Large-scale single-crystal blue phase through holography lithography

Abstract. The blue phase, which emerges between cholesteric and isotropic phases within a three-dimensional periodical superstructure, is of great significance in display and photonic applications. The crystalline orientation plays an important role in the macroscopic performance of the blue phase, where the single crystal shows higher uniformity over the polydomain and monodomain, resulting in higher Bragg reflection intensity, lower hysteresis, and lower driving voltage. However, currently reported methods of forming a single-crystal blue phase based on thermal controlling or e-beam lithography are quite time-consuming or expensive for large-scale fabrication, especially in the centimeter range, thus hindering the broad practical applications of single-crystal blue-phase-based photonic devices. Herein, a strategy to fabricate a large scale single crystalline blue-phase domain using holography lithography is proposed. Defect-free single-crystal domains both in blue phase I and blue phase II with a desired orientation of over 1  cm2 are fabricated based on a nanopatterned grating with periodic homeotropic and degenerate parallel anchoring, with colors from red and green to blue. This holography lithography-assisted strategy for fabrication of a large-scale single-crystal blue phase provides a time-saving and low-cost method for a defect-free single crystalline structure, leading to broad applications in liquid crystal displays, laser devices, adaptive optics elements, and electro-optical devices.


Introduction
The blue phase (BP), existing between the cholesteric phase and isotropic phase (ISO) of liquid crystals within a threedimensional periodical superstructure, possesses three forms of blue phase I (BP I), blue phase II (BP II), and blue phase III (BP III). 1,2 BP III possesses a noncrystalline symmetry with disordered structure, and BP I and BP II exhibit body-centered cubic structure and simple cubic structure, respectively, with a double-twisted cylinder nanostructure. [3][4][5][6] The narrowed temperature range and nonuniformity of the crystalline structure are two important issues that hinder the practical applications of blue phase liquid crystal (BPLC). On one hand, the temperature range of the BP has been extended by polymerization 7,8 or nanoparticle doping, 9,10 leading to useful applications such as displays, [11][12][13][14] lasers, [15][16][17] sensors, [18][19][20] and photonic devices. [21][22][23][24] On the other hand, the crystalline orientation plays an important role in the macroscopic performance of the blue phase, where the single crystal shows higher uniformity over the polydomain and monodomain, resulting in higher Bragg reflection intensity, lower hysteresis, and lower driving voltage. Usually, the BP fragments form inside the volume simultaneously as a phase transition occurs, leading to polydomain BP structures, which consist of many platelets of different orientations. The mismatches in polydomain BPs increase the scattering in the volume and affect the reflectivity of the Bragg reflection and the optical-electrical properties of BPs. [25][26][27][28][29] Recent studies indicate that several methods, such as electric fields, [30][31][32] thermal control, 33 and surface treatments [34][35][36] can be applied to form monodomain BPs, which consist of many single-crystal platelets with one lattice plane orientated in the same direction. The structures of monodomain BPs significantly increase the reflectivity of the Bragg reflection. However, many defects still exist between the separated platelets with a grain boundary. Therefore, to further improve the optical performance of BPs, it is highly desirable to develop methods of fabricating ideal, single-crystal BPs.
Several methods have been proposed to generate a single crystal blue phase. Chen et al. 37 reported the fabrication of an extraordinarily large single-crystal BP I by controlling the selfassembly processes of BPLC. The gradient-temperature technique enables growth of a single crystalline BP with the size of 1 cm 2 . However, long periods of thermal control over several days were required, which leads to low efficiency in fabrication, and the crystal orientation of the BP could not be controlled due to the similar treatment of the substrate compared to traditional BPs. de Pablo et al. proposed a method to form a single crystalline BP II through a nanopatterned surface with binary homeotropic/planar anchoring through e-beam lithography. [38][39][40][41][42] This method is capable of generating a single-crystal BP over a macroscopic region (at a scale of mm 2 ) with designed crystallographic plane orientation based on the simulation of free energy from Landau-de Gennes theory (see Supplementary Material). However, the fabrication is highly dependent on the nanopattern fabricated by e-beam lithography, which is time-consuming and expensive, thus hindering the practical application of singlecrystal BP photonic devices. Therefore, a time-saving and lowcost method, rather than e-beam lithography, to fabricate the nanopattern at a larger scale for large-scale single-crystal BPs is highly desirable.
In this paper, a strategy to fabricate large scale single crystalline BP liquid crystals is demonstrated through holography lithography. Defect-free single-crystal domains both in BP I and BP II with a desired orientation of over 1 cm 2 are fabricated based on a nanopatterned grating with periodic homeotropic and degenerate parallel anchoring. A large-scale single-crystal BP with reflection colors from red and green to blue are realized while varying the pitch of the nanopattern grating from 230 and 190 nm to 170 nm, along with a high reflectance of 44% and 45% to 42% and a narrow bandwidth of 19.0 and 17.0 nm to 14.6 nm, respectively. This holography lithography-assisted strategy for fabrication of a large-scale single-crystal BP provides a time-saving and low-cost method for a defect-free single-crystalline structure that significantly improves the property of the BP, including an increase in the intensity of the Bragg reflection, leading to broad applications such as liquid crystal displays, laser devices, adaptive optics elements, and electrooptical devices.

Results and Discussion
In our experiments, both BP I [with body-center cubic lattice structure, Fig. 1(a)] and BP II (with simple cubic lattice structure, Fig. 1(b)] are investigated. The wavelength of reflected light from the BP is determined by λ ¼ 2n eff a∕ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; n o and n e are the ordinary and extraordinary refractive indices of liquid crystal materials), a is the lattice constant of crystal, and h; k; l are the Miller indices. 1 The BP crystallographic planes are denoted by (hkl), and BP ðhklÞ represents a BP with orientation of the (hkl) plane parallel to the surface.
The anchoring pattern of the substrate is designed based on the morphology of the orientating lattice plane on the surface.  substrate surface and the director of the LC molecule). This region will be treated to be a homotropic surface anchored in a simplified alignment model. The rest of the region represents the defect structure in the crystal lattice, which can be seen as isotropic materials. The pitch along two orthogonal directions is represented by ffiffi ffi 2 p a BPI , and a BPI , where a BPI is the lattice constant of BP I, leading to an effective period of grating formed by the region of blue ellipses to be d BPI ¼ ffiffiffiffiffiffiffi ffi 2∕3 p a BPI . This region will be treated as a degenerate parallel surface anchored in a simplified alignment model. Figure 1(d) shows the morphology of BP II ð100Þ , which is similar to BP I. The region of the blue rectangle with an oblique line represents the long-axis cutting section of the double-twist cylinder, where the LC molecules orient from 0 deg to 45 deg (the angles between the substrate surface and the director of LC molecule). Both the blue rectangle and the rest of the region will be treated as a degenerate parallel surface anchored in a simplified alignment model. The effective period of grating formed by the region of blue circles and the rest is The single crystalline BPs are mediated by the strain induced by the corresponding patterned anchoring conditions with the lower free energy. The grating pattern consists of homeotropic anchoring and degenerate parallel anchoring, resulting from boundary molecular distribution, which successfully induced the formation of single crystalline BPs. 38,39 Figures 1(e) and 1(f) demonstrate the reduced morphology of BP I ð110Þ and BP II ð100Þ planes at the boundary of the crystal lattice with l c ¼ 0, where the blue region represents the homeotropic surface anchoring and the rest, the yellow region, represents degenerate parallel surface anchoring. The reduced morphology of surface anchoring can be further simplified to a grating in both cases, and the duty ratio is defined as d 1 ∶d 2 , where d 1 and d 2 are the corresponding widths of the region with the blue part and the region without the blue part, respectively. The duty ratios are around 0.7: respectively. However, the fabrication process of the duty ratio (0.7:1.3) is much more difficult. Therefore, we try to use a grating with a duty ratio of 1:1 to replace the duty ratio of 0.7:1.3, which shows good and acceptable results in the following experiments. Figures 1(g) and 1(h) demonstrate the simplified grating deduced from Figs. 1(e) and 1(f), respectively. To reduce the difficulty of fabrication, the duty ratio of grating is chosen to be 1:1 in both cases. This simplification process proved to be effective and efficient, leading to a single crystal forming in both the BP I ð110Þ and BP II ð100Þ planes.
In our experiment, two-beam holography lithography was applied to generate the grating on a large scale. Figure 2(a) depicts the schematic illustration of the fabrication process, where a linearly polarized laser beam (the polarization direction is perpendicular to the plane of the optical table) with a wavelength of 325 nm splits into two beams by passing through a beam splitter, and there is interference at the surface of substrate coated with homeotropic alignment material (OTE) and photoresist. For two-beam holography lithography, the obtained interference light field is a grating. The pitch of the formed grating is determined by the formula of 2d sin θ ¼ λ, where d is the pitch of the grating, λ is the wavelength of the laser, and the interference angle θ is half the angle between two interference beams.
The parameters of BP samples (S1, S2, and S3) used in our experiment are shown in Table 1. The data indicate the process of phase transitions and the corresponding information between substrates and lattice parameters; for example, Iso-BP I means this sample is started from an isotropic phase and stabilized at BP I through cooling. Once the pitch is fixed, the corresponding interference angle, lattice constant, and chiral dopant concentration can be calculated. In our experiments, three pitches of grating were chosen to be 230, 190, and 170 nm, and the calculated interference angle θ should be 45.0 deg, 58.8 deg, and 72.9 deg, respectively. The corresponding lattice constant a is calculated The pattern of the grating received by the positive photoresist where the bright region in the light field forming the grating will be developed and removed, while the dark region in the light field forming the grating will be retained for the next developing step [ Fig. 2(b)]. After developing, the O 2 plasma etching was applied [ Fig. 2(c)], where the OTE covered with photoresist (yellow) was kept from etching by O 2 plasma and while the OTE part uncovered with photoresist was etched. After stripping of the photoresist, a grating consisting of the region with OTE (which would lead to perpendicular alignment of the LC) and the region without OTE (which would lead to degenerate parallel alignment of the LC) on substrate were fabricated, as shown in Fig. 2(d). Figure 2(e) shows the orientation of liquid crystal molecules induced by the surface anchoring of the patterned substrate. The patterned homeotropic and degenerate parallel anchoring of the substrate induces periodic orientation of liquid crystal molecules on the patterned substrate and leads to uniform formation of BPs with a cubic structure. The cell with a grating pattern was made up of a bare glass and a glass with grating-patterned OTE, and 5 μm spacers were used to define the cell thickness.
The phase transitions among isotropic phase, BP I, and BP II can be categorized as isotropic phase BP I, BP II-BP I, and isotropic phase BP II during the temperature decrease process. Figures 3(a)-3(c) show the polarization optical microscopy (POM) images of sample S1 in BP I (cooling from isotropic phase at 89.5°C to BP I at 85.7°C with a rate of 0.1°C/min) at the homeotropic, parallel, or grating-patterned alignment of the substrate, leading to polydomain, monodomain, and a single crystal, respectively. Figures 3(d)-3(f) show the POM images of sample S2 in BP I (cooling from isotropic phase at 88.8°C to BP II at 86.3°C and then to BP I at 84.9°C with rate of 0.1°C/min) at homeotropic, parallel, or grating-patterned alignment of the substrate, leading to polydomain, monodomain, and a single crystal, respectively.  Fig. 4(e), which derives from diffractive limitation. The lattice constant of sample S1 is larger than S2 within diffractive limitation; therefore, more Kossel lines can be seen. The Kossel diagrams with distinct Kossel lines indicate a uniform orientation. The Bragg reflection spectra of S1, S2, and S3 are shown in Figs. 4(g)-4(i), respectively. The single-crystal BPs of samples S1, S2, and S3 possess high reflectance of 44%, 45%, and 42% (the theory limitation is 50% due to the circularly polarized light of reflection) at central wavelengths of 648, 540, and 512 nm, and narrow bandwidths of 19.0, 17.0, and 14.6 nm, respectively. According to the relationship of the grating period and the lattice constant for BP I and BP II (d BPI ¼ ffiffiffiffiffiffiffi ffi 2∕3 p a BPI , and d BPII ¼ a BPII ), the calculated lattice constants of induced single-crystal BPs are a BPIðS1Þ ¼ 283.6 nm, a BPIðS2Þ ¼ 233.3 nm, and a BPIIðS2Þ ¼ 170.9 nm, respectively. Compared to the measured lattice constants (λ ¼ 2n eff a∕ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h 2 þ k 2 þ l 2 p ) of 289.3, 241.3, and 161.6 nm, the deviation values between the calculated and measured values of lattice constants Δa are 5.7, 8.0, and 9.3 nm, respectively, which are quite small compared to those previously reported in Ref. 38. The parameters including pitch, calculated and measured lattices, and the deviation values for samples S1-S3 are shown in Table 2.
The reflection spectra and POM textures of BPs are valid proof to differentiate polydomain, monodomain, and single- crystal BPs, as shown in Fig. S3 in the Supplementary Material. The polydomain BPs are easy to differentiate. The spectra of monodomain and single-crystal BPs are quite similar, which makes them difficult to distinguish. Monodomain BPs are formed with pieces of single crystals with the same orientationand show similar Bragg structure colors. The defects and mismatches of angles between pieces of crystalline structures exist in monodomain BPs, while single-crystal BPs exhibit perfect morphology in the POM texture. Figures 5(a)-5(c) show the photo images of fabricated singlecrystal BPs S1, S2, and S3 with a large scale of over 1 cm 2 in red, green, and blue, respectively. In principle, the fabrication size can be further increased by using a larger diameter of laser beam with higher laser power. The large scale of single-crystal BPs based on holography lithography induced grating pattern of the substrate enables defect-free crystalline structures, leading to potential applications in displays, lasers, and electrooptical devices.

Conclusion
We demonstrated a strategy to fabricate a large-scale single crystalline BP through holography lithography. Defect-free single crystals both in BP I and BP II with size over 1 cm 2 are fabricated based on a nanopatterned grating with periodic homeotropic and degenerate parallel anchoring. The grating pattern consisting of homeotropic anchoring and degenerate parallel anchoring resulting from boundary molecular distribution successfully induced the formation of a single crystalline blue phase. A single-crystal BP in BP I ð110Þ , BP I ð110Þ , and BP II ð100Þ planes with reflection color from red and green to blue are realized while varying the pitch of the nanopattern grating from 230 and 190 nm to 170 nm, with a high reflectance of 44% and 45% to 42% at the central wavelengths of 648 and 540 to 512 nm, and narrow bandwidths of 19.0 and 17.0 nm to 14.6 nm, respectively. This holography lithography-assisted strategy for fabrication of a large-scale single-crystal BP provides a time-saving and low-cost method for formation of a defect-free single crystalline structure, leading to broad applications in liquid crystal displays, laser devices, adaptive optics elements, and electro-optical devices.

Fabrication Process
Liquid crystal mixtures preparation: The nematic liquid crystal HTG135200-100 and chiral dopant R5011 were mixed together, stirred at the isotropic phase, and cooled down to the BP.
Substrates preparation: First, the OTE film was developed on the substrates. The substrate glass was cleaned by sonication in (f) POM image of single crystalline BP II formed by S3. Inset: Kossel diagram of BP II ð100Þ . The reflection spectra of (g) S1, (h) S2, and (i) S3. To remove excess silane aggregates in the solution, the samples were stirred in a toluene bath and rinsed with deionized water several times. Then they were blown dry with nitrogen and allowed to cure for 2 h at 150°C in a vacuum oven. After development with OTE, the substrates were spin-coated with photoresist mr-P 1202LIL (4000 r, 30 s) and baked at 100°C for 60 s, and then exposed under two-beam interference for 30 s to get the structure of the grating. A 325 nm He-Cd laser was used as the interference light source. The substrate was developed in developer mr-D 374 for 25 s. The resulting grating pattern was transformed onto the OTE film layer by exposing the sample to oxygen plasma (50 W, 60 s), followed by stripping the photoresist in stripper mr-Rem 660 for 1 min. The cell with the grating pattern was made up of a bare glass and a glass with grating-patterned OTE, and 5 μm spacers were used to define the cell thickness. A liquid crystal mixture was injected into the cell through capillary action. The cell was heated until the mixtures were at the isotropic phase, and then slowly cooled down by 0.1°C per minute until the single crystalline BP was fully formed in the cell.
The cell with homeotropic alignment was made up of a bare glass and a glass coated with OTE, which was an intermediate product in substrate preparation before photolithography.
The cell with parallel alignment was made up of a bare glass and a glass coated with PI. The PI-coated glass was rubbed with fabric beforehand to induce parallel alignment.

Measurements
Optical characterization was performed by using the crosspolarized and reflective mode of the microscope (ECLIPSE Ci POL, Nikon) with a 10× objective. Samples were heated up and cooled down by using a temperature controller hot stage (TS62, INSTEC). Visible spectra of BPs were obtained by spectrometer (USB2000+, Ocean Optics). The He-Cd laser (IK3151R-E, KIMMON) was used to generate two-beam interference. The laser power was 10 mW, and the beam diameter of laser beam was 2 cm.