Ultra-fast-switching flexoelectric liquid-crystal display with high contrast Flynn Castles (SID Student Member) Stephen M. Morris Damian J. Gardiner Qasim M. Malik Harry J. Coles

Abstract — The flexoelectro-optic effect provides a fast-switching mechanism (0.01–0.1 msec), suitable for use in field-sequential-color full-motion-video displays. An in-plane electric field is applied to a short-pitch chiral nematic liquid crystal aligned in the uniform standing helix (or Grandjean) texture. The switching mechanism is experimentally demonstrated in a single-pixel test cell, and the display performance is investigated as a function of device parameters. A contrast ratio of 2000:1 is predicted. Keywords — Liquid-crystal display, flexoelectric, fast switching, high contrast ratio. DOI # 10.1889/JSID18.2.128

1

Introduction

Liquid crystals (LCs) are useful in a wide range of display devices because their optical properties may be manipulated by an applied electric field. The speed of the response of the LC to the electric field will be governed by a number of factors, including the viscosity, the elastic restoring forces, and the specific orientation of the LC molecules.1 Improving the response time of liquid-crystal displays (LCDs) is a primary technical challenge in their development. A faster switching speed will lead to superior quality of moving images, and a suitably fast switch will enable the use of field-sequential-color (FSC) generation. FSC has a number of associated benefits, such as increased resolution, greater brightness, and a potential reduction in cost, due to the fact that a color filter is no longer required.2 The implementation of FSC has been hindered by the restrictively slow response times of conventional display modes. The flexoelectro-optic effect is a naturally fast-switching mechanism seen in short-pitch chiral nematic (N*) LCs, whereby the optic axis is rotated by an electric field applied perpendicular to it.3 The rotation is found to be practically independent of temperature.4 Response times are typically ultra-fast, in the context of LC switching: on the order of 0.01–0.1 msec. The effect was first discovered in, and is usually investigated in, the uniform lying helix (ULH) configuration, in which the helical axis of the N* lies in the plane of the device. The drawback to this configuration is that the ULH structure must usually be formed under the application of an electric field and is inherently unstable.5 An alternative device geometry is generated when the N* is aligned in the Uniform Standing Helix (or Grandjean) configuration, in which the helical axis of the N* stands normal to the plane of the device. The rotation of the optic axis is now created by an in-plane electric field. An electrically

driven optical switch is produced between crossed polarizers. This was first proposed by Broughton et al. in the context of a polarization controller at optical communications wavelengths.6,7 We investigate this device in the context of a fast-switching display without motion blur. We will call this the Uniform Standing Helix Flexoelectric (USHF) display mode. In addition to the fast response in this mode, the LC structure is stable using existing, robust alignment techniques. An excellent dark state is also achievable, leading to a high contrast ratio (typically ≈2000:1). We investigated the primary aspects of the device performance as a function of material and device parameters. We present results based on theoretical modeling, analytic theory, and experiment. The switching mechanism is experimentally demonstrated in a single-pixel test cell. We investigated the switching speed, the quality of the dark state, the electro-optic curves, and the isocontrast curves with and without a compensation film, using well-established theoretical methods. Realistic predictions are generated using existing, experimentally determined material parameters. The structure of the device is shown in Fig. 1(a). The N* is aligned in the USH configuration using anti-planar alignment on the glass surfaces. With no field applied, the helical structure is undistorted, and the device is non-transmissive between crossed polarizers. When an in-plane electric field is applied, the optic axis of the N* rotates, and a birefringence is induced. For a sufficient tilt angle, the device becomes transmissive (the required angle depends on the birefringence of the LC). The short-pitch N* may be considered as a uniaxially birefringent structure with the optic axis along the helical axis. The viewing characteristics of the device are analogous in many respects to that of the vertically aligned nematic (VA) mode LCD8,9 [Fig. 1(b)].

Expanded revised version of a paper presented at the 2009 SID International Symposium (Display Week 2009) held May 31–June 5, 2009 in San Antonio, Texas, U.S.A. The authors are with the Centre of Molecular Materials for Photonics and Electronics, Electrical Engineering Division, Department of Engineering, University of Cambridge, 9 JJ Thomson Ave., Cambridge CB3 0FA, U.K.; telephone +44-122374-8366, e-mail: [email protected]. © Copyright 2010 Society for Information Display 1071-0922/10/1802-0128$1.00

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is small ∆ε ≈ 0 and e is large. Bimesogenic LCs have been developed specifically to have large average flexoelectric coefficients e ~ 10 pC/m and very low dielectric anisotropy ∆ε ˜ 0.11–14 If ∆ε is sufficiently low (but not negative), there will be no dielectric unwinding of the N* helical structure.

3

Response time

The characteristic response time τ of the flexoelectro-optic effect may be derived for small deformations as τ = γP2/(4π2K), where P is the pitch of the N*, γ is an effective viscosity, and K is the average of the splay and bend elastic constants of the LC.15 Here, τ is the time taken for the tilt to fall to 1/e of its initial value, where e is the base of the natural logarithm. From this, we may loosely approximate the 90%–10% natural fall time to be τ90–10 = 2τ, i.e.,

t 90-10 ª FIGURE 1 — (a) The chiral nematic liquid crystal is aligned in the uniform standing helix configuration. An in-plane electric field is applied in the same direction as the surface alignment, which rotates the optic axis via the flexoelectro-optic effect. Crossed polarizers are positioned at ±45° to the direction of the electric field. (b) The short-pitch chiral nematic is effectively a uniaxially birefringent structure, with optic axis along the helical axis. The viewing characteristics of the device are analogous to the VA mode LCD.

2

gP 2 2p 2 K

.

Typical, experimentally determined material parameters for pure bimesogenic LCs are shown in Table 1. Based on these, the predicted response time of the device is sub 0.1 msec for an N* pitch less than ≈360 nm. Such fast response times have been confirmed experimentally in both the ULH and USH geometries.13,6 For the specific value of pitch P = 150 nm, a response time of τ90–10 = 0.017 msec is predicted.

The flexoelectro-optic effect

Conventionally, the switching mechanisms in LCDs exploit dielectric coupling, where, due to the dielectric anisotropy ∆ε, the LC molecules will tend to align in the applied electric field. Flexoelectro-optic switching may be considered as a separate switching mechanism to dielectric coupling, in that it can be seen in LCs even if there is zero dielectric anisotropy ∆ε = 0. The flexoelectro-optic effect in N* LCs is a result of flexoelectricity,10 which is caused by a linear coupling between the distortion of the LC and the applied electric field. The strength of the flexoelectric response is characterized by the splay and bend flexoelectric coefficients es and eb, which appear in the free-energy expression as an additional, flexoelectric, term10,3

fflexo = - E ◊ es n(— ◊ n) + ebn ¥ — ¥ n , where E is the applied electric field and n is the director. In a short-pitch N* under the application of an electric field perpendicular to the helical axis, the flexoelectric effect manifests itself as a fast rotation of the optic axis. This is known as the flexoelectro-optic effect. The average of the flexoelectric coefficients e = (es + eb)/2 dictates the strength of the flexoelectro-optic response for a given electric-field strength. While all LCs are, to some degree, flexoelectric, the effect is usually small and the response of the LC is dominated by the dielectric coupling in most circumstances. However, under certain circumstances, the flexoelectric effect may dominate, particularly if the dielectric anisotropy

4

Field-off (dark) state

The transmission in the field-off (dark) state will dominate the contrast ratio of the device. With no field applied, the LC structure is that of an undistorted N*. Under certain circumstances, the plane of polarization of light travelling along the helical axis of a N* will be rotated by the helical structure. This is the regime in which the twisted-nematic (TN) and super-twisted-nematic (STN) devices operate. However, if the pitch P is suitably smaller than the wavelength of light λ, the plane of polarization of light does not follow the helical rotation. This is the regime in which the USHF device operates. As the pitch is reduced, the optical rotation falls. For sufficiently short pitch, the N* provides an excellent dark state between crossed polarizers. An analogy may be drawn here with the VA device (except that the short-pitch N* i s negatively birefringent). So, how short TABLE 1 — Throughout this work, we use the following typical, experimentally determined values for the material parameters of bimesogenic liquid crystals.13

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FIGURE 2 — Test cells filled with chiral nematic aligned in the uniform standing helix between crossed polarizers. From left to right, the pitch is decreasing (P = 460, 300, 260, 230, 190 nm). For sufficiently short pitch, a uniform dark state is observed.

must the pitch be to give a suitably dark off-state? To answer this question, we investigated the dark state (a) experimentally, (b) using the Berreman 4 × 4 method, and (c) using an analytic approach based on the de Vries equation. A series of test cells were filled with the same liquid crystal (BL003, Merck), but with varying concentrations of chiral dopant (BDH1281, Merck). This gave equivalent samples with varying pitch. Photographs of the test cells (thickness d = 5 µm) between crossed polarizers demonstrate that, as the pitch is reduced, a uniform dark state is attained (Fig. 2). We used the Berreman 4 × 4 method16,17 to investigate the optical properties of the display in general cases. This method is frequently employed to model LC structures and has been found to give results in good agreement with experiment (see, e.g., Ref. 18). Polarizers are implemented using the equivalent polarizer method.19 The Berreman method has shown that in order to produce a dark state the crucial requirement on the pitch is that it must be sufficiently small that the selectively reflective region of the N* (or the photonic band gap) is below visible wavelengths.17 As the pitch is further reduced, the transmitted intensity rapidly reduces to zero. As a specific example in this regime, consider the following typical device parameters: parallel and perpendicular component of the local refractive index n|| = 1.7 and n⊥ = 1.5, pitch P = 150 nm, and device thickness d = 6 µm. At the wavelength of green light, λ = 555 nm, the Berreman method predicts a transmitted intensity in the off-state of Ioff = (2270)–1. This will give the display a contrast ratio of approximately CR ≈ 2000:1+ at normal incidence. In the limit of small pitch the de Vries equation20 may be used to derive an analytic expression for Ioff, resulting in

Ioff

F GG p(Dn) Pd ª sin G GG 4l FG1 - FG l IJ GH GH H nPK 2

2

2

2

I JJ I JJ JJ JJ KK

for Pn|| < λ, where n = (n|| + n⊥)/2 and ∆n = n|| – n⊥.17 For the above device parameters, this equation gives Ioff = (2244)–1, in approximate agreement with the Berreman method. This expression becomes exact in the limit Pn/λ → 0. By way of comparison with experiment, the quality of this dark state has been measured in a different device which uses the same configuration for the off-state. In that case, a contrast ratio of 1000:1 was reported.21

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FIGURE 3 — The tilt of the optic axis of the chiral nematic is plotted as a function of the applied in-plane electric field for various values of the combined quantity eP (where e is the average flexoelectric coefficient and P is the pitch).

5 5.1

Field-on (transmissive) state Tilt as a function of applied electric field

The director profile of the LC is determined using a one-dimensional continuum model with strong planar alignment.22,17 The figure of merit is θmax, the rotation of the optic axis. In the limit of zero dielectric anisotropy ∆ε → 0, the tilt of the optic axis is given as a function of the electric field E by23

tan qmax =

K - 2K 2 + K 3 eP sin qmax . E- 1 2pK 2 2K 2

(1)

(In this situation, the tilt as a function of field is identical to that found in the ULH case.17) The tilt angle is thus dominated by the combination of the average flexoelectric coefficient and the pitch, eP. By using Eq. (1), the rotation of the optic axis as a function of electric field is plotted in Fig. 3 for various values of eP. It is noted that, in the limit of small θmax, Eq. (1) may be approximated by3

qmax ª

eP E, 2p K

where K = (K1 + K3)/2, which describes the linear part of the plots at sufficiently low E.

5.2

Electro-optic curves

We investigated the transmission of the device as a function of the applied electric field using the Berreman 4 × 4 method. For typical device parameters, we ploted the electro-optic curves for various values of the average flexoelectric coefficient e in Fig. 4. It is seen that as e increases, the field value required for full intensity modulation decreases. The driving voltage of the display V may be approximately

FIGURE 6 — Oscilloscope trace of the applied voltage and the resultant transmitted intensity show that the switching mechanism is flexoelectric. FIGURE 4 — Predicted electro-optic curves for typical device parameters at various values of the average flexoelectric coefficient e, calculated using the Berreman 4 × 4 method.

determined from the electro-optic curve by multiplying the electric field required for full intensity modulation EFI by the spacing of the in-plane electrodes V = EFI × de. We constructed a USHF test cell to experimentally demonstrate the switching mechanism. A d = 5 µm thick cell with transparent inter-digitated indium-tin-oxide in-plane electrodes was used. The electrodes spacing was de = 15 µm, and the width of the electrodes themselves was 5 µm. Antiparallel polyimide alignment layers produced a uniform USH texture. A highly flexoelectric mixture of nematic bimesogenic liquid crystals was used (see, e.g., Ref. 12), together with high-twisting-power chiral dopant (BDH1281, Merck). The dielectric anisotropy was less than ~2 (but not negative). To avoid degradation of the N* structure near the electrodes, the mixture was polymer-stabilized according to the process described in Ref. 24. A 1-kHz square-wave signal

was applied. The transmitted intensity as a function of applied electric field is shown in Fig. 5, together with photomicrographs of the test cell. The ability to control the gray scale is apparent. It is seen that the experimental region currently represents only the initial part of the full electrooptic curve. The curve was truncated because at ≈15 V/µm the structure became degraded and did not revert quickly back to the undistorted N* upon removal of the electric field. We are currently working to optimize the device to make the full electro-optic curve experimentally accessible at lower field values. Figure 6 shows that the response of the LC is dependent on the polarity of the field, and hence the device is flexoelectrically driven, as opposed to dielectrically driven (see Ref. 6 for a discussion of this issue). It is noted that the operation of the device will not be significantly degraded by the presence of “twist-jump” domains due to variations in thickness. Such domains create potential problems for conventional N* devices. However, because the pitch in the USHF device is unusually small (~150 nm), it has been argued that the effect will negligible (less than ~0.4% variation in transmission17).

6

FIGURE 5 — Experimental demonstration of USHF switching. (a) Electro-optic curve. (b) Photomicrographs of test cell as a function of applied electric field.

Viewing-angle dependence

We investigated the viewing-angle dependence of the display by calculating the contrast ratio (CR) using the Berreman method. The CR is defined as the ratio of the luminance of the device in the on-state to the luminance in the off-state. To determine the CR, the spectral power density of transmitted light is integrated over the visible range 380–780 nm, weighted by the standard color-matching function of the green component of light.25 We used Standard Illuminant A as the light source. To reduce the expense of the computation, we approximated the short-pitch N* to be a uniaxial, negatively birefringent structure. Figure 7(a) plots the CR as a function of viewing angle – the isocontrast curves – with no optical compensation. The device parameters used for this plot are the same as for Fig. 4, with the average flexoelectric coefficient set to e = 10 pC/m. It may be expected that the viewing angle will be widened using optical compensation films. As a simple example

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Acknowledgments We would like to thank the Engineering and Physical Sciences Research Council (UK) for financial support. One of the authors (FC) gratefully acknowledges Merck.

References FIGURE 7 — Contrast ratio (CR) as a function of viewing angle (a) with no optical compensation and (b) with positive c-plate compensation. Lines denote equal CR contours. Polarizers are at 0° and 90° azimuthal angles, and the electric field E is applied at 45°.

of this, we implemented a c-plate compensation film. The film is chosen such that its phase retardation cancels that of the LC. In this way, the light leakage in the dark state is greatly reduced. The film is required to be a uniaxial positively birefringent structure, with the optic axis normal to the plane of the device. For simplicity, we set the thickness of the film to be equal to that of the LC layer, in which case the required birefringence of the film ∆nfilm is given by ∆nfilm = –∆nN*, where ∆nN* is the effective birefringence of the N*. The c-plate compensated isocontrast curves are plotted in Fig. 7(b). The viewing angle is significantly widened. It is noted that the viewing-angle dependence may be further improved using additional compensation layers (see, e.g., Refs. 26 and 27), and/or a multi-domain electrode structure.28

7

Conclusion

By applying an in-plane electric field to a short-pitch N* LC in the USH configuration, a fast optical switch may be generated, which operates using the flexoelectro-optic effect. We call this the USHF display mode. Some properties of this mechanism have been investigated in the context of a fast-switching display device. Highly flexoelectric materials with low (but non-negative) dielectric anisotropy are required. Using typical experimentally determined material parameters, we predict a response time of τ90–10 = 0.017 msec, together with a contrast ratio at normal incidence of CR ≈ 2000+. In this respect, the USHF device may be considered as an ultra-fast-switching VA device. While the typical driving voltage for the display remains relatively high, further developments in materials with higher average flexoelectric coefficients e may reduce this. The predicted isocontrast curves for the device were plotted, and we demonstrated that the viewing angle may be improved by implementing a positively birefringent c-plate compensation film. Our results suggest the USHF display is a promising candidate for future display devices, and further theoretical and experimental work is being undertaken.

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1 D. Pauluth and K. Tarumi, “Optimization of liquid crystals for television,” J. Soc. Info. Display 13, No. 8, 693–702 (2005). 2 N. Koma et al., “A novel driving method for field sequential color using OCB TFT-LCD,” J. Soc. Info. Display 9, No. 4, 331–336 (2001). 3 J. S. Patel and R. B. Meyer, “Flexoelectric electro-optics of a cholesteric liquid crystal,” Phys. Rev. Lett. 58, 1538 (1987). 4 P. Ruquist et al., “Linear electro-optic effect based on flexoelectricity in a cholesteric with sign change of dielectric anisotropy,” J. Appl. Phys. 76, 7778 (1994). 5 G. Carbone et al., “Short pitch cholesteric electro-optical device based on periodic polymer structures,” Appl. Phys. Lett. 95, 011102 (2009). 6 B. J. Broughton et al., “Optimized flexoelectric response in a chiral liquid-crystal phase device,” J. Appl. Phys. 98, 34109 (2005). 7 H. J. Coles et al., “Flexoelectro-optic liquid crystal device,” Patent No. WO/2006/003441 (2006). 8 S. -T. Wu, “Film compensated homeotropic liquid crystal cell for direct view display,” J. Appl. Phys. 76, 5975 (1994). 9 K. Ohmuro et al., “Development of super-high-image-quality verticalalignment-mode LCD,” SID Symposium Digest 28, 845 (1997). 10 R. B. Meyer, “Piezoelectric effects in liquid crystals,” Phys. Rev. Lett. 22, 918 (1969). 11 B. Musgrave et al., “A new series of chiral nematic bimesogens for the flexoelectro-optic effect,” Liquid Crystals 26, 1235 (1999). 12 H. J. Coles et al., “Strong flexoelectric behavior in bimesogenic liquid crystals,” J. Appl. Phys. 99, 34104 (2006). 13 S. M. Morris et al., “Structure-flexoelastic properties of bimesogenic liquid crystals,” Phys. Rev. E 75, 041701 (2007). 14 H. J. Coles, “Bimesogenic liquid crystals: New materials for high performance flexoelectric and blue phase displays,” Proc. IDW ‘06, 15 (2006). 15 J. S. Patel and S.-D. Lee, “Fast linear electro-optic effect based on cholesteric liquid crystals,” J. Appl. Phys. 66, 1879 (1989). 16 D. W. Berreman, “Optics in stratified and anisotropic media: 4 × 4 matrix formulation,” J. Opt. Soc. Am. 62, 502 (1972). 17 F. Castles et al., “The flexoelectro-optic properties of chiral nematic liquid crystals in the uniform standing helix configuration,” Phys. Rev. E. 80, 031709 (2009). 18 H. G. Yoon and H. F. Gleeson, “Accurate modelling of multilayer chiral nematic devices through the Berreman 4 × 4 matrix methods,” J. Phys. D: Appl. Phys. 40 3579 (2007). 19 H. A. van Sprang, “Angular dependence of the transmission of nontwisted liquid crystal displays,” J. Appl. Phys. 71, 4826 (1992). 20 H. De Vries, “Rotary power and other optical properties of certain liquid crystals,” Acta Cryst. 4, 219 (1951). 21 S. S. Choi et al., “High contrast nematic liquid crystal deivce using negative dielectric material,” Appl. Phys. Lett. 95, 193502 (2009). 22 A. J. Davidson et al., “Investigation Into chiral active waveplates,” J. Appl. Phys. 99, 93109 (2006). 23 S.-D. Lee et al., “Effect of flexoelectric coupling on helix distortions in Cholesteric liquid crystals,” J. Appl. Phys. 67, 1293 (1990). 24 B. J. Broughton et al., “Effect of polymer concentration on stabilized large-tilt-angle flexoelectro-optic switching,” J. Appl. Phys. 99, 023511 (2006). 25 J. Schanda, Colorimetry: Understanding the CIE System (Wiley, 2007). 26 Z. Ge et al., “Extraordinarily wide-view circular polarizers for liquid crystal displays,” Opt. Express 16, 3120 (2008). 27 Z. Ge et al., “Switchable transmissive and reflective liquid-crystal display using a multi-domain vertical alignment,” J. Soc. Info. Display 17, No. 7, 561–566 (2009). 28 A. Takeda et al., “A super-high image quality multi-domain vertical alignment LCD by new rubbing-less technology,” SID Symposium Digest 29, 1077 (1998).

Flynn Castles received his B.A. and M.S. degrees in experimental and theoretical physics (2006) and his M.A. degree (2009), from the University of Cambridge. He is currently working towards his Ph.D. in electrical engineering under the supervision of Prof. H. Coles at the Center of Molecular Materials for Photonics and Electronics at the University of Cambridge. His research interests include liquid-crystal display devices, flexoelectricity in liquid crystals, and liquid-crystal blue phases. He is a member of St. Catharine’s College, Cambridge. Stephen M. Morris obtained his M.S. degree in physics from the University of Southampton (2000) and his Ph.D. in electrical engineering from the University of Cambridge (2005). He subsequently continued as a Research Associate at the Center of Molecular Materials for Photonics and Electronics, working in collaboration with an industrial partner to produce a new hybrid display, which can be viewed in both low- and high-light-level environments. At present, he is currently involved in developing miniature tunable laser light sources for next-generation displays and photonics applications. He is a Fellow of St. Catharine’s College, Cambridge. Damian J. Gardiner received his M.Phys. degree in physics from Southampton University (2001). Subsequently, he worked at the Space Department, Qinetiq Ltd., before moving to Wolfson College, University of Cambridge, where he received his Ph.D. degree. His doctoral thesis was focused on organosiloxane-based bistable materials for use in displays and other applications. Following his Ph.D., he worked at Cambridge Display Technology, Ltd., developing organic electroluminescent and photovoltaic systems. He re-joined the Center of Molecular Materials for Photonics and Electronics, University of Cambridge, in February 2008. He is currently working on a hybrid electroluminescent liquidcrystal project in collaboration with Pelikon, Ltd.

Qasim M. Malik received his M.S. degree in chemistry (2000) from Quaid-I-Azam University Islamabad (Pakistan), researching natural product synthesis (Isocumarine and its dihydro-derivatives). This was followed by his M.Phil. in organic chemistry (2002) from the same institute. The research project was based on synthesis of mesogens comprising of Schiff’s base analogues derived from benzyl amine derivatives. He was then appointed a lecturer in chemistry at APSC Rawalpindi. In 2008, he received his Ph.D. in chemistry from Macquarie University, Sydney (Australia). His Ph.D. involved the synthesis and characterization of liquid-crystal molecules possessing chiral scaffold analogues. He joined the Center of Molecular Materials for Photonics and Electronics, University of Cambridge, in June 2008 and is working on the synthesis and characterization of materials leading to devices and lasing liquid crystals in general. Harry J. Coles is Professor of photonics of molecular materials at the Engineering Department of Cambridge University and Director of the multidisciplinary Cambridge Center of Molecular Materials for Photonics and Electronics, and Fellow of the Institute of Physics. His research interests cover extremely wide areas: synthesis and characterization of liquid crystals, oligomers, and polymers; structure–property correlations; spectroscopic and electro-optic techniques; linear and non-linear optics of liquid crystals; organic lasers; thin-film optical devices and displays; telecommunications and photonic switches/interconnects; and device fabrication. To date, he has published over 200 refereed papers, 26 patents, and some 400 published abstracts. He is Chairman of the multimillion-dollar COSMOS EPSRC funded Basic Technology Research Grant developing new all organic lasers, which involves the Departments of Physics, Chemistry and Engineering. In 2002, he was invited by the British Liquid Crystal Society to give the Ben Sturgeon Memorial Lecture and in April 2003 was awarded the George Gray Medal for his research on Liquid Crystals and their Applications. He is a Professorial Fellow of St. Catharine’s College, University of Cambridge.

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