Fringing Field Effect of the Liquid-Crystal-on-Silicon Devices

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1 Jpn. J. Appl. Phys. Vol. 41 (22) pp Part 1, No. 7A, July 22 #22 The Japan Society of Applied Physics Fringing Field Effect of the Liquid-Crystal-on-Silicon Devices Kuan-Hsu FAN CHIANG, Shin-Tson WU 1 and Shu-Hsia CHEN Institute of Electro-Optical Engineering, National Chiao Tung University, 11 Ta Hsueh Road, Hsinchu 3, Taiwan, Republic of China 1 School of Optics/CREOL, University of Central Florida, Orlando, Florida 32816, U.S.A. (Received January 21, 22; accepted for publication April 11, 22) The fringing field has an important effect on the contrast ratio of liquid-crystal-on-silicon (LCOS) display devices. Computer simulation results of five commonly employed LC operating modes are compared: mixed-mode twisted nematic (MTN) cell, 45 twisted nematic cell, vertical alignment (VA) cell, film-compensated homogeneous cell, and fringe-field switching cell. The slope of the pixel electrodes is found to make an important contribution to the brightness and contrast ratio of each mode. Simulation results indicate that the VA mode has the best contrast ratio when all the pixels are on and off. However, the MTN cell shows the smallest fringing field effect when alternating pixels are switched on and off. [DOI: /JJAP ] KEYWORDS: liquid crystal display, fringe field effect, contrast ratio, sloped electrode, liquid crystal on silicon (LCOS) 1. Introduction Liquid-crystal-on-silicon (LCOS) has been used extensively for large screen projection and near-eye virtual projection displays. 1 3) The demand for ever-increasing resolution leads to smaller pixel sizes. Owing to the high mobility of the silicon wafer, pixel size as small as 8 1 microns has been demonstrated. However, several problems occur as the pixel size decreases. For example, the aperture ratio is decreased and the diffraction loss and fringe field are both increased. Maintaining high brightness and a high contrast ratio for a high-resolution LCOS projector is a challenging task. As the inter-pixel gap becomes comparable to the LC cell gap, the fringe field between the voltage-on and the adjacent voltage-off pixels produces disclination lines. These disclination lines affect the electro optic properties of the cell and reduce the contrast ratio and display brightness. Sloped electrodes have been proposed to minimize the fringe field effect of the LCOS devices. 4) In this study, we analyze how the sloped electrodes affect the contrast ratio of four commonly used LC operating modes: vertical alignment (VA), 5,6) 45 -twisted nematic (TN) cell, 7) 8 and 9 mixed-mode TN (MTN) cell, 8,9) and film-compensated homogenous cell. 1) The fringe-field-switching (FFS) mode 11) which exhibits wide viewing angles for transmissive display is also included for comparison. 2. Cell Structure and Simulation Method Figure 1 shows the cross section of the LC cell structure used for calculating LC director distributions and light efficiency. To make a fair comparison, the pixel size is assumed to be 15 m which corresponds to the SGA 2 m LC layer Al Electrode Glass 15 m ITO layer Fig. 1. LC cell structure used for computer simulations. Cell gap is 2 m, and pixel size and inter-pixel gap are 15 m and 1 m, respectively. Thickness of Al electrodes is.3 m, and electrode slopes are varied from.3 to infinity. ( ) resolution in a.95-inch panel. The pixel gap and the cell gap are assumed to be 1 and 2 m, respectively. We adjust the LC birefringence to obtain the required dn value for each mode. We also vary the slope of the electrode edges as shown in Fig. 1 in order to minimize the fringing field effect. For a rectangular electrode, its slope is infinity. Our simulations are based on the Frank s continuum theory 12) and use the finite element method to calculate the LC directors profiles. Once the LC directors are obtained, we use the 2 2 Jones matrix to calculate the voltagedependent reflectance. Under the crossed-polarizer configuration, the normalized reflectance R? of a LCOS device can be described by the following Jones matrices as R? ¼jMj 2 : 13,14) M ¼½cos 2 sin Š6 4 2 cos i sin sin cos i sin 2 sin sin cos þ i 2 sin sin 3 cos þ i 7 sin 5 zfflffl} fflffl{ 2 3 " # N 1matrices 7 5 zfflffl} fflffl{ sin cos N 1matrices ð2:1þ simonf.eo89g@nctu.edu.tw 4577

2 4578 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al (a) Calculated reflectance with sharp electrode for 8 -MTN mode. 1. (c) Calculated reflectance with slope=1 for 8 -MTN mode (b) Calculated reflectance with slope=2 for 8 -MTN mode. 1. (d) Calculated reflectance with slope=.3 for 8 -MTN mode. Fig. 2. Computer simulated LC reflectance of the 8 -MTN cell with different electrode slopes. dn ¼ 223 nm, ¼ 2. On and off voltages were 6 V and 1.6 V, respectively. The wavelength of the light source was 55 nm. Here, is the angle between the polarization axis and the front LC director, is the twist angle, ¼½ 2 þð 2 Þ2 Š 1 2 and ¼ 2dn, where d is the cell gap, and n is the birefringence. During computer simulations, we divide the LC layer into N slabs. Each slab is treated as a uniaxial film, and the final device reflectance is calculated by integrating the light throughput of each layer. 3. Fringe Field Effect We have calculated and compared the fringing field effect of the 8 -MTN cell, 45 -TN cell, VA cell, film-compensated homogeneous cell, and fringing field switching cell. All the calculations were made at ¼ 55 nm except in the FFS mode ( ¼ 589 nm). The LC parameters used in the simulations are listed in Table I. The simulation results of each mode are discussed in the following. Table I. Parameters of liquid crystals that were used in the simulations for each mode. FCH stands for the film-compensated homogeneous cell. The unit for elastic constants (K 1, K 2 and K 3 ) is pico-neuton and dn is nanometer. K 1 K 2 K 3 dn k? MTN TN VA FCH FFS MTN cell Figure 2 shows the simulated reflectance for the 8 -MTN cell with dn ¼ 223 nm and ¼ 2. In order to obtain a higher contrast ratio, the on pixel is set at 6 V and the adjacent off pixels are set at 1.6 V. The effects of different electrode slopes are investigated. In the 8 -MTN mode, the overall dark state is quite good, except for a weak disclination line at the right-hand edge of the bright pixel. This is attributed to the 2 pretilt angle of the LC cell. As evident from Fig. 2, the fringe field effect decreases as the electrode slope decreases from infinity to 1 and bounces back as the electrode slope is further decreased to.3. Hence, the optimal electrode slope is around TN cell Next, we evaluate the performances of the 45 -TN cell. Figure 3 shows the simulated reflectance for the 45 -TN mode with dn ¼ 44 nm and ¼ 12. The maximum reflectance occurs at 3 V and the adjacent dark pixels occur at 2V. Results with different electrode slopes are included in Fig. 3 for comparison. In the 45 -TN mode, if we decrease the electrode slope, the fringe field effect which appears at the right-hand edge of the bright pixels will also decrease [cf., Figs. 3(a) 3(c)]. As the electrode slope is reduced to 1, the fringe field effect on the right-hand side almost vanishes. However, the fringing field effect on the left-hand side and inside the pixel do not change very noticeably. When the electrode slope is reduced to.3, the disclination lines at both sides of the bright pixels

3 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al V 3V 2V (a) Calculated reflectance with sharp electrode for 45 -TN mode V 3V 2V (b) Calculated reflectance with electrode slope=2 for 45 -TN mode V 3V 2V (c) Calculated reflectance with electrode slope=1 for 45 -TN mode 2V 3V 2V (d) Calculated reflectance with electrode slope=.3 for 45 -TN mode Fig. 3. Computer simulated reflectance of the 45 -TN cell with different electrode slopes. dn ¼ 44 nm, ¼ 12. On and off voltages were 3 V and 2V, respectively. The wavelength of the light source was 55 nm. grow, as indicated by the circles in Fig. 3(d). The optimal performance takes place at electrode slope VA cell Figure 4 shows the simulated reflectance for a vertically aligned cell with dn ¼ 156 nm and ¼ 45 between crossed polarizers. The on pixel is set at 6 V and the adjacent off pixels are set at 1.8 V, which is slightly below the threshold voltage. The performances of different electrode slopes are compared in Fig. 4. In a VA cell, the dark state outside the pixels is excellent. However, the fringing field produces a relatively wide dark line near the right-hand edge of the bright pixels. This dark line splits the bright pixel into two parts. This is a major concern for LCOS projectors employing VA cells. From our simulations, this dark line is not influenced by changing the electrode slope. Conversely, if we keep on decreasing the electrode slope, it will induce a small fringe field effect at the right-hand edge of the bright pixel, as shown in the circled area of Fig. 4(d). It is noteworthy that this dark line would disappear if all the pixels were set at the same voltage (to be discussed later). This stationary state would lead to a very high flat field contrast ratio. However, if the adjacent pixels are not completely on or off, then the dark lines as shown in Fig. 4 will appear. A pixel is split into two unequal parts and the display brightness and contrast ratio are both reduced. 3.4 Film-compensated homogenous cell A homogeneous cell is known for its fast response time. However, its dark state voltage is too high unless a phase retardation film is used. 15) The principal axis of the film is oriented to be orthogonal to the LC axis such that their phase retardations are subtractive: ¼ 4ðd 1n 1 d 2 n 2 Þ ; ð3:1þ where d 1;2 and n 1;2 represent the cell gap and birefringence of the LC cell and compensation film, respectively. Figure 5 shows the simulated reflectance for a homogeneous cell with a uniaxial compensation film. The dn is 184 nm for the LC cell, and 48 nm for the compensation film. The on pixel is set at 4 V (dark state) and the adjacent off pixels are set at 1.5 V (bright state). The performances of different electrode slopes are presented. Figures 5(a) and 5(b) show the optical characteristics of a homogenous cell with and without the compensation film, respectively. As expected, the dark state of the homogeneous cell without compensation film is poor. Adding a compensation film cancels the residual phase retardation of the cell and leads to a good dark state. As evident from Figs. 5(c) 5(e), the fringe field effect still occurs at the right-hand edge of the bright pixel. The sloped electrode is not helpful in reducing the fringe field effect.

4 458 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al V 1.8V (a) Calculated reflectance with sharp electrode for VA mode 1.8V 1.8V (b) Calculated reflectance with electrode slope=2 for VA mode V 1.8V (c) Calculated reflectance with electrode slope=1 for VA mode 1.8V 1.8V (d) Calculated reflectance with electrode slope=.3 for VA mode Fig. 4. Computer simulated reflectance of the VA cell with different electrode slopes. dn ¼ 156 nm and ¼ 45. On and off voltages were 6 V and 1.8 V, respectively. The wavelength of the light source is 55 nm V 1.5V 4V (a) Calculated reflectance with sharp electrode for homogenous cell V 1.5V 4V (b) Calculated reflectance with sharp electrode for film-compensated homogenous cell V 1.5V 4V (c) Calculated reflectance with electrode slope=2 for film-compensated homogenous cell. 4V 1.5V 4V (d) Calculated reflectance with electrode slope=1 for film-compensated homogenous cell. 4V 1.5V 4V (e) Calculated reflectance with electrode slope=.3 for film-compensated homogenous cell. Fig. 5. Computer simulated reflectance of the film-compensated homogenous cell with different electrode slopes. d 1 n 1 ¼ 184 nm for LC, and d 2 n 2 ¼ 48 nm for the compensation film, ¼ 45. On and off voltages were 4 V and 1.5 V, respectively. The wavelength of the light source is 55 nm.

5 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al Analyzer LC layer Electric field /4 plate Reflector w l Glass 2nd ITO Passivation 1 st ITO (a) Cell structure for the FFS mode (b) Cross-sectional view of the interdigital electrodes for the FFS mode. Fig. 6. FFS mode structure used for computer simulations. Width (w) of the interdigital electrode is 3 m, and distance (l) between electrodes is 5 m. Cell gap is 4 m. The cell is operated at normally black mode (Dark when no voltage is applied) Reflectance Reflectance V 5V 1V (a) Calculated reflectance with sharp electrode for FFS mode. (b) Calculated reflectance with electrode slope=2 for FFS mode. Reflectance Reflectance (c) Calculated reflectance with electrode slope=1 for FFS mode. (d) Calculated reflectance with electrode slope=.3 for FFS mode. Fig. 7. Computer simulated reflectance of the FFS mode with different electrode slopes. dn ¼ 296 nm, ¼, and ¼ 3:8. On and off voltages were operated at 5 V and 1 V, respectively. ¼ 589 nm. 3.5 Fringing-field-switching cell There are several ways to construct a FFS cell. Figure 6 shows a commonly configured FFS cell. It uses only one polarizer and a =4 plate between the LC layer and the bottom reflector. The indium tin oxide (ITO) layer which was deposited on the bottom glass substrate is 4 nm thick, and a 15-nm-thick SiO 2 passivation layer was over coated on the ITO layer. Lastly, a second ITO layer was patterned as interdigital electrodes on the passivation layer with the thickness of 4 nm. The width (w) of the interdigitated electrode was 3 m and the distance (l) between electrodes was 5 m. The FFS cell is operated in the normally black (NB) mode in this case. Figure 7 shows the simulated reflectance for different electrode slopes assuming a cell gap d ¼ 4 m, a LC dielectric anisotropy ¼ 3:8, and a birefringence n ¼ :74 at ¼ 589 nm.

6 4582 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al V 1.8V (a) Calculated reflectance with sharp electrodes when all the pixels were turned on(left) and off(right) for VA mode 1.8V V 1.8V 1.8V (b) Calculated reflectance with electrode slope=.3 when all the pixels were turned on(left) and off(right) for VA mode Fig. 8. Computer simulated reflectance of VA mode when all the pixels were turned on (left) or off (right). Performances of different electrode slopes are compared in (a) slope=1 and (b) slope=.3. In the FFS mode, the fringe field effect is quite strong, as its name implies. The LCs are driven by the fringing field resulting from the interdigital electrodes. As shown in Fig. 7, different electrode slopes also greatly influence the optical performances. Overall, there are two main disclination lines, one each sides of the bright pixels. As the electrode slope changes, the transmittance at the center of the bright region also changes. In Fig. 7(c), a relatively uniform reflectance is obtained when the electrode slope is equal to one. However, the poor dark state implies a low contrast ratio. 4. Comparison of Contrast Ratios The contrast ratio of each LC mode discussed above is calculated as below: R Rbright CR ¼ R : ð4:1þ Rdark Here, R R bright is the integrated reflectance of the panel when all pixels are at the bright state, and R R dark is that when all pixels are at the dark state. Table II shows the contrast ratio for each of the five modes studied at different electrode slopes. As expected, the VA mode exhibits the highest contrast ratio when all the pixels were turned on and off (Fig. 8). If we decrease the electrode slopes or reduce the biased voltage, the dark state will be improved further. Table II. Calculated flat field (totally white and totally dark) contrast ratios for the studied LC modes at different electrode slopes. FCH stands for the film-compensated homogeneous cell. Slope 8 -MTN 9 -MTN 45 -TN VA FCH FFS Infinity Figures 9 11 show the calculated reflectance for other modes considered here for the conditions that all pixels were turned on or off. In Table II, we also include the 9 -MTN cell for comparison. Its contrast ratio is impressive because of the natural phase compensation of the two orthogonal boundary layers. A shortcoming is that its maximum light efficiency is 88%. For a display, the occasion when all the pixels are simultaneously on or off is rare. Most of the time, some pixels are on and some are off. Under such circumstances, the contrast ratio listed in Table II is not representative. Nevertheless, to simulate such a random dark/bright pixel configuration is difficult. For simplicity, we assume that on and off pixels alternate and then calculate the average reflectance of the bright and dark states. In our simulations, we calculated the contrast ratios using 3 pixels (dark/bright/ dark) and 5 pixels (dark/bright/dark/bright/dark) and found

7 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al (a) Calculated reflectance with sharp electrodes when all the pixels were turned on(left) and off(right) for 8 -MTN mode (b) Calculated reflectance with electrode slope=.3 when all the pixels were turned on(left) and off(right) for 8 -MTN mode. Fig. 9. Computer simulated reflectance of 8 -MTN mode when all the pixels were turned on (left) or off (right). Performances of different electrode slopes are compared in (a) slope=1 and (b) slope= V 3V 3V (a) Calculated reflectance with sharp electrodes when all the pixels were turned on(left) and off(right) for 45 -TN mode V 3V 3V (b) Calculated reflectance with electrode slope=1 when all the pixels were turned on(left) and off(right) for 45 -TN mode. Fig. 1. Computer simulated reflectance of 45 -TN mode when all the pixels were turned on (left) or off (right). Performances of different electrode slopes are compared in (a) slope=1 and (b) slope=1.

8 4584 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al V 4V 4V (a) Calculated reflectance with electrode slope=1 when all the pixels were turned on(left) and off(right) for film-compensated homogenous cell. 4V 4V 4V 1.5V 1.5V 1.5V (b) Calculated reflectance with electrode slope=.3 when all the pixels were turned on(left) and off(right) for film-compensated homogenous cell V 1.5V 1.5V Fig. 11. Computer simulated reflectance of film-compensated homogenous mode when all the pixels were turned on (left) or off (right). Performances of different electrode slopes are compared in (a) slope=1 and (b) slope=.3. Table III. Calculated contrast ratios for the studied LC modes at different electrode slopes for the dark/bright/dark pixel configuration. FCH stands for the film-compensated homogeneous cell. Slope 8 -MTN 9 -MTN 45 -TN VA FCH FFS Infinity that their results are almost the same. The calculated contrast ratios for the dark/bright/dark pixel configuration are listed in Table III. Owing to its weaker fringing field, the 9 -MTN exhibits a higher contrast ratio than the VA mode. From Table II and Table III, it is evident that the contrast ratios are influenced by the electrode slopes in each mode. Hence, the electrode slope should be taken into consideration in the optimization of LCOS devices. 5. Conclusions In summary, we present detailed analyses of the fringe field effect in five commonly employed LC modes for LCOS projectors. The influences of electrode slopes on the optical performances were analyzed quantitatively. In order to design a high-brightness and high-contrast-ratio LCOS projector, the LC operating modes and electrode slopes must be optimized. From the calculated results, the optical performances of 8 and 9 -MTN, 45 -TN, and FFS modes could be optimized by choosing a suitable electrode slope. However, the FFS mode has a very poor contrast ratio due to the strong fringe field effect, and may not be suitable for application to LCOS devices. On the other hand, the fringe field effect in the film-compensated homogenous cell and VA cell are less sensitive to the electrode slope in the darkbright-dark state. By comparing the contrast ratios among the five LC modes studied, the VA mode is found to exhibit the best flat field contrast ratio due to its perfect dark state. However, the MTN mode showed the smallest fringing field effect when the pixels were operated in the dark-bright-dark state. Acknowledgements This work is partially supported by the National Science Council, R.O.C., under the Contract No. NSC M ) P. M. Alt: Int. Display Research Conf., 1997, M ) Y. Ji and M. E. Stefanov: Proc. Asia Display, 1998, p ) F. Sato, Y. Yagi and K. Hanihara: SID Tech. Dig. 28 (1997) ) K. H. Fan Chiang, S. T. Wu and S. H. Chen: Proc. Asia Display/IDW, 21, p ) K. Ohmuro, S. Kataoka, T. Sasaki and Y. Koike: SID Tech. Dig. 28 (1997) ) A. Van Calster and D. Cuypers: Proc. SPIE 3954 (2) 112.

9 Jpn. J. Appl. Phys. Vol. 41 (22) Pt. 1, No. 7A K.-H. FAN CHIANG et al ) J. Grinberg, A. Jacobson, W. Bleha, L. Miller, I. Fraas, D. Bosewell and G. Myer: Opt. Eng. 14 (1975) ) S. T. Wu and C. S. Wu: SID Tech. Dig. 27 (1996) ) S. T. Wu and C. S. Wu: Displays Technol. & Appl. 2 (1999) ) Y. Fujimura, T. Nagatsuka, H. Yoshimi, S. Umemoto and T. Shimomura: SID Tech. Dig. 23 (1992) ) S. H. Lee, S. H. Hong, H. Y. Kim, D. S. Seo, G. D. Lee and T.H. Yoon: Jpn. J. Appl. Phys. 4 (21) ) F. C. Frank: Discuss. Faraday Soc. 25 (1958) ) S. T. Wu and C. S. Wu: Appl. Phys. Lett. 68 (1996) ) S. T. Wu and D. K. Yang: Reflective Liquid Crystal Displays (John Wiley & Sons, New York, 21). 15) S. T. Wu and C. S. Wu: J. Appl. Phys. 83 (1998) 496.

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