Liquid Crystal Displays. Ernst Lueder

alignment of the Fréedericksz cell in the field-free state. Hence, all results in Equations (3.40) through (3.87) also apply to the DAP cell, which is exposed to an electric field. The DAP cell is as well suited for phase-only modulators, as the pertinent Equations (3.90) and (3.95) also hold if a voltage V is applied. However, for the voltage-dependent refractive index n(V), we obtain , but contrary to the Fréedericksz cell with n┴ for the lower voltage and n|| for the higher voltage. The homeotropic alignment of the molecules in the DAP cell requires special care. It is achieved by a spin-coated monomolecular silane-layer dissolved in ethyl alcohol, which is polymerized in the presence of humidity. The high polarity of silane thus generated anchors the polar LC molecules perpendicular to the surface. If a voltage is applied, all molecules are supposed to tilt in the same direction, since they have to end up all in parallel to each other and parallel to the plane of the substrates. This is realized by a small uniformly oriented pretilt of around 1 ° to 2° off the normal of the surface. A larger pretilt must be avoided, since it degrades the black state. The polymerized silane layer is uniformly rubbed with a carbon fibre brush to generate the grooves for the orientation of the molecules. As an alternative, this pretilted uniform orientation is produced with a very high manufacturing yield by an SiO₂ layer obliquely evaporated or sputtered under an angle of 2° off the normal. This alternative also achieves a very high contrast exceeding 500: 1. The sputtering of this SiO₂ layer is explained in Figure 3.18. The DAP cell is, like a Fréedericksz cell, designed as a λ/2-plate with a retardation Δnd = λ/2, and hence d = λ/2Δn. For most commercially available LC materials exhibiting Δn = 0.08, this leads for λ = 550 nm to a cell thickness of d= 3.4 μ. The reflective version is a λ/4-plate with a thickness of d= 1.7 μ, which is often too thin for a high yield fabrication because small particles could easily cause shorts. The search for electro-optical effects with a larger cell thickness leads to the HAN cells and the Twisted-Nematic cells (TN-cells), which are covered in the next subsection and in Chapter 4.

Figure 3.18 The sputtering of an SiO₂ orientation layer under an oblique angle of 70°

      A reflective DAP cell with a thickness d/2 can be constructed in the same way as a Fréedericksz cell.

       3.2.6 The HAN cell

The Hybrid Aligned Nematic cell (HAN cell) represents a mixture between the Fréedericksz cell and the DAP cell (Glueck, 1995). We investigate the reflective version in Figure 3.19(a), because among untwisted cells they have turned out to be more important. On the plate with the polarizer the LC molecules are in the field-free state in Figure 3.19(a) oriented all in the same direction parallel to the surface of the plate like in a Fréedericksz cell, whereas on the plate with the mirror they are homeotropically oriented. The linearly polarized light enters the cell at an angle α ≠ 0 to the x-axis, as in the transmissive and reflective Fréedericksz cells. The optical anisotropy Δп changes with z described by Δn(z). At z = 0 the light wave encounters the full anisotropy Δn, meaning that Δn(0) = Δn. This is only true for α ≠ 0. At z = d the light encounters no anisotropy as the medium is isotropic with a refraction index n_┴, reflecting in Δn(d) = 0. Assuming a linear change of Δn(z) we obtain Δn(z) in Figure 3.19(b), leading to an effective retardation R of

      (3.96)

Figure 3.19 The reflective HAN cell. (a) Cross-section; (b) optical anisotropy An(z)

We know from Equations (3.45) and (3.54) that a retardation of λ/4 transforms linearly into circularly polarized light as desired at the mirror of a reflective cell. From (1/2) Δnd = λ/4 we obtain

(3.97)

      This is twice the thickness of the reflective Fréedericksz and DAP cells, resulting in a higher fabrication yield. This advantage of the HAN cell was brought about by lowering the effective birefringence. We shall encounter the same effect again with TN cells.

The reflection of the circularly polarized light in the field-free state is depicted in Figure 3.20(a) (Glueck, 1995). After the reflection the wave reaches the polarizer rotated by 90° and is blocked. If a field is applied in Figure 3.20(b), the molecules orient themselves due to Δε > 0 in parallel to the field, birefringence does not take place, and the reflected wave passes the polarizer. The cell is normally black.

      For the homeotropic alignment of the molecules, an obliquely evaporated or sputtered SiO₂ orientation layer is again a good solution.

Figure 3.20 The operation of a reflective HAN cell. (a) In the field-free state; (b) if a voltage is applied

       3.2.7 The π cell

      So far we have not dealt with the time needed to switch an LC cell from the black state to the white state, or vice versa. Dynamics of a cell are based on mechanical properties of the LC material, and will be discussed in Section 3.2.8. Some information on switching speed can, however, be derived from the field of directors. That’s how a very fast switching cell, the π cell, has been found (Bos and Koehler, 1984), as will be outlined later in this chapter.

The Fréedericksz cell and the TN cell exhibit a uniform alignment of the molecules with a pretilt α in the opposite direction on the substrates, as shown in Figure 3.21(a) for the on-state of the cell. After the electric field has been switched off, the molecules relax to the off-state, resulting in a low of LC material and a tilting of the molecules. The molecules around the centre of the cell are exposed to a torque, causing aback-flow of the material and trying to rotate them through a large angle to the position in the off-state. This slows down the switching process. Figure

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