickness d, tilt angle θ and the φ orientation were used as determined from the Theta Scans for the following tting procedure of the spectroscopic Mueller matrix data. However, a φ-oset was allowed for the transmission data to account for a dierent sample adjusting. Reection and transmission data were tted simultaneously but individually for each ROI. Then, to obtain Kramers-Kronig consistency of the dielectric tensor components, the t was parameterized with sets of Lorentz and Tauc-Lorentz oscillators as listed in Figure S10.
The parameterization was conducted with a self-programmed routine in Python using the The uncertainty values of the t results (error table in Figure S10) were obtained from the t-parameter covariance matrix that is provided by the Levenberg-Marquardt (LM) t routine. It should be noted that these values are estimates based on the assumption that only S17 the dependent variables (i.e. the measured MM data) are subject to a measurement uncertainty (standard deviation). In contrast, the LM routine does not consider the uncertainty values of the independent measurement parameters, most notably the probing wavelength and the AOI. Hence, the uncertainty values provided in S10 do not consider e.g. the intrinsic bandwidth of the monochromator (about 0.01 eV-0.03 eV for the applied spectral range).
Thus, the LM-estimated uncertainty values of e.g. an oscillator resonance energy may be much smaller (about 10 =4 eV) than the monochromator's resolution. The total precision or uncertainty of the measurement of any resonance energy, of course, cannot be better than the energy resolution of the applied instrumentation. The nal best t result for jointly tting of all ROIs for the dielectric tensor is displayed in Figure S11 together with the individual ts for each ROI. In Figure S12 the data are shown in the representation as complex refractive index N , real refractive index n in (a) and extinction coecient k in (b). Here, the vibronic progression as typical for the UDC 14 is clearly visible as a shoulder in the extinction coecient, blue curve Figure S12 (b).
The peak position of the measured / calculated absorbance spectra, Figure S12 (c) and

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Calculated polarized absorbance spectra can be seen in Figures S12 (c) and (d).
Note that in our previous studies 3,17 the assignment of UDC and LDC to the crystallographic axes was interchanged due to the ambivalence in interpreting simple polarized absorbance spectra under normal incidence. The unique assignment of dielectric tensor components to the crystallographic axes was only possible by imaging Mueller matrix ellipsometry. S21