1 Introduction

1.1 General

The method of immersion transmission ellipsometry (ITE) [1] and [2] allows highly accurate determination of the absolute three-dimensional refractive indices of anisotropic ultra-thin films at one single wavelength. Therefore, no assumptions are necessary about using a specific dispersion model. The method is combined with conventional ellipsometry in transmission and reflection. Polarisation elements or retarders as well as the LC of course can be characterised by this method more accurately than in the past, because they are much thicker (in the μm range). In fact, because almost any film can be anisotropic to some degree, this measuring method has a wide applicability in quality control and research and development. One important example is the anisotropy of phase shift masks in semiconductor technology. Another one would be aligned organic light emitting diodes (OLEDs) [3]. In future, the method might also serve to characterise thin films with thicknesses below 100 nm, which are used as aligning layers in liquid crystal displays (LCDs), and for the fabrication of polarisation elements such as thin polarisers, retarders or polarisation gratings.

Anisotropic films with different optical properties in all three spatial directions are important for optical technologies, such as LC (liquid crystal) technologies. The standard technique to align anisotropic LC layers is to use an anisotropic surface, such as a rubbed polyimide film or a photoalignment layer [4]. A photoalignment layer is a thin film, whose surface is made anisotropic either by irradiation with polarised light or by irradiation with unpolarised light under oblique incidence or under a combination of both irradiation schemes.

If one could determine the orientation gradient within such a photoalignment layer, one would be able to predict in which way LC layers would be aligned by this anisotropic surface and make a pre-choice of alignment layers before preparing LC (liquid crystal) cells or retarders.

The ITE technique in combination with standard reflection and transmission ellipsometry gives information about the absolute refractive indices, which influence the optical properties of optical functional layers used in industrial applications. The absolute average refractive index gives hints to the density of the material after preparation. Its development during irradiation is also of interest in case of photodecomposition or a change in free volume [5]. The absolute refractive index is also useful, if UV/Vis absorption data are Kramers–Kronig transformed as described in [6]. A statement about the lumped anisotropy of the UV absorption data at wavelengths below 200 nm is then possible, without measuring at these wavelengths.

1.2 Theory and state of the art

The task of determining orientation gradients has been tackled for layers around 1 μm using generalised ellipsometry [7]. Here, we show that using our measurement cell standard ellipsometry (in transmission, immersion/transmission and reflection) without introducing s- and p-light coupling can determine orientational gradients in deep-sub-μm films. This technique therefore is complementary to the waveguide spectroscopy technique, which is used for 1-μm-thick films and thicker films [8, 9, 10].

Reflection ellipsometry measurements can be carried out for two perpendicular orientations of a biaxial layer: Either the polarisation of the orienting light is parallel to the plane of incidence of the measuring light or perpendicular. The ellipsometric parameters Ψ and Δ in dependence on the incidence angle could now be fitted to the theoretical equations, in order to obtain the three refractive indices and the thickness of the film.

Difficulties with the accuracy are, however, encountered in reality: Even for Ψ and Δ of a very thin uniaxial layer with refractive indices \(n_{x} = n_{y} \ne n_{z}\) (z is the film normal) nearly the same values result from the fit as for an isotropic layer with a quite different effective refractive index (Fig. 1).

Fig. 1
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Comparison of reflection, transmission and immersion transmission ellipsometry. The difference in Ψ and Δ for two different layers is depicted. Layer A: n x = n y = 1.666, n z = 1.666, d = 60.0 nm. Layer B: n x = n y = 1.63869, n z = 1.6, d = 63.0 nm. Δ From ITE is in this case more sensitive to anisotropy by a factor of 10 than Δ from conventional (transmission) ellipsometry

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1.2.1 Short description of immersion transmission ellipsometry (ITE)

An older method, described in [11], is immersion ellipsometry in reflection. In this method, the ambient medium of the investigated layer is varied in order to remove the ambiguities present in the evaluation of the conventional ellipsometry measurements. We, in turn, perform immersion ellipsometry in transmission (Figs. 1, 2), also because the transmission properties of an optical functional layer in transmission are more important for the application than the reflection properties. In order to remove the ambiguities, measurements in two different ambient media in transmission are performed. Also, the thickness should be determined by combination of the results with the results of reflection ellipsometry. (Of course, the thickness could also be measured by other techniques, such as X-ray measurements or atomic force microscopy.)

Fig. 2
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Scheme for immersion transmission ellipsometry (ITE)

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One ambient medium is air (as in conventional transmission ellipsometry) and the second one is formed by placing the layer (with the substrate) between two hemispheres (Fig. 2), made from the substrate material (in this case quartz glass SQ1). For optical contact, an immersion liquid is used. This system is then investigated by transmission ellipsometry at different angles of incidence. The method was termed immersion transmission ellipsometry (ITE).

2 Evaluation of orientation gradients by ITE in experimental thin films

We had in the past successfully applied ITE for spin-coated and photo-oriented azobenzene containing side-chain polymer films (Fig. 3 shows the chemical structure) [2] without assuming a gradient. First a few words about the coordinate system chosen: The x- and y-directions are in the plane of the film, the z-direction perpendicular to it, for photo-oriented films the x-direction is the direction parallel to the polarisation of the irradiating light. The data from the measurements in the two different media were combined in the following way: The average of the three refractive indices in the three spatial directions was assumed to have several different values, and the birefringence Δn zx = n z − n x was a free fit parameter, which was determined from the fit to a orthogonal biaxial model assuming no gradients. For the transmission ellipsometry measurement in air (only Δ was considered) and for the ITE measurement, dependencies were determined between the assumed average refractive index values and the resulting birefringence Δn zx. Each dependency was in itself unambiguous. But the two dependencies (one for air and one for immersion) were different. Therefore, their common point should represent the real value. And indeed, the two dependencies had their common point exactly where the ITE measurement alone had predicted the values to be.

Fig. 3
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Chemical structure of the investigated azobenzene-HEMA-copolymer

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However, different anisotropies resulted, when evaluating the reflection measurements, which can be due to gradients along the z direction. Therefore, we here evaluated the data with a combined fit to reflection and transmission data and allowed for gradients, too. The average refractive index N = 1/3(n x + n y + n z) was assumed to be constant throughout the film. We are therefore investigating gradients of the anisotropy or orientation of the molecules and not gradients of the absolute refractive index. The individual indices n x, n y and n z (but not their average) were allowed to vary along the z direction. This leaves us with the birefringences Δn yx (in-plane) and Δn zx (out-of-plane) as functions of the z-coordinates. For the calculation of the ellipsometric parameters of the films containing these orientational gradients, we used the Berreman method (10 linearly varying sub-layers replaced the original one-layer model) modified by [12] under consideration of special cases for faster calculation, such as no tilt angle or no twist angle.

The raw data are shown in Fig. 4. In Table 1, the results of the evaluation of ITE measurements of five polymer films, which have been made by spin-coating, are listed. In Fig. 5, the orders are schematically depicted. The chemical structure of the polymer is depicted in Fig. 3. It has an azobenzene side-chain suitable for photo-orientation and a nematic liquid crystalline phase, suitable for amplification of the inscribed order by annealing. The state of two of the five films has been changed by irradiation at 488 nm, and one of them has been annealed in the liquid crystalline phase. The biaxial orientation gradients were assumed to be linear. Earlier, a one-layer model evaluation of the data to the films I, J and E has been published [2].

Fig. 4
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Simulation (solid lines) and experimental data compared for five thin films of the copolymer

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Table 1 Results for orientation gradients from ITE combined with reflection and transmission ellipsometry obtained with the assumption of no tilt gradient
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Fig. 5
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Schematic depiction of the orders in the thin films, determined by ITE in combination with reflection ellipsometry

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We assumed the following standard deviations of the measured data: In air: 0.5°, ITE: 0.1° and reflection 5.0°. The estimated errors in Table 1 stem from the Levenberg–Marquardt-algorithm and probably underestimate the real errors. A higher weight of the air measurement by assuming 0.1° standard deviation, too, did not give substantially different results (see below). Δn yx is the difference between the two in-plane refractive indices n y and n x. grad Δn yx is then defined by dividing by two the difference between Δn yx at the air interface and Δn yx at the substrate interface. grad Δn zx is given correspondingly.

The values for the average refractive index correspond well to data, obtained earlier by investigating this polymer using waveguide spectroscopy [8]. This is true for all films, apart from film E.

The fresh thin films (I and C) seem to be more planar at the air interface, compared to the substrate interface. This can be inferred from the sign of the gradient of the out-of-plane birefringence grad Δn zx. The out-plane birefringence is smaller at the air interface than at the substrate interface (see definition of grad Δn zx). The thicker film (A), in turn, is less planar at the air interface. The thinner films are optically denser: Obviously, they seem to contain less free volume or less solvent. The annealed film (E) is the densest, as expected.

For film C, it has to be stated that the reflection data had exceptionally bad quality. This is reflected by a significant influence of the different weighting of the air transmission measurement on the apparent film thickness. In the other cases, this weighting gave no bigger differences. This underlines the high accuracy of the method for normal data. Even the orientation gradients are well reproduced.

The photo-oriented film J after irradiation did not have a substantial gradient, which shows that the light energy was sufficient to get orientation throughout the whole sample thickness. When using this first model (Table 1) for the irradiated and annealed film E, the in-plane birefringence was higher than after irradiation only. This is the well-known amplification effect by liquid crystalline self-organisation. However, the film thickness did change, when comparing to older results of a one-layer model [2]. Also, the absolute refractive index seemed to be quite high. When looking at a second model, an almost uniaxial alignment with tilt gradient resulted. This is one possible macroscopic order for nematic liquid crystals between surfaces.

Film E can be fitted with a better fit quality to the following, almost uniaxial (nematic), model (the resulting thickness corresponds exactly to an atomic force microscopy measurement, which gave 147 nm) (Table 2): The model corresponds to an average tilt angle of zero and an interfacial tilt angle, which is the same at both interfaces, however, with a different sign. This kind of order can be found in low molecular liquid crystals in vertically aligned nematic (VAN) displays [13]. Here, the in-plane order in the middle of the layer stems from the photo-irradiation and in the LC cells from the effect of the electric field acting on the negative dielectric anisotropy of the molecules used for VAN displays. Here, in contrast to a multi-domain VAN order, one has only degeneracy in one spatial direction. A multi-domain order could, however, be achieved by photo-patterning.

Table 2 Alternative, better solution for film E
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In fact, this film might be useful as alignment layer for a single-domain VAN display because of the pre-tilt angle of 70° and −70° at the air interface, which should give homeotropic alignment. This homeotropic alignment can evolve into in-plane alignment under an electric field.

3 Conclusions

The applicability of ITE combined with conventional reflection ellipsometry and transmission ellipsometry has been successfully extended to determine orientation gradients. This was demonstrated in films thinner than one μm by more closely investigating different stages of photo-oriented layers (fresh, irradiated, annealed). The method can be accompanied by AFM in order to further strengthen the confidence in the results. The technique might in the future even be useful to predict the pre-tilt angle of a liquid crystal aligned by such a thin film interface, by ellipsometrically measuring the tilt gradient of the aligning layer in advance and taking the value at the air interface of the anchoring layer (which becomes the LC interface) as pre-tilt angle. The results in this paper are very encouraging in this direction. Aligning layers have a thickness of about 50 nm, and film thicknesses as low as 100 nm were investigated here.

Of course, the method should be able to investigate thicker layers, such as the oriented LCs themselves, retardation films or polarisation films, much more accurately, than possible so far.