1. INTRODUCTION

Ellipsometry is a well-established, nondestructive and noninvasive linear-optical technique for characterizing the properties of materials by means of polarized light [1–4]. The method has been extended over the years to cover the infrared (IR) spectral range, and is nowadays successfully used to measure a plethora of ambient- and stimuli-dependent physical and chemical sample properties. These include film thicknesses, refractive and absorption indices, free-carrier concentration, mobility and effective masses, chemical composition, interdiffusion and cross-linking, as well as molecular adsorption, orientation, and molecular interactions [5–14].

Due to the ever-growing demand in the scientific community and from industry to investigate samples of increasing complexity, such as structured, biomimetic, and thin-film-covered surfaces, there is an increased need for optical methods such as ellipsometry to provide access to the sample’s dielectric, structural, anisotropy, and depolarizing properties. Depolarizing samples in particular cannot be addressed by classical ellipsometry in the Jones formalism. Within the Stokes formalism, though, all of the aforementioned properties are accessible via the sample’s $4\times 4$ Mueller matrix (MM)—a general description of the sample’s polarimetric properties that fully characterizes its polarization response [15]. MM ellipsometry has therefore gained recent attention as an advanced characterization technique in science and metrology [16–24].

MM ellipsometry is especially interesting in the IR where excitations of vibrational modes can be studied. IR MM ellipsometry thus opens up new analytical possibilities for investigations of thin films and structured surfaces, in particular with regard to molecular orientation, binding, and interactions at interfaces. However, laboratory IR ellipsometry is intrinsically challenging due to the low optical throughput, the nonideal properties of optical components such as wire-grid polarizers, the low brilliance of radiation sources such as globars, and the low specific detectivity of frequently used room-temperature-operated broadband IR detectors.

Our premise for this paper was to design and build a laboratory IR MM ellipsometer with as high an optical throughput as possible, capable of performing highly sensitive MM measurements of nanometer-thin films and surfaces with μm-sized structures. Commercially available IR MM ellipsometers mostly use pyroelectric detectors, and are not optimized for high optical throughput. Furthermore, common MM ellipsometers operate with fixed polarizers and rotating retarders in order to sufficiently sample the polarization space with mixed polarization states. Conveniently, these ellipsometers can measure the complete $4\times 4$ Mueller matrix, or the partial MM if only one retarder is used. However, typical IR retarders based on total internal reflections exhibit maximum transmittances of merely 50% to 70%. In a dual-compensator design, all measurements are made in the presence of the two retarders, and hence all MM elements are affected by low throughput. While such a design can be advantageous for spreading experimental noise across the various MM elements [25,26], it comes at the expense of sensistivity. This is especially relevant for MM elements in the upper-left $2\times 2$ block, which, for non-depolarizing samples, are associated with the amplitudes of the anisotropic complex reflection coefficients [27]. These MM elements usually contain key information in the IR for many samples, and can be measured most sensitively without retarders.

For these reasons, we opted for a different design approach, namely, to work with a liquid-nitrogen-cooled photovoltaic detector for increased detectivity, with non-continuously rotating tandem polarizers for optimized polarization control, and with optional and retractable retarders for enhanced throughput. Furthermore, all optical elements were chosen or designed large enough not to act as beam-restricting apertures. This novel IR ellipsometer generates and projects almost pure polarization states. It acquires subsets of four MM elements at a time. In detail, the upper-left $3\times 3$ block of the MM is obtained without retarders for maximum signal-to-noise ratio, whereas the fourth row and/or column is measured with retarder(s) inserted into the optical path. Besides reduced spectral noise, this approach offers increased temporal resolution ($<1\min$) if only parts of the Mueller matrix are of interest. It also allows one to selectively spend less or more measurement time on specific MM elements, which is very useful when certain elements show stronger or weaker IR signatures, respectively.

The ellipsometer covers the spectral range of $7000–800{\mathrm{cm}}^{-1}$, and can reach root mean square (RMS) noise levels below ${10}^{-4}$ in the normalized MM elements. IR MM ellipsometry with such sensitivity is of high interest for research of thin-film materials with complex anisotropy and/or depolarizing properties. With sub-minute time resolutions for partial MM measurements, the ellipsometer bears great potential for industrial applications such as in-line monitoring or process and quality control. It is also highly relevant for numerous scientific investigations, for instance, of adsorption or growth processes at solid–liquid interfaces, which demand both thin-film sensitivity and sufficiently short measurement times.

This paper is outlined as follows: in the first part, we give a brief overview of the optical set-up, introduce the measurement principle and necessary equations for obtaining the sample’s MM, and then address issues of instrument alignment, calibration, and accuracy. In the second part, we demonstrate the capabilities of the new MM ellipsometer and provide several examples of measurements and modeling of complex samples. These include structured gratings on silicon wafers and thin polymer films under various ambient conditions.

2. EXPERIMENTAL SET-UP AND CHARACTERIZATION

A. Optical Configuration

The IR MM ellipsometer is schematically depicted in Fig. 1. It operates both in reflection, with possible incidence angles between ${\varphi }_0=45°$ and 90°, and in transmission with arbitrary ${\varphi }_0$. Transmission mode is useful for measuring transparent bulk and thick-film samples, but also for instrument calibration, as will later be explained in detail. Reflection mode provides the highest sensitivity for characterizing nanometer-thin films.

 

Fig. 1. Schematic of the IR Mueller-matrix ellipsometer operating in reflection mode (top) with autocollimator (AC) and adjustable sample stage, or in transmission mode (bottom) with rotatable sample mount.

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The input arm of the ellipsometer is fixed, whereas the sample stage and analyzer arm are mounted on a motorized $2\vartheta$ goniometer stage independently angle-adjustable within the plane of incidence (2-Circle Goniometer 423, Huber Diffraction and Positioning Equipment, Germany). A standard Fourier-transform IR (FT-IR) spectrometer (Tensor 37, Bruker, Germany) with a globar as radiation source is coupled to the ellipsometer.

The ellipsometer itself consists of two sets of rotating tandem polarizers (polarizer and analyzer), a tilt- and depth-adjustable sample rotation stage with autocollimation unit, optional and retractable non-rotating retarders, and a highly linear photovoltaic mercury-cadmium-telluride (MCT) detector (KLD-1-J1-3/11, Kolmar Technologies, USA).

The two tandem polarizers are each comprised of two properly aligned KRS-5 wire-grid polarizers (25 mm clear aperture, 0.25 μm wire spacing, Specac Ltd, England) in order to suppress unwanted leaking polarization states, thereby improving the polarization control of the ellipsometer.

Our retarder design consists of a KBr prism for two phase-shifting attenuated total reflections, and two gold mirrors to bring the transmitted light back onto the axis of the ellipsometer arm [28]. The prism’s facet angles (51.5°) and the incidence angles on the gold mirrors ($\approx 25°$) were chosen to achieve an almost achromatic response very close to a 90° phase shift between $p$- and $s$-polarization over the entire spectral range. The retarder unit is mounted on a motorized translation stage that reproducibly moves the retarder into, or out of, the optical path.

An off-axis parabolic mirror focuses the IR globar radiation exiting the spectrometer onto the sample, resulting in a range of incidence angles and a small spot size dependent on the FT-IR spectrometer’s Jacquinot aperture. For a maximum aperture setting of 1.5 mm, which still guarantees a linear detector response, the spot size perpendicular to the incidence plane is about 2 mm. Incidence angles range between ${\varphi }_0\pm 2.4°$, as is typical for IR ellipsometers with non-brilliant radiation sources. Optical modeling of experimental data can, if necessary, easily take into account, such as angle distributions.

The outgoing light passing through the analyzer is focused onto the detector’s $1{\mathrm{mm}}^2$ large detection element. Importantly, the detector is also mounted on a translation stage to ensure optimal focusing with maximum photon collection.

The whole instrument, including the FT-IR spectrometer, is constantly purged with dried air ($\text{r.H.}\ll 0.1\%$) to provide atmospheric stability with minimal IR absorption due to ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ vapor.

B. Measurement Principle

The ellipsometer works with a polarization-state generator (PSG) in the input arm and a polarization-state analyzer (PSA) in the output arm that sample the polarization space with a sufficient number (four) of polarization states in order to calculate quadruples of MM elements. PSG and PSA comprise a polarizer and a retractable retarder. Data collection is based on a rotating-polarizer/rotating-analyzer configuration. For maximum optical throughput we opted to acquire the upper-left $3\times 3$ MM block without retarder, whereas the fourth row and/or column is obtained with retarder in the optical train.

Using the MM calculus [27], the output Stokes vector ${\mathrm{S}}_{\mathrm{out}}$ at the detector, characterizing the light’s polarization state after interaction with sample and ellipsometer optics, is derived from

Ideal PSGs and PSAs can generate and analyze the pure orthogonal polarization states ${[1,\pm 1,0,0]}^{\mathrm{T}}$, ${[1,0,\pm 1,0]}^{\mathrm{T}}$, and ${[1,0,0,\pm 1]}^{\mathrm{T}}$. As illustrated in Fig. 2, corresponding intensity measurements are always selective towards four MM elements. Hence, four intensity measurements with two of these ± vectors in the PSG and PSA lead to a set of four equations that are solvable for a subset of four MM elements [27].

 

Fig. 2. Quadruples of MM elements obtaintable via different combinations of polarizer/analyzer/retarder settings.

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These equations have to be generalized when source prepolarization, polarizer diattenuation, and other nonidealities come into play. For this, we parameterized the tandem polarizers as linear diattenuators [27] with diattenuation $D=\frac{1-c}{1+c}$, where $c$ is the inverse extinction ratio ($c=r/q$ in Ref. [27]).

We first evaluate Eq. (1) without retarders (${\mathrm{R}}_1={\mathrm{R}}_2$ = identity matrix), for negligible circular source prepolarization ($s_3=0$), keeping only terms with expected contributions $>0.0001$. Quadrupels of MM elements are then acquired via

The above formulas require knowledge of polarizer diattenuation and source prepolarization, both of which can be determined from transmission measurements ${\tilde{X}}_n$ of air:

 

Fig. 3. Left: intensity-normalized Stokes-vector components of the FT-IR source, as measured in front of the first polarizer. Right: diattenuation of single and tandem wire-grid polarizers.

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A crucial ellipsometer component is the detector. Its response must be highly linear because of the extreme dynamic range of the detected signals. Otherwise, the MM will suffer from unrecoverable errors. Nonlinearity manifests itself as a nonzero baseline in $I_{{\alpha }_1,{\alpha }_2}$ below the detector cutoff (here at $800{\mathrm{cm}}^{-1}$) and, in extreme cases, as obvious modulation artifacts at the high-wavenumber end of the $I_{{\alpha }_1,{\alpha }_2}$ spectrum [29]. Since the ellipsometer operates with a rotating analyzer, the detector should also be polarization insensitive, obeying ${\mathrm{D}}_{1j}=[1,0,0,0]$.

Linearity of the detector was tested via transmission measurements of air by restricting the IR beam waist using different iris diaphragms. The detector was found to be linear when operated below 90% of its maximum dynamic range. Measuring the detector’s polarization sensitivity via ${\mathrm{D}}_{1j}=[1,{\mathrm{D}}_{12},{\mathrm{D}}_{13},0]$, with

C. Alignment and Calibration of Optical Components

A visible (VIS) laser inserted in the optical path was used to determine the ellipsometer’s central axis, the plane of incidence perpendicular to that axis, and the alignment of all optical elements with respect to that plane [30]. A major cause of systematic errors related to misalignments is beam wander. It occurs when the light’s path through the set-up is disturbed upon interaction with the optical parts, or because of environmental changes such as temperature drift. Beam wander can result in differently illuminated areas on the detector element, leading to baseline errors in the calculated MM. We used the VIS laser to meticulously adjust polarizer and retarder alignment for minimal beam wander and maximum transmission of IR radiation.

Deviations in sample tilt from the plane of incidence also induce beam-wander-like effects on the detector. The same holds true if the sample plane does not cross the central ellipsometer axis. While $\mathrm{\Psi }/\mathrm{\Delta }$ measurements are pretty robust against those misalignments, we found that proper sample alignment is mandatory for reliably measuring the block-offdiagonal MM elements. The correct sample tilt (to within 1 arcmin) is set utilizing an autocollimation stage with VIS light under normal incidence. Sample depth is then adjusted maximizing the photon count at the detector. The additional VIS laser can be exploited to ensure that light reflected off the sample travels along the same path as during instrument calibration in transmission.

With all optical elements properly aligned, the polarizer offsets with respect to the plane of incidence could be determined. This was achieved to $\pm 0.05°$ accuracy via calibration and sample measurements [Eqs. (9) and (2)] of isotropic thin polymer films. In a minimization procedure, polarizer and analyzer offset were varied until the block-offdiagonal MM elements showed baselines of zero with vanishing polymer vibrational bands. Retarder alignment was performed in a similar fashion orienting the fast axes to 0° for vanishing block-offdiagonals. Experimentally, the phase shifts were within $\sin {\mathrm{\Delta }}_{\mathrm{Ret}}=0.997$ and 0.999.

D. Instrument Operation and Characterization

One advantage of using tandem polarizers is working with much better defined, almost pure polarization states. A drawback is that fast intensity measurements with crossed polarizers can become difficult because the centerburst of the interferogram is buried within the noise, which leads to baseline errors at the high- and low-wavenumber end of the Fourier-transformed spectrum. We therefore advise to measure cross polarization by accumulating a larger number $N$ of interferogram scans.

In the following, we consider ${\mathrm{M}}_{11}$-normalized MM elements. In order to assess accuracy, noise propagation, and measurement time, we performed MM measurements of air in dependence of $N$. Noise is minimized because the ellipsometer works with almost pure polarization states inscribing an octahedron in the Poincaré sphere [25]. The ellipsometer achieves remarkable and unprecedented signal-to-noise levels in the mid-IR range between $4000{\mathrm{cm}}^{-1}$ and $800{\mathrm{cm}}^{-1}$, as shown in Fig. 4. The noise follows a $1/\sqrt{N}$ behavior, as is expected for additive Gaussian noise. For air, as well as for samples with high reflectivities such as thin films on metals, an RMS noise of about 0.0001 (0.00005) is reached for $N=32$ (128) at $4{\mathrm{cm}}^{-1}$ spectral resolution and 40 kHz scanner velocity. Compared to MM elements in the fourth row and column, elements in the upper-left $3\times 3$ block exhibit 1.5–1.8 times less noise, as they are measured without retarders.

 

Fig. 4. RMS noise (top) between $4000{\mathrm{cm}}^{-1}$ and $1000{\mathrm{cm}}^{-1}$ of selected MM elements (bottom) of dry air at two different spectral resolutions. The insets show examplary intensity spectra measured in an unpurged (humid) and purged (dry) ellipsometer chamber.

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With the above settings, acquisition of a MM takes about 13 min (32 min). For $N\lesssim 64$, measurement times are dominated by the time it takes to position polarizers and retarders. Using faster polarizer rotation and retarder positioning velocities, temporal resolutions of 2 min seem feasible for a complete MM acquisition with acceptable RMS noise; 15 s should be possible for a partial measurement of four MM elements.

3. RESULTS AND DISCUSSION

A. Structured Trapezoidal ${\mathsf{SiO}}_{\mathsf{2}}$ Gratings

A first application of the new MM ellipsometer is the profile determination of μm-sized trapezoidal ${\mathrm{SiO}}_2$ gratings on silicon substrates, schematically depicted in Fig. 5. The gratings were prepared by chemical vapor deposition of a 1000 nm thick ${\mathrm{SiO}}_2$ layer on a Si wafer, followed by photolithography processing (transfer of the mask’s shadow cast, 7.5 s illumination with UV light, development of photo resist, and buffered oxide etch with $\mathrm{HF}:{\mathrm{NH}}_4\mathrm{F}=12.5\%:87.5\%$ to remove exposed oxide).

 

Fig. 5. Structure parameters of trapezoidal ${\mathrm{SiO}}_2$ gratings on Si.

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Structure parameters of the gratings are their height (H), the trapezoid lengths at the base (${\mathrm{B}}_x$, ${\mathrm{B}}_y$) and top (${\mathrm{T}}_x$, ${\mathrm{T}}_y$), and their period lengths (${\mathrm{P}}_x$, ${\mathrm{P}}_y$). All parameters are on the order of μm and therefore give rise to complex MM spectra in the IR spectral region, especially if the gratings have unequal structure sizes in $x$ and $y$ directions.

Figure 6 shows measured and fitted MM data of a ${\mathrm{SiO}}_2$ grating in dependence of azimuthal sample rotation. If the plane of incidence is parallel or perpendicular to a symmetry axis (e.g., at 0° azimuth), the MM looks pseudo-isotropic, i.e., all block-offdiagonal elements are zero. Upon azimuthal rotation, anisotropy effects are rotated through the various matrix elements rendering the block-offdiagonals highly sensitive towards the grating’s profile parameters and orientation.

 

Fig. 6. Measured azimuth-dependent MM data (${\varphi }_0=50°$) of a trapezoidal ${\mathrm{SiO}}_2$ grating on Si compared to fitted data according to the optical model in Fig. 5. The fourth column shows several symmetries of the Mueller matrix. Measured spectra were smoothed at the high-wavenumber end because of noise due to the grating’s low reflectivity ($<0.2$). Gray and colored lines are raw and smoothed data, respectively. The legend lists nominal azimuths (0.5° offset).

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The MM of symmetric structures is expected to exhibit various symmetries [15,31] as a consequence of the electromagnetic reciprocity theorem, e.g., ${\mathrm{M}}_{12}-{\mathrm{M}}_{21}=0$, ${\mathrm{M}}_{13}+{\mathrm{M}}_{31}=0$, and ${\mathrm{M}}_{23}+{\mathrm{M}}_{32}=0$. Broken symmetries in measured MM data can be regarded as markers for deviations from an ideal grating. As shown in the fourth column in Fig. 6, the symmetries are observed up to differences from zero of about 0.3% at larger azimuths. We attribute these deviations to defects also seen with scanning electron microscopy (SEM).

In order to quantify grating profile and orientation, we performed rigorous coupled-wave analysis (RCWA) simulations [32,33] (SpectraRay software, SENTECH Instruments GmbH) to fit the measured MM data. As seen in Fig. 6, the experimental MMs are well described by the fitted ones. An overall offset in sample azimuth of 0.5° from the nominal orientation was determined from the fit. Profile parameters as a result of RWCA are listed in Table 1 and compared to nominal values obtained from SEM measurements. The two methods agree remarkably well, yielding very similar results. Ellipsometry, however, is clearly advantageous, as it is nondestructive, much faster than SEM, and theoretically deployable for process control and in-line monitoring in various environmental conditions.

Table 1. Nominal and Fitted Profile Parameters of the Measured ${\mathsf{SiO}}_{\mathsf{2}}$ Grating: Height (H), Periods (${\mathsf{P}}_{\mathsf{x},\mathsf{y}}$), Base, and Top Lengths (${\mathsf{B}}_{\mathsf{x},\mathsf{y}}$, ${\mathsf{T}}_{\mathsf{x},\mathsf{y}}$)^a

View Table

B. Time-Resolved Monitoring of Polymer Relaxation

To demonstrate the achievable time resolution of the ellipsometer, we monitored changes in the transmission MM of a multidirectionally stretched, 11 μm thick low-density polyethylene foil (Papstar GmbH, Germany). The measurement geometry is depicted in Fig. 7 at the bottom-right. The data in the figure show measured MM differences between the foil’s non-equilibrium states under tension and the equilibrium state after 1585 s of relaxation. We chose to acquire selected representative MM elements, in this case [${\mathrm{M}}_{11}$, ${\mathrm{M}}_{12}$, ${\mathrm{M}}_{31}$, ${\mathrm{M}}_{32}$], resulting in a temporal resolution of 47 s.

 

Fig. 7. Time-resolved (47 s) transmission MM difference spectra measured between tensioned and relaxed states of a stretched low-density polyethylene (LDPE) foil. The schematic (bottom-right) shows the measurement geometry of the foil stretched across the sample stage.

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In a simplistic view, the MM elements ${\mathrm{M}}_{12}$ and ${\mathrm{M}}_{31}$ can be associated with $x–y$ and $\pm 45°$ linear dichroism, respectively, while ${\mathrm{M}}_{32}$ can be related to circular birefringence [27]. All three elements are nonzero, which is expected because the polymer foil was stretched in multiple directions within the sample plane. The foil’s effective optical axes are thus oriented in some oblique angles with respect to the ellipsometer coordinate system.

The vibrational signatures around $2900{\mathrm{cm}}^{-1}$ and $1460{\mathrm{cm}}^{-1}$ correlating with the foil’s vibrational fingerprint have distinct shapes in the various entries of the MM, and decrease in amplitude as the polymer foil relaxes and becomes less anisotropic. Upon relaxation, the foil thickness increases, causing shifting and diminishing interference oscillations in $\delta {\mathrm{M}}_{12}$ and $\delta {\mathrm{M}}_{31}$. The observed nonzero baselines of the different MM elements in the non-equilibrium states could be a result of stretching-induced directional differences in polymer density leading to anisotropy of the complex refractive index. Optical modeling can, in principle, quantify such differences but is beyond the scope of this paper. Similarly, optical modeling could reveal in detail which of the above-discussed MM elements are affected by rotation, retardation, and diattenuation, as well as by depolarization.

Sub-minute time resolution and access to a sample’s anisotropy and depolarization properties render IR MM ellipsometry a promising technique for rheology, relaxation, and related studies, again with applications in process and quality control.

C. Ex Situ Studies of Thin and Ultrathin Polymer Films

We now utilize the ellipsometer to measure, and consequently characterize, vibrational MM spectra of nanometer-thin polymer films. As model surfaces, we investigate silicon substrates covered with thin films of spincoated and annealed poly(glycidylmethacrylate) [PGMA] [13,34], a widespread polymer finding applications in surface functionalizations and as a molecular linker. We prepared three PGMA films of 118.0 nm, 68.0 nm, and 7.7 nm thicknesses, as schematically depicted in Fig. 8, and measured them in reflection at ${\varphi }_0=65°$ incidence angle. Figure 9 shows experimental and fitted MMs. All block-offdiagonal MM elements are zero, indicating that the films are isotropic. The remaining nonzero elements are connected to the classical amplitude ratio $\tan \mathrm{\Psi }$ and phase difference $\mathrm{\Delta }$ via ${\mathrm{M}}_{12}={\mathrm{M}}_{21}=-\cos 2\mathrm{\Psi }$, ${\mathrm{M}}_{33}=+\sin 2\mathrm{\Psi }\cos \mathrm{\Delta }$, and ${\mathrm{M}}_{43}=-\sin 2\mathrm{\Psi }\sin \mathrm{\Delta }$.

 

Fig. 8. Thin PGMA films (118 nm, 68 nm, and 7.7 nm) on Si substrates studied in reflection at the solid–air interface.

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Fig. 9. Measured (colored) and fitted (black) MM spectra of thin, isotropic PGMA films of various thicknesses.

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The PMGA spectra are dominated by the carbonyl-stretching vibrational band [$\nu (\mathrm{C}═\mathrm{O})$] around $1735{\mathrm{cm}}^{-1}$ as well as several bands between $1300{\mathrm{cm}}^{-1}$ and $1100{\mathrm{cm}}^{-1}$ associated with vibrations of the polymer’s ester and epoxy groups. Other, less intense, bands between $1500{\mathrm{cm}}^{-1}$ and $1300{\mathrm{cm}}^{-1}$ and below $1000{\mathrm{cm}}^{-1}$ are related to alkyl bending and epoxy ring-deformation modes, respectively. All PGMA bands are resolved in the measured data of the two thicker films. For the ultrathin film, the carbonyl and ester bands are well above the limit of detection ($3\sigma$ level), and so are the vibrational features around $1200{\mathrm{cm}}^{-1}$ from the 1.2 nm thin native ${\mathrm{SiO}}_2$ layer. The weaker PGMA fingerprint bands are slightly above the noise level, which is about $\eta ({\mathrm{M}}_{ij})=\pm 0.00015$, $\eta (\mathrm{\Psi })=\pm 0.005°$, and $\eta (\mathrm{\Delta })=\pm 0.02°$ between $2000{\mathrm{cm}}^{-1}$ and $1000{\mathrm{cm}}^{-1}$. Those weak bands could, nonetheless, be resolved by accumulating more interferogram scans.

For all three films, we used the MM data to calculate polarization degree [35] and phase polarization degree [36]:

The measured data were fitted with an isotropic layer model describing PGMA’s dielectric function by a sum of vibrational oscillators associated with the various molecular vibrations [37]. Film thickness as well as oscillator shapes and amplitudes were fitted simultaneously for the thickest film. The obtained dielectric function was then used to determine the thicknesses of the two thinner films. One might expect that the annealing process during film preparation induces certain ordering or reorientation effects of the polymer segments. Some uniaxial anisotropy might therefore be present, especially for the thinnest film, in which anchoring to the substrate leads to the formation of tail–train–loop conformations [34]. However, employing a uniaxial model did not improve the fit results, indicating that the films are indeed isotropic.

The fact that the vibrational spectra of the 7.7 nm thin film can be modeled with the isotropic dielectric function of the thicker film implies that both films are structurally and chemically identical. Otherwise, effects such as band shifts or changes in band composition would be observed. Position and shape of the $\nu (\mathrm{C}═\mathrm{O})$ band, for instance, are prominent markers for molecular interactions and chemical environment [14], which seem to be very similar for the three films.

These first IR MM studies of thin films show that the technique has great potential for thin-film analysis, particularly with respect to film homogeneity via the depolarization information contained in the MM, and to film anisotropy and molecular interactions correlated with the vibrational fingerprint.

D. In Situ Studies of Polymer–${\mathsf{H}}_{\mathsf{2}}\mathsf{O}$ Interfaces

The previously discussed 68.0 nm thick PGMA film now serves as a test surface for the first in situ MM study of a thin organic film at the solid–liquid interface to water. The film was prepared on a wedge-shaped (1.5°) silicon substrate and is hence suitable for usage in our in situ flow cells [38]. With the cell tilted within the plane of incidence to select the inner reflex (Fig. 10), the wedge’s backside was illuminated under ${\varphi }_0=57.3°$ resulting in a non-attenuated total reflection (nATR) incidence angle of 12.6° at the Si–PGMA interface.

 

Fig. 10. Left: liquid flow cell with thin polymer film on Si wedge measured in backside reflection. Right: measured and fitted in situ ellipsometric data of a 68 nm thick, isotropic PGMA film at the polymer–air and polymer–water interface.

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Measured and fitted spectra of the film, first in contact with air and then with water at room temperature, are plotted in Fig. 10. Being an isotropic sample, only the block-diagonal MM elements are nonzero, and it is thus equivalent to calculate and analyze conventional $\mathrm{\Psi }$ and $\mathrm{\Delta }$ spectra. In absolute ellipsometric spectra, the strong vibrational bands of bulk water domininate and mask the polymer bands [37]. The figure therefore shows referenced spectra with respect to a clean silicon-wedge surface. As a result, upward-pointing PGMA bands and downward-pointing residual water bands are observed. The bending mode $\delta ({\mathrm{H}}_2\mathrm{O})$ at $1650{\mathrm{cm}}^{-1}$ and the libration modes ${\nu }_{\mathrm{L}}({\mathrm{H}}_2\mathrm{O})$ below $1000{\mathrm{cm}}^{-1}$ [39] are a consequence of the difference in optical contrast at the substrate–film–ambient and the substrate–ambient interfaces. Amplitudes and shapes of the water bands are related to PGMA film thickness and hydration [14].

Optical modeling based on an effective-medium approach [14] confirms the hydrophobic nature of the film. There is no substantial amount of swelling ($<1\mathrm{nm}$ thickness change, $<5\%$ water content) and no significant redshift of the carbonyl stretching mode, $\nu (\mathrm{C}═\mathrm{O})$. The latter would point towards the presence of hydrogen-bond interactions between the polymer’s ester group and surrounding water molecules.

These first in situ measurements of isotropic films with the new MM ellipsometer compare well with data obtained with established in situ IR ellipsometry [37]. The instrument thus proves to be promising for studies of more complex samples with thin-film anisotropy and/or structure, which is the aim of ongoing and future projects.

4. CONCLUSIONS AND OUTLOOK

We developed a broadband IR MM ellipsometer with high optical throughput for sensitive MM measurements of ultrathin films and structured surfaces. The ellipsometer was successfully used to obtain high-quality MM data of complex samples, such as trapezoidal oxide gratings, anisotropic polymer foils, and ultrathin polymer films. In conjunction with optical calculations based on RCWA and different layer models, we demonstrated the ellipsometer’s applicability for various research questions from the thin-film community but also for industry-related problems such as quality and process control.

The device achieves sensitivities of less than ${10}^{-4}$ in the normalized MM elements, which opens up new possibilities for polarimetric measurements. It is expected that this unrivaled sensitivity can be even further increased by at least 30% by using ${\mathrm{BaF}}_2$ wire-grid polarizers, which have better transmissivity and diattenuation properties than KRS-5 polarizers. Furthermore, a tunable IR laser could be coupled to the instrument [40] providing additional noise reduction with simultaneously increased temporal resolution.

We anticipate that the ellipsometer will help to satisfy the growing demand from science and industry for a sensitive and accurate IR MM ellipsometer to characterize complex samples.