Chapter 9 Electro-optic Properties of LCD

Transcription

1 Chapter 9 Electro-optic Properties of LCD 9.1 Transmission voltage curves TVC stands for the transmittance-voltage-curve. It is also called the electro-optic curve. As the voltage is applied, θ(z) and φ(z) changes. Therefore the transmission will also change. T = T(θ(z,V), φ(z,v)) The TVC has to be calculated numerically. Commercial software are available for such calculations. One can estimate the TVC from the parameter space diagrams. Basically, the most important change is that n -> 0. So it is like a vertical line drawn on the PS pointing towards the x-axis. Select and nonselect voltages: It is common to call the lower voltage near the Frederick transition the nonselect voltage (V ns ) or the off voltage (V off ), and the higher voltage the select voltage (V s ), or the on voltage (V on ). For the normally black LCD, the names are correct. But for the normally white LCD, the on-off nomenclature can be confusing. It is better to use the V s and V ns terminology. 1

2 The following is the TVC for normally white 90 o TN and 180 o STN and 40 o STN displays. Transmittance Voltage 45 twist 70 twist 90 twist 40 Transmittance Voltage

3 Notice that the 45 o twist case shows a sharp transition. That transition can be further optimized to dominate the TVC by varying d/p. It is the basis of STN optimization. 9. Contrast ratio The contrast ratio is defined as CR = T ( Vs ) T ( Vns) or T ( Vns) T ( Vs ) whichever is larger than unity. There are possibilities because the LCD may be normally bright or normally dark. The transmission depends on the wavelength. So we can define an average CR as <CR> = Thi ( λ) f ( λ) dλ Tlo where f(λ) is the photopic response curve of the human eye. Typical CR of TN display is 0:1. STN can be as bad as 5:1. AMLCD can be as good as 00:1. The CR determines the number of grayscales that the display can have. It does not make much sense to have a lot of grayscale if the CR is not high. CR depends on the steepness of the TVC and the ratio of the select to nonselect voltage. This ratio is called the selection ratio. Steep TVC means the selection ratio does not have to be too large for good contrast. 3

4 Some definitions: V 10, V 50 and V 90 are the voltages at 10% 50% and 90% transmission respectively for a NB display. The steepness coefficient is defined as V p = 90 1 V10 Steep TVC corresponds to small p. Empirically p = K d n ln K11 λ p also increases with Φ and increases with decreases with increasing pretilt angle. ε. It also ε 9.3 Viewing angle References: A. Lien, Appl Phys Lett 57, 767 (1990) P. Yeh, J Opt Soc Am, 7,507 (1983) All the above formulas are only valid for normal angle of incidence. Obviously, the transmittance depends on the angle of incidence of the light or the viewing direction. The viewing direction is defined using the clock 4

5 Viewing direction θ y-axis φ x-axis 6 o clock: (θ, φ) = (45 o, 90 o ) 1 o clock: (θ, φ) = (45 o, -90 o ) Most LCDs are optimized for 6 o clock viewing. The viewing angle is shown in a polar plot. It is usually calculated using the Berreman 4x4 matrix approach. It is also possible to use the extended x Jones matrix to analyse such problems. The viewing angle depends on the voltage which affects θ(z) and φ(z) inside the LC. At each voltage, one can plot the transmittance as a function of (θ, φ). The contrast ratio is defined as the ratio of transmittance between the bright and dark states. For the normal TN, 5

6 the bright state is the low voltage nonselect state; while the dark state is the higher voltage select state. For segment TN LCD, the nonselect voltage is zero volt for convenience. Extended x matrix: (Ref. P Yeh, Optical Waves in Layered Media, Wiley 1988) The usual Jones matrix is defined for normal incidence. If the incidence angle is not normal, we have double refraction and difficult boundary conditions matching. p polarizer θ ο o y,s α φ D 1,e x z K i In the general geometry, it is easier to define the x-axis to be on the plane of incidence. Hence the input LC director will not be on the x-axis. It is at angle φ to the x-axis. Also the polarizer is defined relative to the x-axis, not the input LC director. For the case of wave incident from an isotropic medium to a uniaxial medium, we can match the boundary conditions 6

7 and take care of double refraction by converting the s and p wave into the e and o waves inside the crystal E E e o R p,e R s, e E = ( ) ( ) R p,o R s, o ( ) ( ) E p s where R( p, e) = R( e,p) = p e R( s,e) = R( e,s) = s e R( p, o) = R( o,p) = p o R( s,o) = R( o,s) = s o In the above diagram, s = y p = cos θ x sin θ z o and e depends on φ R is the coordinate transformation matrix from (p, s) to (e, o) axes. Therefore the Jones vector of the output after going through the uniaxial medium is given by E E p s ' R( e,p) R( o,p) exp( ik ezh) ' = σ R( e,s) R( o, s) 0 0 R( p, e) R( s, e) E exp( ik ozh) R( p, o) R( s, o) σ E p s E p = J E s For a single uniaxial layer, the problem is straight-forward. Now for the LC cell, we have to divide the LC into many layers and the c-axis of each layer is different form the next. How do we match the boundary conditions? There are approached to the extended Jones matrix. Lien et al match the E field or H field B.C. Yeh et al assumes a zero 7

8 thickness isotropic layer to aid the B.C. matching. In that case, the overall Jones matrix is simply J = J J J J J J N N 1 n 3 1 where the J n s are given above. Such calculations are necessarily numerical. In general, higher twist more symmetrical better viewing angles. Also, the homeotropic state always poor viewing angle. Therefore, new LCD modes such as (0, π) BTN or chiral nematic or in-plane switching modes all try to get rid of the high voltage homeotropic state and all have excellent viewing angles. One can also draw the contrast polar plot using any commercial software, by specifying the operating voltages. Here is an example for TN designed for 6 o clock viewing. 8

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11 Interesting case: calculate the viewing angle of a cross polarizer system without any LC cell. Use the above geometry, P in = cos α x + sin α y P out = sin α x - cos α y Therefore s P in = sin α p P in = cos θ cos α Let (ζ, η) be the unit vectors parallel and perpendicular to the projection of P in onto the (p, s) plane. So ς = sinα s + cosα cosθ p where = sin α + cos α cos θ The field before entering the polarizer is given by E = 1 Eo s + 1 Eo e jψ p where ψ is a random phase. Assuming a perfect polarizer, only the ζ component passes through. The output field is therefore E = 1 1 ts E o (ζ s)ζ + tp E o e jψ (ζ p)ζ where t s and t p are the Fresnel transmission coefficients. Now if we pass this through a cross polarizer, i.e. polarizer angle = α+π/, we shall have the same formulas, but with α replaced by α+π/. Then after some algebra, it can be 11

12 shown that the transmission through this cross polarizer system is given by T = T 4 s T p sin φ cos φ sin θ (1 sin θ sin φ)(1 sin θ cos φ) This is an interesting result. It shows that even a perfect cross polarizer system will have leakage when viewed at oblique angle of incidence. There is no leakage for φ = 0 o or 90 o. Maximum leakage occurs at φ = 45 o. In that case, T = T 4 s T p sin θ ( sin θ ) (Exercise: Plot T as a function of θ.) 9.4 TVC at oblique angles of incidence The TVC at oblique angles of incidence has to be calculated numerically. The TVC can depend on the viewing angle very strongly. The following is an example for a second minimum TN display viewed along the 6-1 o clock direction. One interesting observation, the steepness of the TVC depends on the viewing angle the multiplex ratio will also depend on the viewing angle. 1

13 These curves are calculated at 45 o incidence angle. It should be noted that for the 1 o clock position, there is almost no contrast at all. On the other hand, the 6 o clock case has a low threshold and an image reversal. 9.5 Wide viewing angle displays The viewing angle of TN and STN displays are limited mainly by the homeotropic state. These displays rely on a high voltage homeotropic state as either the bright or dark state. The homeotropic state is highly birefringent and the birefringence depends strongly on the viewing angle. It is possible to eliminate this homeotropic state using some new designs, such as in-plane-switching (ISP), inverse chiral nematic mode, and the use of bistable TN (BTN) displays. The common feature in all of these displays is that both the on and off states are twisted nematic states. The homeotropic state is not used. 13

14 For the BTN, the horizontal viewing angle can be as large as 180 o, which is the same as an emissive CRT! Here is an actual measured result for BTN: 14

15 The viewing angle can be calculated using a commercial software. Since there is no applied voltage, the calculation is straightforward. 15