A. Adamski, H. Pauwels, K. Neyts, C. Desimpel, G. Stojmenovik, S. Vermael ... fast speed, high contrast ratio, wide viewing angle, high resolution and full grey ...
P-33: The Non-uniform Theory Simulations of the Continuous Director Rotation Mode of FLCD’s A. Adamski, H. Pauwels, K. Neyts, C. Desimpel, G. Stojmenovik, S. Vermael LC group, ELIS, Ghent University, St. Pietersnieuwstraat 41, B-9000 GENT, Belgium
Abstract We introduce the theoretical model of LC material with the phase sequence I-N*-SmC* as a material having suitable properties for multimedia applications (fast speed, high contrast and full grey scale capabilities). We present the structure and investigate the switching and the optical response of the device taking into account material and technological parameters. We explain the mechanism of the continuous switching mode and prove the ability of using grey levels.
1.
Introduction
A lot of effort has been put into a solution for liquid crystal displays for video and multimedia applications. Today these applications have very high technological requirements such as: fast speed, high contrast ratio, wide viewing angle, high resolution and full grey scale capabilities. The commercially available displays only partially fulfil these demands. A number of different solutions have been reported up to now. One must mention here the actively addressed TN [1] and IPS [2] displays using nematic LC materials which have relatively low speed. Smectic materials on the other hand give faster switching times which can be achieved by the combination of high PS materials with a polysilicon thin film transistors TFT matrix [3]. Unfortunately this is an expensive solution so one tends towards lower PS materials in combination with amorphous silicon transistors [4]. The optimum is some trade-off between the speed, the resolution, the driving voltage and the cost price of the display. In this paper we present a theoretical investigation of a monodomain FLC structure which exhibits the majority of the demands described above. We consider a material having a phase sequence I-N*-SmC*. This material was reported not to show zigzag defects (in contrast with the SSFLC) and due to its bookshelf structure it provides good electrooptical quality [5]. The director configuration is presented on Fig. 1a. (b)
x
(a) E>0
layer2 ϕ0 P0 layer1
P ϕ
rubbing direction
2Θ
rs laye ctic e m s Θ
90−Θ rubbing direction
Figure 1. (a) Director configuration and (b) monodomain and smectic layers inclination The monodomain is created by cooling down the LC material in a parallel rubbed sample from the isotropic, through the nematic to
the smectic C* phase with the application of a monopolar pulse in the transition region between N* and SmC*. This leads to the homogeneous alignment of the molecules along the rubbing direction. The smectic layers are then not perpendicular to the rubbing direction (because of the absence of SmA phase) but inclined with an angle 900-Θ (Fig. 1b). The monopolar pulse causes alignment of the molecules along the same side of the cone what leads to a monodomain structure instead of spontaneous multidomains. We believe that this technique allows uniform alignment without any stripe textures [6], and therefore domain wall motion and related domain switching is not included in the theoretical model.
2.
The Model
The previous model introduced by H. Pauwels [7] assumes a uniformity along the thickness of the LC, therefore a monostable state can be specified by only one variable. This model includes the dielectric interaction, which becomes important for high positive values of dielectric anisotropy of the material. This interaction leads to asymmetric CDR T-V characteristics between positive and negative driving voltage. Another model introduced by T. Nonaka and H.R. Duebal [4] also assumes a uniformity and gives similar continuous results. It contains the effect of the chevron structure and does not include the influence of dielectric torque. This model is confirmed by experimental measurements. Our model assumes a non-uniformity along the thickness of the sample, i.e. the position of the molecule on the smectic cone can change along the depth of the LC. It means that molecules in the bulk can have different states than the ones at the top or the bottom of the cell. This is caused by introducing two anchoring parameters, namely: polar and non-polar interaction. The model is based on the following energy expression: −
∂W ∂ 2ϕ 1 ∂ϕ (1) = EPS sin ϕ + α 2 − ε 0 E 2 ⋅ ∆ε cos 2 Θ sin 2ϕ = η 2 ∂ϕ ∂t ∂x
The first term of the equation describes the alignment of the spontaneous polarisation PS along the electrical field E, the second one expresses the tendency of the director to be parallel to the electrodes and the final term favors the alignment of the director along the electrical field for positive ∆ε. η is the viscosity of the LC medium. Two boundary conditions are crucial in this case:
α
TOP
∂ϕ = mγ 1 sin 2ϕ BT − γ 2 sin ϕ BT m AR sin ϕ BT ∂x BOTTOM
(2)
The parameters in this equation have the following meaning: γ1 – describes the non-polar interaction – the molecules prefer to be parallel to the glass substrates γ2 – describes the polar interaction – the polarisation of the molecules tends to point into the alignment layer AL AR – rubbing energy – the molecules prefer to align along the rubbing direction
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Figure 2. Time evolution during switching from the dark to the bright state for different values of rubbing strength AR Switching time for PS=19 nC/cm2 is around 500 µs, timestep 25 µs γ1 is a symmetric contribution in Equation 2. γ2 introduces an asymmetry for the boundaries – one surface interaction is weaker than the other one and allows the molecule to switch towards the other side of the cone. AR introduces an asymmetry between the positive and the negative driving voltage.
(Fig. 2b) only the molecules on the weak surface switch. Finally for large AR value (Fig. 2c) molecules at the borders stay in their fixed positions namely aligned with the rubbing direction. The switching time is relatively small in all cases therefore this material could lead to fast applications.
From the technological point of view the value of the rubbing strength AR can be expressed as the following [8]: 2πrR AR = Nl 1 + v
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where: N – number of rubbing treatments, l – pile impression of the rubbing cloth on the substrate ,r – number of rotations of the rubbing roll, R – radius of the rubbing roll, v – translation velocity of the substrate relative to the roll.
3.
– –
AR1 small (smaller than anchoring forces) – bottom surface weaker than the top one AR2 moderate (in the range of anchoring forces) – bottom surface weak, top surface strong AR3 high (higher than anchoring forces) – bottom and top surface both strong
The simulation program is able to calculate the distribution of the ϕ-angle (position of the molecule on the smectic cone) along the thickness as well as an average transmission throughout the sample. The results can be displayed in function of time as well.
3.1
Switching
First we simulate the switching to see how the molecules behave in the bulk and at the borders for different values of AR. Typical values of the parameters are: γ1=1⋅10-4 N/m, γ2=5⋅10-5 N/m, AR1=48, AR2=96, AR3=144 J/m2. The driving voltage is high enough to switch the molecules in the bulk from their starting positions towards the other sides of the cone. The simulations in Fig. 2 represent the positions of the molecules along the cell thickness. The state of the molecule is described by the angle ϕ on the smectic cone (see Fig. 1a). The molecules behave differently at the borders for different values of AR. For small AR (Fig. 2a) both surfaces allow them to switch to the opposite side of the smectic cone, for moderate AR
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Results of Simulations
Our aim is to investigate the switching of the LC material with the phase sequence I-N*-SmC* for different alignment conditions of the molecules and thus the influence of the technology on the optical response of the display. For the standard values of the anchoring forces we choose different values of rubbing parameter and divide our simulations in three general cases: –
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Figure 3. The soultion of Equation 2 for different values of parameter AR The differences at the borders are explained by the boundary conditions for various AR. Fig. 3 presents the plot of the boundary conditions (Eq. 2) for different values of parameter AR at the top and the bottom of the simulated structure. For small AR both derivatives change sign therefore both surfaces allow border molecules to switch to the opposite side of the cone. For high AR the rubbing force becomes dominant, the sign of derivatives remain unchanged and switching at the borders does not occur. We also mention the influence of the spontaneous polarisation PS on the switching behavior, not only as the change of the switching time, but also as the influence on the state of molecules in the border regions. The higher the PS value the easier the molecules at the borders switch for the same value of AR.
3.2
Optical Response
We simulate the optical response of the sample with two different switching profiles: (a) all molecules including borders switch to the opposite side of the cone (see Fig. 2a) and (b) only bulk molecules switch (see Fig. 2c). The simulations are performed with the following parameters: d=2.1 µm, ε1=5.2, ε2=ε3=4.8, Θ=22.5 0, λ=550 nm, ∆n=0.13.
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decreasing pulse whereas for high AR they follow the driving wave. The transition for small AR and 1.25 V pulse (saturation voltage) exhibits interesting behavior (Fig. 5). The fast change of the transmission, indicated by the circle in Fig. 5, is related with overcoming the anchoring forces and the switching of the border molecules to the other side of the cone (see Fig. 2a). This switching leaves the cell in a different local energy minimum and thus the molecules do not relax back when a 0V pulse is applied (hysteresis). For large AR hysteresis does not occur because the border molecules do not switch at all.
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One of the crossed polarizers is situated along the rubbing direction. The applied waveform is a monopolar square wave with 10 ms pulse width and varying amplitude.
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Figure 5. Optical response for small AR value and different applied voltages
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The different switching behavior depending on the AR value leads to two different transmission-voltage characteristics namely: normal switching (bistability with hysteresis) and so called CDR switching (Continuous Director Rotation mode). Switching with hysteresis possesses only two states: the black and the white one whereas CDR-mode has also stable intermediate states. These states are fully controlled by the driving voltage and allow the FLC-cell to produce grey levels.
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Figure 4. Transmission for different values of rubbing strength for (a) increasing and (b) decreasing driving pulse Figure 4 presents the time variation of the transmission in two cases of different rubbing strength. Fig. 4a corresponds with the increasing square wave from 0 to 2.5 V with a 0.25 V step. In the first case (small AR) the molecules, for a certain VSAT (saturation voltage), switch from the dark to the bright state and stay in this state even with short 0 V switch-back pulse. For high AR (second case) the molecules follow the driving wave – they switch with the positive pulse and relax back with 0 V pulse. The output transmission is proportional to the driving voltage. Fig. 4b shows a similar simulation with a decreasing square wave from 2.5 to 0 V with a 0.25 V step. The response of the device looks the same. For small AR switched molecules do not relax back with the
Fig. 6a presents the simulation of the transmission-voltage characteristics for a low value of AR and two different values of PS, namely 9 and 19 nC/cm2. The optical transmission varies from 0 to 1 with a small hysteresis loop in both cases. Fig. 6b (moderate AR) shows a similar behavior for the higher PS value but a different continuous switching for the smaller PS value. For large AR (Fig. 6c) the continuous mode occurs in both cases. This means that the CDR-mode is observed only for high value of AR (without any influence of PS) as well as for moderate value of AR when PS is sufficiently small.
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Figure 6. Transmission-voltage characteristics for different values of rubbing strength AR and spontaneous polarization PS
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Figure 7. Total interface interaction energy for different voltages applied, V0=0 V, V1 γ 2 > 2γ 1 − AR
(4)
It is important to mention the switching times in the case of CDR mode. We define the switching time as a change of the transmission between 10 % and 90 % of the opposite states. tON depends strongly on the driving voltage and varies between 6 ms and 500 µs. The higher the driving voltage the shorter the tON. tOFF is almost independent (it slightly depends on the last position of molecules on the smectic cones but we can assume that it is constant). Both switching times depend of course on the spontaneous polarization and viscosity of the LC. Returning to the switching and comparing it with the optical characteristics we can conclude that switching of the molecules at the borders leads to hysteresis in the optical behavior whereas their fixed positions (strong rubbing interaction) favor CDRmode. This can be visualized by the energy distribution of the molecules in the LC medium.
3.3
4.
The stable solutions on the graphs are marked with a dot. Fig. 7a and 7b correspond with a switching cycle with hysteresis. The stable solution remains in the same position up to some threshold value and afterwards it relaxes to the other minimum level. The same cycle occurs when switching in the opposite direction. Fig. 7c represents the CDR-mode with stable solutions controlled
Conclusions
In this paper we presented an improved model of the material with a phase sequence I-N*-SmC*. We showed that this material has all suitable advantages for high-demand applications. We visualised the real non-uniform switching of the molecules and the influence of the border regions on the optical characteristics of the device. We confirmed that CDR-mode provides full grey scale capabilities and is fully controllable by the driving voltage. We showed that not only material properties are essential but also the technology and manufacturing is very important. We investigated the influence of both the material (PS) and the technology (AR) parameters on the optical response of the device. We hope that our theoretical investigations will be useful for designing and manufacturing real working devices.
5.
Energy State
We simulate the interface interaction energy under the assumption of uniform ϕ for different voltages to see the minimum energy state (stable position) among all possible solutions. One of the simulations is performed without the influence of AR which represents the presence of the SmA phase (Fig. 7a). The minimum energy when no electric field is applied is equally distributed so the molecules can align along both sides of the cone with the same probability (Fig. 7a, V0). Introducing the AR parameter gives a preferable direction for the orientation of the director but still two local minima exist (Fig. 7b, V0). Finally the high value of AR forces the molecules to align only along the rubbing direction, the energy level has only one possible minimum (Fig. 7c, V0).
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by the applied voltage. One must emphasize the absence of hysteresis. This behavior leads to a continuous movement of the director on the smectic cone and allows to control the grey levels.
References
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[2] Matsumoto, S., Seyama, S., Ukai, Y., Unate, T., Moriya, M., Inada, T., Saigusa, K., Euro Display ‘96, p.445, 1996
[3] Okumura, H., Akiyama, M., Takatoh, K., Uematsu, Y., SID’98 Digest, p.1171, 1998
[4] Dubal, H.R., Nonaka, T., Li, J., Ogawa, A., Hornung, B., Schmidt, W., Wingen, R., Liquid Crystals vol.26, no.11, p.1599, 1999
[5] Hatano, T., Yamamoto, K., Takezoe, H., Fukuda, A., Jpn. J. Appl. Phys. 25, p.1762, 1986
[6] Asao, Y., Togano, T., Terada, M., Moriyama, T., Nakamura, S., Iba, J., Jpn. J. Appl. Phys. 38, p.5977, 1999
[7] Pauwels, H., Zhang, H., Dubal, H.R., SID’00, p.72, 2000 [8] Verweire B., Fornier, J., Cnossen, G., Ferroelectrics, vol. 213, p.133, 1998
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