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The anchoring energy of liquid crystals was shown to be tunable by surface nanopatterning of periodic lines and spaces. Both the pitch and height were varied using hydrogen silsesquioxane negative tone electron beam resist, providing for flexibility in magnitude and spatial distribution of the anchoring energy. Using twisted nematic liquid crystal cells, it was shown that this energy is tunable over an order of magnitude. These results agree with a literature model which predicts the anchoring energy of sinusoidal grooves.
© 2015 Optical Society of America
1. Introduction
Optical devices employing liquid crystals (LCs) require alignment layers to establish a preferred orientation of the LC molecules on a substrate. Liquid crystal displays (LCDs) require a strong, uniform anchoring layer across large substrates [1]. Other functionalities require that the LC orientation vary spatially across a substrate [2], leading to a need for preparing surfaces with varied anchoring energies, such that they change both in orientation and magnitude in a predefined spatial pattern [3]. The anchoring energy is the magnitude of the free energy penalty for LC which aligns perpendicular to the preferred direction. If the preferred LC orientation is in the plane of the substrate, then there are two anchoring energies: azimuthal, which refers to LC orientation in the same plane but in a perpendicular direction; and polar, referring to orientation perpendicular to the substrate. Frequently, the polar anchoring energy is significantly larger than the azimuthal anchoring energy, and techniques need to be developed to only modulate the azimuthal energy.
Currently, most LC anchoring methods employ chemical alignment “templating” techniques. These involve ordering of thin films of anisotropic molecules from which LCs adopt their alignment. This monolayer effect is due to Van der Waals interactions between the alignment molecules and the LC [4], resulting in high anchoring energies (≥ 10−4 J/m2).
The most common form of chemical anchoring is a rubbed polyimide layer on the surface of a substrate. The polymer chains are aligned to the direction of the rubbing and transfer their orientation to the LCs. Anchoring with rubbed polyimide, because it requires physical rubbing, is inherently a spatially coarse method and thus lacks the ability to vary its energy or alignment direction over small length scales. Usually, the resulting anchoring energy is large and spatially uniform, as desired by the application, such as in LCDs. Spatial control over small distances has been demonstrated with the related “nanorubbing” of polyimide alignment layers using an atomic force microscope (AFM) tip to score the polyimide [5, 6, 7].
Chemical alignment can also be achieved with photoalignment layers [8, 9]. These are thin layers of materials (the most common of which are organic molecules containing azo (-N=N-) moieties), which can be aligned with linearly polarized light, and thereby serve as a template for the alignment of the LC [10]. By leveraging photolithography techniques, photoaligned layers offer greater ability to pattern anchoring energies across a single substrate. It has also been shown that modulating the exposure time can increase the anisotropy found in the photoaligned layer and thus increase the anchoring energy [11]. Additionally, by exposing the substrate with multiple sources of light, interference patterns can be produced in the alignment layers [12]. This technique ultimately falls short in its ability to provide truly arbitrary anchoring layers with variable strength and direction over small length scales (≤ 1μm).
Mechanical anchoring with nanogrooves is the least mature LC alignment technology, but can be highly versatile and useful in solving some of the challenges associated with preparing novel LC devices. The anchoring effect of grooves was first studied by Berreman in 1972 [13]. Berreman showed that LC molecules, given the opportunity, will align parallel to grooves on a surface, and he derived the energy penalty incurred when LCs align in the plane of the substrate, but perpendicular to the grooves, i.e. the azimuthal, anchoring energy. As seen in Fig. 1(a), aligning parallel to the grooves allows the LC molecules to have uniform alignment; however, by aligning perpendicular to the grooves, the LC molecules are forced to constantly change orientation, as shown in Fig. 1(b). This ultimately increases the elastic energy present in the LC, making perpendicular alignment an unfavorable configuration.
Fig. 1: LC molecules deposited onto ridges and aligning parallel (a) and perpendicular (b) to the ridges. In (a), the molecules can all have uniform alignment while remaining tangent to the substrate; however, in (b) the LC molecules must constantly change their orientation.
As shown in [13], the azimuthal anchoring energy WA of sinusoidal grooves in the x–z plane, whose profile is represented by z = A sin(qx), where A is the groove depth and q is the spatial frequency of the grooves, is:
In this expression, K is the average of the LC’s splay deformation constant K11 and its bend deformation constant K33, and Λ = 2π/q is the groove pitch.Equation (1) assumes an infinite out-of-plane, i.e., polar anchoring energy Wp. When Wp is finite, Faetti [14] showed that Equation 1 is modified to:
Note that Wa in Eq. (2) indeed reduces to the Berreman equation for large values of Wp. The above correction is often neglected because of the fact that the product of Λ and Wp is often large compared to πK. For example, in [15], the value of K is ∼ 10−11 N, and the corresponding anchoring energies are ∼ 10−4J/m2. Therefore, for pitches Ω larger than ∼ 1 μm, the Faetti correction in [14] becomes negligible. Indeed, in Reference [16], where larger periods of 500 – 900 nm were patterned, Eq. (1) was sufficiently accurate to fit the experimental data. It is also important to note that at the relatively large dimensions of [16], the value of Wa in Eq. (1) that is obtainable using this method is relatively small. However, with the fine periods afforded by electron beam lithography, which is used to pattern the grooves for the present report, the reduction in azimuthal anchoring energy becomes significant.
The emergence of new high resolution patterning technologies enables a radical extension of previous experimental studies in this field. In particular, electron beam lithography has the ability to pattern dense lines and spaces to pitches as small as ∼ 40 nm, and semi-isolated lines ≤ 10 nm in width. This process, coupled with appropriate etch techniques, provides for much higher azimuthal anchoring energies. Furthermore, the flexibility afforded by this approach allows one to pattern a wide range of groove geometries. These patterns can vary in pitch and direction along very short length scales (≤ 1μm). The strong inverse cubed dependence of the anchoring energy on groove pitch (Eq. (1) or (2) above) allows for large variations in anchoring energy with small variations in pitch, thus enabling whole new classes of LC devices with complex alignment geometries. In this paper we demonstrate the power and flexibility afforded by these new technologies, in agreement with the expectations of Eqs. (1) and (2).
2. Experimental
2.1. Nanopatterning and liquid crystal cell fabrication
The demonstration of these new capabilities of variable anchoring energies was carried out by assembling a twisted nematic LC cell which included the commonly used LC 5CB, with input and output glass plates into which we etched arrays of nanogrooves. The nanogroove dimensions were varied, with pitches ranging from 150 to 250 nm and the depth from 18 to 26 nm. In general, patterning consists of two steps: lithography and etching. However, in these experiments we have simplified the process in such a way as to dispense with the need for etching: the patterned resist was chemically and optically similar to the fused silica substrate, and thus, instead of etching the grooves into the substrate we utilized the patterned resist in the measurements of anchoring energy. The lithography was carried out with an electron beam system operating at 100 kV accelerating voltage, and the resist was a negative tone inorganic resist, hydrogen silsesquioxane (HSQ) [17]. Crosslinking of HSQ was obtained at doses of 575 μC/cm2, the field size was 4 mm2, and all samples were patterned on fused silica substrates. The depth of the grooves was determined by the thickness of the HSQ after exposure and developing.
In order to achieve the desired dimensions, the HSQ was diluted to 2% solids in methyl isobutyl ketone, and spin speeds of 2000, 3000, and 4000 RPM were used to generate different HSQ thicknesses of 26, 22, and 18 nm, respectively. Furthermore, two additional thin films had to be applied to the HSQ, and after exposure – removed: EL11, a copolymer dissolved in ethyl lactate [18], was diluted to a concentration of 8.8% solids in solution and spun on the HSQ-coated sample at 3000 RPM (350 nm thick), followed by the evaporation of 50 nm of chromium. The role of the EL11 copolymer was to serve as a buffer between the HSQ and the Cr; without it, the exposed HSQ exhibited considerable overexposure and limited spatial resolution. The Cr layer was needed to provide both a path to electrical ground and a reflection layer which the electron beam lithography tool uses to probe the local height of the substrate. After exposure the chromium was etched from the wafers using Cr etch type 1020 [19]. The samples were then rinsed with acetone to remove the EL11 layer, and the HSQ was then developed in tetramethyl ammonium hydride (AZ 300MIF) for 2 minutes at 50°C. Finally, the wafer was rinsed with isopropyl alcohol (IPA) and blown dry with nitrogen.
An example of the HSQ nanogrooves obtained in this way is shown in Fig. 2. It is noteworthy that the resultant HSQ had some roughness as seen in the AFM scans. This roughness is apparently due to the interaction of the resist with the glass substrate, since it was not present on similar test gratings in HSQ on silicon wafers.
Fig. 2: Liquid crystal anchoring ridges written in hydrogen silsesquioxane patterned on fused silica substrates, using electron beam lithography. The pitch is 200 nm and the height of the ridges is 19 nm.
The LC cell was assembled with the two patterned fused silica substrates facing each other and separated by a 3 μm spacer. This spacer was a UV-crosslinkable polymer, SU-8 [20], which also acted as the bonding layer between the two plates. The SU-8 was spun onto the fused silica discs, prebaked at 90°C for one minute, then exposed with 365 nm light and post-exposure baked for 5 minutes at 90°C. The SU8 was then developed using SU8 developer for 30 seconds with slight agitation. Afterwards, the wafers were rinsed with IPA and blown dry with N2.
Pairs of substrates were sandwiched together with a 90° offset, such that the nano groove arrays were perpendicular to each other. The substrates were pressed together with 1 psi of pressure and hardbaked at 160°C for at least 12 hours. This completed the crosslinking process and the fusion of the two layers of SU8. Using a micropipetter, 10 μL of the LC were wicked into the cavity while in the isotropic state with the cell heated to 40°C. The filled cells were then cooled to room temperature before measurement and assumed a twisted configuration as shown in Fig. 3. The LC used in these studies was the commercially available 5CB, whose elastic constants are: K11 = 6 pN, K22 = 4.5 pN, K33 = 9.9 pN [21].
Fig. 3: Representation of a twisted nematic liquid crystal cell. The LC molecules twist between two substrates with perpendicular anchoring layers, which are represented by the red lines.
2.2. Measurement of anchoring energy
The twisted nematic LC cell, prepared as described above was used to measure the twist angle, and the twist angle was used in turn to determine the azimuthal anchoring energy via Eq. (3):
where K22 is the twist elastic constant of the LC molecules, d is the thickness of the cell, θ is the twist angle, and θd is the “design” twist angle which is the rotation between the preferred alignment direction on each substrate [22, 23]. In our setup, θd = 90°. To measure the twist angle, each LC cell was placed between two linear polarizers whose relative angles of rotation are varied at multiple wavelengths. At the wavelength corresponding to the local adiabatic condition, the maximum transmission through the LC cell and the two polarizers is obtained at a fixed relative angle, i.e., the angle between the polarizer and the analyzer is independent of their orientation with respect to the LC director. It can be shown [22] that this adiabatic condition exists when the twist angle θ is balanced by the accumulated phase change along the cell length, so that: where γ is the intensity of the light transmitted through the liquid crystal cell, β = πdΔn/λ, d is the thickness of the cell, Δn is the birefringence of the liquid crystal at a given wavelength λ, and m is an integer. Figure 4 shows two traces of analyzer angle vs. polarizer angle at maximum transmission. At 440 nm, the LC cell is at its adiabatic point, while at 460 nm it is not, as evidenced by the linear and oscillatory curves, respectively. These results were obtained with nanogrooves where the pitch was 100 nm and the depth was 18 nm. For each set of nanogrooves, the wavelength corresponding to the respective adiabatic point was obtained. The corresponding twist angle was then calculated using Eq. (4). For a given input polarization, the analyzer is rotated to find the maximum transmission at a particular test wavelength. The difference in angle between the polarizer and analyzer at maximum transmission is equal to the twist angle when adiabatic condition is satisfied.Fig. 4: Analyzer angle required to achieve the maximum transmission versus the polarizer angle, on and off the local adiabatic point.
3. Results and discussion
The azimuthal anchoring energy for the nanogrooves at different pitches and depths was calculated using Eq. (3), and the results are plotted in Fig. 5. For our experiments, a K22 value of 4.5 pN and d = 1.5 μm were used in Eqs. (3) and (4). Because of the functional dependence of the anchoring energy on the twist angle θ, for higher azimuthal anchoring energies θ approaches 90°, which also increases the uncertainty in the measurements. Indeed, this is observed in Fig. 5, which plots the data on a linear scale. It should be noted that Eq. (3) predicts that the fractional uncertainty is approximately constant, as evidenced by our data. The theoretical prediction for the azimuthal anchoring energy is also shown in the plot, as calculated from Eq. (2), where one adjustable parameter was used to fit all the data, namely the polar anchoring energy. The value of Wp is unknown for the fused silica substrates; however, reported literature values for 5CB on similar glass surfaces range from 1 × 10−5 J/m2 ≤ Wp ≤ 1 × 10−3 J/m2 [24]. Using a standard least squares fit, Wp was found from the data in Fig. 5 to be 7.1 × 10−5 J/m2.
Fig. 5: Anchoring energies obtained with various groove depths and pitches, superimposed on the data is the anchoring energy predicted by Eq. (2) with Wp = 7.1 × 10−5J/m2
From Fig. 5, the absolute magnitude of anchoring energies measured experimentally, as well as the qualitative trends with nanogroove pitch and depth, are in good agreement with those predicted by theory. Furthermore, the quadratic dependence on groove depth is also confirmed quantitatively for all pitches, as shown in Fig. 6. Note, however, that unlike in Fig. 5, in Fig. 6 each set of grooves of a given pitch was fit with an independent polar anchoring energy. It is noteworthy, that the polar anchoring energies calculated in this fashion increase as the pitch is decreased: from 1.8 × 10−5 J/m2 at a 250 nm pitch, to 3.9 × 10−5 J/m2 at a 200 nm pitch to 1.9 × 10−4 J/m2 at a 150 nm pitch. This coupling between azimuthal and polar anchoring energies is in agreement with previous experiments reported in the literature [25], and modeling work shows that higher azimuthal anchoring energies can increase the order parameter for LCs, which in turn increases the polar anchoring energy [26, 27, 28]. The results in Fig. 5 also show that when using one universal value of the polar anchoring energy, the quantitative dependence of the azimuthal energy on the pitch is significantly steeper than that predicted by Eq. (2). One reason for this discrepancy may be the increased deviation of the groove shapes from sinusoidal with decreasing pitch and increasing depth, due to the significant surface roughness of grooves produced in this manner, Fig. 2. Equation (2) applies to each Fourier component of the steeper-than-sinusoid profiles, and the cubic dependence on the higher spatial harmonics would cause a strong increase of the anchoring energy compared to the sinusoidal model.
Fig. 6: The anchoring energy is plotted versus the square of the groove depth. Each period is shown with the line for which Wp was optimized.
4. Conclusions
We have demonstrated that patterned nanogrooves using electron beam lithography can be used to control the magnitude of the azimuthal anchoring energy of liquid crystals, and that these amplitude variations can also be different for different spatial domains. Additionally, electron beam lithography offers the flexibility to pattern nanogrooves of various orientations on a single substrate, thus allowing for a wide range of alignment patterns. This approach provides a powerful method to engineer complex geometries of LC devices, thus enabling new applications of LCs.
Acknowledgments
The authors would like to thank Brian Kimball (NSRDEC) and Silvija Gradečak (MIT) for helpful discussions. This work was sponsored by the U. S. Army Natick Soldier Research Development and Engineering Center under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, recommendations and conclusions are those of the authors and are not necessarily endorsed by the United States Government.
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