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4.2.2 The supertwisted nematic LC cell (STN-LCD)
ОглавлениеLinear polarized light is fed into the STN cell (Scheffer and Nehring, 1998) again with α = 0 in Figure 4.1. The twist angle β at z = d is, however, β > π/2, with values typically between π and 3(π/2). With the twist angle β in Equation (4.49) and a in Equation (4.48), we rewrite γ in Equation (4.47) with p from Equation (4.49) as
With γ in Equation (4.64), and β0 in Equation (4.50), Equation (4.52) governing the field-free state provides for the coordinates x′ and y′ with the angle ψ in Figure 4.1, and again, drawn in Figure 4.5
(4.65)
leading to
Figure 4.5 Angles and coordinates for an STN display
and
For
Equations (4.66) and (4.67) yield
(4.69)
and
Osx′ reaches its maximum
(4.71)
for
If the axis x′ of the analyser is at an angle ψ = −α to the x-axis, the maximum intensity passes the cell. For energy reasons the intensity in the y′ -direction must be zero, which is met in Equation (4.70). The direction x′ for maximum intensity is shown by dashed lines in Figure 4.5. The condition in Equation (4.68) for maximum intensity yields for a from Equation (4.64)
(4.73)
with the first realizable value for v = 2. For β = 3(π/2), we obtain the values
(4.74)
From Equation (4.64), we calculate the thickness
For λ = 550 nm, β = 3(π/2), and Δn 0.05 the thickness is d = 14.5 μm. As the thickness in Equation (4.75) is proportional to β, STN displays operate with thicker cells than regular TN displays.
The intensity passing the analyser at an angle ψ describes the normally white state, with the maximum for ψ = −α. If a high enough field is applied, the linear polarized light reaches the analyser at the angle α, resulting (according to Figure 4.5) in a component
For α = π/4, and hence ψ = −α = π/4, we obtain Ea = 0 independent of λ. This normally white state exhibits an excellent black state, and works with crossed polarizers.
For the optimum ψ = −α and the normally black state, the analyser has to be placed, due to Equation (4.70), in the y′ -direction, which is for ψ = −α = −π/4 parallel to the polarizer. In this case, however, Osy holds only for one wavelength in Equation (4.75). The white state after a field has been applied fully passes the analyser.
As the normally white state exhibits a black independent of wavelength, it is the preferred mode of operation.
If the large thickness of an STN cell is decreased, the transmission falls below optimum and some luminance is sacrificed, but a wider viewing angle is obtained. The reason for this will be explained in the chapter on compensation foils later.
The larger twist angle β in supertwist nematic LCDs has a pronounced effect on the transmitted luminance versus voltage curve in Figure 4.6 by rendering the transition from the white state to the black state much steeper. As will be explained in Chapter 12, this enhanced steepness is required for addressing an STN cell with a larger number of lines without losing too much contrast. The increase in steepness with increased β is now explained phenomenologically. In the transition from, let’s say, the white state to the black state, the LC molecules have to be tilted by a torque stemming from the applied electrical field. They finally end up parallel to the field. A smaller torque is needed if the molecules exhibit a larger twist angle from layer to layer as the restoring force by the vertically neighbouring molecules becomes weaker. Hence, a smaller voltage is required to achieve the tilt angles.
Figure 4.6 Transmitted luminance and midlayer tilt versus the voltage across an STN cell with a twist of β = 240°, an off-voltage of 2.58V and an on-voltage of 2.75V for addressing 240 lines (Reproduced from Scheffer and Nehring, 1998 with permission of Annual Reviews.)
A calculation of this effect is based on fluid mechanics and liquid crystal continuum equations (Degen, 1980), where the mechanical parameters K11, K22 and K33, the dielectric constants ε┴ and ε||, the pretilt angle at the orientation layers and, of course, the twist angle β and d/p play a role. The calculations are similar to the electro-optical investigations of TN cells in Section 4.1, because propagation matrices based on the mechanical properties are established for a sequence of twisted layers, and are finally multiplied.
Figure 2.12 shows that the tilt of the molecules is larger in the midlayer due to the restoring forces of the molecules anchored on top of the orientation layer. Figure 4.7 depicts the midlayer tilt versus the voltage VLC across the cell with twist angles β as a parameter. The larger is β, the greater is the slope of the curves. For β = 3π/2(270°) the curve rises perpendicularly in the centre portion. For β greater than 270° the curves become double-valued, causing bistability and hysteresis. Therefore, the twist must not exceed 270°. STN cells use twists between 180° and 270°, where 240° is often encountered as the electro-distortional curves are steep, but sufficiently removed from bistability.
To sustain these large twists, chiral compounds have to be added. The chiral dopant imparts an intrinsic twist, given by d/p, to the helical structure. On the other hand, the twist angle is also imposed by the angular difference ΦT of the rubbing directions. A matching of the two constraints requires d/p = ΦT/2π. In practical STN cells d/p > ΦT/2π is chosen, which compresses the helical structure in order to avoid the phenomenon of stripes. These stripes are generated if the condition that the local optic axis changes orientation only along the spatial coordinate perpendicular to the layer is not met (Nehring and Scheffer, 1990). They result in scattering of light, rendering the display unacceptable.
In Figure 4.8, the influence of the pretilt on the electro-distortional curve is depicted. The larger the pretilt, the smaller the voltage needed to tilt the molecules. This is understandable, as the molecules with larger pretilt are already rotated in the right direction.
Figure 4.7 Midlayer tilt versus voltage of an STN cell with twist angle β as a parameter (Reproduced from Scheffer and Nehring, 1998 with permission of Annual Reviews.)
Figure 4.8 The influence of the pretilt angle on the electro-distortional curve of the midlayer in an STN cell (Reproduced from Scheffer and Nehring, 1998 with permission of Annual Reviews.)
Finally, Figure 4.6 shows both the midlayer tilt and the transmitted luminance versus VLC for a twist of 240°. The transition from white to black is considerably steeper than for the regular 90° TN cell in Figure 2.13. It exhibits an extended linear range leading to a good grey scale operation. It is interesting to note that a sufficient black state occurs even when the midlayer has not yet reached 90°. In Figure 4.6, the display assumes a desired grey shade if voltages in between the on-voltage (fully black) and the off-voltage (fully white) are applied. The off and on voltages are 2.58V and 2.75 V, respectively representing a comparatively small voltage difference for switching a display with 240 lines.
The voltage-induced change of the orientation of the LC molecules also affects the colour appearance of an image. This is demonstrated in Figure 4.9, where the luminance vs. the wavelength of the display in Figure 4.6 is shown. For an off-voltage of 2.58 V, the colouring is greenish-yellow. With increasing voltage, the display becomes bluer, ending up with dark blue at the on-voltage of 2.75 V. This mode is called the yellow mode, which is used in inexpensive displays. Other colours are generated with larger values for dΔn. More on this colour generation is presented in Section 4.3.
