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Abstract
A slim beam deflector that satisfies both a large steering angle and a large area can be very useful in various applications. However, a smaller electrode pitch for a large steering angle and enlargement of its area are trade-off relations due to the limited number of control channels in an electrically tunable beam deflector system. For a large steering angle in the active area where actual diffraction occurs, an indium tin oxide electrode of 2 µm pitch was implemented through a stepper lithography. The via-hole process was developed to expand the reduced active area due to the small electrode pitch. We developed a beam deflector with 7200 controllable channels in an active area of ${14.4}\;{\rm mm} \times 14.4\;{\rm mm}$. The maximum steering angle is 7.643° at a wavelength of 532 nm.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. INTRODUCTION
Recently, beam deflectors have been researched and developed for an eye tracking system in holographic displays [1]. A slim beam deflector system can be applied to the compact eye tracking system and a liquid crystal (LC)-based non-mechanical-type beam deflector is a suitable candidate because it is much more flexible and requires less volume compared to the mechanical type [2–4]. The electrically tunable beam deflector using LC steers the incident beam at a desired angle by changing the refractive index of LC to form a phase profile [5]. A non-mechanical beam deflector based on LC could be categorized into two reflective and transmission types. Between them, it has been found that the reflective one has an advantage of a high fill factor with a small electrode pitch due to the availability of silicon substrates for the application of a spatial light modulator [6]. However, a long optical path is required to apply the reflected light to the system, and it is a fatal disadvantage in terms of a slim form factor. For this reason, a transmission-type beam deflector with an indium tin oxide (ITO) electrode on a glass substrate is suitable for making compact devices [7,8].
The main role of the beam deflector in the eye tracking is to steer the image into the viewer’s eyes, and a grating pattern with small pitch is required for a large steering angle. The area where incident light actually diffracts through a beam deflector is called the active area. It is essential to develop a large active area with a large steering angle for the eye tracking system in holographic displays. However, increasing the active area and the beam steering angle are in a trade-off relationship with each other because the total active area must be decreased as the electrode pitch decreases within the same controllable channels in the driver module. To solve this problem, we introduced and developed various methods in the fabrication process. First of all, a stepper (step and repeat projector) lithography for reducing the pitch of the electrode pattern is introduced to realize a small ITO electrode in the active area. By introducing the via-hole process, the size of a unit bank derived from the existing ITO electrodes with small pitch was increased 10 times. A pad area, molybdenum (Mo) electrodes for connecting driving channels to each ITO electrode in the active area, has a relatively large electrode pitch and a large area compared to the active area. A mask aligner lithography was applied to cover a large area, and a mix-and-match process was also developed to connect the ITO and Mo electrode patterns created by the stepper and the mask aligner lithography.
The main purpose of this study is to develop a large-area transmission-type beam deflector based on LCs at a large steering angle. The driving module is also developed to steer the incident beam in connection with the eye tracking system for the slim holographic display.
2. BEAM DEFLECTOR SYSTEM ARCHITECTURE
Figure 1 depicts the system architecture of a large-area transmission-type beam deflector. The beam deflector system plays an important role in steering the image to the viewer’s eyes based on the eye position provided by the eye-tracking sensor.
A. Beam Deflector Driver Module
A beam deflector driver module consists of three major parts: a control module, a driver board, and driver integrated circuits (ICs). The control module is used to modify the viewer’s eye positions using lookup tables based on the driving algorithm for the diffraction efficiency and the angular accuracy. After this modification, driving algorithm data is forwarded to the driver board through a high-speed application programming interface. The driving algorithm data from a control module is stored sequentially in a buffer of the driver board for a real-time undistorted image processing control, and it will be transferred to the following driver ICs. Each driver IC has 360 channels and a total of 720 channels from two driver ICs are embedded for individual channel activations.
The maximum output driving voltage per channel is $\pm10\;{\rm V} $, from 0 V to 20 V. Each channel of driver ICs transmits different voltages to the ITO electrodes on the lower glass substrate in accordance with data received from the driver board.
B. Liquid Crystals Blazed Grating in the Beam Deflector Cell
Figure 2 shows the concept of the beam deflector using LCs. A beam deflector cell consists of a bare ITO electrode on the upper glass substrate, high birefringence nematic LCs, and one-dimensional-patterned ITO electrodes on the lower glass substrate, as shown in Fig. 2(a). Each ITO electrode can be individually controlled according to the signal from the driver module, so the effective refractive index of LCs is changed across the neighboring electrodes. When an external voltage is applied to the upper and lower electrodes, the phase changes of LCs occur according to each ITO electrode and its position-dependent change of optical phase profile can be described by a sawtooth-like function, as shown in Fig. 2(a). It could deflect the incident lights optically like the prism [9–12].
Fig. 2. Concept of beam deflector: (a) the effective refractive index of the LC in the beam deflector cell, (b) continuous and wrapped phase.
The phase retardation, which is the relative change due to the propagation, through a beam deflector device was shown in Eq. (1) and larger than ${2}\pi$ phase modulation is required to satisfy the phase-matching condition, as shown in Fig. 2(b):
where $ \lambda $ is the wavelength of the light, and $ d $ is the height of the medium. Birefringence $\Delta n$ is given in Eq. (2): where $ \theta $ is the tilt angle of the optic axis of liquid crystal along with the $ x $ axis in Fig. 2(a). When the molecules are moving when the electric field is applied, its refractive index ${n_{\rm eff}}(\theta)$ varies with the optic axis of liquid crystal, as shown in Eq. (3):The birefringence is defined as the difference between the $ n_e $ and $ n_o $ of a fully oriented nematic phase propagating orthogonal and parallel to the optic axis, respectively. The maximum birefringence occurs when $\theta = 0^\circ$ in the absence of an applied external voltage whereas the minimum birefringence occurs when $\theta = 90^\circ$ in response to the maximum applied external voltage.
In order to secure a sufficiently large phase retardation, the typical methods are to increase the cell gap to secure a long optical path and to apply LC mixtures having a large refractive index. However, those methods have fundamental disadvantages. First of all, increasing the cell gap requires high driving voltage in addition to the driving speed being lowered. Also, most of the electric fields are generated to the neighboring electrodes in the lower substrate rather than upwards to the upper substrate at a long distance. In particular, this phenomenon becomes more prominent when the gap between the electrodes on the lower substrate is reduced due to a fine pattern. This phenomenon is called the fringing-field effect, which leads to a reduction in efficiency.
As a result, the method of wrapped phase as shown in Fig. 2(b) is a good solution for implementing a large diffraction angle with maintaining the minimum cell gap of ${2}\pi$ phase modulation. An absolute value of phase modulation can be wrapped into the interval $[{0},{2}\pi\!]$ or $[- \pi ,\pi\!]$, which produces a plot with a phase jump of ${\sim}2\pi$. The method of wrapped phase does not affect the actual value of phase modulation, since phase is a relative quantity. For this reason, when removing discontinuities from the wrapped phase at every ${2}\pi$, the wrapped phase is equivalent identically to the original unwrapped phase.
The total channel number for a unit prism $ n $ is defined in Eq. (4):
where the total channel number, $ m $, is decided as 720 according to the number of driver ICs and $ i $ is defined as the total number of unit prisms. Obviously, the minimum of 2 and the maximum of 720 channels are required to make a unit prism.The maximum and the minimum steering angles are determined by the channel number of prisms and the electrode pitch relatively. Steering angle $ \theta $ can be derived in Eq. (5):
where $ \lambda $ is the wavelength of the light, and the electrode pitch is $ p $. When the wavelength of the light and the electrode pitch are fixed, the steering angle is determined by modulating the number of prisms using the driving module system which could be capable of independent driving channel. In Eq. (5), the maximum steering angle ${\theta _{{\max }}}$ is 7.643° at the wavelength of 532 nm when the total number of unit prisms, $ i $, is 360 and the electrode pitch, $ p $, is 2 µm. On the other hand, the smallest angle, which could be also called angular resolution, is 0.021° when the total number of unit prisms, $ i $, is 1.A continuous beam deflector also needs fast operating materials, which can be ensured by the high birefringence LCs with low viscosity, in combination with a small cell gap. A high birefringence of LC material, $\Delta {n} = 0.32$, was developed to secure the 2$ \pi $ phase modulation within a minimal cell gap. The details of LC parameters are shown in Table 1. The maximum phase delay at the wavelength of 532 nm is 2.91$ \pi $ in Eq. (1) when the cell gap is set to 2.5 µm, and this value allows a margin of the effects of the anchoring forces near the substrate.
Table 1. Material Parameters of Nematic Liquid Crystal Mixture, at Room Temperature
C. Design of the Beam Deflector Cell
A small electrode pitch creates a large diffraction angle, and thereby increases the viewing angle. The typical lithographic equipment, a mask aligner and a stepper, are used to transfer electrode patterns onto a substrate and perform alignment and exposure of wafers. In the case of the mask aligner equipment, the feature to be formed on the wafer is the same as the mask size, whereas a stepper equipment is used to increase the resolution of a mask (a so-called reticle). There are hard and soft contact modes within a mask aligner lithography, and the hard contact mode is used to achieve a good physical contact. This enables critical dimension down to 3 µm. In our previous work, patterned-ITO electrodes with a pitch of 6 µm (3 µm electrode width and 3 µm spacing) were fabricated by using a contact aligner [13]. In contrast to the mask aligner, a stepper’s reticle does not make contact with the wafer, but rather the light is focused by the use of projection optics. The development of lithography fabrication with a stepper equipment makes the critical dimension down to 0.5 µm for realizing a 2 µm electrode pitch (1.5 µm electrode width, 0.5 µm spacing) with patterned-ITO electrodes by the NSR-2205i12D Model, i-Line stepper, with 5∶1 reduction magnification an exposure area is 22 mm square [${17.96}\,({H})\;{\rm mm} \times 25.2\,({V})\;{\rm mm}$].
In order to determine the proper linewidth of the electrode and its gap at a pitch of 2 µm, it is required to simulate the effect of the fill factor of an ITO electrode. To simplify the simulation, one-dimensional Fraunhofer wave propagation was used, while no fringe field is assumed which means the electric field exists only on the area of electrodes and the electric flux is normal to each electrode surface. The simulated complex profiles are a combination of the following phase and amplitude profiles in Fig. 3.
Fig. 3. Simulated (a)–(c) phase profiles, (d)–(f) amplitude profiles. (a) $\varphi (x){|_{\theta = \frac{{{\theta _{{\max}}}}}{4}}}$, (b) $\varphi (x){|_{\theta = \frac{{{\theta _{{\max}}}}}{2}}}$, (c) $\varphi (x){|_{\theta = {\theta _{{\max}}}}}$, (d) $a(x){|_{f = 100\%}}$, (e) $a(x){|_{f = 50\%}}$, and (f) $a(x){|_{f = 25\%}}$.
One-dimensional Fraunhofer diffraction is used to calculate the diffraction efficiency in Eq. (6):
The simulation results on the diffraction efficiencies versus diffraction angles are plotted in Fig. 4 for various fill factors of an ITO electrode. The definition of the fill factor is the portion occupied by the width of the electrode excluding the gap in the overall pitch. For example, when the width of the electrode is 1.5 µm and the gap is 0.5 µm at a pitch of 2 µm, the fill factor is 0.75. When the widths of an electrode are 2, 1.5, 1, and 0.5 µm at a pitch of 2 µm, the fill factors are 100%, 75%, 50%, and 25%, respectively. The result clearly shows that the larger fill factor leads to the higher diffraction efficiency. This is because an increase in the amount of phase profile caused by the electric field from ITO electrodes gives rise to an increase in the diffraction efficiency.
Fig. 4. Simulation results of the diffraction efficiency as a function of diffraction angle according to the fill factor of an ITO electrode.
Although the diffraction efficiency is almost perfect when the optical fill factor is as high as 100%, it is not possible in practical device fabrication or in driving. For this reason, the maximum fill factor of 75% is selected for an ITO electrode which corresponds to a linewidth of the electrode of 1.5 µm and 0.5 µm spacing.
In order to fabricate the transmission-type beam deflector cell, electrode patterns for an LC-based blazed grating is fabricated with a transparent ITO on the lower glass substrate. For the large steering angle, it is designed and fabricated with a fine pattern of 2 µm electrode pitch. The cross-section image of the ITO pattern on the lower glass substrate is captured by scanning electron microscopy in Fig. 5(a) and the ITO electrode grating of the beam deflector cell is shown in Fig. 5(b).
Fig. 5. (a) Scanning electron microscope (SEM) image of ITO electrodes on a glass substrate; (b) structure of a transparent ITO electrode grating.
Due to the total number of independent driving channels limited to 720 and the 2 µm electrode pitch corresponding to each channel, the active area can only be made into a small area of ${1.4}\;{\rm mm} \times 1.4\;{\rm mm}$. Such a small electrode pitch can be integrated into an embedded system; however, the active area also decreases in direct proportion to the electrode pitch. Figure 6 shows that the architecture of the beam deflector cell and the via-hole process is introduced to repeat the unit block of the active area to overcome the conflicting between the maximum beam steering angle with small electrode pitch and large active area.
A total of 720 electrodes associated with two driver ICs are grouped into a unit bank. The unit bank is repeated 10 times by the process of via-hole in the stepper lithography, resulting in a final active area of ${14.4}\;{\rm mm}\times 14.4\;{\rm mm}$ with 7200 channels. To give a specific input value to the channel in the same order of each bank, it is necessary to physically connect the channels in the same order. Through the via-hole process, the 720 channels in the same order of each bank are electrically connected and this enables controlling all the input values of the 10 times repeated unit bank.
Finally, it is possible to control 7200 electrodes corresponding to a large active area of ${14.4}\;{\rm mm} \times 14.4\;{\rm mm}$ while maintaining the ITO pattern of 2 µm and a driving board with 720 channels. An advanced driving algorithm was developed to control the whole channels without any stripe noise by using the via-hole process [14].
A stepper lithography has one of the main roles in microfabrication for the submicrometer electrode pattern but faced problems of a limited die size compared to the mask aligner lithography. Except for the active area that requires a fine pattern, it is better to apply the mask aligner lithography for the pad area due to its relatively large pattern size and a large area. The so-called mix-and-match process refers to a mix process for exchanging and a match process for connecting electrode patterns fabricated by the stepper lithography and the mask aligner lithography. The overlapping of the patterns created using two different fabrication processes was captured using a microscope. As shown in Fig. 7, the ITO electrode patterns in the upper active area and the Mo electrode patterns in the lower pad area are well aligned. The upper and lower electrode pitches are both equal to 20 µm; the upper ITO electrode pitch is the same as that of a 2 µm micropattern described in Fig. 6 with 10 unit banks and the lower Mo electrode was designed accordingly.
Fig. 7. Layout of the beam deflector cell and the optical microscope image of the line connection between the active area and pad area.
D. Fabrication Process of the Beam Deflector Cell
Figure 8 shows the whole process of a stepper and a mask aligner lithography on the lower glass substrate, including the multilayer and via-hole process for the fine-patterned-ITO electrode in the active area and patterned-Mo electrode in the pad area for input signal.
Fig. 8. Process of photolithography to form the lower substrate of the beam deflector. (a) Align key (stepper); (b) signal line in the main area (stepper); (c) signal line in the pad area (aligner); (d) VIA in the main area (stepper); (e) contact in the main area (stepper); and (f) pad open in the I/O area (aligner).
First of all, Mo is deposited and etched to make an align key for adjustment of the mask in the stepper lithography in Fig. 8(a). Silicon dioxide for a passivation layer and ITO for electrodes in the active area are then deposited by chemical vapor deposition and sputtering, respectively, on the lower glass substrate in Fig. 8(b).
A mask for fine patterns of a 2 µm electrode pitch is applied to the specific area for a large steering angle. The critical dimension of the stepper lithography is 0.5 µm, and the line space was removed by dry etching. Moving to the mask aligner lithography, a signal line for the pad is pattered for connection to the driving channels of driver ICs in Fig. 8(c).
The process of via-hole is developed and optimized to connect 720 channels in the same order of each bank in Fig. 8(d). The size of via-hole is defined as ${1}\;\unicode{x00B5}{\rm m} \times 1\;\unicode{x00B5}{\rm m}$ in consideration of the process condition and resistance for driving capability of a driver module. Finally, the channels in the same orders could be connected by the process of contact with Mo in Fig. 8(e). Finally, a pad open process is carried out to apply an external signal through the flexible printed circuits board (FPCB) in Fig. 8(f). Chip on film driver ICs were connected to this Mo pad on the lower glass substrate by using the anisotropic conductive film bonding.
The actual beam deflector cell is shown in Fig. 9. The square in the upper middle is the active area that LCs are filled for changing optical phase profile, where ITO electrodes with 2 µm pitch are patterned for large steering angle. In addition, Mo electrodes for connecting the signal coming from the driver board to the ITO electrodes in the active area are patterned below the active area. Finally, there are two driver IC connection pads with 360 channels each in the bottom area and they are connected through the FPCB.
3. EXPERIMENTS
Figure 10 shows the phase retardation according to the variable applied voltages to the beam deflector cell. Driving voltages applying to ITO electrodes on the lower glass substrate are from 0 V to 20 V; a negative and a positive gamma could be defined from 0 V to 10 V and from 10 V to 20 V, respectively, when a common voltage of 10 V is applied to the bare ITO electrode on the upper glass substrate.
Fig. 10. Experimentally measured phase retardation as a function of the applied voltages in the beam deflector cell.
Figure 11 depicts the diffraction efficiency of our LC beam deflector where a linearly polarized beam from a laser at a wavelength of 532 nm. This means that the beam deflector exhibits a polarization-dependent response, and a linearly polarized plane wave should be aligned with the optical axis of the liquid crystal.
Fig. 11. Experimentally measured diffraction efficiency of a LC beam deflector as a function of the diffraction angles.
The diffraction efficiency of the beam deflector can be defined and measured as the ratio of ${{ I }_{{\rm str}}}/\!{{I}_{{\rm off}}}$, where ${{ I }_{{\rm str}}}$ is the intensity of the steered beam and ${{ I }_{{\rm off}}}$ is the intensity of the non-steered beam at 0th order. The diffraction efficiency starting at 100% decreases gradually as the diffraction angle increases and becomes 12% at the maximum diffraction angle of angle 7.643° at the wavelength of 532 nm. The difference between the diffraction efficiency calculated through the simulation shown in Fig. 4 and the measured diffraction efficiency shown below is because the correlations between the quantization error and the fringe effect in real LC behavior are reflected in experimentally measured diffraction efficiency.
Figure 12 shows the picture taken at a distance of 1 m when the incident beam is steered 2° and the maximum 7.643°. As mentioned earlier, it is clearly seen that the light intensity is weakened at the maximum angle compared to the smaller angle since the diffraction efficiency is decreased.
Fig. 12. Captured images of the steered beam: (a) steering angle of 2°, (b) the maximum steering angle of 7.643°.
4. CONCLUSION
In this paper, a large-area transmission-type beam deflector with large diffraction angle is proposed based on the development of a new architecture. To solve the issues of trade-off relation between a large beam steering angle and a large active area within the limited number of driving channels, the process of via-hole is developed to enlarge the total active area to ${14.4}\;{\rm mm} \times 14.4\;{\rm mm}$ while maintaining a 2 µm electrode pitch from the use of stepper lithography. The driver module is also designed and implemented to steer the beam to the desired angle in real time. It is demonstrated that a large incident beam could be deflected to the maximum steering angle of $\pm7.643^\circ$ at the wavelength of 532 nm.
The further study is being conducted to increase the driving speed and diffraction efficiency of the beam deflector system for the advanced eye tracking system which could be applied to slim holographic display systems.
Disclosures
The authors declare no conflicts of interest.
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