Application of antiferroelectric liquid crystals with high tilt

232.4 The direction of the optic axes for a ferroelectric liquid crystal... deforma-352.12 The direction of the optic axes for an antiferroelectric liquid crystal.. A further subdivision

Liquid Crystals with High Tilt

Koen D’havé

Promotor: prof dr ir H Pauwels

Proefschrift ingediend tot het behalen van de graad van Doctor in de Toegepaste Wetenschappen: Elektrotechniek

Vakgroep Elektronica en Informatiesystemen Voorzitter: prof dr ir J Van Campenhout Faculteit Toegepaste Wetenschappen Academiejaar: 2001-2002

Tai ngay!!! Ban co the xoa dong chu nay!!!

Acknowledgement

1 Introduction 1

1.1 The current display market 1

1.2 Liquid crystal displays 3

1.2.1 The liquid crystal phase 3

1.2.2 Liquid crystal displays; layer by layer 6

1.3 Quantification of the image quality 10

1.4 An overview of this work 12

2 Ferroelectric and antiferroelectric liquid crystals 15

2.1 SmC and SmC* phases 15

2.1.1 Structure 15

2.1.2 Dielectric tensor 17

2.1.3 Optical properties 21

2.1.4 Ferroelectric liquid crystal displays 22

2.2 The SmCa and SmCa* phases 28

2.2.1 Structure 28

2.2.2 Dielectric tensor 30

2.2.3 Optical properties 33

2.2.4 Antiferroelectric liquid crystal displays 36

2.3 The first goal 38

3 Alignment of AFLCs 39

3.1 Prototype cells 39

3.2 Optimization of the buffing parameters 42

3.3 Compensating the rubbing directions 45

3.4 Obliquely evaporated SiOx 49

3.5 Conclusion 51

4 Orthoconic antiferroelectric liquid crystals 53

4.1 Uniaxial anticlinic conditions 53

4.2 Isotropic anticlinic conditions 56

4.3 A solution for the dark state problem of an AFLCD 56

4.4 Orthoconic antiferroelectric liquid crystals 58

4.5 Phase modulation by means of OAFLCs 61

4.5.1 Polarisation switches 61

4.5.2 An alternative construction for an OAFLC display 63

4.5.3 Ternary phase modulation 64

4.6 The pretransitional effect in AFLCDs 70

4.7 Conclusion 73

4.8 The second goal 74

5 Reflective AFLCDs 75

5.1 Normally bright mode 75

5.2 Normally dark mode 77

5.2.1 A λ/4 film between liquid crystal layer and mirror 77

5.2.2 A λ/4 film between polariser and liquid crystal layer 80

5.3 Conclusion 82

5.4 The third goal 82

6 Light scattering polymer dispersions of OAFLC 83

6.1 Polymer Dispersed Liquid Crystals 83

6.2 OAFLC in a polymer matrix 85

6.3 The influence of the material parameters 86

6.3.1 Extinction in a light scattering medium 86

6.3.2 Anomalous diffraction 87

6.3.3 Influence of the tilt angle 91

6.3.4 Influence of the birefringence 93

6.3.5 Viewing angle dependency of the transparent state 93

6.3.6 Conclusion 96

7 Conclusions 97

7.1 Achievements 97

7.2 Some remarks 98

A Data sheets 99

A.1 CS4001 99

A.2 W107 100

A.3 W107a 102

A.4 W107b 104

A.5 W123 106

A.6 W124 108

A.7 W129 110

Bibliography 113

232.4 The direction of the optic axes for a ferroelectric liquid crystal

27

2.7 The operation of the Twisted Smectic Mode in the SmC* phase.This mode is similar to the twisted nematic mode The electro-optic behaviour is ‘normally bright’

2.8 The operating principle of the V-shaped switching mode in theSmC* phase Note that the choice of the directions of polariser andanalyser differ from the TS-mode The electro-optic behaviour isalso reversed

29

2.9 A schematic illustration of the difference between (a) synclinic and(b) anticlinic behaviour

30

2.10 A representation of a full pitch length of the helix in the SmCa*

pha-se The helix represented here is an idealized structure To be moreprecise the director in adjacent layers of the unit cell does not make

a phase angle difference of exactly 180°

32

2.11 The position of the glide mirror plane and the symmetric tion with respect to the ideal anticlinic structure When the symme-tric deformation reaches 90°, one obtains a synclinic state At thatmoment the angle ψ describes the phase angle of the SmC phase.This description will allow us to determine the direction of theprinciple axes and their matching refractive indices in a more sim-plified manner

deforma-352.12 The direction of the optic axes for an antiferroelectric liquid crystal

372.13 The working principle of an AFLCD

43

3.3 The alignment (left) obtained for a cell of which only one substratereceived an optimal buffing treatment The right part of that pictureshows the deformation of the structure when applying even smallelectric fields The other picture (right) shows the structure afterprolonged addressing of such a cell

45

3.4 The straightening of the smectic layers by an electric field The vrons, which are created due to shrinkage of the layers during cooldown, endure a straightening torque Instead of creating a books-helf structure, a defect structure in the plane of the cell, which is cal-led the striped texture, is obtained Between crossed polariser onesees a grid of alternating bright and dark lines

4.1 The necessary tilt angle as a function of the symmetric deformationwith respect to the ideal anticlinic structure in order to obtain auniaxial phase The parameters used are: , and

57

4.2 Approximation of the striped texture by an alternating bookshelfstructure The slow axis for a normal AFLC (a) alternates, for anAFLC with 45° tilt (b) the optic axis is perpendicular to the layernormal and can therefore not alternate, there is no slow axis in thatcase

58

4.3 This sequence shows the switching from the anticlinic state to thesynclinic state for the orthoconic antiferroelectric material W107.Note that the defect structure is not visible in the dark anticlinic sta-

te For the bright state the defect structure is of minor importance

59

4.4 The switching process for a “non-aligned” OAFLC sample betweencrossed polarisers The layer normal is oriented parallel to thesubstrates

60

4.5 The rotation of an OAFLC sample between crossed polarisers.From the structure outside the pixel area we can conclude that thestructure inside the pixel can not be a perfect alignment of the ma-terial Nevertheless the transmission through the pixel is practical-

ly zero for all angles

66

4.9 Discretisation of the phase profile for pixelated devices One can ther modulate the thickness or the refractive index in order to mo-dulate the relative phase shifts between the pixels

72

4.14 Director profile obtained after exceeding the Fréederickszthreshold

76

5.1 A schematic representation of the optical geometry for the

normal-ly bright mode of a reflective AFLCD The anticlinic state is in thiscase the bright state

n1 = 1.5 n2 = 1.51

n3 = 1.7

5.2 A schematic representation of the optical geometry for a normallydark mode of a reflective AFLCD wherein the quarter wave film isplaced between the liquid crystal layer and the mirror Theswitched synclinic states are now the bright states

79

5.3 Visualisation of the solutions for an optimal bright state The dottedline represents the locus of the solutions corresponding to the firstand second maxima

80

5.4 A schematic representation of the optical geometry for a normallydark mode of a reflective AFLCD wherein the quarter wave film isplaced between the polariser and the liquid crystal layer The syn-clinic states are the bright states

846.1 The principle behind PDLC devices

91

6.4 The influence of the tilt angle on the relative scattering cross section

of the droplets PDOAFLC in the anticlinic state The parameterswhich are used here are: , and Thepolarisation is taken to be along the axis corresponding to Forthe polarisation perpendicular to it, , thus according tothe axis belonging to , the sensitivity of the tilt angle is found to

93

6.6 The influence of the birefringence on the scattering properties Forall curves an equally good index matching is assumed This impliesthat the curves for both perpendicular polarisations are almostequal

94

6.7 The viewing angle dependency of the transparent state for a

nemat-ic PDLC The parameters whnemat-ich are used here are: ,

101A.3 Helical pitch of W107, measured through selective reflection

103A.7 Threshold field of W107a, measured with a square wave of 10 Hz

1.1 The current display market

Next to the cathode ray tube, Liquid Crystal Displays (LCD) havebeen the most successful display technology so far In September 1999Stanford Resources predicted an annual growth of the number offActive Matrix Liquid Crystal Displays (AM-LCD) of about 18% untilthe year 2005 [1] This implies a doubling over a period of 4 years Ifone observes the position of the liquid crystal display in the flat paneldisplay market [2], one finds that no less than 90% of that market iscontrolled by this technology

About 50 years ago it was thought that flat panel displays, at thattime Electro-Luminescent (EL) displays, would soon replace the clas-sic Cathode Ray Tube (CRT) Today the CRT still rules supreme overthe two most important application areas, television and desktopmonitors

Television is by far the most important application area for the CRT.Although digital techniques are already quite common in audio appli-cations, such techniques for video applications have been delayed forquite some time Now, however, they are considered for imminentrelease Development of sound digital compression- and decompres-sion techniques allow for television images of superior quality The socalled ‘high definition television’ (HDTV) is nearing reality Theenhanced image quality is partially due to the nature of digital trans-mission and partially due to the larger amount of pixels (at least 4

times as much pixels as a standard TV) Research has shown that theaverage user always positions himself at the same distance withrespect to a display, independent of the size of the screen is If onewants to enjoy a higher resolution, one thus has to build larger dis-plays [3] For very high resolutions the diagonal of the screen ought to

be in the range of 60 inch, which is out of reach for the ogy and barely feasible with the current plasma technology It there-fore seems that for television applications the classic CRT-technologywill have to endure a competition with projection technology How-ever within that technology the CRT is still an option Apart from liq-uid crystal based projectors and micro mechanical light valveprojectors, CRT-projectors have been available

CRT-technol-The sudden appearance of the portable computer has created anew consumers’ market which is entirely dominated by liquid crystaldisplays No other technology has been able to threaten that position

so far, although the Organic Light Emitting Diode (OLED) technique,

in the long run, might sneak in Desktop monitors of personal puters were until quite recent entirely CRT dominated Neither theirbulk nor their power consumption were considered severe draw-backs Today, however, a fair amount of companies do believe in spaceand power saving arguments In many offices liquid crystal displaysare gradually replacing the CRT monitors The image quality of anLCD has become comparable to that of classical CRTs The elegantappearance of a liquid crystal display contributes to its popularity andcan by itself already justify its cost Stanford Resources, one of themost well-established market and technology research businesses ofthe display market, predicts an annual growth of the AM-LCD desk-top monitors of 45% for the next 5 years [1]

com-Opposed to other successful flat panel display technologies, liquidcrystal displays do not emit light They modulate light originatingfrom an external source There exist a number a possibilities to achievethis goal:

• By means of controlled absorption the amplitude of a beam oflight can be modulated This is the mechanism behind the ‘dich-roic dye’ type LCD [4]

• By means of controlling the scattering the direction of a lightbeam can be modulated ‘Dynamic scattering’ and ‘Polymer Dis-persed Liquid Crystal’ types build on this principle [5,99]

• The polarisation of light can be modulated by means of led birefringence ‘Twisted Nematic’ (TN) and ‘Supertwisted

control-Nematic’ (STN) are the best known representatives for devicesbased on this effect [6,7].

Reflective LCDs use the ambient light as the light source to be ulated In contrast to light emitting technologies this mechanism pro-vides a good readability in high luminance environments This andthe fact that liquid crystals fulfil two other important demands, a lowpower consumption and low driving voltage, justify the success ofthis type of displays for applications such as mobile telephones, elec-tronic video games, digital cameras, electronic agendas, etc

mod-Transmissive LCDs are more common for e.g computer screens.Instead of modulating the reflectance of the ambient light, they use ahigh luminance light source placed behind the display panel Thistype of display is well suited for indoor applications, such as desktopmonitors The readability of transmissive LCDs in high luminanceenvironments is rather weak In order to combine both properties ofreflective and transmissive LCDs a new technology has emergedcalled ‘transflective’ [8]

Other appealing properties of LCDs apart from their low powerconsumption are the possibility to create displays with high informa-tion content through use of an active matrix, the possibility to createfull colour screens and the possibility to further miniaturise the tech-nology However the currently dominating liquid crystal technology,the TN AM-LCD, is rather slow, the image depends on the angle of theviewing direction with respect to the screen, the useful temperaturerange is limited and the displays are not robust If one of the foremen-tioned properties is of utmost importance, one will revert to other flatpanel technologies as there are electro-luminescent displays (ELD) orfield emission displays (FED) To conclude this matter, for screens oflarger proportions (>75 cm) plasma displays (PDP), projection screens(>150 cm) and light emitting diode walls (LED wall) will be chosen

1.2 Liquid crystal displays

1.2.1 The liquid crystal phase

A material designated as a liquid crystal has a liquid crystal phase.This is a phase between solid and liquid which only appears in certainmaterials, also called mesogenic materials The liquid crystallinephases can be subdivided by the amount of order they posses This is

possible because the molecules show a certain orientational order,while they show no or limited positional order in various degrees.Apart from the liquid crystal phase there is a mesophase called plasticcrystal phase or disorder crystal phase [9] In such a phase the mole-cules do have positional order but lack orientational order The nameplastic crystal phase originates from the ease with which such materi-als can be deformed.

One can also differentiate between two main types of liquid talline materials: the lyotropic and the more known thermotropickinds The lyotropic liquid crystals are often simply obtained by mix-ing rod or disk shaped molecules in an isotropic solvent [10] Besidesthe temperature also the concentration determines the stability of themesophase For thermotropic liquid crystals the stability of the phasedepends only on the temperature Thermotropic liquid crystals areused in most cases of ‘technological’ applications such as displays,temperature and pressure sensors On the other hand lyotropic liquidcrystals are responsible for countless ‘biological’ processes

crys-The liquid crystal phases are usually divided in ‘nematic’ and

‘smectics’ The former term is used when only orientational order ispresent in the material The latter is used when next to orientationalorder also positional order is a characteristic of the material The smec-tic liquid crystals themselves then are further subdivided according totheir degree of order Another important property of a liquid crystal isits possible chiral nature To put it shortly, a liquid crystal is chiral ifthe mirror image of the structure can not be made to coincide with theoriginal structure by any means of rotations and translations Theusual example is that of our own hands Chirality has far-reachingconsequences for liquid crystals, it is not only responsible for helicalstructures but it is also a source for possible polarity A description ofknown liquid crystal phases can be found in reference [11]

The nematic liquid crystal phase

Rigid rod shaped molecules have a tendency to lie parallel to eachother, such that orientational order results If we put such a materialbetween two glass plates and place it between crossed polarisers, wewill see a large amount of defects The untreated glass surface has noclear preferential direction This results in different domains being cre-ated inside the liquid crystal layer in contact with that surface When

we look at a nematic material in a glass vial, it has a milky whiteappearance This is due to the light scattering caused by the domain-walls The average direction of the molecules at any point inside the

liquid crystal layer is given by the director n Since the molecules have

no head or tail (or pack in such a way that we can not distinguish

them), n and -n denote the same direction.

In most applications the formation of domains has to be pressed In order to do so, a thin liquid crystal layer is sandwichedbetween two carefully treated surfaces These surfaces impose bound-ary conditions on the liquid crystal molecules in contact with them.When the phase is chiral, a helical structure develops in the mate-rial When we move in a direction perpendicular to the director, thedirector itself rotates around that direction (see Figure 1.1) The dis-

sup-tance over which the director makes a full rotation of 360° is called the

pitch p of the material According to the sense of the rotation the helix

can be called left or right handed The name cholesteric which is oftengiven to chiral nematics has a historical origin The first chiral nematicliquid crystals were derived from cholesterol

The smectic liquid crystal phases

On top of the orientational order the molecules seem to order selves in ‘layers’ The molecules not only adopt the direction fromeach other but also which to be next to one another This results in aone-dimensional positional order as schematically illustrated in Fig-ure 1.1 The correlation between the layer normal and the orientationorder gives rise to a division of the smectic phases In this way oneuses the term ‘orthogonal smectics’ when the layer normal coincideswith the director as it does in e.g the SmA phase When these two

them-Figure 1.1: A schematic comparison between the nematic (N), the cholesteric(N*) and the smectic A (SmA) phases

order

N*

directions make a certain angle, as it does in the SmC phase, one usesthe term ‘tilted smectics’ A further subdivision is then based on thedegree of positional order inside the layers and/or the correlation ofthe orientation of the director in subsequent layers.

Chirality in tilted smectic phases gives again rise to the creation of

a helical structure in the material This time, however, the directordescribes more or less a screw line when we move along a directionperpendicular to the layers inside the material Another consequence

is polarity which will be described further in chapter 2

The two most important representatives of smectic liquid crystalphases from a technological viewpoint, are the SmC* and the SmCa*phases Because of their importance for this thesis, chapter 2 will beentirely devoted to their description and their application to electro-optic devices

1.2.2 Liquid crystal displays; layer by layer

Without an appropriate ‘container’ the properties of liquid crystalscan not be exploited Figure 1.2 shows a cross section of the pixels of a

typical matrix display, not drawn to scale The different layers fied in the figure are as follows:

identi-(1) Polariser/Analyser; These laminates respectively determine theentrance and exit polarisations

(2) The substrate; It needs to be as flat as possible and impregnable

to moist and gas It contributes to the structural stiffness of the

Figure 1.2: A schematic cross section of the pixels of a typical liquid crystaldisplay The purpose and the materials used for the different layers are fur-ther explained in the text

entire display To these purposes glass is an obvious choice.Originally soda-lime glass was used but it has gradually beenreplaced by borosilicate and aluminosilicate glass types Alsomonocrystalline silicon wafers for reflective miniature applica-tions are used Quite recently flexible substrates are being con-sidered, however those demand extra gas-barrier layers.

(3) The ion barrier; These serve the purpose of shielding the liquidcrystal from ionic impurities present in the glass substrate Usu-ally a sputtered combination layer of SiO2 and Si3N4 is entrustedwith this job By using high quality borosilicate and aluminosili-cate glass an ion barrier becomes unnecessary

(4) The black matrix; Its purpose is to prevent light leakage fromareas outside the pixel surface in order to increase the contrast.For active matrix displays it also has to shield the semiconduc-tor element from the intense illumination from the backlight andambient light This task is usually accomplished by a sputteredchromium layer covered with an insulating layer A more mod-ern material is a strongly absorbing polyimide that can bedeposited by spincoating, in that case an insulation layer is nolonger needed

(5) The colour filters; They are necessary to recreate all coloursthrough additive mixing in a triad of elements which build up atrue pixel Today polyimides which can be printed or deposited

by spincoating are used Earlier materials were based on tine

gela-(6) The electrode; If one wishes to apply an electric field over theliquid crystal layer a conductive layer is necessary On top ofthat it has to be transparent on at least one of the substrates Tothis means a sputtered and etched layer of indium-tin-oxide(ITO) is used More recently research into transparent conduct-ing polymer layers has made strong advances and has alreadygiven birth to a commercial product However these polymerlayers do show a lower transparency and higher resistivity forwhich they offer user friendliness and possibly even flexibility

in return For reflective displays one uses pure aluminium orpalladium-silver-copper alloys

(7) The alignment layer; This material is necessary to push a certainorientation on the liquid crystal in contact with it For this jobone uses polyimide layers as their properties can be tailored tomeet various needs Such polymers can be deposited through

spincoating or different printing techniques An alternative sists of evaporated siliconoxide and germanium layers Theevaporation mechanism limits the effective substrate size forthese materials.

con-The distance between the two substrates is kept constant through use

of ‘spacers’ Most common materials for this purpose are polymer orsiliciondioxide spheres with precise diameter Nowadays most manu-facturers are trying to switch to ‘post spacers’ These are little islandscreated by applying a photolithographic technique to a layer with pre-cise and uniform thickness deposited on top of the alignment layer

Passive matrices

By etching the electrodes in a one-dimensional stripe pattern,obtained on both substrates and crossed while assembling, a matrix ofpixels is formed Picture elements are created everywhere a stripeelectrode of one substrate crosses a stripe electrode on the other sub-strate One substrate serves as rows while the other serves as columns

In this way writing a picture consists of selecting each row tially by applying a certain voltage at the row electrode, voltageswhich represent the data for pixels belonging to the selected row arethen applied to the columns During the selection window each pixel

sequen-of a selected row receives a voltage which is the subtraction sequen-of thevoltage on the column the pixel belongs to and the selection voltage.Because pixels which do not belong to the selected row also receivethe data voltages, a strong non-linearity (the effect is not proportional

to the cause) is required from the liquid crystal In reality this impliesthat a sharp threshold is needed to avoid crosstalk problems Nematicliquid crystals react on the RMS-value of the applied voltage whichmeans that there is a limit to the number of rows a multiplexablematrix can contain This limit was first calculated by Alt and Pleshko[12] For liquid crystal technologies which react on the amplitude andsign of the voltage itself (this requires polarity) and show hysteresis(the effect lags behind in comparison to the cause) this limit does notapply and larger matrices can still be addressed The factor which thendetermines the feasibility of the passive matrix addressing is theswitching speed of the liquid crystal

Active matrices

In order to avoid the problem of strong non-linearity in the switchingproperties of the liquid crystal, one can in fact render the matrix itself

non-linear This principle implies that we have to build in at least onetransistor or one diode in each element of a pixel It requires a precisecontrol over the properties of such elements on rather huge surfaces incomparison to normal semiconductor technologies For this reasonsuch a solution was for a long time considered to be too cumbersome.However due to intensified efforts and money streams it has becomethe standard matrix solution A small calculation reveals that a liquidcrystal display with only VGA resolution ( ) contains no lessthan 307,200 working transistors on a surface with a diagonal of about

14 inch and if you would prefer colours 921,600 transistors are sary Because of these stunning amounts it is even short to miraculousthat this technology works at all Nowadays resolution requirementshave increased further such that in a ‘normal’ XGA AM-LCD onelooks at 2,359,296 working transistors

neces-The forementioned transistor serves as a switch neces-The electrode linesnecessary to operate this three-terminal switch are all located on thesame substrate The real construction of a substrate thus becomes evenmore complex The transistors are of a thin film field-effect type Incommercial leaflets and specifications one usually refers to the activematrix with the term TFT which is short for Thin Film Transistor Byfar the most applied material so far for the semiconductor element hasbeen ‘amorphous Hydrogenated Silicon’ (a-H:Si) Other possibilitiesinclude polycrystalline Silicon (p-Si) and cadmiumselenide Whenmonocrystalline silicon wafers are used as substrates, a standardCMOS process can be used for the creation of the active matrix Themost difficult parts to manufacture are the post-process light shieldsand reflective electrodes The other substrate of an AM-LCD displaycontains one big common electrode

The gates belonging to pixels located on the same row are nected to each other by a row electrode In this way they can all beselected simultaneous by applying a voltage to their common rowelectrode Because all pixels of the entire matrix receive the same volt-age on the other substrate, the data has to be passed through the data-bus column lines, connected to the drain of each transistor within acolumn The source of the transistor is connected to the pixel elec-trode The switching process is similar to the charging of a capacitor.When the next row is selected, the transistors of the previous row nolonger conduct and the data applied for the now selected row can nolonger create crosstalk in the non selected rows In addition to this theswitching process of the liquid crystal can continue even long after therow has been deselected This is because the charge put on the pixelduring the selection window is now the driving force for the switch-

con-480×640

ing process In practical devices an extra storage capacitor is necessary

to prevent charge leakage from the pixel during the entire frametime.There are thus two elements present which drastically reduce theeffective surface of a pixel for transmissive displays

1.3 Quantification of the image quality

There are several different aspects to the quality of a true display.Because each application has a set of different demands, it is not use-ful to try to concentrate the quality of the displayed image into onesingle number For instance the speed with which a new image can bedisplayed is of lesser importance for screens displaying only alphanu-meric information, as it is for screens used for video applications Forthis reason the properties of a display are divided into separate cate-gories [13] The spatial block applies to the dimensions of the screenand the spatial sensitivity of the human eye Another category, thespectral one, portrays the possibilities connected to the colour rendi-tion of the screen The sensitivity to changes of the light intensity inthe time domain forms a third category The luminance category,which describes the sensitivity to the light intensity itself is a fourthand final category

Figure 1.3: A schematic comparison between (a) a passive matrix and (b) anactive matrix

DATA

DATA

Because the CRT has dominated the display market for a very longtime, the Figures of Merit (FOMs) of a display needed to be adaptedfor use with flat panel screens The most important category wherechanges were necessary was the time domain This is a consequence ofthe fundamental difference of the driving method [13] A seconddomain where changes were needed, is that of the viewing angledependence of the image A CRT is a light emitting display The phos-phors can with good approximation be considered as lambertian emit-ters, therefore the dependence on the viewing direction is negligible.The properties of the liquid crystal layer in an LCD are indeed verydepended on the viewing direction This prompted the creation of anentirely new FOM in the luminance category.

A large portion of this thesis is devoted to the extinction of lightcaused by a liquid crystal layer between crossed polarisers For thisreason I will further describe three properties from the entire setwhich can be traced to this problem

In the liquid crystal world one often encounters the word contrastwhere one actually means the contrast ratio Since the contrast isdefined as

(1.3)

this is only true when the low luminance is negligible in comparison

to the high luminance measured A contrast ratio of 10:1 is deemedacceptable, a contrast ratio of 5:1 is considered to be the absolute use-ful minimum

The extinction of the liquid crystal layer between crossed polarisers

is clearly related to the low luminance mention above Under ideal cumstances the contrast ratio can be augmented by increasing theluminance of the source which will increase the luminance of the

cir-bright state L B This is of course only true if the luminance of the dark

state, L D, is not increased proportionally Therefore a high quality ofthe extinction is necessary

Grey scale

Displays with high information content generally have grey scalecapabilities This means that individual pixels can adopt a desiredbrightness somewhere between the minimum and maximum value.For a full colour display each pixel can adopt 256 grey shades Becausethe sensitivity of the eye is rather logaritmic, they must be chosenequidistant on a log-scale Such an amount of grey levels is only usefulwhen the high and the low limit of the luminance are located far fromeach other or thus the contrast ratio is sufficiently high

Colour saturation

The usual way of rendering colours in a liquid crystal display is bymeans of a triad of elements Each element of the triad has a differentcolour filter, red, green or blue Because of the additive colour mixingthe saturation of a colour depends on the luminance in the dark state

of the other elements in the triad This implies that also colour tion is controlled by the extinction However the relation between col-our and extinction is not straight forward for a birefringent layerbetween crossed polarisers This can be derived from the transmissioncharacteristics plotted in Figure 1.4

satura-1.4 An overview of this work

Antiferroelectric liquid crystals are closely related to ferroelectric uid crystals, their properties and application to displays will be thesubject of chapter 2 For AFLCDs the extinction between crossedpolarisers has been a long standing problem It can be traced back tothe poor alignment of those materials and thus chapter 3 describes afew experiments related to this alignment problem A sound androbust solution to the extinction problem is presented in chapter 4.Along the way a lot of questions and ideas develop, which are mainly

liq-related to the use and the properties of the proposed materials A littlestep is made in the direction of phase gratings and in that same chap-ter a larger step into the realisation of a switchable phase grating usingferroelectric liquid crystals is taken A detailed description of thedesign and assembly of the spatial light modulators is however notincluded in this thesis Further also the dynamic properties of theextinction are investigated A problem which occurs when trying touse AFLC materials in reflective displays is eliminated in chapter 5,while chapter 6 houses a new light scattering variant which will bemodelled.

Figure 1.4: The wavelength dependency of the transmission of a birefringentlayer between crossed polarisers The optical thickness of the layer was opti-mised for a wavelength of 550 nm The best choice is k=0, corresponding to aoptical thickness of λ/2 That plot shows least curvature and hence has thelowest wavelength dependency The curve with k=1 corresponds to an opti-cal thickness of 3λ/2

Ferroelectric and

antiferro-electric liquid crystals

This chapter treats the two most important smectic phases, not only for this work but also from technological point of view From the structure of the phase one can determine the dielectric and hence also the optical properties of the material Because these two phases have a large potential for flat panel displays, their application to electro-optic devices will be discussed.

matically the difference between the SmA and SmC structures The

angle enclosed by n and k is called the tilt angle and is usually noted as

θ The fact that the molecules tilt away from the layer normal meansthat the director is confined to a conical surface of which the layer nor-mal is the axis

When the phase is chiral, a helical structure will develop The axis

of the helix coincides with the layer normal, whereas the helix in the

N* phase develops in a direction perpendicular to the director itself.The consequence of this, is that the helix in the SmC* phase is repre-sented by a combined ‘twist-bend’ deformation with respect to theSmC structure [15] Figure 2.2 portrays the helix by using the position

of the director in subsequent layers For a more detailed discussion ofthe elastic properties themselves, I refer to [16] and [17,18]

Figure 2.1: A schematic illustration of the difference between (a) the SmAand (b) the SmC phases

Figure 2.2: A representation of a full pitch length of the helix in the SmC*phase

k=n

(a)

n k

9

10

zp

In 1974 R B Meyer showed that the symmetry of the SmC* phaseallows for a polarisation to appear perpendicular to the plane spanned

by k and n [19] This plane is commonly referred to as the tilt plane.

Because the director in an undisturbed SmC* structure spirals aroundthe layer normal, no net polarisation will result When we apply anelectric field which is not along the helix axis, the field will couple tothe polarisation and will unwind the helix In 1980 N A Clark and

S T Lagerwall showed that the helix can be unwound by means of thesurface interactions and as such the liquid crystal obtains ferroelectricproperties [20] This mechanism has been called surface stabilization,one also uses the term ‘Surface Stabilized Ferroelectric Liquid Crys-tals’ (SSFLC) The typical feature of ferroelectricity is the hysteresis inthe reversal of the polarity by means of applying an electric field

2.1.2 Dielectric tensor

Although one also uses the term director n for this phase, there is a

fundamental difference with the director in the N, N*, SmA and SmA*phases In the latter phases the dielectric properties are constant in adirection perpendicular to the director, this is no longer true for theSmC and SmC* phases Therefore the material is characterized bythree different eigenvalues There are now two axes for which the die-lectric properties perpendicular to those directions are constant For

this reason such materials are called biaxial and one uses the term optic

axes for the mentioned directions.

The matrix representation of the dielectric tensor in the principalaxes system, which is connected to the molecules themselves, is diago-nal and all elements are different On the other hand uniaxial nematicand smectic A phases have only two elements which differ from eachother

(2.1)

If we would like to determine the dielectric properties in an axes tem which does not coincide with the principal axes system, we cancalculate those from the transformation The columns

sys-of the transformation matrix T are unit vectors along the directions sys-of

the principal axes system as it is oriented with respect to the chosen

axes system This implies that we can build up T through

tion of appropriate rotation matrices The principal axes system isusually called the qpn-system Here we chose the rotations in such away that they represent phenomenological features of the liquid crys-tal The first obvious candidate is the tilt angle θ Because the director

is positioned on the smectic cone the second choice is a phase angle ϕwith respect to a fixed reference position Liquid crystals are mostcommonly used in a so called sandwich-geometry, a thin layer of liq-uid crystal sandwiched between two substrates The most ideal layer

structure is the bookshelf structure, with smectic layers oriented

per-pendicular to the substrates (see Figure 2.5) It has been known forquite some time now that this layer structure is difficult if not impossi-ble to obtain One finds that the layers make a certain angle withrespect to the substrates and that this angle usually varies throughoutthe liquid crystal layer [21] This angle is our third candidate, it is mostcommonly denoted as δ Figure 2.3 shows a summary of the phenom-

enological angles The fixed reference axes system chosen for thiswork, also called laboratory axes system, is based on the bookshelfgeometry We chose the yz-plane for the substrates and the xy-planefor the smectic layers If a helix is present it will therefore developalong the z-axis when the layers are perpendicular to the substrates If

we would like the principal axes system to be the same as the onefound in literature [22,23], an extra but just ‘technical’ rotation is nec-essary We can now transform our xyz-system into the qpn-system by

means of the described rotations and obtain the matrix T.

Figure 2.3: A review of the phenomenological angles

(2.2)Each matrix represents a rotation around the intermediate axis i

The columns of T, from left to right, are unit vectors according to the

directions of the principal axes q, p and n in the xyz-system If weadapt this further to the example of the bookshelf geometry, thus for, we find the following components for the dielectric tensor

0 1 0θsin

In the model described above, the polarisation P is along the p-axis,

positive according to the direction shown in Figure 2.3 In the tory axes system that direction is given by the second column of the

labora-transformation matrix T.

If one would like to take the helix into account, we can replace ϕ by

in which The pith of the helix is represented by

p One then obtains the following components

(2.9)

Apart from components with a periodicity equal to the pitch, there arealso components which show a periodicity equal to half the pitch.Therefore the reflection spectrum of the SmC* phase can portray twopeaks The peak corresponding to the half pitch periodicity is called

the half pitch band The other peak thus corresponds to the periodicity

of the pitch itself That second peak is called the full pitch band For

light incident along the helix axis the full pitch band disappears Thiscan easily be explained because only the components which will con-tain crossterms as a function of the z-field have a periodicity equal tothe pitch On top of that the wavelength which corresponds to the half

pitch band is then equal to the pitch of the material multiplied by n eff.This effective refractive index is in its most generally case dependent

on the tilt angle (a derivation of that formula can be found in graph 4.1) However one usually assumes it to be around 1.5 The full

para-εxx = ε1cos2θsin2ϕ+ε2cos2ϕ+ε3sin2θsin2ϕ

εxy = εyx = –ε1cos2θcosϕsinϕ+ε2cosϕsinϕ–ε3sin2θcosϕsinϕ

εxz = εzx = ε1cosθsinθsinϕ–ε3cosθsinθsinϕ

εyy = ε1cos2θcos2ϕ+ε2sin2ϕ+ε3sin2θcos2ϕ

εyz = εzy = –ε1cosθsinθcosϕ+ε3cosθsinθcosϕ

pitch band is only visible for light which does not propagate along thehelix axis.

2.1.3 Optical properties

The linear optical properties of liquid crystals are entirely defined bythe direction of the principal axes system and there matching refrac-tive indices If we neglect the absorption of the liquid crystal andassume that it is also non-magnetic, those refractive indices are given

principal axes are given by the columns of the transformation matrix

T If we have a set of angles (θ, ϕ, δ), the optical properties of the rial are completely defined The difference is usuallyreferred to as birefringence or optical anisotropy The difference

is called the optical biaxiality

The optical properties along any given direction can be obtainedthrough a geometrical construction on the refractive index ellipsoid.Described in the principal axis system, it has the equation

(2.10)

wherein x', y' and z' are taken along q, p and n respectively We form the wavevector k to the principle axes system and construct the plane perpendicular to k’ which runs through the origin The curve

trans-obtained by the section of this plane with the index ellipsoid is in itsmost general form an ellipse The principle directions of this ellipse

are along the eigenpolarisations of light propagating along k and

described in the principal axes system The length of the principalaxes of the ellipse are equal to the refractive indices belonging to thosepolarisations This method can be found in many different textbooks[24] Strictly speaking, this method only applies to light incident per-pendicular to the interface

To calculate the transmission through a stack of arbitrary orientedliquid crystal layers, one usually has a choice of numerical simulationpackages The most powerful method is based on the multiplication of matrices, this method is know as the ‘Berreman formalism’ [25]

In order to be able to use this formalism one needs to calculate the lectric tensor in the fixed laboratory frame Another method uses spe-cific knowledge of the refractive indices and the eigenpolarisations Touse this method, which is better known as the ‘Jones calculus’ [26],one needs to calculate these parameters first taking into account the

orientation of the medium The advantage of this method is the fastermultiplication of matrices However one can only take a perpen-dicular light incidence into account and all reflections are neglected.The ‘extended Jones calculus’ [26], introduces the possibility to takeoblique incident light into account without increasing the dimensions

of the matrices to be multiplied, but also this method in principleneglects the reflections An excellent treatment of all these differentoptical matrix formalisms can be found in references [28,29]

The direction of the optic axes can also be found using the tive index ellipsoid Since light which propagates along these direc-tions does not encounter any birefringence, the section with the indexellipsoid is in fact a circle The optic axes are always found in the planespanned by the principle axes connected to the smallest and largestrefractive indices, and are oriented symmetric with respect to theseaxes For ferroelectric liquid crystals one usually finds that

refrac- Therefore the optic axes are located in the qn-planerefrac- If wetakeβ to be the angle between n and an optic axis, it is given by

directions for the director n Because the position of the director is

cou-pled to the layer normal and the latter one is assumed to be fixed inspace, this also creates two preferential directions for the polarisationconnected to those of the director If we assume that the director is

±0βcos

parallel to the substrates in both states, the polarisation will always beperpendicular to the substrates If we now apply an electric field alongthe substrate normal, the polarisation will align itself in the direction

of the field Each deviation between those two directions leads to atorque If we reverse the field the polarisation will even-tually change its direction and because it is coupled to the director it

Figure 2.4: The direction of the optic axes for a ferroelectric liquid crystal

Figure 2.5: The bookshelf geometry of an SSFLCD and its electro-optic cation between crossed polarisers

will drag the director along with it over the smectic cone to the otherextreme state If we take away the field the current state will remain If

we apply a field which is lower than the threshold field the liquidcrystal does not switch It is this hysteretic behaviour which allows theuse of a passive matrix for devices

The optical effect is based on the switching of the slow axis (or fast

axis) of a birefringent layer placed between crossed polarisers Often

the term optic axis or effective optic axis is used for this but strictlyspeaking this axis is not necessarily an optic axis of the medium It is

in fact the direction of the eigenpolarisation which propagates withthe slowest velocity hence endures the highest refractive index Wehere limit ourselves to perpendicular incident light In that case theslow axis for both stable states coincides with the director We thusswitch between two states which are separated an angle 2θ from eachother but the birefringence of both states is equal By using the JonesCalculus, one can calculate the normalised transmission of a birefrin-gent layer between crossed polarisers

(2.13)

In the above formula α represents the angle between the polarisingdirection of the polariser and the slow axis, λ is the wavelength of the

incident light, d is the thickness and ∆n the birefringence of the liquid

crystal layer If we now put the polariser along the director in one ofthe stable states and the analyser perpendicular to it, we obtain a darkstate The director in the other state thus makes an angle withthe polariser If we want an optimal bright state the first condition is tohave an FLC material with a tilt angle of 22.5° From the second factor

one concludes that the product d∆n must be equal to a half

wave-length to make the bright state optimal

The above description is in fact too simplified In reality the layersare rarely perpendicular to the substrates, instead they form a socalled chevron profile [21,30] A consequence of these chevrons is thatthe stable states no longer represent polarisations perpendicular to thesubstrates If we take away the field, the position of the directorrelaxes back to an energetic more favourable state governed by thechevron angle as illustrated in Figure 2.6 The slow axis thus switchesover a significantly smaller angle than 2θ Obtaining a uniform chev-ron direction is a technological challenge by itself The usual solution

consists of the use of alignment materials which generate a high pretilt

for the molecules with respect to the surfaces

α = 2θ

In order to obtain a larger switching angle one can exploit the lectric couple Opposed to the nematic phase, where the dielectric ani-sotropy is entirely responsible for the switching mechanism, it is only

die-a seconddie-ary effect for FLCs In fdie-act it is the dielectric bidie-axidie-ality whichplays an important role for these materials [31] When , an AC-field will try to reorient the p-axis, which is connected to the higher value, along the electric field direction such that the ideal switchedstates are better approached and thus the effective switching angle isincreased [32,33] For this effect quite high fields are required whichare delivered by the purposely designed crosstalk embedded in thedatavoltages meant for other pixels There exist a number of rathercomplicated addressing schemes to accomplish this task The ferroe-lectric and the dielectric torques are given by [34]

(2.14)

Because the dielectric torque is independent of the sign of the electricfield it can be used in a number of different ways Another example isthe possibility to finalise the switching with it In this method one

Figure 2.6: The chevron profile in an SSFLCD and the stable states in whichthe material can be switched In order to keep a constant layer spacing at thesurfaces, the layers have to tilt when the layer thickness decreases due to theincreasing tilt angle of the material If this phenomenon occurs in oppositedirections at both surfaces a chevron with a sharp tip is created For the situa-tion represented here, without surface pretilt, both chevron directions areequally probable and optically identical If both directions are present in onecell, they give rise to the characteristic zig-zag or lightning defects

switches the director over the smectic cone by means of the tric torque just as far as necessary in order to define the direction ofthe switching but the switching mechanism is completed by exploit-ing the dielectric biaxiality This finalisation step can take place evenwhen the next rows are being selected The advantage of this mecha-nism is that the row selection time can be shortened Such addressingschemes have also been developed [35] If one applies high electricfields the dielectric contribution to the switching may not beneglected, it gives rise to a minimum in the switching time and thismechanism gives the name to the -principle [36,37,38] Switch-ing times of about 30 µs are quite normal for FLCs, with usefulminima even down to 6 µs at the expense of higher driving voltages.

ferroelec-In spite of the enormous potential that this technology posses, therehave been only a few attempts to create a commercially viable productbased on this bistable effect By far the most critical parameter is thealignment of the material Not only is a uniform chevron profilerequired, it also has to remain unchanged when applying electricfields, a problem which may not be underestimated because all of theabove described techniques which use the dielectric torque requirerather high fields Also the sensitivity to chocks and pressure sets highdemands on the robustness of the display Although that problem is

no longer considered to be insuperable Quite recently new materialswhich do not form chevrons were discovered [39,40]

Monostable technology

A problem inherent to the bistable technology is the absence of naturalgrey levels One has to rely on time or space integration [16] Anotherpossibility consists of the use of an active matrix, in that case hystere-sis is no longer a requirement There exist in essence two differenttypes of monostable technologies which make use of ferroelectric liq-uid crystals

The first method takes advantage of the SmC* phase without pressing the helix An important requirement for the liquid crystal isthat the pitch is very small (preferably smaller than the wavelength oflight) Under field free conditions the liquid crystal is than uniaxialwith its optic axis along the layer normal If we apply a field the helix

sup-is unwound and results in an optically biaxial liquid crystal layer ofwhich the slow axis makes a certain angle with respect to the layernormal As a first approximation, this angle is linearly dependent onthe applied field but saturates for high fields to a value equal to the tiltangle when the helix is completely unwound The direction in which

τV min