Ghent University - Faculty of Engineering

Department of Electronics and Information Systems

Head of Department: Prof. dr. ir. J. Van Campenhout

Philips Research

Department of Display Applications and Technologies

Head of Department: dr. ir. A. Saalberg-Seppen

Modelling of the static and (hydro)dynamic switching

behaviour in ultra-wide viewing angle LCDs

by

Pieter Vanbrabant

(Pieter.Vanbrabant@UGent.be)

Master dissertation submitted to obtain the Electrical Engineering degree

Academic year 2006-2007

Promoter: Prof. dr. ir. K. Neyts

Industrial supervisor: dr. ir. N. Dessaud

COMPANY

CONFIDENTIAL

Acknowledgments

This work was realized at the Display Applications and Technologies group of Philips Researchlocated at the HighTech Campus in Eindhoven. It was very inspiring to spend six intensivemonths in such a positive and professional research environment. I would like to thank all groupmembers for their warm welcome and kindness. A special word of thanks for Nathalie Dessaudand Jan Stroemer is certainly at its place: Nathalie motivated me from the first day with herenthusiasm, helped me on any kind of problem that occurred and provided many good ideasfor the VA part of this work. I also would like to thank Jan for his interesting discussions andremarks on the IPS part and his practical tips and tricks.

I would like to thank the promoter of this thesis, Prof. Kristiaan Neyts for the discussions onmy work, his flexibility and the provided opportunity to acquire experience at Philips Research.

Special thanks to my parents Martin & Marleen and sister Paulien for all their extra-academicalsupport and motivation. Last but not least, I would like to thank Lien for her love and patience.

I hereby provide permission to make this assertation available for consultation and to copy partsof this work for personal use. Any other use is subjected to the restrictions of the copyright law,especially the obligation to mention the reference explicitly in quoting results of this work.

Eindhoven, 31 May 2007

Pieter Vanbrabant.

ii

Modelling of the static and (hydro)dynamic switching

behaviour in ultra-wide viewing angle LCDs

by

Pieter Vanbrabant

Master dissertation submitted to obtain the Electrical Engineering degree

Academic year 2006-2007

Ghent University - Faculty of Engineering

Department of Electronics and Information Systems

Head of Department: Prof. dr. ir. Jan Van Campenhout

Philips Research

Department of Display Applications and Technologies

Head of Department: dr. ir. Ans Saalberg-Seppen

Promoter: Prof. dr. ir. Kristiaan Neyts

Industrial supervisor: dr. ir. Nathalie Dessaud

Summary

Ultra-wide viewing angle Liquid Crystal Displays (LCDs) based on the Vertically Aligned (VA)and In-Plane Switching (IPS) modes are currently used in high-end mobile and television ap-plications. Both the VA and IPS modes feature highly important advantages such as a wideviewing angle, low operation voltage, excellent contrast ratio and are therefore interesting forwider application in the consumer market segment. Based on results of both simulations and ex-periments, this work targets to provide a better understanding of some aspects of the switchingproperties of IPS and VA-LCDs, which should ultimately lead to a progression in performanceof these technologies.

It is shown through experiments and simulations that the light transmission of IPS-LCDs canbe optimized for both the area above and between the pixel electrodes by selecting an optimumelectrode configuration. This leads to a new kind of hybrid Fringing-Field/In-Plane Switchingcell, which has not been discussed in literature yet according to our knowledge. An optimizationof the liquid crystal material used in the presented hybrid cell will lead to an improved design,which could provide better performance than the conventional optimum IPS cells.

The occurrence of backflow is a known phenomenon which affects the switching behaviour,severely limiting the performance of VA-LCDs. To take this effect into account in simulations,the hydrodynamic Leslie-Ericksen theory needs to be included in the simulation model. Using arecent procedure to estimate material specific viscosity coefficients, a good agreement betweenexperimental and simulated switching profiles affected by backflow are obtained at room tem-perature.

It is important to know the effect of temperature variations on the switching behaviour becausethe temperature range for proper display performance puts a high requirement on LCDs for mo-bile applications. Therefore, an experimental study was performed for VA-LCDs to probe theinfluence of temperature on the switching behaviour. It was observed that a better switchingbehaviour is obtained with increasing temperature. To obtain a better understanding of theeffect of temperature, the simulation model ought to be extended to take temperature varia-tions into account. However, not much quantitative information is known about the variationof the liquid crystal material parameters with temperature. Therefore, an approach based ona combination of measurements and fittings was developed to extract these variations. Modifi-cations to the viscosity estimation procedure were presented to obtain more accurate viscositycoefficients at temperatures exceeding 25◦C. The extension of the simulation model allowed tosimulate temperature effects accurately in the voltage range which is important for practicaldisplay applications.

The simulation model was used to extract a standard overdrive scheme. It is shown experi-mentally that applying such scheme in VA-LCDs can lead to a considerable improvement inperformance over a restricted temperature range. However, it is pointed out that the perfor-mance of such a driving scheme is too sensitive to temperature variations to be applicable inpractical display applications. Using the developed simulation model, it was possible to extracta temperature compensating overdrive scheme. It is shown experimentally that the switchingperformance of VA-LCDs can be increased considerably by using this scheme instead of the con-ventional driving scheme used nowadays. Therefore, the presented temperature compensatingoverdrive scheme has a high potential for application in future VA-LCDs.

Key words: Liquid Crystal Display (LCD), In-Plane Switching (IPS), Vertically Aligned (VA),backflow, overdrive scheme

Modelling of the static and (hydro)dynamic switching behaviour inultra-wide viewing angle LCDs

Pieter Vanbrabant

Supervisors: Nathalie Dessaud1, Jan Stroemer1, Kristiaan Neyts2

Abstract—Two aspects of the static and dynamic behaviour of ultra-wideviewing angle LCDs are considered. First, we present a hybrid fringing-field/in-plane switching cell geometry for which the static transmission bothabove and between the electrodes is optimized. Second, the effect of tem-perature on the switching behaviour of VA-LCDs is investigated throughexperiments and simulations including the hydrodynamic Leslie-Ericksentheory. This leads to a temperature compensating overdrive scheme whichimproves the switching performance of VA-LCDs considerably.

Keywords— Liquid Crystal Display (LCD), In-Plane Switching (IPS),Vertically Aligned (VA), backflow, overdrive scheme

I. INTRODUCTION

ULTRA-WIDE viewing angle Liquid Crystal Displays(LCDs) based on the Vertically Aligned (VA,[1]) and In-

Plane Switching (IPS,[2]) mode are currently investigated foruse in high-end mobile and television applications. Both theVA and IPS mode feature important advantages such as a wideviewing angle, low operation voltage, excellent contrast ratioand are interesting for wider application in the consumer marketsegment, previously dominated by the well-known Twisted Ne-matic (TN,[3]) mode. Based on the results of both simulationsand experiments, we target to provide a better understanding ofsome aspects of the switching properties of IPS and VA-LCDs.This should ultimately lead to a progression in performance ofthese technologies.

II. A HYBRID FRINGING-FIELD/IN-PLANE SWITCHINGCELL GEOMETRY

Various IPS samples with an electrode width L varying be-tween 4µm-8µm, electrode gap G of 4µm to 20µm and an opti-mum cell thickness of 5µm were considered. Fig.1 shows theobtained experimental voltage-transmission characteristics forthe optimum samples.

Fig. 1. Experimental voltage-transmission characteristics for the consideredcells. The electrode geometry is denoted in the legend: xLyG denotes a cellwith an electrode width of xµm and electrode spacing of yµm.

It appears from Fig.1 that optimum transmission is obtained at6V for a geometry L = 6µm and G = 4µm, which will be

1 Philips Research Laboratories, Department of Display Applications andTechnologies, Eindhoven, The Netherlands

2 Ghent University, Department of Electronics and Information Systems,Ghent, Belgium

denoted as 6L4G. Two-dimensional simulations with a com-mercial package ([4]) of this cell geometry were performed tounderstand why optimum performance is obtained for this par-ticular geometry. Fig.2 shows the resulting transmission profilealong one unit cell for a 10V driving voltage. An investiga-

Fig. 2. Simulated transmission profile along one unit cell with 6L4G electrodegeometry for a 10V driving voltage (the electrode at the highest resp. lowestpotential is denoted by a red resp. blue rectangle).

tion of the simulated transmission profile points out that a highaverage transmission is obtained through contributions of areasboth above and between the electrodes. The high transmissionarea above the electrodes is typical for fringing-field switching(FFS,[5]) designs, while IPS designs are characterized by hightransmission areas between the electrodes. As the transmis-sion of 6L4G is determined by an interplay between both thefringing-field and in-plane switching effect, this cell can be re-ferred to as having a new hybrid FFS/IPS geometry. Currently,a maximum transmission value of 67% is obtained for the cell ata 10V driving voltage. We suggest a further liquid crystal ma-terial optimization to decrease the driving voltage for optimumtransmission and to reduce the low transmission areas along thecell. The optimized design obtained in this way could lead to anincrease in performance compared to conventional IPS designs.

III. 1D-MODELLING OF BACKFLOW IN VA-LCDS

In case a voltage step with amplitude exceeding a certainthreshold voltage VBF is applied in VA-LCDs, a reverse flowphenomenon occurs, referred to as backflow. This effect inducesunder crossed polarizers a double-peaked transmission profileupon switching which leads to a drastic increase in switchingtimes, thereby severely limiting the possibility to provide videocontent to the user. In order to model the effect of backflowon the switching behaviour, the hydrodynamic Leslie-Ericksentheory ([6]) needs to be included in simulations. This requiresthe 4 Miesowicz viscosity coefficients ηij of the material to beknown, which increases the complexity of the simulation modeldrastically. Until now, reported simulations on the occurrence ofbackflow ([7]) used the ηij values of the MBBA material, oneof the only materials for which these coefficients were measuredaccurately, [8]. As illustrated in Fig.3, a better agreement be-tween experimental and simulated switching profiles affected bybackflow is obtained with a commercial one-dimensional simu-lation package ([9]) by using material specific estimates whichwere obtained according to a recent procedure ([10]).

Fig. 3. Simulated (left) and experimental (right) switching profile illustratingthe occurrence of backflow in VA-LCDs. A 6V voltage step was applied tothe sample at t = 0ms.

IV. THE EFFECT OF TEMPERATURE ON THE SWITCHINGBEHAVIOUR OF VA-LCDS

The temperature range for which proper display functioningmust be guaranteed puts a high requirement on LCDs for mobileapplications. An experimental study was performed to probethe effect of temperature on the switching behaviour of a VAsample. Fig.4 presents the obtained switching times as a func-tion of voltage for different temperatures. Fig.4 shows that the

Fig. 4. Experimental turn on times as a function of voltage for different temper-atures.

turn on time τon decreases with temperature for all voltages.Furthermore, the backflow threshold voltage VBF at which theturn on times start to increase drastically (4.5V-5V) is shiftedto higher voltages for increasing temperatures. Consequently, abetter switching behaviour is obtained at higher temperatures.To take temperature effects into account in the simulationmodel, the variation of the liquid crystal material parameterswith temperature needs to be known. However, not much quan-titative information on the effect of temperature on the materialis known as it is hard to measure these variations accurately.Therefore, a heuristic approach based on a combination of rel-atively simple measurements (static voltage-transmission char-acteristic, turn off times, etc.) and fittings was developed to ex-tract the profile of material parameters such as the anisotropy indielectric permittivity ∆ε, the Frank elastic constants Kii(i =1, 2, 3) and the rotational viscosity γ with temperature. The pro-cedure to estimate the viscosity coefficients ηij was modified toobtain accurate values at temperatures exceeding 25◦C. Usingthe extracted and estimated parameters, the simulation modelwas extended to model the effect of temperature on the switch-ing behaviour of VA-LCDs. Fig.5 shows the simulated turn ontime graph for different temperatures. Comparing Figs.4 and 5shows a remarkable agreement between the simulated and ex-perimental characteristics. A quantitative assessment of the rel-ative error on the simulated turn on times points out that theswitching behaviour is modelled accurately (max. 25% error onτon) for the voltage range of practical importance for displayapplications (i.e. V ≤ VBF ).

Fig. 5. Simulated turn on times as a function of voltage for different tempera-tures.

V. A TEMPERATURE COMPENSATING OVERDRIVE SCHEMEFOR VA-LCDS

The use of an overdrive scheme is a common way to obtainfaster grey scale transitions in LCDs ([11]). Using solely the re-sults of simulations, such a scheme was extracted for transitionsbetween the black state and various grey scale levels at 25◦C.Although much faster transitions were obtained at 25◦C, wepointed out experimentally that a conventional overdrive schemeis too sensitive to temperature variations to be applicable in prac-tical displays. Using the ability to take temperature effects intoaccount in simulations, extra overdrive schemes were extractedfor {35◦C, 45◦C, 55◦C, 65◦C, 75◦C}. By sensing the opera-tion temperature and selecting the most appropriate scheme, thetemperature sensitivity of a single overdrive scheme can be elim-inated and a temperature compensating overdrive scheme is ob-tained. It is shown experimentally that satisfying grey scale tran-sitions are obtained for the complete temperature range 25◦C-80◦C: compared to the conventional static driving scheme usedin VA-LCDs used nowadays, the grey scale error of this schemeis decreased (max. 10% error compared to a 200% error for theconventional scheme at 75◦C) and a considerable faster switch-ing is obtained (up to two times faster). This illustrates thepower of the simulation model presented: simply by perform-ing simulations according to this model, it is possible to extractvaluable overdrive schemes at any desired temperature. As theswitching performance is increased considerably by using thetemperature compensating overdrive scheme, such a scheme hasa high potential for application in future VA-LCDs.

VI. CONCLUSIONS

A hybrid FFS/IPS cell design which features an improvedtransmission profile above and between the electrodes has beenproposed. The backflow phenomenon in VA-LCDs was revised:a more accurate modelling and a new approach to include tem-perature effects has been proposed. As an application, a temper-ature compensating driving scheme was developed, which in-creases the switching performance of VA-LCDs drastically.

REFERENCES

[1] M. Schiekel et al., Appl. Phys. Lett., vol.19, pp.391-393, 1971[2] M. Oh-e et al., Appl. Phys. Lett., vol.67, pp.3895-3897, 1995[3] M. Schadt et al., Appl. Phys. Lett., vol.18, pp.127-128, 1971[4] 2dimMOS, autronic-Melchers, Karlsruhe, Germany[5] S. Lee et al., Appl. Phys. Lett., vol.73, pp.2881-2883, 1998[6] S. Chandrasekar, Liquid Crystals (2nd edition), Cambridge University

Press, 1992[7] N. Dessaud et al., IDW’06, LCT7-2, 2006[8] H. Kneppe et al., Mol.Cryst.Liq.Cryst., vol.65, 23, 1981[9] DIMOS, autronic-Melchers, Karlsruhe, Germany[10] H. Wang et al., Liq.Cryst., vol.33, pp.91-98, 2006[11] H. Nakamura et al., SID’01 Digest, 32(1), 1256, 2001

Modellering van het statisch en (hydro)dynamisch schakelgedrag vanLCD’s behorende tot de ”brede kijkhoek”-klasse

Pieter Vanbrabant

Begeleiders: Nathalie Dessaud1, Jan Stroemer1, Kristiaan Neyts2

Abstract— Twee aspecten van het statisch en dynamisch gedrag vanLCD’s behorende tot de ”brede kijkhoek”-klasse worden behandeld. Westellen een celgeometrie voor die aanleiding geeft tot een hybride Fringing-Field/In-Plane Switching schakelgedrag, wat zowel boven als tussen deelektrodes voor hoge lichttransmissie zorgt. Verder wordt de temperatuur-afhankelijkheid van het schakelgedrag van Vertically Aligned (VA)-LCD’sgerapporteerd in overeenstemming met experimentele bevindingen ensimulaties die rekening houden met de hydrodynamische Leslie-Ericksentheorie. Tot slot wordt een schema voor overdrive aansturing voorgestelddat temperatuurseffecten in rekening brengt en het schakelgedrag vanVA-LCD’s gevoelig verbetert.

Sleutelwoorden— Liquid Crystal Display (LCD), In-het-vlak draaiendedirector/In-Plane Switching (IPS), Verticale Alignering/Vertically Aligned(VA), backflow, overdrive aansturing

I. INLEIDING

Liquid Crystal Displays (LCD’s) met schakelmodes gebaseerdop Verticale Alignering (VA,[1]) of in-het-vlak draaiende direc-tor (In-Plane Switching - IPS, [2]) worden momenteel gebruiktin de toplaag van TV en mobiele toepassingen. Belangrijkevoordelen zoals een brede kijkhoek, een lage werkspanning eneen hoge contrast ratio maken zowel de VA als IPS mode interes-sant om aangewend te worden in een breder toepassingsdomein.Wij proberen om, gebruikmakend van zowel experimenten alssimulaties, een beter inzicht te verschaffen in enkele aspectenvan het schakelgedrag van VA en IPS-LCD’s om uiteindelijk eenprogressie in performantie van deze technologieen te bekomen.

II. EEN HYBRIDE FFS/IPS CELGEOMETRIE

Er werd een vergelijking gemaakt van de transmissie-eigenschappen van IPS samples met varierende elektrodege-ometrie. De breedte L van de elektrodes in de samples varieerttussen 4µm-8µm, terwijl de afstand G tussen de elektrodes eenwaarde aanneemt in het interval 4µm-20µm. Fig.1 toont de ex-perimentele spanning-transmissie karakteristieken van de bestpresterende samples. Fig.1 geeft aan dat optimale transmissie

Fig. 1. Experimentele spanning-transmissie karakteristieken van debeschouwde samples. De elektrodegeometrie wordt als volgt aangegeven inde legende: xLyG symboliseert de cel waarvoor L = xµm en G = yµm.

bekomen wordt voor een celgeometrie met L = 6µm en G =4µm, die in wat volgt wordt aangeduid als 6L4G.

1 Philips Research Laboratories, Department of Display Applications andTechnologies, Eindhoven, Nederland

2 Universiteit Gent, Vakgroep Elektronica en Informatiesystemen, Belgie

Het schakelgedrag van de 6L4G-structuur werd gesimuleerdmet een commercieel 2D-simulatiepakket ([3]) om te be-grijpen waarom voor deze structuur optimale transmissie-eigenschappen bekomen worden. Fig.2 toont het gesimuleerdetransmissieprofiel van 6L4G voor een 10V stuurspanning. Dit

Fig. 2. Gesimuleerd transmissieprofiel van een 6L4G-eenheidscel voor een 10Vstuurspanning (de rode resp. blauwe rechthoeken duiden elektrodes op eenhoge resp. lage potentiaal aan).

profiel toont aan dat voor deze structuur zowel boven als tussende elektrodes hoge transmissiewaarden bekomen worden. Con-ventionele IPS ontwerpen worden gekarakteriseerd door hogetransmissiewaarden tussen de elektrodes, terwijl voor Fringing-Field Switching (FFS,[4]) ontwerpen typisch een hoge trans-missie bekomen wordt boven de elektrodes. Aangezien dehoge gemiddelde transmissie van de 6L4G-structuur bekomenwordt door bijdragen van zowel de IPS en FFS zones, kun-nen we de structuur van de 6L4G-cel benoemen als een nieuwehybride FFS/IPS geometrie. Momenteel wordt een maximaleceltransmissie van 67% bekomen voor een 10V stuurspanning.We stellen een verdere optimalisatie voor van het gebruiktevloeibaar kristal om de stuurspanning voor optimale transmissiete verlagen en de lage transmissiezones te reduceren. Het de-sign dat op deze manier zal bekomen worden, kan aanleidinggeven tot een structuur die beter presteert dan conventionele IPSontwerpen.

III. 1D-MODELLERING VAN BACKFLOW IN VA-LCD’S

Wanneer een VA-LCD pixel wordt aangestuurd met eenspanningstap waarvan de amplitude V een zekere drempel-waarde VBF overschrijdt, treedt een vloeistofstroming op waar-naar gerefereerd wordt als backflow. Dit effect induceerteen slingerend transmissieprofiel tijdens het schakelen, watleidt tot een sterk verhoogde schakeltijd. Om dit effect temodelleren in simulaties moet de hydrodynamische Leslie-Ericksen theorie in rekening worden gebracht, [5]. Hiervoorzijn 4 Miesowicz viscositeitscoefficienten ηij vereist, wat decomplexiteit van het simulatiemodel verhoogt. Conventionelesimulaties van het backflow effect ([6]) gebruiken typisch deηij waarden van MBBA, het enige vloeibaar kristal waarvoor deviscositeitscoefficienten nauwkeurig bepaald werden, [7]. Zoalsin Fig.3 geıllustreerd wordt, kan er een betere overeenkomsttussen gesimuleerde en experimentele transmissieprofielenbekomen worden met een 1D-simulatiepakket ([8]) door gebruikte maken van materiaalspecifieke schattingen van ηij , die kun-nen bekomen worden met een recent gerapporteerde procedure([9]).

Fig. 3. Het optreden van backflow in VA-LCD’s: gesimuleerd (links) en exper-imenteel (rechts) schakelprofiel. Op t = 0ms werd het sample met een 6Vspanningsstap aangestuurd.

IV. DE INVLOED VAN TEMPERATUUR OP HETSCHAKELGEDRAG VAN VA-LCD’S

Het temperatuursinterval voor aanvaardbare prestatie legteen strenge eis op voor LCD’s die gebruikt worden inmobiele toepassingen. Daarom werd een experimentelestudie uitgevoerd om het effect van temperatuursvariaties ophet schakelgedrag van VA-LCD’s na te gaan. Fig.4 toontde schakeltijd als functie van de aangelegde spanning voorverschillende temperaturen.

Fig. 4. Experimentele schakeltijden als functie van de stuurspanning voor ver-schillende temperaturen.

Fig.4 toont dat bij toenemende temperatuur de schakeltijd τon

afneemt en dat de drempelspanning VBF (4.5V-5V) waarvoorde schakeltijden sterk toenemen (als gevolg van backflow) ver-schuift naar hogere spanningen. Bijgevolg wordt bij toene-mende temperatuur een beter schakelgedrag bekomen. Om tem-peratuurseffecten in rekening te brengen in simulaties moetende variaties van de materiaalparameters met temperatuur gekendzijn. Aangezien het echter moeilijk is om deze variaties methoge nauwkeurigheid te bepalen, is hierover weinig kwanti-tatieve informatie beschikbaar in datasheets of in de literatuur.Daarom werd op basis van metingen en fittings een heuristiekeprocedure ontwikkeld die toelaat om de belangrijke materiaal-parameters af te leiden als functie van de temperatuur. Deprocedure voor het schatten van de viscositeitscoefficientenwerd gewijzigd, aangezien deze methode aanleiding geeft totonfysische waarden voor η22 voor een temperatuur T > 25◦C.Het simulatiemodel van de vorige sectie kan uitgebreid wor-den om temperatuursvariaties in rekening te brengen bij hetmodelleren van het schakelgedrag van VA-LCD’s door gebruikte maken van de afgeleide en geschatte materiaalparameters.Fig.5 toont de gesimuleerde schakeltijden bekomen met ditmodel als functie van de spanning. Er is duidelijk een goedeovereenkomst tussen de experimentele (Fig.4) en gesimuleerde(Fig.5) schakeltijden. Een kwantitative beoordeling van de re-latieve fout op de gesimuleerde waarden van τon geeft aan dathet schakelgedrag op nauwkeurige manier gesimuleerd wordt(max. 25% fout op τon) voor het spanningsinterval dat van prak-tisch belang is voor beeldschermtoepassingen (i.e. V ≤ VBF ).

Fig. 5. Gesimuleerde schakeltijden als functie van de stuurspanning voor ver-schillende temperaturen.

V. EEN TEMPERATUURSCOMPENSERENDE OVERDRIVEAANSTURING VOOR VA-LCD’S

Het gebruik van een overdrive aansturing is een gekendemanier om sneller te schakelen tussen opeenvolgende grijswaar-den in LCD’s ([10]). Een dergelijk overdrive schemawerd afgeleid voor 25◦C door enkel gebruik te maken vangesimuleerde karakteristieken. Hoewel een sneller schakel-gedrag bekomen wordt in een beperkt temperatuursinterval,werd er experimenteel aangetoond dat de prestatie van eendergelijke overdrive aansturing te gevoelig is aan temper-atuursvariaties om toepasbaar te zijn in praktische beeld-schermtoepassingen. Extra overdrive schema’s werden afgeleidvoor {35◦C, 45◦C, 55◦C, 65◦C, 75◦C}, gebruikmakend van demogelijkheid om het schakelgedrag van VA-LCD’s te simulerenbij verschillende temperaturen. De temperatuursgevoeligheidvan een enkel schema kan worden geelimineerd door in situde temperatuur te bepalen en het meest geschikte schemate selecteren. Er werd experimenteel aangetoond dat opdeze manier correcte grijswaardenovergangen bekomen wor-den voor het volledig temperatuursinterval 25◦C-80◦C: de foutop de bekomen grijswaarde wordt voor het temperatuurscom-penserend schema drastisch gereduceerd (max. 10% fout t.o.v.200% fout bij 75◦C voor het conventionele statisch aanstuur-schema gebruikt in huidige VA-LCD’s) en gebeurt het schake-len veel sneller (tot tweemaal sneller). Gelet op de aanzienlijkeverbetering in prestatie van het schakelgedrag is het duidelijkdat het voorgestelde aanstuurschema een groot potentieel heeftvoor toepassing in toekomstige VA-LCD’s.

VI. BESLUIT

Een hybride FFS/IPS celgeometrie werd voorgesteld waar-voor zowel boven als tussen de elektrodes hoge lichttrans-missie bekomen wordt. Het dynamisch gedrag van VA-LCD’s werd beschouwd: een betere modellering en een nieuwemethode om temperatuurseffecten in rekening te brengen wer-den voorgesteld. Als toepassing werd een aanstuurschemaontworpen dat temperatuurseffecten in rekening brengt en daar-door de schakelprestaties van VA-LCD’s gevoelig verbetert.

REFERENCES

[1] M. Schiekel et al., Appl. Phys. Lett., vol.19, pp.391-393, 1971[2] M. Oh-e et al., Appl. Phys. Lett., vol.67, pp.3895-3897, 1995[3] 2dimMOS, autronic-Melchers, Karlsruhe, Germany[4] S. Lee et al., Appl. Phys. Lett., vol.73, pp.2881-2883, 1998[5] S. Chandrasekar, Liquid Crystals (2nd edition), Cambridge University

Press, 1992[6] N. Dessaud et al., IDW’06, LCT7-2, 2006[7] H. Kneppe et al., Mol.Cryst.Liq.Cryst., vol.65, 23, 1981[8] DIMOS, autronic-Melchers, Karlsruhe, Germany[9] H. Wang et al., Liq.Cryst., vol.33, pp.91-98, 2006[10] H. Nakamura et al., SID’01 Digest, 32(1), 1256, 2001

Contents

Acknowledgments ii

Overview iii

Extended abstract v

Extended abstract (Dutch version) vii

List of Abbreviations xii

List of Symbols xiii

1 Introduction 1

2 Liquid Crystal Displays 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Basic principles behind LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2.1 Liquid Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2.2 Changing the orientation of liquid crystal molecules . . . . . . . . . . . . 42.2.3 Polarization of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.4 Polarized light in an uniaxial birefringent layer . . . . . . . . . . . . . . . 72.2.5 LCD devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Different LC modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Twisted Nematic (TN) mode . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.3 In-Plane Switching (IPS) mode . . . . . . . . . . . . . . . . . . . . . . . . 112.3.4 Fringing-Field Switching (FFS) mode . . . . . . . . . . . . . . . . . . . . 112.3.5 Vertically Aligned (VA) mode . . . . . . . . . . . . . . . . . . . . . . . . . 122.3.6 Optically Compensated Bend (OCB) mode . . . . . . . . . . . . . . . . . 14

2.4 Driving schemes for LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.1 Passive matrix driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4.2 Active matrix driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Measuring and simulating LCD’s 173.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Description of the samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 Description of the setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

ix

x3.2.3 Measurement modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.4 Electrical driving schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.5 Temperature control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.6 Calibration of the setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Simulation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.1 DIMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 2dimMOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Implementation of the Jones matrix formalism . . . . . . . . . . . . . . . 21

4 Theoretical and experimental investigation of the IPS mode 224.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2 Measurement of IPS cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Sample information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Voltage-transmission characteristics . . . . . . . . . . . . . . . . . . . . . 23

4.3 Two-dimensional simulations of IPS . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.1 Simulation procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3.2 The use of dielectric layers in 2dimMOS . . . . . . . . . . . . . . . . . . . 264.3.3 Calculating the local polarization state . . . . . . . . . . . . . . . . . . . . 26

4.4 Analysis of IPS on local scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4.1 Simulating the voltage-transmission characteristics . . . . . . . . . . . . . 274.4.2 Static behaviour of the 6L4G cell . . . . . . . . . . . . . . . . . . . . . . . 294.4.3 Comparing the 4L4G, 6L4G and 8L4G cells at 6V . . . . . . . . . . . . . 344.4.4 Voltage-transmission behaviour of the 6L4G IPS cell . . . . . . . . . . . . 36

4.5 Further optimization of the hybrid FFS/IPS cell . . . . . . . . . . . . . . . . . . 414.6 Comparing the hybrid FFS/IPS cell with an existing IPS design . . . . . . . . . 424.7 Conclusion of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 The impact of fluid flow on the switching behaviour in VA-LCDs 445.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.2 Experiment: the dynamic response of VA cells . . . . . . . . . . . . . . . . . . . 455.3 Leslie-Ericksen theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.4 Modelling the switching behaviour in VA-LCDs with a 1D simulation model . . . 49

5.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.4.2 Determining the alignment boundary conditions . . . . . . . . . . . . . . 495.4.3 Estimating the viscosity parameters . . . . . . . . . . . . . . . . . . . . . 535.4.4 Simulating the switching behaviour in VA-LCDs . . . . . . . . . . . . . . 55

5.5 Description of the backflow phenomenon . . . . . . . . . . . . . . . . . . . . . . . 585.6 Conclusion of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6 The influence of temperature on the switching behaviour of VA-LCDs 636.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.2 Experimental study of the effect of temperature on the switching behaviour of

VA-LCD’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3 Temperature dependency of ∆ε, γ and Kii . . . . . . . . . . . . . . . . . . . . . . 65

6.3.1 Influence of T on ∆ε . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.3.2 Influence of T on Kii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.3.3 Influence of T on γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

xi6.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.4 Simulating the effect of temperature on the switching in VA-LCDs . . . . . . . . 706.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.4.2 The use of the default estimates for ηij . . . . . . . . . . . . . . . . . . . . 706.4.3 Methodology to obtain better estimates of ηij . . . . . . . . . . . . . . . . 716.4.4 Simulating the temperature dependency of the switching behaviour in VA-

LCDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.4.5 Verification of the model for a different LC . . . . . . . . . . . . . . . . . 786.4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.5 Conclusion of Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

7 A temperature compensating overdrive scheme for VA-LCDs 857.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2 The conventional LCD overdrive scheme . . . . . . . . . . . . . . . . . . . . . . . 85

7.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2.2 Extracting an overdrive scheme . . . . . . . . . . . . . . . . . . . . . . . . 877.2.3 Experimental verification of the overdrive scheme . . . . . . . . . . . . . . 907.2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.3 Towards a temperature compensating overdrive scheme . . . . . . . . . . . . . . 957.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.3.2 Temperature dependency of ∆n . . . . . . . . . . . . . . . . . . . . . . . . 957.3.3 Applying overdrive schemes at different temperatures . . . . . . . . . . . 97

7.4 Conclusion of Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

8 Conclusions 102

A Jones matrix implementation 105A.1 Theory of the Jones matrix formalism . . . . . . . . . . . . . . . . . . . . . . . . 105A.2 Implementation of the Jones matrix formalism in matlab . . . . . . . . . . . . . . 106A.3 ImportDataFile.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Bibliography 111

List of Abbreviations

AM Active MatrixCRT Cathode Ray TubeDAQ Data AcQuisitionEVA Enhanced Vertical AlignmentFEM Finite Element MethodFFS Fringing-Field SwitchingIPS In-Plane SwitchingITO Indium Tin OxideLC Liquid CrystalLCD Liquid Crystal DisplayMVA Multi-domain Vertically AlignedOCB Optically Compensating BendPM Passive MatrixPDP Plasma Display PanelPVA Patterned Vertical AlignmentTBA Tilt Bias AngleTFT Thin Film TransistorTN Twisted NematicVA Vertically Aligned

xii

List of Symbols

αi Leslie viscosity coefficientc light speed∆ε dielectric permittivity anisotropy∆n refractive index anisotropy (birefringence)D dielectric displacement field vectorε dielectric permittivity tensorε|| longitudinal dielectric permittivityε⊥ transversal dielectric permittivityE electrical field vectorfe electrostatic energy densityfelastic elastic energy densityfelectric electrical energy densityfsurface surface interaction energy densityftotal total free energy densityγ rotational viscosityΓ phase retardationηij Miesowicz viscosity coefficientk wave vectorkB Boltzmann constantK11 elastic splay constantK22 elastic twist constantK33 elastic bend constantλ wavelengthL liquid crystal directorn refractive index tensorn|| longitudinal refractive index (ne)n⊥ transversal refractive index (no)ne extraordinary refractive indexno ordinary refractive indexω pulsationS order parameterTc clearing temperatureVBF backflow threshold voltage

xiii

Chapter 1

Introduction

Liquid Crystal Displays (LCDs) have become very popular and well-known during the lastdecades due to their low weight, slim size and low power consumption. First appearing in digi-tal wrist watches, alarm clocks and small alphanumeric displays used in for example calculators,LCDs started penetrating the consumer electronics market. Nowadays, LCDs dominate the mo-bile and flat computer monitor market segment. Together with Plasma Display Panels (PDP),LCDs have replaced the Cathode Ray Tube (CRT) technology in TV applications.

Although the first generation of LCD panels was characterized by having a limited viewing angle,more recent ultra-wide viewing angle technologies have solved this issue. Two LCD switchingtechnologies that belong to the class of ultra-wide viewing angle LCDs will be considered inthis work: the Vertically Aligned (VA) and In-Plane Switching (IPS) modes. Currently, thesetechnologies are already used in high-end mobile and television applications. Both the VA andIPS mode feature highly important advantages such as a wide viewing angle, low operation volt-age, excellent contrast ratio and are therefore interesting for wider application in the consumermarket segment, previously dominated by the well-known Twisted Nematic (TN) mode. Wetarget to obtain a better understanding of some aspects of the switching behaviour of IPS andVA-LCDs, which should ultimately lead to an increase in performance of these technologies.

Chapter 2 gives a general introduction on the fundamental principles behind LCDs such as liq-uid crystals, light polarization, various switching modes etc. As the switching behaviour of IPSand VA-LCDs will be investigated by means of experiments and simulations, the experimentalsetup and simulations packages used will be described briefly in Chapter 3. The influence of thecell geometry parameters on the static transmission profile in IPS-LCDs will be considered inChapter 4.

The description of the (hydro)dynamic switching behaviour of VA-LCDs forms the core part ofthis work. The impact of fluid flow on the switching behaviour of VA-LCDs at room tempera-ture will be investigated and modelled in Chapter 5. It is also important to consider the effectof temperature variations on the switching phenomena, as the temperature range for properoperation puts a high requirement on displays for mobile applications. Therefore, the influenceof temperature on the switching behaviour of VA-LCDs is investigated and modelled in Chapter6. As an application of the model obtained in Chapters 5 and 6, a new driving scheme to obtainfaster and better switching over the whole temperature range in VA-LCDs will be presented inChapter 7. The conclusions of this work will be summarized in Chapter 8.

1

Chapter 2

Liquid Crystal Displays

2.1 Introduction

The aim of this chapter is to describe the fundamental principles behind Liquid Crystal Displays(LCDs). The basic properties of liquid crystals and light polarization will be introduced and aschematic pixel layout will be presented in the first section. Every pixel in a LCD acts as a lightvalve. Depending on the initial alignment of the liquid crystal molecules, various modes existwhich change the light transmission differently. These different modes and their properties willbe addressed in section 2.3. The chapter is concluded with an overview on the electrical drivingschemes for LCDs.

2.2 Basic principles behind LCDs

It will be described in this section how the properties of light propagating through a liquidcrystal layer can be changed. To do this, the most important properties of liquid crystals andlight polarization will be discussed. The section will be concluded by considering a typical LCDpixel layout.

2.2.1 Liquid Crystals

The liquid crystalline state, also called mesophase, features properties that are typical for boththe solid and liquid state. As in solids, liquid crystal molecules (mesogens) point, on average,along a common axis, called the director L = [Lx, Ly, Lz]. The molecules are not bound, buthave a translational freedom as in the liquid state. The difference in orientational order betweenthe solid, liquid crystalline and liquid phase is sketched in Fig.2.1.The director profile is mostly described in a fixed coordinate system where θ and φ representrespectively the inclination angle between the molecule and the z-axis and the angle betweenthe inclination plane and the xz-plane, as shown in Fig.2.2.To quantify the order present in the material, the order parameter S can be defined as, [1]:

S =< 3 cos2 ϑ− 1 >

2, (2.1)

where ϑ is the angle between the director and the longitudinal direction of each molecule andthe sign < x > averages the argument x over a sufficient number of molecules. In a materialwhere all molecules point in the same director direction, the order parameter S is equal to 1 (as

2

3

(a) solid (b) liquid crystalline (c) liquid

Figure 2.1: Sketch of the orientational order in the solid, liquid crystalline and liquid phase.

Figure 2.2: Defining tilt and twist angle for the liquid crystal director.

the cosine factor is equal to 1) as in a crystal. In a material with less ordering, the variationsin ϑ lead to a lower value of S. In a complete isotropic material, ϑ takes for every molecule arandom value in the interval [0, π] and the order parameter becomes zero in this case. For liquidcrystal materials, the order parameter typically varies between 0.3 and 0.9. The exact valueof S depends on the material parameters, but also on temperature. In liquid crystal materialsused for display applications, the interaction between the different liquid crystal molecules isin competition with the thermal motion of the molecules (thermotropic liquid crystals). At acertain high temperature, referred to as the clearing temperature Tc, the material becomes anisotropic liquid.

The liquid crystalline phase can be further divided into several categories with decreasing orderparameter, for example: smectic C, smectic A and nematic. For display applications, the nematicphase is very important. There is a directional order in this phase, but no positional order of thedifferent molecules with respect to each other. The macroscopic properties of a nematic liquidcrystal layer possess uniaxial symmetry. If the z-axis is oriented along the molecular director,the tensor of refractive indices in this coordinate system therefore reduces to, [1]:

n =

n⊥ 0 00 n⊥ 00 0 n||

,where n|| denotes the refractive index along the longitudinal direction of the molecule while n⊥symbolizes the refractive index in the transversal field of the molecule. One uses the notation no

4resp. ne more frequently to indicate the ordinary resp. extraordinary refractive index for lightpolarized perpendicular resp. parallel to the director. The anisotropy in refractive index, alsoreferred to as the birefringence, is defined as ∆n = ne − no. The birefringence of the nematicliquid crystals used in display applications typically varies between 0.05 and 0.30.In contrast to the nematic phase, the smectic A and smectic C phase feature both orientationaland positional ordering. The molecules in these phases are on average positioned in planes, sothey are closer to the crystalline phase than the nematic phase.

2.2.2 Changing the orientation of liquid crystal molecules

The actual profile of the director orientation corresponds to the configuration for which the totalfree energy is minimum. For practical display applications, the free energy density consists ofcontributions of the elastic energy (denoted by felastic), energy related to the applied electricalfield (denoted by felectric) and energy related to the interaction between the liquid crystal andthe surface (denoted by fsurface):

ftotal = felastic + felectric + fsurface. (2.2)

The three different contributions will be considered in this subsection.

Elastic energy

The director profile in a liquid crystal layer can be deformed due to external electrical or magneticfields or boundary conditions. The free energy related to elastic deformation depends on thedirector orientation and the variation of this director (first derivative) and can be calculated ateach point by means of the Frank-Oseen expression, [2]:

felastic =12

[K11(∇ · L)2 +K22(L · (∇× L))2 +K33(L× (∇× L))2

]. (2.3)

As can be seen in Eqn.2.3, the elastic energy consists of three terms defined as the splay,twist and bend contributions, each having its own deformation type. It can be shown that thedeformations correspond respectively to the variations

[∂Lx∂x ,

∂Ly

∂y

],

[∂Lx∂y ,

∂Ly

∂x

]and

[∂Lx∂z ,

∂Ly

∂z

].

These three basic deformation types are shown in Fig.2.3.

Figure 2.3: Splay, twist and bend deformation in liquid crystal layers, [3].

5The parameters K11,K22 and K33 in Eqn.2.3 are the elastic constants of the liquid crystalmaterial for splay, twist and bend deformations respectively. These material constants arerelated to the energy required for the respective deformations. The total deformation energy isthe integrated value of the local deformation free energy density function over the liquid crystallayer.

Influence of the electrical field

As mentioned before, liquid crystal molecules possess uniaxial symmetry due to their specialchemical structure. If the z-axis is again oriented along the director of the liquid crystal, thedielectric tensor of the uniaxial material can be written down as:

ε =

ε⊥ 0 00 ε⊥ 00 0 ε||

. (2.4)

Consequently, the dielectric anisotropy is calculated as ∆ε = ε||−ε⊥. In the standard coordinatesystem defined in Fig.2.2, the dielectric tensor is transformed to, [4]:

ε =

ε⊥ + (ε|| − ε⊥) sin2 θ cos2 φ (ε|| − ε⊥) sin2 θ sinφ cos2 φ (ε|| − ε⊥) sin θ cos θ cosφ(ε|| − ε⊥) sin2 θ sinφ cosφ ε⊥ + (ε|| − ε⊥) sin2 θ sin2 φ (ε|| − ε⊥) sin θ cos θ sinφ(ε|| − ε⊥) sin θ cos θ cosφ (ε|| − ε⊥) sin θ cos θ sinφ ε⊥ + (ε|| − ε⊥) cos2 θ

. (2.5)

When an electrical field E is applied to a dielectric material, the field induces a dielectricdisplacement field D = εE. The corresponding energy density felectric can be calculated as, [1]:

felectric = −12[ε⊥|E|2 + ∆ε(L · E)2]. (2.6)

Liquid crystal molecules always tend to reach an equilibrium state for which the free energyis minimized. The switching behaviour of the liquid crystal molecules when an electrical fieldis applied depends on the sign of the dielectric anisotropy ∆ε. As the first term in Eqn.2.6is constant, the expression for felectric can be minimized by making the second term as smallas possible. For a positive dielectric anisotropy ∆ε, this can done by maximizing the scalarproduct between the director and the electrical field. This condition is satisfied when E and L

are parallel. Therefore, liquid crystal molecules with ∆ε > 0 show the tendency to align parallelto the electrical field lines.In case ∆ε < 0, the elastic energy is minimized by making the scalar product E · L as smallas possible. This factor becomes zero when the director is perpendicular to the electrical field.Consequently, in case ∆ε < 0 the liquid crystals will try to orient perpendicular to the electricalfield lines.

Interface interaction

The interaction between the surface and the liquid crystal molecules has a determining rolein the macroscopic orientational order of the liquid crystal. One speaks of strong anchoringif the interaction between the interface and the liquid crystal molecules is so strong that theorientation of the director (azimuth and pretilt) at the interface is completely determined bythe surface conditions. In the case of weak anchoring, deviations of the preferential directionwill occur. These variations have a certain energy cost which is expressed by the surface energydensity fsurface. In case of weak anchoring, this extra cost has to be added to Eqn.2.2.

6Different models to describe fsurface exist in literature, depending on the exact interface ge-ometry. For example, if there is a preferred boundary direction, denoted by Lpref , the surfaceenergy in the model described by Rapini and Papoular can be calculated as, [5]:

fsurface =Ks

2(1− (L · Lpref )2). (2.7)

2.2.3 Polarization of light

Light waves can be considered as electromagnetic waves propagating in a certain direction andhaving a certain polarization state. This polarization state describes the direction of oscillationof the electrical field in the plane perpendicular to the propagation direction. Any polarizationcan be described as a (complex valued) linear combination of two orthogonal components. Incase both orthogonal components are in phase, the direction of the transversal electrical fieldhas a fixed direction, so a linear polarization state is obtained, as shown in Fig.2.4(a). When theorthogonal components have equal amplitudes and a quadrature phase difference, the transverseelectrical field describes a circle in time, leading to a circular polarization state as shown inFig.2.4(b). Depending on the sign of the phase difference, one can further distinguish left (+90degrees) and right (-90 degrees) handed circular polarization states. An elliptical polarizationstate is obtained (Fig.2.4(c)) in case the orthogonal components are not in phase and either donot have the same amplitude and/or are not ninety degrees out of phase. If the phase differencebetween the orthogonal polarization components varies randomly, the light is unpolarized.

(a) linear (b) circular (c) elliptical

Figure 2.4: The three basic polarization states, [6].

Polarized light can be obtained from unpolarized light by using a polarizer (mainly linear andcircular). A polarizer transmits one polarization state and absorbs the component orthogonalto that polarization. Consequently, the obtained polarized light beam will only have half of theintensity of the original unpolarized light beam.

72.2.4 Polarized light in an uniaxial birefringent layer

Solving the Maxwell equations for uniaxial media in a principal coordinate system (so thatthe dielectric tensor reduces to the tensor from Eqn.2.4) leads to two plane wave solutions(eigenmodes) for the electrical field. It can be shown that the eigenmodes have correspondingrefractive indices n1 and n2:

n1 = no (2.8)

n2 =1√

cos2 θn2

o+ sin2 θ

n2e

. (2.9)

As the two eigenmodes ’see’ a different refractive index upon propagating through the uniaxialmedium, both modes have a different phase velocity. Consequently, after propagation overa distance d through the medium, there will be a phase difference or retardation Γ which iscalculated as:

Γ = (k1 − k2)d

=2πλ

(n1 − n2)d

=2πλ

no −1√

cos2 θn2

o+ sin2 θ

n2e

d. (2.10)

As follows from the discussion in subsection 2.2.3, the polarization state of light can be alteredby changing the phase difference between the orthogonal components of the electrical field.It can now be understood that this is possible when light is transmitted through an uniaxialmaterial. At the first interface, the incident electrical field splits up in the two eigenmodesof the uniaxial crystal. Next, the two eigenmodes propagate with a different phase velocitythrough the material, which leads to an extra phase difference Γ after transmission through thematerial. This change in phase difference between the orthogonal polarization components leadsto a change in polarization state.

The most common liquid crystals for LCDs can be categorized in the class of uniaxial materials.The liquid crystal layer in display applications can not be considered uniform, as the orientationof the molecules varies across the layer. However, the layer can be divided into subsequent slices(slabs) that are thin enough to be considered as homogeneous. The discussion above is directlyapplicable to such elementary liquid crystal layers. It is possible to describe the change of thelight polarization through subsequent elementary layers by using the Jones matrix formalism(see appendix A). In this way, the light transmission through the whole liquid crystal layer canbe described.

2.2.5 LCD devices

Fig.2.5 shows a schematic drawing of a liquid crystal device. Light from the unpolarized backlightbecomes polarized by means of the first polarizer. Depending on the orientation of the liquidcrystal, the polarization state can be influenced as discussed in subsection 2.2.4. The initialorientation of the liquid crystal molecules is determined by polymer alignment layers. Theorientation of the liquid crystal molecules can be changed externally by creating an electrical

8field between the transparent Indium Tin Oxide (ITO) electrodes, so also the polarization statecan be controlled indirectly in this way. Therefore, by carefully designing the liquid crystalmaterial and the cell geometry, one can reach a situation where the phase retardation in case anelectrical field is applied leads to a polarization state which is ideally orthogonal to the initialpolarization state. The second polarizer (after the liquid crystal layer) blocks one of these twopolarization states, so the setup can act as a light valve. The pixel layout created in this wayblocks or transmits light, depending on the presence of an external electrical field. Grey scalesare obtained by applying an intermediate field strength.

Figure 2.5: Schematic LCD pixel layout with typical dimensions (drawing not to scale).

To apply an electrical field over the liquid crystal layer, electrodes are positioned around thislayer. The electrodes in Fig.2.5 are drawn at the top and bottom of the liquid crystal layer sothe electrical field is applied across the whole layer, but also other geometries are possible andthey will be discussed in the next section. The cell gap d between the substrates is realized byusing incompressible spacer balls or cylinders that are spread over the bottom substrate. Dueto the incompressibility of these spacers, the gap is maintained after the top substrate is laidover the bottom substrate. Except for a small opening, the whole structure is glued together.This opening is used to fill the cell structure with the liquid crystal material. This is done undervacuum conditions where the unfilled cell structure is immersed in liquid crystal material. Dueto capillarity action, the liquid crystal material fills the whole cell. Afterwards, the opening isclosed with polymer glue. A heating step can be applied to obtain a more uniform liquid crystallayer over the cell. Finally, the cell is sandwiched between crossed or parallel polarizers.

To make a display, a lot of pixels are aligned in a matrix structure. By controlling the lighttransmission (intensity) of every pixel, an image can be created. In order to add color to theimage, every pixel is divided into three subpixels. By putting a different color filter (e.g. red,green and blue) above each area, a color impression can be created by controlling the intensitiesof these areas (trichromatic principle).

Various standard designs with different electrode geometries and alignment of the liquid crystallayer will be discussed in the next section.

92.3 Different LC modes

2.3.1 Introduction

A brief overview on various methods for pixel switching will be presented in this section. Thisoverview serves as a first introduction to compare the different available technologies, eachfeaturing a different way of switching when an electrical field is applied. Before turning to thedifferent switching modes, it will be considered how the predefined director orientation in theoff-state can be obtained.

The liquid crystal molecules show the tendency to align themselves due to intermolecular forces.However, this alignment is only in microscopic domains. Therefore, it is necessary to controlthe macroscopic orientational order of the liquid crystal externally to secure proper operationof the liquid crystal display. This is done by giving the top and bottom of the liquid crystallayer a fixed orientation (pretilt and pretwist) in space by rubbing of polymer alignment layers,[7]. The non-fixed molecules in the layer orient themselves in such a way that the elastic energyin the liquid crystal layer is minimized. As a result, the initial orientation of the whole liquidcrystal can be controlled. For example, if there is a difference ∆φ in pretwist between the topand bottom alignment layer, a homogeneous twist profile φ(z) = z∆φ/d over the complete crosssection minimizes the elastic energy, [8].Next to the pretwist, also an initial pretilt is necessary to ensure that all liquid crystals switchin the same direction when an electrical field is applied. For example, consider the case whereall molecules are initially oriented completely horizontally. If a vertical electrical field is applied,the molecules with ∆ε > 0 will tend to align parallel to the field lines. The molecules howeverpossess the freedom to turn to a vertical orientation either in a clockwise or counter-clockwisedirection, as depicted in Fig.2.6.

Figure 2.6: Ambiguous switching behaviour if no pretilt is present.

It is necessary to avoid this situation, as undesirable domains would originate where moleculesswitch in different directions. Therefore, in analogy with the pretwist, it is necessary to givethe liquid crystals an initial inclination. This leads to a better defined switching behaviour, asshown in Fig.2.7.

10

Figure 2.7: Well defined switching behaviour if pretilt is present.

2.3.2 Twisted Nematic (TN) mode

In a Twisted Nematic (TN) LCD, the liquid crystal molecules are put between two glass plateswith transparent ITO electrodes with crossed polarizers placed on top and bottom. The liquidcrystal molecules show a gradual twist across the cell in the off-state, due to a 90◦ pretwistdifference for the directors at the top and bottom substrate (see Fig.2.8). In this case, the lin-early polarized light propagates through the liquid crystal layer, guided along the twisted liquidcrystals. Consequently, the light polarization gradually turns and finally becomes orthogonalto the initial polarization state just before the analyzer. All light is transmitted because thepolarizers are crossed.

Figure 2.8: Operating principle of the TN cell, [9].

If a voltage is applied between the electrodes, the liquid crystal molecules (positive ∆ε material)orient parallel to the vertical field lines, so the twisted structure disappears. The light polariza-tion is no longer rotated, as the phase retardation Γ from Eqn.2.10 is zero when θ = 0. As thepolarizers are crossed, all light is absorbed at the second polarizer so a black pixel is obtained.The arrangement sketched above with crossed polarizers is called the normally white mode asall light is transmitted in the off-state. If the polarizers are parallel to each other, the display isoperating in the normally black mode: the pixel appears black in the off-state while all light istransmitted in the on-state. The normally white mode is however mostly preferred in TN-LCDs,as this mode shows a better neutral black and provides a wider viewing angle.The advantages of twisted nematic cells are a low operating voltage and a high contrast ratio.The viewing angle of TN cells is insufficient for large panel displays. In order to improve theviewing angle of the TN cells, retardation films can be used.

112.3.3 In-Plane Switching (IPS) mode

Soref proposed in 1973 a design in which inter-digital electrodes are arranged parallel to eachother on the same substrate. If a voltage is applied, an electrical field originates in the trans-verse plane, [10]. Consequently, the liquid crystal molecules are rotated in the plane, leadingto so-called In-Plane Switching (IPS) as shown in Fig.2.9. As indicated in Fig.2.9, the gap G

between the electrodes is typically much larger than the electrode width L.

Figure 2.9: Operating principle of the IPS cell, [11].

The polarizers are crossed and the front polarizer is parallel to the rubbing direction. Conse-quently, no retardation occurs in the off-state and the polarization state remains unchanged. Asthe polarizers are crossed, all light is blocked by the analyzer (dark pixel). If an electrical field isapplied, the molecules reorient parallel (positive ∆ε material) to the field lines, causing a phaseretardation of the incoming light. If the cell geometry is designed well, the liquid crystal layeracts as a quarter wavelength plate (the light polarization is turned by 90 degrees), so all lightis transmitted by the analyzer. To make sure that all molecules turn in the same direction, apretwist can be introduced.Due to the symmetry of the fringing field, the liquid crystal directors above the middle of theelectrodes remain unchanged, leading to low transmission values in this area.

As the liquid crystal molecules are rotated in-plane, the viewing angle of IPS-LCDs is wider andmore symmetric than that of the TN-LCDs.

2.3.4 Fringing-Field Switching (FFS) mode

The basic structure of FFS cells is very similar to that of IPS cells, except for the much smallerelectrode gap, which is in this design typically smaller than the electrode width, [12]. Due tothis geometry, the electrical field parallel to the substrate can not be formed out, but insteadparabolic shaped field lines (fringing fields) are obtained, as shown in Fig.2.10. There is a smallvertical offset between the fingers of the inter-digital electrodes for a further enhancement of theparabolic field lines.

12

Figure 2.10: Operating principle of the FFS cell, [12].

In contrast to IPS cells, the fringing-field component is dominant in this design. Due to thisfield component, also liquid crystal molecules above the electrodes reorient when an electricalfield is applied. Therefore, no dead zone prohibiting transmission above the electrodes appearsas in IPS-cells and a higher average cell transmission is obtained. Typically, FFS-LCDs providewide viewing angle characteristics.

2.3.5 Vertically Aligned (VA) mode

In the Vertically Aligned (VA) mode, liquid crystal molecules with a negative ∆ε value areinitially oriented vertically (referred to as homeotropic alignment, [13]) between two glass plateswith ITO electrodes, as shown in Fig.2.11. The liquid crystal layer is placed between crossedpolarizers.The homeotropic alignment is realized by using polymer alignment layers. The fabricationprocess can be rubbing free which leads to a cheaper process chain with a higher yield.

Figure 2.11: Operating principle of the mono-domain VA cell, [14].

When no electrical field is applied, the liquid crystal molecules stay aligned vertically and noretardation occurs. Consequently, there is no polarization change and all light is absorbed bythe analyzer (dark pixel) which leads to an excellent dark state, independent of wavelength andtemperature. When a voltage is applied between the electrodes, the vertical electrical field causes

13the liquid crystal molecules to align perpendicularly to the field lines. As the directors becomeoriented horizontally, the retardation is different from zero, leading to a change in polarization.If the cell is designed carefully, the linear polarization state is turned by 90 degrees so all lightis transmitted by the analyzer (white pixel). A small pretilt is necessary to let all moleculesswitch in the same direction in mono-domain VA-LCDs.The threshold voltage for switching is given by, [8]:

Vth = π

√K33

ε0|∆ε|, (2.11)

while the switching on and switching off times are proportional to, [8, 15]:

τon ∝ γd2

ε0|∆ε|(V 2 − V 2th)

(2.12)

τoff ∝ γd2

ε0|∆ε|V 2th

. (2.13)

The main advantages of the VA mode are the low operation voltage and the excellent contrastratio (due to the excellent dark state).In order to improve the viewing angle, various approaches to achieve multi-domain VA (MVA)cells have been investigated, [16, 17, 18]. One principle is shown in Fig.2.12.

Figure 2.12: Operating principle of the MVA cell, [11].

As can be seen in Fig.2.12, each pixel has different domains. The initial director alignment(pretilt) is different for each domain. As shown in Fig.2.12 by purple triangles, one way to achievethis is to insert real protrusions. The protrusions are formed by coating the ITO electrodes with apolymer, etching this layer with a special mask and depositing the alignment layer. The domainsare automatically controlled by the slope of the protrusions. In the off-state, the liquid crystalmolecules are oriented vertically as in a mono-domain VA cell. When a potential difference isapplied between the electrodes, the protrusions assist the liquid crystal molecules to tilt alongthe slopes. The retardation corresponding to this orientation turns the polarization and the lightis transmitted by the analyzer. Wider viewing angles can be obtained as neighbouring subpixelshave complementary viewing characteristics due to the different orientation of the directors.A combination of real and virtual protrusions that are created by fringing electrical fields nearthe edges of a patterned ITO slit can also be used to create multi-domain VA cells, as shown inFig.2.13.

14

Figure 2.13: Virtual protrusions in MVA cells, [19].

Other possibilities are the enhanced vertical alignment (EVA, [20]), patterned vertical alignment(PVA, [21]) and polymer-stabilised vertical alignment techniques (PSVA, [19]).

2.3.6 Optically Compensated Bend (OCB) mode

The principle of the OCB mode is shown in Fig.2.14. Just as in VA and TN cells, the liquidcrystal is put between two glass plates with etched ITO electrodes and crossed polarizers areused.

Figure 2.14: Operating principle of the OCB cell.

In the off-state, the director profile in the OCB cell shows a splay configuration. When thevoltage between the electrodes exceeds a certain threshold voltage, the director profile changesto a first bend state, indicated as state I. For even higher voltages, a second bend state IIis reached in which the directors align parallel to the electrical field. The operating principleof OCB cells is based on the very fast switching between these two bend states (I and II),which implies that the voltage applied between the electrodes needs to be kept above a criticalvoltage at all time to avoid relaxation to the splay state. In the first bend state, the obtainedretardation turns the linear polarization state by 90 degrees, so all light is transmitted by thesecond polarizer. In the second bend state, the directors are oriented vertically, so no change inpolarization is obtained and all light is blocked by the analyzer.An interesting feature of the OCB mode is the fact that the retardation in the upper and lowerpart of the cell compensate each other (hence the name OCB), which leads in theory to excellentviewing angle properties.

152.4 Driving schemes for LCDs

To create an image on the display, one has to be able to impose the given grey levels at a pre-scribed time onto the individual pixels. This is done electronically by applying the appropriatedriving voltage across each pixel in the LCD. In time, the driving scheme is divided into framesof fixed duration. The pixel driving voltages can only be changed at the start of every frame, soduring one frame the provided image is ideally kept fixed. Two addressing schemes are commonfor LCDs: passive and active matrix driving. Both methods will be described shortly in thissection.

2.4.1 Passive matrix driving

In the Passive Matrix (PM) driving scheme, the pixels are situated at each cross section of amatrix conductor pattern, as can be seen in Fig.2.15. As the liquid crystal material is sandwichedbetween the electrodes, each pixel behaves as a capacitor.

Figure 2.15: Passive matrix driving configuration, [22]. The pixels are symbolized by rectangles whichdenote capacitive impedances.

In the line-at-a-time addressing, one line of the matrix is activated by a row driver and theappropriate driving voltages for this line are provided by a column driver. In this way, eachpixel of the line is driven at the appropriate voltage. After this, the next line is selected bythe line driver and the sequence is repeated. It is obvious that the pixels in the passive matrixmust maintain their state until they are refreshed again. In the next cycle, the driving voltagesare inverted to avoid the occurrence of a net DC-voltage which would degrade the liquid crystalmaterial (dissociation of the ingredients in the liquid crystal material).The maximum number of rows that can be addressed using the passive matrix scheme can becalculated. Alt and Pleshko showed that the contrast ratio reduces with an increase in thenumber of lines to be addressed, until no distinction is possible between the ’on’ and ’off’ states.Consequently, the use of the passive driving scheme is not applicable for use in displays with alarge number of pixels.

162.4.2 Active matrix driving

In the Active Matrix (AM) driving scheme, an active switching element (e.g. a Thin FilmTransistor, TFT) is incorporated on each cross point of the matrix layout, as shown in Fig.2.16.This allows the pixel to be isolated from the matrix when it is not being addressed.

Figure 2.16: Active matrix driving configuration.

In one row, the transistor gates are connected to the row electrode of the line. The sources in acolumn are connected to the column electrode and the drain contacts are connected to the pixelelectrodes.Just as in the passive driving scheme, one line is selected by the row driver (gate voltages of thetransistors in this row becomes high) and the appropriate driving voltages for the pixels in thisline are provided by the column driver to the sources of the transistors. The drain takes overthe source voltage and the pixel, again acting as a capacitor, is charged. After the signal at thegate electrode is removed, the charge across the pixel is stored until the next refresh cycle (thedrain voltage has become independent of voltage variations at the source because the gate signalis low). As the charge stored in each pixel (capacitor) is kept fixed using the active switch, theAM driving scheme leads to an almost flicker-free image. This in contrast to the PM drivingscheme where the transmission decays due to a continuous discharge of the capacitor. Just aswith passive matrix driving, the voltage polarity is altered in subsequent refreshment cycles.

Chapter 3

Measuring and simulating LCD’s

3.1 Introduction

The objective of this work is to gain better insight in some aspects of the switching behavior ofIPS and VA-LCDs. The followed approach is based on the results of simulations and experimentsthat are performed in a parallel manner. This chapter describes the framework in which thesesimulations and measurements are performed. Therefore, an overview will be given of theexperimental setup and the simulation software that are used.

3.2 Experimental setup

3.2.1 Description of the samples

In order to investigate the properties of IPS and VA liquid crystal modes, various test sampleswere fabricated. Each sample consists of several areas which can be addressed by applying avoltage between the appropriate electrodes. Therefore, each cell can be considered as a singlepixel that can be driven to obtain an on, off or intermediate grey scale state. The test areashave much larger dimensions (about 1cm2) than the picture elements of real LCD panels (about100µm2), which makes measurements more practical. A typical layout of a test sample is shownin Fig.3.1.

Figure 3.1: Typical layout of the test samples used in measurements. The 9 zones depicted as activeareas denote the different test cells.

17

183.2.2 Description of the setup

The experimental setup resembles the conventional LCD setup from subsection 2.2.5 as muchas possible. An overview picture of this setup is shown in Fig.3.2.

Figure 3.2: Overview picture of the experimental setup. Following devices can be distinguished on thispicture: (a) computer showing a LabVIEW interface, (b) optional oscilloscope, (c) data acqui-sition (DAQ) card, (d) multimeter for voltage read-out from the photomultiplier, (e) optionalsignal generator, (f) capacitance meter, (g) active matrix driving devices, (h) photomultipliercontroller, (i) temperature controller, (j) polarizing microscope, (k) photomultiplier, (l) hotstage.

The test sample is inserted in the hot stage in which the temperature can be controlled precisely.After the setup is calibrated, the cell is driven to a certain voltage provided by the digital outputof a data acquisition card (DAQ), which is controlled by a computer. The cell is observed with apolarizing microscope in which the orientation of the top and bottom polarizers can be controlledto align the setup as in a real display (crossed polarizers). A photomultiplier is placed on topof the microscope. The photomultiplier detects the amount of light coming from a specificarea of the cell. When the setup is calibrated properly, the output of the photomultiplier is avoltage which is linear to the detected light intensity. This output is connected to the analoginput of the DAQ card. The whole setup is controlled by a LabVIEW program which providesthe appropriate voltage sequence to the output of the DAQ card and reads the data from thephotomultiplier.

3.2.3 Measurement modes

Different types of measurements will be performed with the presented setup: the voltage-transmission, time-transmission and voltage-capacitance modes.

Voltage-transmission measurement

In this scheme, the transmission is measured as a function of the voltage applied between the cellelectrodes. The voltage profile is applied in a staircase sequence. Each step lasts sufficiently long

19so that a director profile close to the equilibrium configuration is obtained before the transmissionvalue is captured by the DAQ card. In this way, a voltage-transmission characteristic is extractedby the LabVIEW program. Finally, the measurement results are exported to a text file.

Time-transmission measurement

In the time-transmission measurement, a single voltage step is applied between the electrodesand the cell transmission is captured continuously (10kHz sample rate). In this way, the dy-namic transmission profile upon switching can be measured. The resulting time-transmissioncharacteristic is exported to a text file.

Voltage-capacitance measurement

In the voltage-capacitance scheme, a staircase voltage profile is applied and the capacitancebetween the electrodes is measured by a capacitance meter as a function of voltage.This scheme will be applied in chapter 6 to measure the transversal and longitudinal dielectricpermittivity of liquid crystal materials used in a VA samples with a cell gap d ≤ 4.2µm. This canbe done in following way: First, the capacitance C0 of the unfilled sample (fabricated as discussedin subsection 2.2.5) is measured. Next, the VA sample is filled with the liquid crystal material.When no voltage is applied, the directors remain in their initial orientation, perpendicular tothe substrate. The capacitance of the pixel according to this orientation equals:

Coff = ε||ε0A

d= ε||C0, (3.1)

where A denotes the electrode area. The value of ε|| can be calculated by taking the ratio betweenthe experimental values of Coff and C0. To calculate ε⊥, a similar procedure can be followed.In this case, a sufficiently high voltage is applied so that the liquid crystal molecules are orientedparallel to the electrodes (perpendicular to the field lines). In this case, the capacitance of thepixel changes to:

Con = ε⊥ε0A

d= ε⊥C0. (3.2)

Taking the ratio Con/C0 leads to the value of ε⊥. It was shown in [23] that the contribution ofthe fringing field is negligible for this scheme, as long as the cell gap remains smaller than 5µm.Therefore, we only expect a small error on the extracted values of ε|| and ε⊥.

3.2.4 Electrical driving schemes

In the measurement modes described above, the potential was applied continuously to the elec-trodes. By inserting an external hardware device, also measurements can be done simulatingactive matrix driving. This device converts the voltage provided by the output of the DAQ tovery short voltage pulses of 50µs every 0.5ms which are applied over the test sample. After thevoltage pulse is applied in every period, the cell is isolated by an active switch. This situationcorresponds to the active matrix driving scheme discussed in subsection 2.4.2.

3.2.5 Temperature control

The setup is equipped with a Mettler-Toledo temperature control system. This system consists ofa FP82HT hot stage, a thermal measuring cell, in which the temperature is controlled by a FP90central processor. This temperature control system provides a precision on the temperature in

20the hot stage of±0.4◦C. The transmission of the sample inserted in the hot stage can be measuredwith the microscope through an opening in the hot stage.

3.2.6 Calibration of the setup

In order to obtain useful experimental results, the setup must be calibrated carefully. Thiscalibration can be done manually in LabVIEW by setting minimum and maximum transmissionvalues which serve as a 0% resp. 100% transmission reference in the measurements. The zeroreference was set by blocking the input of the photomultiplier with a sheet. As the 100% trans-mission reference should correspond to the situation where all light passing the first polarizeris transmitted, this reference was set by measuring the light intensity through the hot stage(without sample inserted) when the polarizers were oriented parallel to each other. In order tooperate the photomultiplier in its linear region, its output for the 100% transmission referencemust be higher than -0.5V. This requirement can be met by adjusting the backlight intensity sothat the output of the photomultiplier coincides with the desired value just above -0.5V.

3.3 Simulation techniques

This section gives a brief overview on the software that is used to perform simulations in thecoming chapters. These simulations can provide a lot of additional information on what ishappening on micrometer scale in the cell, leading to a better understanding of the switchingbehavior. Without going into detail, the calculation methods on which these programs are basedwill be described shortly. This is important to understand the possibilities and restrictions ofeach of these software packages. A description of how the software is used in simulations will begiven at the appropriate places in the coming chapters.

3.3.1 DIMOS

DIMOS ([24]) is a software package of Autronic-Melchers GmbH that can be used to calculatethe electro-optical properties of LCDs. It is assumed that the LCD is composed of plane parallellayers where the lateral extensions are much larger compared to the thicknesses of the singlelayers. In DIMOS only one spatial variation of the layer parameters along the layer normal isconsidered. Consequently, it is not possible to simulate two-dimensional effects (e.g. fringing-field effects) using this package.

Arbitrary multilayer structures consisting of isotropic, uniaxial and biaxial materials can bedefined with an arbitrary orientation of the optic axis. For nematic liquid crystal layers, thestatic and dynamic deformation profiles of the liquid crystal layer induced by an external fieldcan be calculated. These deformation profiles can be presented to the user by means of molecularplots that show the director orientation along a cross section at different time steps.

The director calculation in DIMOS is based on a minimization of the total free energy expressionfrom Eqn.2.2 by using the Ritz relaxation method, [25]. Using this method, both static anddynamic director profiles can be calculated. Once the director profile along the cross section isknown, the static or dynamic optical transmission of the system can be calculated. In DIMOS,two matrix methods are implemented to calculate the optics of the liquid crystal cell. Thefirst method is the Jones matrix method, which is discussed in more detail in appendix A.In contrast to the Jones matrix formalism, the Berreman method ([26]) uses 4x4 matrices to

21describe the liquid crystal layer. This method is more general as the calculated quantities followdirectly from the Maxwell equations. Just as with the Jones formalism, inhomogeneous layersare approximated by a series of homogeneous slabs. Disadvantages of this more exact methodare the increase in calculation time and the decrease of the numerical stability.

The DIMOS software will appear to be very useful as also flow phenomena in liquid crystallayers can be simulated in this package. This will be discussed in chapter 5.

3.3.2 2dimMOS

Just as DIMOS, 2dimMOS ([27]) is also a commercial product of Autronic-Melchers. In contrastto the one-dimensional DIMOS, 2dimMOS allows variation of the molecular orientation in twospatial dimensions so that lateral effects can be taken into account. Both the calculation of thetwo-dimensional electrostatic potential and the director profile are calculated by means of theFinite Element Method (FEM). The dielectric and liquid crystal areas are divided into smalltriangles. A mesh is defined by the edges and vertices of these triangles. The potential valuesand director orientation are calculated at each vertex assuming a linear spatial variation withineach triangular element.

Just as in DIMOS, the director calculation is based on the minimization of the expression fromEqn.2.2. The calculation of the electrical potential U starts at the expression for the electrostaticfree energy density fe, [4]:

fe =12∇U · ε · ∇U.

Because of the mutual dependence between the director orientation and potential distribution,the electrostatic potential is recalculated after the director configuration has changed by a certainamount. After the director profile is known, the optical transmission is calculated. In 2dimMOSthis is done exclusively by using the Jones matrix formalism.

In both DIMOS and 2dimMOS, the transmission and the director profile can be exported to atext file, so that the data can be further processed by other programs to extract e.g. switchingtimes, transmission values etc.

3.3.3 Implementation of the Jones matrix formalism

Using the 2dimMOS simulation software, the transmission profile and director configuration(azimuth and inclination) along the lateral dimension of the cell geometry can be extracted.In order to better understand the transmission profile along the cell, it is interesting to haveinformation on the polarization states along the cell after transmission through the liquid crystallayer (just before the second polarizer). Unfortunately, it is not possible to extract this informa-tion from the simulation software. However, taking the extractable information on the directororientation into account, it is possible to calculate the various polarization states by using theJones matrix formalism. Therefore, this formalism was implemented in Matlab, as discussed inappendix A. The Jones formalism will be very useful in the description of IPS cells in chapter 4.

Chapter 4

Theoretical and experimental

investigation of the IPS mode

4.1 Introduction

The goal of this chapter is to investigate how the switching behaviour of IPS-LCDs depends onvarious cell parameters such as the gap G between the electrodes, the width of the electrodes Land the cell thickness d by using results from measurements and simulations. Simulations provideessential information on the local transmission and director profile to assess and quantize thephenomena that determine the switching behaviour on local scale. The experimental resultsprovide less detailed information, as only the average transmission over a number of cells can bemeasured, but are crucial to verify the results of simulations and allow for extraction of unknownmaterial parameters.

We will first compare the transmission behaviour of cells with different electrode geometries(filled with the same liquid crystal material). The results of measurements and simulations willreveal for which electrode geometry optimum transmission is obtained. The next step is thento investigate why some cell geometries feature better transmission behaviour, by using a localanalysis of the transmission profile. A good understanding of the phenomena that appear willlead to further optimization of the existing IPS cell design.

4.2 Measurement of IPS cells

4.2.1 Sample information

The considered IPS cells all have a cell thickness d = 5µm and a pretwist φ = 80◦ and pretiltθ = 88◦ (see Fig.2.2), but feature different electrode geometries. All cells were filled with theliquid crystal material LC-IPS of which the known material parameters are listed in Table 4.1.

Table 4.1: Known material parameters of LC-IPS (20◦C datasheet values).

no ne ε|| ε⊥ K11(pN) K33(pN) γ(Pa.s)1.5266 1.8181 21.0 5.5 14.6 29.9 0.185

The electrode width L (see Fig.2.9) of the samples varies from 4µm to 8µm (steps of 2µm),while the gap G between the electrodes takes values between 4µm and 20µm (steps of 4µm).

22

23In what follows, the electrode geometry will be indicated as xLyG where x and y representrespectively the electrode width and gap between the electrodes (expressed in micrometer). Forexample, 4L4G indicates the sample having electrodes with a width of 4µm, spaced apart by4µm. Unfortunately, the cells 4L12G, 4L16G and 6L16G were not functioning.

4.2.2 Voltage-transmission characteristics

Applying a voltage between neighbouring electrodes results in an electrical field that causes theliquid crystal to reorient. This reorientation changes the retardation which alters the light po-larization, so light can be transmitted through the crossed polarizers. The voltage-transmissioncurve, which describes the light transmission as a function of the voltage applied between theelectrodes, is one of the most important characteristics of LCD cells. This characteristic wasmeasured for all samples at 25◦C by using the experimental setup described in subsection 3.2.The polarizers are crossed and oriented such that the first polarizer has the same orientation asthe rubbing direction (pretwist). This is done to achieve a good dark state, an important issuefor LCDs. The results are shown in Fig.4.1.

Figure 4.1: Experimental voltage-transmission characteristics for the considered IPS samples.

It follows from Fig.4.1 that cell structures with an electrode gap G = 4µm are best performing at6V. The voltage range in the experiments was limited to 6V because problems with a first seriesof samples occurred when higher driving voltages were applied (probably due to ion migration).The ranking of best performing samples can and will change at higher driving voltages.

244.3 Two-dimensional simulations of IPS

One has to know which effects take place on micrometer scale to describe the behaviour of In-Plane Switching. The most obvious route to follow is that of two-dimensional simulations. Thissection will explain step by step how these simulations can be used for modelling the switchingbehaviour of IPS cells.

4.3.1 Simulation procedure

Entering the cell geometry

The first step is to enter the IPS cell geometry in the simulation program. This is done by drawingelectrodes, dielectrics and liquid crystal layers on a scaled grid and entering the appropriatematerial parameters. Figure 4.2 shows the typical layout of the 6L4G cell in 2dimMOS.

Figure 4.2: IPS 6L4G - Entering the geometry of the IPS cell in 2dimMOS. Each rectangle in the gridrepresents an area with 2µm x 1µm dimensions. The grey and green area define the liquidcrystal layer resp. glass substrate, while the blue polygons represent the cell electrodes.

The red resp. black lines in Fig.4.2 were added afterwards and represent the boundary betweendifferent IPS unit cells and the x-axis. The x-axis with origin in the middle of the inner cellwill remain the same in all coming simulations. Three IPS cells were simulated together inevery simulation, while only the data of the middle cell was retained. This was done to excludesimulation errors on the electrical field lines that appear at the boundary of the geometry becauseno periodic boundary conditions for the field lines could be taken into account.The boundary conditions on the orientation of the liquid crystal molecules at the interfaces(tilt and twist angles) and calculation parameters (time step, number of liquid crystal slabs andtotal number of elements etc.) must be defined properly before a simulation can be started. Theelectrical field lines, director profile and local transmission are calculated for every time step.

Calculating the electrical field lines

A static or varying electrical potential profile can be assigned to each electrode. The oddelectrodes were assigned as zero potential reference, while the even electrodes are connected tothe same potential (inter-digital electrodes). After this potential is defined, the electrical fieldlines can be calculated.

25Calculating the director profile

As explained in subsection 2.2.2, the liquid crystal molecules with ∆ε > 0 try to align parallelto the electrical field lines. Taking the boundary conditions and the obtained field lines intoaccount, 2dimMOS calculates the director profile for every time step (typically a time step of0.1ms was chosen for stability and accuracy). The IPS director profile in the middle cell ofFig.4.2 is shown in the lower part of Fig.4.3 for a 10V driving voltage .

Figure 4.3: IPS 6L4G - Director and transmission profile for a static 10V driving voltage between theelectrodes. The green lines in the liquid crystal layer denote the equipotential surfaces ac-cording to the field lines calculated in the previous part. The red electrode is at the highestpotential.

The local director profile can be divided in three zones, as indicated in Fig.4.3. In the middleof the electrodes, zone (1), there is no change in the orientation of the liquid crystal moleculesacross the cell because there is no electrical field. In zone (2) around the edges of the electrodes,the liquid crystals are oriented diagonally according to the shape of the electrical field lines. Thedirector profile in the middle between the electrodes (zone 3) is mainly horizontal with (almost)zero twist, as there is no vertical field component. The area (1) above the electrodes where thereis no change in reorientation extends over about one micrometer. The areas (2) and (3) wherethe director profile is oriented diagonally or horizontally are more or less equal in size.

Calculating the local transmission

Once the director profile is known, the retardation introduced by the subsequent liquid crystalslabs can be calculated. This is done in 2dimMOS using the Jones matrix formalism, which isdiscussed in appendix A. Depending on the orientation of the entrance polarizer and analyzer(the same configuration as in the experimental setup is chosen here), the light transmission ofthe IPS cell can be calculated. The local transmission along the middle IPS cell in Fig.4.2 for astatic 10V driving voltage is shown in the upper part of Fig.4.3. The local transmission profileof the 6L4G cell will be discussed extensively in section 4.4.

264.3.2 The use of dielectric layers in 2dimMOS

The glass substrate (dielectric layer εr = 3.5) was included in the simulation example discussedabove (Fig.4.3). The alignment layers were left out because they are too thin to have a largeinfluence on the shape of the electrical field lines.Simulations were performed where the glass substrate was left out in the cell geometries. Theresults of these simulations were very comparable as in the case where the glass substrate wastaken into account and removing the dielectric layers allows us to reduce calculation times. Asan example, Fig.4.4 shows the transmission profile according to a 10V driving voltage for thesame cell geometry as in Fig.4.3, but without taking the glass substrate into account.

Figure 4.4: IPS 6L4G - Transmission and director profile for a static 10V driving voltage between theelectrodes (no glass substrate simulated used).

By comparing Figs.4.3 and 4.4, it appears that the presence of the dielectric layer indeed doesnot have a great influence on the results of the simulations. The only noticeable difference is thefact that the transmission profile is more smoothened in case the dielectrics are present. Theaverage transmission values are very comparable (68% resp. 67%). Consequently, it is justifiedto omit this layer to obtain an increase in calculation stability. Therefore, the simplified cellgeometry will be used for all coming simulations.

4.3.3 Calculating the local polarization state

Both the local transmission and director profile are calculated by 2dimMOS. The director profilecontains for every cross section information on the twist and inclination angles. Using thisinformation, the polarization state at every place in the cross section can be calculated by thematlab implementation of the Jones formalism (see appendix A). This is a powerful tool tounderstand the transmission profile along the cell. Furthermore, it indicates if and how thetransmission along the cell can be optimized (e.g. by achieving a better match in polarizationstate through a change of the cell thickness).

274.4 Analysis of IPS on local scale

The simulation procedure discussed in section 4.3 will be used here to obtain a better under-standing of the switching behaviour of the considered test samples. The first goal is to investigateif the experimental voltage-transmission characteristic can be reproduced by using simulations.The next step is then to investigate why some cell geometries feature better transmission be-haviour, by using a local analysis of the transmission profile. This good understanding will leadto further optimization of the existing cell design.

4.4.1 Simulating the voltage-transmission characteristics

Extracting the value of K22

The value of the twist elasticity constant K22 plays a determining role in the switching be-haviour of IPS-LCDs, as the in-plane switching principle is based on a change in twist of theliquid crystal molecules. Values for K22 are however rarely found in datasheets, because it isvery hard to determine the value of this parameter experimentally. Therefore, a heuristic fittingis necessary to obtain the value of K22 for input in 2dimMOS. This was done by adjusting K22

in simulations until a good match was found between the experimental and simulated voltage-transmission characteristic of the 8L8G cell, which was chosen as reference sample.As discussed in the previous section, two-dimensional simulations provide the user the trans-mission data at every place on the grid. The average cell transmission (as measured in theexperiment) is then calculated by averaging out the local transmission profile along the cen-ter cell. By stepwise applying different voltages, a voltage-transmission characteristic can beextracted. Fig.4.5 illustrates the good match between the simulated and experimental voltage-transmission characteristic obtained after K22 was fitted. The obtained value K22 = 4pN willbe used for all simulations throughout the whole chapter.

Figure 4.5: IPS 8L8G - Experimental and simulated (best fitting) voltage-transmission characteristic.

28Simulated voltage-transmission characteristics

The voltage-transmission characteristics were simulated for all cell geometries. The results areshown in Fig.4.6.

Figure 4.6: Simulated voltage-transmission characteristics for the considered IPS samples.

We obtained good agreement between the results of experiments and simulations (Fig.4.1 andFig.4.6 respectively). This indicates the validity of the simulation model and the material param-eters that were used. The cell structures with an electrode gap of 4µm show high transmissionfor a given voltage (e.g. 6V). It follows both from simulations and experiments that the 6L4Ggeometry is the optimum cell structure.

The optimum cell thickness

Next to the electrode geometry, also the cell thickness d plays an important role in the switchingbehaviour of IPS-LCDs, because it has a direct influence on the switching behaviour. Indeed,the obtained retardation after transmission through the liquid crystal layer is directly relatedto the cell thickness, as is clear from Eqn.2.10. The cell thickness of the 6L4G cell was variedin voltage-transmission simulations to determine its optimum value. Figure 4.7 shows somesimulated characteristics for values of the cell thickness in the interval [2.5µm,12.5µm].

From Fig.4.7, 5µm appears to be the optimum cell thickness in the 0V-10V voltage range.Therefore, all the IPS-samples considered in this chapter have a 5µm cell thickness.

29

Figure 4.7: IPS 6L4G - Simulated voltage-transmission characteristic for different values of the cell thick-ness.

4.4.2 Static behaviour of the 6L4G cell

As mentioned in subsection 4.4.1, the simulated and experimental voltage-transmission char-acteristics show that the 6L4G electrode configuration leads to the best performance of theconsidered cell geometries. Therefore, the static behaviour of this cell will be studied in moredetail.

Voltage-transmission characteristic

An obvious first step in the investigation of the static behaviour of the 6L4G cell is to considerthe complete voltage-transmission characteristic which is shown in Fig.4.8.

Figure 4.8: IPS 6L4G - Simulated voltage-transmission characteristic.

30It can be seen in Fig.4.8 that the transmission first increases with the amplitude of the voltageapplied between the electrodes. This is due to the stronger field that occurs at higher voltageswhich forces more liquid crystal molecules to reorient, thereby resulting in a higher retardationand transmission. Of course, when the retardation becomes too high, the change in polarizationdirection exceeds the optimum shift. In this case, the transmission will become suboptimumas the polarization direction is not anymore parallel to the analyzer direction (in the case ofcrossed polarizers). From Fig.4.8, it follows that the optimum transmission is reached for a 10Vdriving voltage. In what follows, we choose to investigate the local transmission first for a 6Vdriving voltage, according to the maximum voltage applied in the experiments.

Local transmission profile at 6V

Fig.4.9 shows the local transmission and director profile of the 6L4G geometry for a 6V drivingvoltage, as simulated in 2dimMOS.

Figure 4.9: IPS 6L4G - Simulated local transmission and director profile for a static 6V driving voltage.The transmission values indicated in the left upper corner incorporate the 50% loss at thefirst polarizer.

The transmission profile along the cell in Fig.4.9 consists of high transmission contributions atthe edges of the electrodes and in the area between the electrodes. To understand this transmis-sion profile better, we will consider the local polarization states calculated by using the matlabimplementation of the Jones matrix formalism (see appendix A). Fig.4.10 shows the obtainedpolarization states after transmission through the liquid crystal layer (so just before the ana-lyzer). Due to the inherent symmetry of the unit cell shown in Fig.4.9, it is not necessary tocalculate the polarization states along the complete cell. It is in good approximation sufficientto calculate the polarization state only along one quarter of the cell (x ∈ [0 : 5µm]) of Fig.4.9.Obviously, the polarization states along the rest of the cell are easily obtained by mirroring andtranslating the calculated polarization states. The approximation mentioned follows from thesmall pretilt angle which breaks the symmetry of the cell parts for x < 0 and x > 0, but theintroduced error stays negligible as the pretilt is very small.

31

Figure 4.10: IPS 6L4G - Polarization states along the interval x ∈ [0, 5µm] for a static 6V driving voltage.The red line indicates the direction of the analyzer.

One can understand the transmission profile shown in Fig.4.9 by using the information providedby Fig.4.10. Obviously, the more the polarization ellipse is oriented along the analyzer axis,the greater the light transmission after the analyzer will be. This can be represented morequantitatively by plotting the polarization components that are parallel and orthogonal to theanalyzer. Fig.4.11(a) repeats the transmission profile from Fig.4.9 while Fig.4.11(b) shows thepolarization components parallel and orthogonal to the analyzer as calculated from Fig.4.10,restricted to a quarter of the cell. The red dots in Fig.4.11(b) correspond to the transmissionvalues as calculated by 2dimMOS (zoom of the Fig.4.10(a)), while the blue and green curves arecalculated using the matlab implementation of the Jones formalism. The electrodes are drawnat the bottom of the x-axes in Fig.4.11 for an easier interpretation of the plots (the red and bluerectangles denote the electrodes at respectively higher and lower potential).

Figure 4.11: IPS 6L4G - Position vs. transmission profile (top) and position vs. polarization amplitude(bottom) when 6V is applied between the electrodes. The blue resp. green line in thebottom plot represent the polarization component parallel resp. orthogonal to the analyzerafter transmission through the liquid crystal layer (just before the analyzer).

32As can be seen in Fig.4.11(b), the polarization component along the analyzer (transmissioncomponent) calculated using matlab perfectly coincides with the results obtained by 2dimMOSwhich indicates that the Jones formalism was implemented correctly.

Four different areas {(1),(2),(3),(4)} can be distinguished in Fig.4.11(b), depending on the am-plitude of the polarization component parallel to the analyzer (transmission component). Area(1), is a low transmission area (less than 50% local transmission) above the first part of theelectrode. The low transmission is due to the very weak electrical field above the middle ofthe electrode, so almost no reorientation of the liquid crystal molecules occurs. Fig.4.12 showsthe tilt and twist angles across the thickness of the cell at various cross sections. As can beseen for x between zero and 1.2µm, the average tilt and twist angles across the cell thicknessin the first part of area (1) stay relatively close to the initial pretwist (80 degrees) and pretilt(88 degrees). As almost no reorientation occurs, there is a very low change in retardation. Thisis clearly visible from the polarization states at {0µm, 0.25µm, 0.5µm, 0.75µm and 1µm} inFig.4.10, which are similar to the initial linear polarization state (perpendicular to the analyzerdirection which is shown in red). As the top and bottom polarizers are crossed, this leads tolow transmission values.

In area (2), a higher transmission range (more than 50% local transmission) appears above thesecond part of the electrode. The liquid crystal molecules are oriented diagonally accordingto the electrical field lines in this area (see Fig.4.9). Due to this diagonal alignment there ismainly a change in retardation due to the change in inclination angle, which leads to the hightransmission area. This is also visible in the polarization states for x between 1.2µm and 3.05µmin Fig.4.10. As can be seen, the polarization is turned step by step towards the analyzer axiswhich improves transmission. This switching behaviour could also be referred to as fringing-field switching, in analogy with the similar behaviour of the FFS mode, described in section2.3.4. The change in retardation between adjacent positions in the interval x ∈[1.2µm,3.05µm]is mainly caused by a change in twist as the inclination angle stays more or less constant in thisinterval (see Fig.4.12).

Area (3) is a second lower transmission area (less than 50% local transmission) just next to theelectrodes. As can be seen from Fig.4.12, both the twist and inclination angles vary in this area(x ∈ [3.05µm, 3.6µm]). The reason for the lower transmission values in this area follows fromthe polarization states between 3µm and 3.6µm on Fig.4.10: as the retardation keeps risingmonotonically after area (2), the polarization keeps on turning clockwise. As the optimum statewhere the polarization direction is almost parallel to the analyzer axis was already obtainedin the FFS area, one moves away from this optimum. Consequently, the transmission valuesstart decreasing. At x = 3.25µm, a minimum transmission value is reached as the polarizationdirection is clearly perpendicular to the analyzer axis. As the direction of the polarization keepson turning in the same direction, the transmission values increase again as the polarization di-rection again approaches the analyzer axis.

Area (4) indicated in Fig.4.11 shows a high transmission contribution (more than 50% local trans-mission) which is due to true in-plane switching. As can be seen in Fig.4.12 for x ∈[3.6µm,5µm],the tilt angle in this area is close to 90◦ and the twist angle approaches 0◦, so the liquid crystalmolecules are almost completely switched in their plane (see Fig.4.9). The change in retardationbetween adjacent positions is due to a change in inclination as the twist profile stays more orless constant. As visible in Fig.4.10, the polarization states for x ∈[3.6µm,5µm] are orientedcompletely parallel along the analyzer axis which explains the high transmission.

33

Figure 4.12: 6L4G - Tilt and twist angle profiles across the cell thickness for various cross sections.

344.4.3 Comparing the 4L4G, 6L4G and 8L4G cells at 6V

According to Figs.4.1 and 4.6, the 6L4G geometry shows the highest transmission of the con-sidered cells for a 6V driving voltage. It will be investigated here why this cell shows a betterswitching behaviour than the comparable 4L4G and 8L4G cells.Before starting, one could wonder why the samples with the smallest electrode spacing performoptimum at 6V. The strength of the electrical field E is inversely related to the electrode spac-ing. Consequently, a smaller gap leads to a stronger field which forces the mesogens to reorientmore strongly. If the gap is chosen too large, the electrical field will not be strong enough tocause all liquid crystal molecules to turn. Apparently, there exists a certain optimum electrodegap (which also depends on the cell thickness) for which exactly all liquid crystal moleculesare reoriented along the field lines. If the gap is chosen to be smaller than this optimum, thetransmission is expected to be lower as the in-plane switching area is restricted in size.

In order to compare the behaviour of 4L4G and 8L4G with 6L4G, the simulated local transmis-sion and polarization components of these cells are shown in Figs.4.13 and Figs.4.14.

Figure 4.13: IPS 4L4G - Position vs. transmission profile (a) and position vs. polarization amplitude(b) when 6V is applied between the electrodes. The blue resp. green line in the bottomplot represent the polarization component parallel resp. orthogonal to the analyzer aftertransmission through the liquid crystal layer (just before the analyzer).

As indicated on Figs.4.13 and 4.14, four different transmission areas can be distinguished in asimilar way as done for the 6L4G cell. We now define low (resp. high) transmission areas aszones where the local transmission at every place is below (resp. above) 50%. In order to makea quantitative comparison, the dimensions of the four transmission areas were extracted for thethree electrode geometries from Figs.4.11(b), 4.13(b) and 4.14(b). The results are summarizedin Table 4.2.

35

Figure 4.14: IPS 8L4G - Position vs. transmission profile (a) and position vs. polarization amplitude(b) when 6V is applied between the electrodes. The blue resp. green line in the bottomplot represent the polarization component parallel resp. orthogonal to the analyzer aftertransmission through the liquid crystal layer (just before the analyzer).

Table 4.2: Transmission areas for 4L4G, 6L4G and 8L4G cells according to Figs.4.11(b), 4.13(b) and4.14(b). The values between brackets denote the relative size of the areas for each cell.

(1) Low transmission (2) FFS (3) Low transmission (4) IPS4L4G 0-0.9µm (22.5%) 0.9-2.3µm (35%) 2.3-2.8µm (12.5%) 2.8-4µm (30%)6L4G 0-1.2µm (24%) 1.2-3.05µm (37%) 3.05-3.6µm (11%) 3.6-5µm (28%)8L4G 0-2.1µm (35%) 2.1-3.75µm (27.5%) 3.75-4.3µm (9.2%) 4.3-6µm (28.3%)

Table 4.2 reveals that the size of the lower transmission area (3) is nearly independent of theelectrode width. Indeed, this area extends over about 0.55µm for the three cells. The FFS andIPS area should be as large as possible for an optimum design, while the low transmission areasshould remain as small as possible.Comparing 4L4G with 6L4G in Table 4.2 shows that the low transmission areas (1) and (3) arerelatively seen of comparable dimensions for both cells. It becomes however clear from Figs.4.11and 4.13 that 6L4G has a higher average transmission because of higher transmission values inthe FFS and IPS area.Comparing the transmission areas of 8L4G with 6L4G in Table 4.2 reveals that 8L4G is mainlyperforming worse than 6L4G because of a larger first low transmission area (1), as the equallyimportant FFS and IPS contributions are about equal in absolute size. The electrodes in the8L4G geometry are so wide that the increase in electrode width compared to 6L4G only haslead to a larger area where the field is too weak to cause a reorientation of the mesogens. As thelow transmission area is more extended, the average transmission is lower than the optimum.

36It can be concluded that, next to the gap G between the electrodes, also the electrode width Lis a very important parameter of the cell geometry. If this width is chosen too small, not enoughadvantage can be taken of the FFS effect. When the electrode width is too large, there is animportant negative contribution of a ’dead zone’ above the electrode where the electrical fieldis too weak to cause a reorientation of the liquid crystal, thereby leading to a low transmission.

4.4.4 Voltage-transmission behaviour of the 6L4G IPS cell

The static behaviour of the 6L4G cell at 6V was described in the previous subsections as thiscell is so interesting because of its optimum performance. The change in local transmissionprofile along the complete voltage-transmission characteristic in Fig.4.8 will be considered inthis subsection. In particular, it will be explained why optimum transmission is reached at 10V.

Low driving voltages V ≤ 2.5V

The electrical field between the electrodes is too weak for low voltages to cause a reorientationof the liquid crystal molecules. Therefore, there is almost no change in retardation, which leadsto a low transmission profile. This is illustrated in Fig.4.15 which shows the transmission andpolarization components along the cell for a 2.5V driving voltage.

Figure 4.15: IPS 6L4G - Position vs. transmission profile (a) and position vs. polarization amplitude(b) for a 2.5V driving voltage. The blue resp. green line in the bottom plot represent thepolarization component parallel resp. orthogonal to the analyzer after transmission throughthe liquid crystal layer (just before the analyzer).

It is not possible to make a distinction between different transmission areas in Fig.4.15 as theswitching behaviour of the cell did not start completely yet for a 2.5V driving voltage. Thisalso becomes clear from Fig.4.16 which shows the different polarizations states along the cell for2.5V.

37

Figure 4.16: IPS 6L4G - Polarization ellipses along the cell for a 2.5V driving voltage. The red lineindicates the direction of the analyzer.

It is clear from Fig.4.16 that, along the whole cell, the polarization states after transmissionthrough the liquid crystal layer are still very similar to the initial polarization state after thefirst polarizer (direction perpendicular to the analyzer). This confirms that the retardation dueto reorientation of the liquid crystal molecules is too low at 2.5V.

Intermediate driving voltages 2.5V≤ V <10V

In the range 2.5V-10V the average transmission increases with voltage as the electrical fieldbecomes stronger to reorient a larger part of the liquid crystal molecules. This is illustrated inFig.4.17, which shows the transmission profile and polarization components along the cell for5V and 7.5V driving voltages.

Figure 4.17: IPS 6L4G - Position vs. transmission profile and position vs. polarization amplitude for5V and 7.5V driving voltages. The blue resp. green lines in the bottom plots represent thepolarization component parallel resp. orthogonal to the analyzer after transmission throughthe liquid crystal layer (just before the analyzer).

The FFS (area ’2’) and IPS area (area ’4’) can be clearly distinguished in the transmission profilefor 5V (Fig.4.17(b)) and 7.5V (Fig.4.17(d)). Furthermore, it becomes clear by comparing thesize of these high transmission areas for 5V and 7.5V that both the FFS (2) and IPS (4) areasgrow with increasing voltage at the expense of the low transmission areas (1) and (3), therebyleading to a higher average transmission. Fig.4.18 shows the polarization ellipses along the cellfor the 5V and 7.5V driving voltage.

38

(a) 5V (b) 7.5V

Figure 4.18: IPS 6L4G - Polarization ellipses for a 5V (a) and 7.5V (b) driving voltage. The red lineindicates the direction of the analyzer.

In the case of a 5V driving voltage (Fig.4.18(a)), the polarization first starts to turn in counterclockwise direction, while it turns around x =0.5µm into clockwise direction. After this transi-tion point, the polarization continues to turn in clockwise direction. Consequently, at a certainplace the polarization direction becomes parallel to the analyzer (FFS area ’2’). The directionof the polarization state continues to turn which leads to the second lower transmission area’3’ as the polarization direction becomes less parallel to the analyzer. Finally, the polarizationdirection becomes again parallel to the analyzer which again leads to a higher transmission area(IPS area ’4’).

The polarization ellipses for a 7.5V driving voltage in Fig.4.18(b) are more linear (lower elliptic-ity) than the polarization states according to a 5V driving voltage (Fig.4.18(a)), because of thehigher retardation due to the stronger field for the 7.5V case. As the linear component alongthe analyzer direction is greater, a more efficient light transmission is obtained. When a 7.5Vdriving voltage is applied, another important phenomenon occurs in the evolution of the polar-ization profile (Fig.4.18(b)). In contrast to the situation for a 5V potential, the polarization firstrotates in counter-clockwise direction, but changes close the edge of the electrode (x = 2.25µm)to a clockwise direction for the 7.5V driving voltage. Consequently, instead of only obtainingonce the situation where the polarization direction is parallel to the analyzer in area (2), theoptimum situation is reached twice. This leads to the occurrence of two peaks in the FFS area(2) in Fig.4.17(d): the polarization direction first turns in counter-clockwise direction towardsthe analyzer in the first part of this area. After the optimum transmission is reached when thepolarization is parallel to the analyzer (x=1.5µm) the polarization continues to turn in this di-rection, away from the analyzer, which leads to a lower transmission in the FFS area (minimumobtained at 2µm). Next, the polarization turns back to the analyzer in clockwise direction, sothe transmission increases until the polarization is again parallel to the analyzer, leading to thesecond optimum obtained at 2.5µm. After this second optimum is obtained, the polarizationkeeps turning in clockwise direction, so the transmission becomes lower (transition area ’3’). Theeffect that the rotation direction of the polarization suddenly changes is clearly very positive, asboth the important FFS area becomes larger and a higher average transmission value over thisarea is obtained as the polarization stays at any place close to the optimum orientation.

39The optimum driving voltage V=10V

The voltage-transmission characteristic in Fig.4.8 shows that the highest transmission is obtainedfor a 10V driving voltage. Fig.4.19 shows the local transmission profile and the polarizationcomponents along the cell for this optimum driving voltage.

Figure 4.19: IPS 6L4G - Position vs. transmission profile (a) and position vs. polarization amplitude(b) for a 10V driving voltage. The blue resp. green line in the bottom plot represent thepolarization component parallel resp. orthogonal to the analyzer after transmission throughthe liquid crystal layer (just before the analyzer).

The local transmission profile from Fig.4.19(a) is very similar to the profile corresponding to a7.5V driving voltage (Fig.4.17(c)), but higher transmission values are reached in the FFS (2)and IPS (4) area because of a more pronounced reorientation of the liquid crystal molecules(especially a higher twist). The evolution of the polarization states along the cell for a 10Vdriving voltage are shown in Fig.4.20.

Figure 4.20: IPS 6L4G - Polarization ellipses along the cell for a 10V driving voltage. The red lineindicates the direction of the analyzer.

40The polarization ellipses shown in Fig.4.20 are similar to the profile corresponding to a 7.5Vdriving voltage (Fig.4.18(b)), except for the more advantageous polarization states for x ∈[0.75µm,1.25µm] which lead to an extra high transmission contribution. Therefore, a moreefficient light transmission is obtained for 10V compared to the 7.5V driving voltage.As mentioned before, the 6L4G cell shows a better performance than the other samples. It isclear from the discussion above that, in contrast to the name ’IPS’ cell, this cell is performing sowell because of transmission contributions of both FFS and IPS areas (’2’ and ’4’ in Fig.4.19).Therefore, the cell is better referred to as a hybrid Fringing-Field/In-Plane Switching cell, asboth the in-plane and fringing-field switching are equally important (because the areas in whichthey take place are about equal) and as they reach their maximum transmission contributiontogether at the same field strength. This hybrid switching behaviour has not been discussed inliterature yet according to our knowledge.

Driving voltages V > 10V

If the driving voltage is larger than 10V, the retardation exceeds the value for which the op-timum shift in polarization was obtained. Therefore, the high transmission areas will decreasewith increasing voltage, as illustrated in the transmission and polarization component profile inFig.4.21 for 12.5V and 15V driving voltages.

Figure 4.21: IPS 6L4G - Position vs. transmission profile (top) and position vs. polarization amplitude(bottom) for a 12.5V and 15V driving voltage. The blue resp. green lines in the bottomplots represent the polarization component parallel resp. orthogonal to the analyzer aftertransmission through the liquid crystal layer (just before the analyzer).

Fig.4.22 shows the polarization states along the cell for the 12.5V driving voltage. As can beseen, the increase in retardation due to a larger reorientation of the liquid crystal molecules(more twist) makes the polarization of the light become more elliptical compared to the 10Vcase, as can be observed by comparing the polarization states in Figs.4.20 and 4.22 at e.g.x ∈ {1.5µm, 2.5µm, 4.25µm, 5µm}. Consequently, the polarization component perpendicularto the analyzer becomes greater at the expense of the transmission component.

41

Figure 4.22: IPS 6L4G - Polarization ellipses along the cell for a 12.5V driving voltage. The red lineindicates the direction of the analyzer.

4.5 Further optimization of the hybrid FFS/IPS cell

The previous section considered the switching behaviour of the optimum 6L4G cell extensively.It followed from the discussion that both the cell thickness and electrode geometry are optimumfor this design. Therefore, the main opportunity to further improve the performance lies inmaterial optimization.

All the considered cells were filled with the same liquid crystal material LC-IPS. Followingthe strategy presented above to select the best electrode geometry, a new optimization of thematerial parameters ∆ε, K22 and K33 could be performed. The importance of the material op-timization can not be underemphasized, as it will lead to an important two-folded improvement.First, a lower optimum voltage can be reached by increasing ∆ε and decreasing the values ofK22 and K33. The increase in dielectric anisotropy ∆ε will increase the torque experienced bya single liquid crystal molecule when an electrical field is applied. Therefore, a lower electricalfield strength will be required to achieve the same reorientation compared to the case where∆ε is lower. Decreasing the operation voltage is a necessary requirement for mobile displayapplications for the purpose of lower power consumption.A comparable reasoning can be made when the values of K22 and K33 are decreased, as theliquid crystal molecules will twist resp. bend more easily. Consequently, one could expect thatthe mesogens will reorient more along the electrical field lines, so a lower field strength wouldbe required to cause the same reorientation. This would again lead to a decrease of the voltagethat needs to be applied to reach a certain director profile.

Next to a reduction of the voltage required to cause switching, also an increase in transmis-sion should be obtained after optimizing the liquid crystal material parameters. For example,consider again Fig.4.19(b): an interesting increase in average transmission could be obtainedby reducing the first low transmission area above the middle of the electrode (x between 0 and0.7µm in Fig.4.19(b)), which is due to the weak field above the middle of the electrode. Theadjacent higher transmission area is due to the fringing field component which leads to a diago-nal orientation of the liquid crystal molecules. Consequently, it would be very interesting if theFFS area could be extended towards the middle of the electrode (x = 0µm) at the expense ofthe lower transmission area. This could be obtained by lowering the K33 material constant, sothe liquid crystal molecules reorient more along the (still weaker) field lines close to the middleof the electrodes. Every extra reorientation that could be obtained will lead to an increase ofthe average cell transmission.

424.6 Comparing the hybrid FFS/IPS cell with an existing IPS

design

In this section, the optimum 6L4G cell will be compared with an existing standard optimumIPS design ([28]). Standard IPS displays are designed such that the transmission is completelydetermined by the zone between the electrodes. Therefore, the electrode width L is typicallymuch smaller than the gap G between the electrodes in such designs. The cell thickness dis chosen to maximize the normalized light transmission in the middle between the electrodeswhich is given by, [29]:

T

T0= sin2(2ψ) sin2

(π∆ndλ

),

where ψ denotes the angle between the crossed polarizers and the liquid crystal director. Tomaximize the normalized transmission, the cell gap d should be chosen as:

d =λ

2∆n

The IPS structure presented in [28] uses a 4L13G geometry and a cell thickness of 4µm. Thepretilt and pretwist used in the design were equal to 89◦ resp. 80◦. The experimentally obtainedoptimum transmission was reached at a 9.5V driving voltage. A simulation of the structure wasperformed in [28] and the result is repeated here in Fig.4.23.

Figure 4.23: IPS 4L13G - Simulated transmission and director profile for a 9.5V driving voltage, [28].

As can be seen in Fig.4.23, the transmission in the 4L13G cell is completely due to in-planeswitching of the liquid crystal molecules, as high transmission values are only obtained in theareas between the electrodes. This is in contrast to the switching behaviour shown in Fig.4.19,where the transmission profile is determined by contributions of both fringing-field and in-planeswitching.

43The average transmission of the 4L13G cell is shown in the right upper corner of Fig.4.23 (theo-retical maximum possible value is 50% as 2dimMOS takes the 50% loss of the first polarizer intoaccount). As can be seen, the transmission obtained for the structure is 38.4% which is equiva-lent to 76.8% light transmission if the (always present) loss at the first polarizer is not considered.The transmission of the 6L4G reaches about 67% (Fig.4.8), clearly a lower value than for thestandard optimimum IPS design. However, a liquid crystal material optimization still needs tobe done in order to get the maximum performance out of the hybrid FFS/IPS 6L4G cell. Itbecomes clear by comparing Figs.4.19 and 4.23 that the hybrid fringing-field/in-plane switchingcell described above could eventually lead to better performing (FFS/)IPS cells for mobile andtelevision applications. As can be seen, a higher transmission is obtained above the electrodes inthe hybrid design compared to the pure IPS cell where the transmission is minimum over almostthe whole electode area. As mentioned before, the FFS/IPS 6L4G cell unfortunately also showstwo lower transmission areas. Figure 4.19 however shows that these areas are of comparabledimensions as the low transmission area in the IPS design from Fig.4.23. Consequently, the useof the hybrid FFS/IPS cell could open perspectives on a higher transmission cell when the liquidcrystal material is further optimized for the 6L4G geometry.

4.7 Conclusion of Chapter 4

The influence of the cell geometry on the switching behaviour of IPS samples has been describedin this chapter. It appeared from measurements and simulations that a cell with an electrodewidth L = 6µm and an electrode gap G = 4µm leads to the best transmission performance.An investigation of the local transmission profile of this cell showed that optimum transmissionis obtained through an interplay between both the fringing-field and in-plane switching effect. Ithas been shown that both phenomena are equally important for the average cell transmission andthat they should be optimized together. Therefore, the switching behaviour in the considered6L4G cell can be described as hybrid FFS/IPS. We believe that this interesting phenomenoncould be further improved, eventually leading to a better performing cell than existing standardIPS cell designs. However, an important optimization of the liquid crystal material still needsto be done.

Chapter 5

The impact of fluid flow on the

switching behaviour in VA-LCDs

5.1 Introduction

The Vertically Aligned (VA) liquid crystal mode shows a very high contrast ratio because of itsexcellent black state, caused by the initial homeotropic alignment. This vertical alignment canbe obtained in a rubbing free process which leads to a cheaper fabrication process with a higheryield. By using multi-domain structures (MVA) and compensation foils, good viewing angleproperties can be obtained. The collection of these advantages have made the VA technologybecome one of the major attractive technologies for LCDs.

According to Eqn.2.12, one expects the switching turn on time to decrease when a higher pixeldriving voltage is applied. Unfortunately, this is not always the case in reality: when a high elec-trical field is applied, the switching mechanism can become more complex, due to a reverse flowcreated by the liquid crystal molecules that are reorienting. This complex switching mechanism(e.g. featuring twist reorientation) finally leads to higher switching times. As a consequence,conventional overdriving technologies for faster switching become unsuitable and the possibili-ties of VA-LCDs to show video content are limited.

A good understanding of how the liquid crystal molecules behave in case of reverse flow willbe the first step to avoid or compensate this effect, immediately improving the performance ofVA-LCDs. This chapter will describe in more detail this reverse flow phenomenon, sometimesreferred to as backflow. The first section will discuss some experimental observations of back-flow, clearly illustrating its negative impact. The Leslie-Ericksen hydrodynamic theory, used insimulations to describe the flow phenomena, will be briefly introduced. It is not easy to simu-late the switching behaviour affected by backflow correctly, due to many degrees of freedom inthe simulation model. Therefore, a stepwise approach will be given to obtain a good simulationmodel. This is crucial to gain insight in the mechanisms behind the complex switching behavior.A detailed analysis of these mechanisms will be given in the last section.

44

455.2 Experiment: the dynamic response of VA cells

This section discusses the switching behavior of a mono-domain VA cell (starting from its blackoff-state) when a voltage step with varying amplitude is applied across the electrodes. Themono-domain was obtained by weak rubbing of the polymer alignment layer. The cell wasassembled ’anti-parallel rubbed’ with a cell gap of 4.2µm. The anti-parallel rubbing leads toparallel directors (same pretilt θ) at the top and bottom substrate, as shown in Fig.5.1.

Figure 5.1: The use of anti-parallel rubbing to obtain directors with the same pretilt θ at the top andbottom substrate. The green layers denote the polymer alignment layers.

The cell was filled with the liquid crystal material ’LC-A’. The known material properties ofLC-A are listed in Table 5.1.

Table 5.1: Material parameters LC-A material (datasheet values at 20◦C). The clearing temperature Tc

indicated by an asterisk corresponds to the value measured experimentally (see subsection6.3.1).

no ne ε|| ε⊥ K11(pN) K33(pN) γ (Pa.s) Tc(◦C) T ∗c (◦C)

1.48 1.56 3.5 7.4 13.8 14.8 0.185 90 95

Using the experimental setup from section 3.2 in time-transmission mode, the transmission pro-files at 25◦C were measured for different voltage amplitudes. The sample was observed undercrossed polarizers, with the polarizers making an angle of 45◦ with the rubbing direction. Thisconfiguration will be maintained for all coming measurements on VA samples. Fig.5.2 showssome experimental switching profiles for different voltage steps.

For switching from 0V to 4.5V (Fig.5.2(a)), the transmission in the switching profile for a 4.5Vvoltage step is monotonically increasing from the black state to the static transmission value.The transmission reaches its static value of 84% after about 30ms. The transmission profile is inagreement with the expected switching behaviour of the liquid crystals in the VA mode: when avoltage step is applied, the liquid crystal molecules reorient gradually from their initial verticalalignment to a horizontal orientation. This is accompanied by a gradual increase in retardation,leading to a gradual increase in transmission.

46

Figure 5.2: Experimental time-transmission characteristics at 25◦C for various voltage steps. At t = 0msthe voltage across the electrodes is changed from 0V to the value indicated in the plot title.(LC-A 4.2µm sample)

When the amplitude of the voltage step is further increased to [4.8V,5V,6V,10V], the switchingprofile changes drastically and a double peaked transmission characteristic appears, accompa-nied by a strong increase in switching time. For example, the switching time (defined here asthe time required to reach 90% transmission) from 0V to 5V becomes about 300ms in Fig.5.2(c).For switching from 0V to 6V, the switching time is more than 350 ms (Fig.5.2(d)). However,the switching time does not keep increasing monotonically with the voltage. The switching ontime for a 10V voltage step is again about 300ms (Fig.5.2(e)).

Fig.5.3 shows the switching time for the sample as a function of the amplitude of the voltagestep. This curve was obtained experimentally by performing similar measurements as those thatlead to the transmission profiles in Fig.5.2.

47

Figure 5.3: Experimental voltage-switching time characteristic at 25◦C (LC-A 4.2µm sample).

As indicated, the graph in Fig.5.3 can be divided in three zones. The switching times in the firstzone Z1 are relatively low, while the third zone Z3 features high switching on times. A transi-tion area Z2 appears in between Z1 and Z3. It is clear that there appears a certain thresholdvoltage VBF ≈ 4.5V for this sample at room temperature for which the switching time starts toincrease drastically. At voltage amplitudes exceeding VBF , the switching time becomes aboutone order of magnitude greater than the switching times for voltages under this threshold.The drastic change in the switching characteristic above a certain voltage indicates that a dif-ferent, more complex, mechanism is governing the reorientation of the liquid crystal molecules.This mechanism leads to a more time consuming reorientation which leads to a degradationin performance. The remaining of this chapter will be devoted to the description of this phe-nomenon.

5.3 Leslie-Ericksen theory

It was already mentioned in the introduction that Eqn.2.12 suggests that the switching timedecreases when the amplitude of the voltage step is increased. However, it was shown in theprevious section that this is only true for a limited voltage range ([0V,4.5V] in Fig.5.3), as theswitching time is increased drastically for voltages above a certain threshold value VBF . In thedescription of the dynamic behaviour of the homeotropic liquid crystal cell in [30], it was pointedout that fluid motion of the liquid crystal should be taken into account, as this flow effect canhave an influence on the director orientation. The restricted validity of Eqn.2.12 is caused bythe fact that fluid flow was not considered in its derivation ([8, 15]).The fluid motion of the liquid crystal molecules can play a crucial role in the reorientation uponswitching in the VA mode, [31]. Therefore, it is necessary to couple the equations that governthe motion of the director with those of the fluid. This problem is solved in the Leslie-Ericksen

48theory ([32],[33],[15]), a continuum theory which describes the mechanical behaviour of liquidcrystals of the nematic type by formulating constitutive equations and general conservation lawsof mass, energy and momentum. According to this theory, the motion of nematic liquid crystalsis governed by the following equations:

ρ.vi = Fi + tji,j (5.1)

ρ1

..li = Gi + gi + πji,j (5.2)

vi,i = 0, (5.3)

where the subscripts i and j denote x, y or z components. The subscript j preceded by a commadenotes differentiation with respect to the jth coordinate. Eqn.5.1 describes the balance of forcesacting on the fluid where ρ denotes the density of the fluid, vi is the fluid velocity, Fi is thebody force and tij is the stress tensor. Eqn.5.2 expresses the balance of torques acting on thedirector where ρ1 is the moment of inertia per unit volume associated with the director, li is theith component of the director L, Gi and gi is the external resp. internal body torque and πij

denotes the ith component of the surface torque across the xj plane. Finally, Eqn.5.3 expressesthe incompressibility of the fluid.The stress tensor tij can be separated into a static and a hydrodynamic part. The hydrodynamicpart is characterized by six Leslie viscosity coefficients αi that describe the viscosity propertiesof the liquid crystal material. Only five of these coefficients are independent, as four of the Leslieviscosity coefficients are related to each other by the Parodi relation, [34]:

α6 = α2 + α3 + α5, (5.4)

while furthermore, [32]

γ1 = α3 − α2 (5.5)

γ2 = α3 + α2,

where γ1 is equal to the rotational viscosity (previously denoted in the text by γ). This vis-cosity coefficient γ expresses the viscous torque exerted on the director during rotation of themolecule around its axis or during shear flow when the orientation of the director is kept fixed.The rotational viscosity is a very important material parameter of liquid crystal materials, asthe relaxation times for switching are highly dependent on this coefficient, as can be seen inEqns.2.12 and 2.13. The Leslie viscosity coefficients mainly have an influence on the shape ofthe time-transmission characteristic.

Alternative formulations of the Leslie-Ericksen theory make use of the so-called Miesowicz shearviscosity coefficients ηij , [15]. It was already mentioned that the flow of the liquid crystal influ-ences the orientation of the molecules. On the other hand, the values of the viscosity coefficientsof the anisotropic liquid crystal depend on the orientation of the molecule. Consequently, thereis anisotropy in the viscosity coefficients as well. Therefore, there are three principal viscos-ity coefficients {η11, η22, η33} belonging to the three principal directions of orientation of themolecule, [35]. This is depicted in Fig.5.4.A fourth viscosity coefficient η4 is needed to characterize the shear viscosity, [37]. This coeffi-cient is defined for a director orientation parallel to the bisector of the two first principal axes(defined by the director orientation in Figs.5.4(a) and 5.4(b)). However, the Helfrich viscosity

49

(a) η11 (b) η22 (c) η33

Figure 5.4: Director orientations according to which {η11, η22, η33} are defined, [36].

coefficient η12 is mostly used in addition to the Miesowicz coefficients instead of η4. This η12

coefficient is defined as, [37]:η12 = 4η4 − 2(η11 + η22).

The Miesowicz viscosity coefficients are directly related to the Leslie viscosity coefficients αi as,[4]:

η11 =12(−α2 + α4 + α5) (5.6)

η22 =12(α3 + α4 + α6) (5.7)

η33 =α4

2(5.8)

η12 = α1. (5.9)

A thorough understanding of the details of the Leslie-Ericksen theory is not essential to under-stand the switching mechanisms governing the switching in VA-LCDs, but it is important tocouple the equation of motion of the director with that of the fluid in the simulation model toobtain accurate simulations of the switching behaviour.

5.4 Modelling the switching behaviour in VA-LCDs with a 1D

simulation model

5.4.1 Introduction

In this section, the switching behaviour of the VA test cells described in section 5.2 will besimulated using the one-dimensional commercial software package DIMOS, which features theoption to include flow effects by solving the Leslie-Ericksen equations. As mentioned before,it is not straightforward to obtain a good model for simulating the switching behaviour whenfluid flow is taken into account. Therefore, this section is divided into several subsections thathighlight the different steps of the approach that was followed. The results of the simulationsin this section will lead to a better understanding of the switching mechanism that leads to thedramatic time-transmission profile shown in the lower plots of Fig.5.2.

5.4.2 Determining the alignment boundary conditions

As mentioned in subsection 2.3.5, the initial vertical alignment in VA cells is obtained by usingpolyimide alignment layers. These layers anchor the liquid crystal molecules at the interfaceperpendicular to the substrates. In order to allow a one-dimensional modelling of the samples,

50an extra rubbing step was added to the fabrication process to have the same pretilt θ for alldirectors along the substrate (see Fig.5.1). Therefore, all directors will reorient in the samedirection upon switching (single domain VA configuration). The goal of this subsection is todetermine the director orientations at the substrate interfaces by a fitting procedure in order toinclude these configurations as boundary conditions in the simulation model. In case no extrarubbing step would have been performed, the pretilt would be 0◦. If a voltage is then applied, arandom orientation of the liquid crystal molecules would occur, creating non-controllable mul-tidomains.

The average pretilt angle θ (defined in Fig.2.2) over the sample area was measured experimen-tally with a commercial Tilt Bias Angle (TBA) setup as 2◦. It is however not straightforwardto measure the pretilt and pretwist angles separately at the top and bottom substrate in anexperimental way. Therefore, a fitting of these angles (top and bottom) in the model is prefer-able. This was done by performing various simulations where the material parameters were keptconstant, but the pretwist and pretilt angles in the boundary conditions were changed. There isno intention to have an azimuthal angle (pretwist) between the directors at the top and bottomsubstrate, but a very small error of azimuthal alignment error in the fabrication process can havea crucial influence on the dynamics of the VA cell, [38]. Therefore, it is important to take thissmall deviation also into account by choosing the right boundary conditions in the simulationmodel.

The fitting procedure was done once for the VA sample for switching between 0V and 5V. Theset of pretilt and pretwist angles was chosen for which the best fitting of the switching responsein Fig.5.2(c) is obtained. To illustrate this procedure, the results of various simulations areshown in Fig.5.5. In these simulations, the upper pretilt angle was fixed to θ = 2◦ while thelower pretilt angle was set to θ′ = θ+∆θ. The azimuthal error between the directors at the topand bottom substrates is denoted by ∆φ. The viscosity coefficients of MBBA from [39] wereused to perform these simulations.Fig.5.5 shows that the alignment boundary conditions indeed have a very large influence on thedynamic response of the VA sample. For example, in case there is no deviation in pretilt at thetop and bottom substrate, the ’bump-free’ VA switching behaviour can be observed (∆θ = 0,Fig.5.5(a)). However, a slight asymmetry in the anchoring at the top and bottom substrate canbe introduced due to thermal agitation during the rubbing step, which leads to a deviation inpretilt ∆θ 6= 0. In this case, the complex switching profile is obtained for the slightest differencein pretwist ∆φ 6= 0. By comparing Figs.5.5(a)-(c), it is also clear that the time-transmissionprofile can change drastically for different values of ∆θ. However, there seems to be a certainpretilt deviation (∆θ = 1.5◦) at which the switching behaviour stays more or less the same, evenwhen ∆θ is further increased. It is also visible that the deviation in twist ∆φ of the directorsat the top and bottom substrate has a large influence. For example, for all values of ∆θ theconventional smooth VA switching behaviour is observed when ∆φ = 0. However, even a smalldeviation in twist ∆φ 6= 0 immediately leads to the more complex switching behaviour when∆θ 6= 0, confirming the results in [38]. As visible in Fig.5.5 when ∆φ 6= 0, the value of this devi-ation plays an important role in the switching behaviour when ∆θ ≤ 1◦. For example, considerFigs.5.5(b)-(c): it is clear that the time-transmission profile changes considerably depending onthe value of ∆φ. However, once ∆θ ≥ 1.5◦, the deviation ∆φ clearly has less influence on theswitching profile.

51

Figure 5.5: Simulated time-transmission characteristics when a 5V amplitude voltage step is applied att = 0ms (LC-A 4.2µm sample). The difference in pretilt and pretwist between the directorsat the top and bottom substrate are mentioned (expressed in degrees) in the title resp. legendof the subplots. The MBBA viscosity coefficients were to obtain these results.

52The observations above showed that once ∆θ ≥ 1.5◦, the time-transmission profile remains moreor less unchanged for values of ∆φ 6= 0. Furthermore, it is clear that the shape of the time-transmission curves for ∆θ ≥ 1.5◦ and ∆φ 6= 0 agrees with the experimental switching behaviourfrom Fig.5.2(c) very well. Therefore, we chose to use ∆θ = 1.5◦ as the boundary condition forthe pretilt of the directors at the top and bottom substrate (meaning that the pretilt at thetop and bottom substrate is equal to 2◦ resp. 3.5◦). The boundary conditions for the twist atthe top and bottom substrate were determined by the ∆φ value for which the best agreement(without taking the time scale into account) between the fitted (Fig.5.5(d)) and experimental(Fig.5.2(c)) time-transmission curve is found. Although there is not much difference betweenthe shape of the curves for subsequent values of ∆φ, the curve according to ∆φ = 2.0 was judgedto show the highest resemblance.

We found that the twist constant K22 has a large influence on the time scale of the switchingcharacteristics in VA-LCDs. This is illustrated in Fig.5.6, where simulated time-transmissioncharacteristics for a 6V voltage step are shown for varying values of K22 (all other parametersare kept constant).

Figure 5.6: Simulated time-transmission characteristics for varying values of K22 when a 6V voltage stepis applied at t = 0ms. Except for K22, all material parameters are kept constant.

As can be seen in Fig.5.6, an increase in the value of the twist elastic constant K22 (twistdeformation becomes harder) indeed leads to a faster switching response (less twist). As itis very hard to measure the value of K22 accurately, we decided to compare the experimentalswitching profile to the shape rather than the curve itself of the simulated transmission profilefor determination of ∆φ and ∆θ. Afterwards, a fitting of K22 can be applied to adjust the timescale. The value for K22 obtained with such a fitting is 4.275pN. This value was used to generatethe plots in Fig.5.5.

535.4.3 Estimating the viscosity parameters

The Leslie viscosity coefficients of LC-A need to be known to include the Leslie-Ericksen theoryin simulations. It is however difficult to measure or estimate these viscosity coefficients ([4]). Asdone in [40], a common approach is to use the viscosity parameters at 20◦C of the MBBA liquidcrystal material, the only material for which the viscosity coefficients were measured accurately,[39]. Recently, a new method for estimating the Leslie coefficients of liquid crystals was publishedby Wang et al, [41].

Description of the Wang et al. approach

The work reported is based on the Imura-Okano theory ([42]), in which all six Leslie coefficientsare derived in terms of the order parameter S:

α1 = A1S2 (5.10)

α2 = −(B1 + C1)S − (B2 + C2)S2 (5.11)

α3 = −(B1 − C1)S − (B2 − C2)S2 (5.12)

α4 = 2ηis − aS +A3S2 (5.13)

α5 =(

32a+B1

)S + (A2 +B2)S2 (5.14)

α6 =(

32a−B1

)S + (A2 −B2)S2, (5.15)

where the coefficients a, Ai, Bi ,Ci (i = 1, 2, ...) are assumed to be weakly temperature dependentand ηis is the flow viscosity of the liquid crystal material in the isotropic state:

ηis = ηo exp(

E

kBT

), (5.16)

where E is the activation energy of molecular diffusion, kB is the Boltzmann constant and ηo isa proportionality constant. Note that the Parodi relationship (Eqn.5.4) is satisfied for the αi inEqns.5.10-5.15. If the temperature T is not too close to the clearing temperature Tc, the orderparameter can be expressed as, [43]:

S =(

1− T

Tc

)β

, (5.17)

where β is a material constant and the temperature is expressed in Kelvin. For many liquidcrystal materials, β ≈ 0.22. In [41], the MBBA viscosity coefficients at different temperatureswere used to fit the coefficients a,Ai, Bi, Ci on this data. The results are listed in Table 5.2.

Table 5.2: Parameters obtained from fitting MBBA data to Eqns.5.10-5.15, [41]. All values are in unitsof Pa.s

A1 A2 A3 A4 A5

-0.0417 0.1729 -0.0829 -0.2072 0.0748B1 B2 C1 C2 ηo a

-0.1442 0.4004 -0.1568 0.4179 4.33.10−9 -0.0437

54Assuming that these fitted coefficients are weakly material dependent, the Leslie coefficients cannow be estimated from Eqns.5.10-5.15 for any material if Tc and E are known. The rotationalviscosity γ then follows from Eqn.5.5. It was shown experimentally that this approach leads tosatisfying results for the α4, α5 and α6 coefficients, but modifications in the theory were neededto obtain better estimates for α1, α2 and α3. Especially the value calculated for the rotationalviscosity γ using the estimates for α2 and α3 in Eqn.5.5 was not in agreement with experimentalresults. Therefore, Wang et al. proposed some modifications to obtain more accurate viscositycoefficients. A better estimate for α1 was found if a third order term in S is included in Eqn.5.10:

α1 = (A4S +A5)S2, (5.18)

where A4 and A5 were again fitted from the MBBA data (see Table 5.2). Instead of calcu-lating γ from the estimates for α2 and α3, better estimates were obtained by calculating α2

and α3 from the Parodi relationship and the value of γ, which is now required to be known(datasheet or measurement). Instead of {γ, α3} now {α2, α3} become dependent variables inthe set {α1, α2, α3, α4, α5, α6, γ}.As the α3 coefficient for MBBA is much smaller in absolute value than the other αi, Wangsimply proposed to neglect α3 and approximate Eqn.5.5, leading to a new estimate for α2:

α2 ≈ −γ. (5.19)

Taking the modifications from Eqns.5.18-5.19 into account, satisfying results were obtained fordifferent (non-VA) materials.

We propose here a more correct approach than the approximation in Eqn.5.19 by using Eqn.5.5in combination with the Parodi relation from Eqn.5.4 to solve for the unknowns α2 and α3 (α5

and α6 are calculated by using Eqns.5.14 and 5.15). This leads to:

α2 = α3 − γ (5.20)

α3 =α6 − α5 + γ

2. (5.21)

Although the presented fitting scheme is still an approximation based on the validity of theImura-Okano theory, Eqns.5.16-5.17 and the assumption that the coefficients from Table 5.2 arematerial independent, it allows however to take a certain degree of material dependency intoaccount, which is more correct than using the MBBA coefficients for all liquid crystal materials.Therefore, this fitting scheme will be exploited where it is applicable and modifications to itstheory will be made where necessary (as the theory was only verified for materials with ∆ε > 0).

Estimating the viscosity coefficients of LC-A

From Table 5.1 it follows1 Tc = 95◦C and β = 0.22 is assumed2. The order parameter for LC-Aat 25◦C can then be calculated (Eqn.5.17):

S =(

1− 25 + 273.1595 + 273.15

)0.22

≈ 0.6941.

The activation energy of LC-A will be taken equal to the value E = 0.414eV of MBBA, similarto the approach followed in [41]. The value of α4 can be adjusted manually afterwards to obtain

1We prefer to use the value of Tc that was measured experimentally, see subsection 6.3.12From private discussion with the material supplier: β ≈ 0.22 is a common value for similar VA materials.

55the best similarity between simulated and experimental time-transmission profiles. This will bediscussed further in the next chapter where temperature effects will be considered. Using thecalculated value of S, E = 0.414eV, the datasheet value for γ at 20◦C (we neglect the variation ofγ with temperature here) from Table 5.1 and the coefficients listed in Table 5.2, the αi viscosityparameters can be calculated from Eqns.5.18, 5.20, 5.21, 5.13, 5.14 and 5.15. The results aresummarized in the first two lines of Table 5.3. Alternatively, we can translate the obtainedLeslie viscosity coefficients αi to the Miesowicz notation by using Eqns.5.6-5.9. The results arelisted in the third and fourth row of Table.5.3.

Table 5.3: Estimated Leslie and Miesowicz viscosity coefficients for LC-A at 25◦C. All coefficients are inunits of Pa.s. The listed values are obtained by using the 20◦C datasheet value of γ.

α1 α2 α3 α4 α5 α6

-0.0332 -0.1853 -0.0003 0.0766 0.1306 -0.0550η11 η22 η33 η12

0.1962 0.0107 0.0383 -0.0332

5.4.4 Simulating the switching behaviour in VA-LCDs

Using the datasheet values listed in Table 5.1, the estimated viscosity coefficients from Table5.3 and the boundary conditions from the subsection 5.4.2, various simulations on the switchingbehaviour in VA-LCDs were performed. The results of these simulations are discussed in thissubsection. Both the experimental curves and estimated viscosity coefficients were obtained for25◦C, but as a first approximation we decide to discard variations of the parameters listed inTable 5.1 (values at 20◦C) with temperature. Temperature effects will be studied extensively inthe next chapter.

The time-transmission characteristics obtained with the simulation model described above areshown in Figs.5.7 and 5.8. For comparison, the equivalent experimental characteristics are alsoshown in Figs.5.7 and 5.8.

From Figs.5.7 and 5.8, it is clear that there is a good agreement between the experimentaland simulated results, especially in Fig.5.7. In this figure, both the shape and timing of thetime-transmission characteristic are modelled quite accurately. It is interesting to notice thatwhen the applied potential is below the threshold voltage VBF for reverse flow (defined insection 5.2), the monotonic increasing transmission profile is simulated correctly. But, for voltageamplitudes exceeding 4.5V, also the more complex time-transmission behaviour is correctlysimulated. For voltage steps with amplitude V ≥ 8V (see Fig.5.8), the simulation results are lessaccurate. However, the simulated characteristics clearly show the same trend as observed in theexperiments: the first peak in the switching characteristic keeps growing for increasing voltages.The value of the second maximum in the simulated step response is however too high comparedto the experimental response. The relative influence of the viscosity coefficients depends on thevoltage, since their effect depends on the director orientation (which strongly depends on theapplied electrical field). Therefore, any inaccuracy in the estimates of the ηij (which will alwaysappear in the estimation process) will become better visible at higher voltages as a discrepancybetween the simulated and measured transmission curves. This is clearly observed in Fig.5.8.

56It should be emphasized that by using the relatively simple one-dimensional simulation modelpresented here, it was possible to perform simulations that model the complex switching be-haviour in VA LCDs quite accurately. Better simulation results were obtained compared to [40]as, based on the fitting presented in subsection 5.4.3, more accurate viscosity coefficients wereused.

Figure 5.7: Simulated (left) and experimental (right) transmission profiles for switching from 0V to thevoltage indicated in the plot titles (LC-A 4.2µm sample).

57

Figure 5.8: Simulated (left) and experimental (right) transmission profiles for switching from 0V to thevoltage indicated in the plot titles (cont, LC-A 4.2µm sample).

585.5 Description of the backflow phenomenon

As mentioned in section 3.3, the conventional strategy used in simulation packages is to firstcalculate the field lines, afterwards the director profile is calculated (optionally taking fluid flowinto account) and finally the light transmission is calculated for every time step. According tothe results presented in subsection 5.4.4, it is clear that the presented simulation model describesthe physical switching of the liquid crystal molecules quite accurately. In order to understandthe mechanism that leads to the observed complex time-transmission profile, we now want todiscuss the director profile upon switching.

Fig.5.9 shows a molecular plot which gives a 3D impression of the director orientation at varioustime steps when a 4.5V step is applied at t = 0ms.

Figure 5.9: Simulated director profile at different time steps upon switching (LC-A 4.2µm sample). Att = 0ms a 4.5V voltage step is applied.

The evolution of the director profile upon reorientation agrees with the expected switchingbehaviour in VA-LCDs. After the voltage step is applied at t = 0ms, the liquid crystal moleculestilt in counter-clockwise direction (according to the initial pretilt, see the plot at t = 0ms) to aposition perpendicular to the electrical field lines as ∆ε < 0 which leads to a gradual increase inretardation. As the liquid crystal layer is sandwiched between crossed polarizers, this gives riseto the smooth time-transmission profile as observed in the transmission profile for switching from0V-4.5V in Fig.5.7. As can be seen on Fig.5.9, the director profile reaches a stable configurationat about 25ms. This is in agreement with the switching time observed on Fig.5.3 and thetransmission profile for 0V-4.5V switching in Fig.5.7.We observed no difference in results when similar simulations are performed that do not includethe Leslie-Ericksen theory. In this case, Eqn.2.12 remains valid and the determining materialparameters for the switching behaviour are γ, ∆ε and K33.

59The director profile upon switching becomes completely different when a voltage exceeding 4.5Vis applied, as shown by the drastic change of the time-transmission characteristic (e.g. seeFig.5.2,5.7 or 5.8). This is visible in Figs.5.10 and 5.11 that show molecular plots of the directorprofile for switching between 0V-6V (the voltage step is applied at t = 0ms).

Figure 5.10: Simulated director profile at different time steps (0-9ms) upon switching (LC-A 4.2µm sam-ple). At t = 0ms a 6V voltage step is applied.

Figure 5.11: Simulated director profile at different time steps (10-400ms) upon switching (LC-A 4.2µmsample). At t = 0ms a 6V voltage step is applied.

60First, consider the director configuration in Fig.5.10 at t = 1ms. In contrast to the situation onthe plot in Fig.5.9, not all directors switch immediately in the same direction. Indeed, it is clearthat the lower directors initially tilt in counter clockwise direction, while the upper directorsswitch in clockwise direction. This can be explained physically by taking the fluid motion of theliquid crystal molecules into account. According to the pretilt direction shown in the molecularplot at t = 0ms (slightly tilted to the left), the molecules try to reorient themselves in a counter-clockwise direction which creates a fluid motion that influences the neighboring molecules bymeans of viscous forces. Due to the viscosity effect, subsequent molecules tend to switch theirhead resp. tail in the same direction (so that the directors point in opposite directions), asshown schematically in Fig.5.12.

Figure 5.12: Neighboring directors switch in opposite directions due to viscous interaction.

Depending on the position of the molecules considered, this flow effect can determine the switch-ing behaviour if the amplitude of the applied voltage step is sufficiently large. If the viscousforces are stronger than the interaction between the neighboring molecules, the molecules canbe forced, due to the fluid motion, to tilt in opposite directions. Therefore, this effect is referredto as reverse flow or backflow. As can be seen in Fig.5.10 at t = 1, 2 and 3ms, backflow takesplace as the directors in the upper part of the structure are tilted in the opposite direction of thedirectors in the lower part. Because of the asymmetry introduced by the boundary conditions(∆θ = 1.5◦), the directors in the black state at the bottom substrate are already 1.5◦ more tiltedtowards the horizontal state (90◦ inclination). This makes their reorientation (when a voltagestep is applied) towards the on-state easier than for the directors in the upper part. Therefore,the lower molecules will start reorienting first, thereby creating a fluid motion which will causethe upper molecules to tilt in the ’wrong’ direction.

When a driving voltage is applied across the cell, the configuration in which all directors areoriented horizontally in the same direction is the most favorable as for this case the free energyis minimized. Therefore, the liquid crystal molecules will reorient until this configuration isreached. This is achieved through a twisting of the liquid crystal molecules, as this deformationis the most favourable because K22 << K11,K33 for most liquid crystal materials. Startingfrom the configuration at t = 3ms in Fig.5.10, the twist deformation turns the liquid crystalmolecules in the upper part until they become parallel to the directors in the lower part of thestructure. The twisting direction is determined by the initial pretwist difference between the topand bottom directors. As can be seen in Figs.5.10 and 5.11, the twist process is very slow as ittakes about 400ms until the stable director configuration is reached. This immediately explainsthe extremely slow switching behaviour for higher voltages observed earlier.

61It is not straightforward to explain the transmission values and timing of the two intermediatemaxima that appear in the time-transmission responses observed under crossed polarizers inFigs.5.7 and 5.8. However, it is clear that in case of backflow there is no gradual increase inretardation upon switching as both the twist and tilt angles of the directors change across thecell thickness in a complex way. Consequently, the average retardation as a function of time alsochanges in a complex way, harder to predict. Apparently, two intermediate optima appear thatgive rise to the local maxima observed in Figs.5.7 and 5.8.

As mentioned before in subsection 5.4.2, a fitting of the (unknown) twist deformation constantK22 mainly leads to a scaling of the time axis of the time-transmission characteristic in casebackflow occurs. It is now easy to understand this physically. It follows from the descriptionabove that the twist deformation plays a dominant role in the switching mechanism of the liquidcrystal when backflow occurs. Therefore, as changing K22 is physically equivalent to enhancingthe twist deformation (decrease of K22) or making this deformation less favorable (increase ofK22), this immediately leads to a slower respectively faster switching response once the thresholdvoltage for backflow occurrence is exceeded (as illustrated in Fig.5.6).

Figure 5.3 shows that after the drastic increase in switching time (occurrence of backflow),the response time decreases again for higher voltages. In this third zone, backflow still occursas shown in Fig.5.8. The response becomes faster in this case as the liquid crystal moleculesrespond faster due to the stronger electrical field.

It is remarkable that the values of the two intermediate minima that occur in the simulated stepresponse in Figs.5.7 and 5.8 are always lower than the values obtained by experiment. This isprobably due to the occurrence of domaining of the liquid crystal molecules. In reality, not allliquid crystal molecules twist back in the same direction because the (unintended) pretwist forthe top and bottom directors varies randomly across the sample. Consequently, the directionin which the directors twist back also varies across the sample and the sample area becomesdivided into microscopic areas (domains) where the directors twist back after backflow in thesame direction. Therefore, at every time step upon switching there appear small deviationsin retardation between the domains due to the different twist directions. This leads to localmicroscopic variations in transmission over the sample upon switching. The experimentallyobtained time-transmission curves in the right column of Figs.5.7 and 5.8 show the transmissionaveraged out over the sample (and therefore also over the different domains). As the simulationmodel used here is one-dimensional, only one cross-section of the sample is considered (onedomain!). Therefore, it is obviously not possible to take domaining into account which can leadto small discrepancies in transmission values between simulations and measurements, especiallywhen fast variations are considered. The use of two- or three-dimensional simulation software(capable to take flow effects into account) could eventually lead to better results as domainingcan also be taken into account. It should be emphasized that this kind of domaining is clearly aconsequence of the backflow phenomenon and does not occur at lower voltages for which there isno backflow. Fig.5.13 shows pictures taken by using a microscope of the transmission across thesample upon switching at different time steps after a 10V voltage step was applied at t = 0ms.The occurrence of domaining can be observed as the non-uniformity in transmission over thesample (different domains feature different transmission values).A test cell similar to the LC-A 4.2µm sample was used to take these pictures. From Fig.5.13, itseems that the switching behaviour for this cell is somewhat slower. This is probably due to asmall deviation in cell gap which can occur due to small variations in the fabrication process.

62

Figure 5.13: Experimental observation of the occurrence of domaining in VA-LCDs at different time steps.A 10V voltage step was applied at t = 0ms.

5.6 Conclusion of Chapter 5

In this chapter, the switching behaviour of VA-LCDs was investigated by using experiments andsimulations. At a certain voltage the switching time of the reorientation of the liquid crystalsincreases drastically, due to the backflow phenomenon. A simulation model was presentedwhich is capable to take this flow effect into account. In contrast to conventional simulationsof the backflow effect that use the viscosity coefficients of MBBA, material dependent viscositycoefficients (obtained by a fitting procedure) were used. This clearly lead to better simulationresults. Although this model is only one-dimensional, a good agreement between simulationsand experiments was found. The simulation model will be extended in the next chapter toincorporate the effect of temperature on the switching behaviour of VA-LCDs.

Chapter 6

The influence of temperature on the

switching behaviour of VA-LCDs

6.1 Introduction

Important advantages such as its excellent contrast ratio, low operation voltage and the rubbing-free process, make the VA-LCD technology attractive for mobile applications. The temperaturerange for proper operation puts an extra requirement on LCDs in these applications. Therefore,an important question arises: how does the switching behaviour change with temperature?

The results of an experimental study on the effect of temperature on the switching behaviourof VA-LCDs will be reported in section 6.2. A next step is to extend the simulation modelpresented in section 5.4 to take temperature effects into account. It already became clear that itis not straightforward to describe the switching behaviour of VA-LCDs in an accurate way due tothe many degrees of freedom in boundary conditions, elasticity constants, viscosity coefficientsetc. To obtain a model which is capable of taking temperature effects into account, the systembecomes even more complex as variations of all parameters with temperature need to be takeninto account. However, such a model would be very valuable as the switching characteristic couldbe predicted or estimated at any temperature. This would allow to optimize the driving schemefor different temperatures, which would lead to an important improvement in performance ofVA-LCDs.

6.2 Experimental study of the effect of temperature on the

switching behaviour of VA-LCD’s

Time-transmission experiments were performed at different temperatures to probe the effect oftemperature on the switching response of VA-LCDs. These experiments were carried out byusing the experimental setup and temperature control system described in section 3.2. The VAsample used in the experimental part of the previous chapter is again considered for the exper-iments in this section. For all measurements, the driving voltage was changed at t = 0ms from0V to a value in the interval 3V-10V. Unfortunately, it was not possible to perform measure-ments at temperatures below 25◦C by using the existing setup. The turn on times τon (0%-90%transmission) were extracted from the experimental time-transmission curves to plot τon as afunction of voltage for different temperatures, as shown in Fig.6.1.

63

64

Figure 6.1: Experimental voltage-turn on time characteristic at different temperatures (LC-A 4.2µm sam-ple).

It is very apparent from Fig.6.1 that the characteristics for all temperatures feature the samecurve shape. As explained in the previous chapter, the response time first decreases graduallyuntil a certain threshold voltage VBF is reached. At this value, the response time suddenlyincreases to much higher switching times due to the occurrence of backflow. The switchingtimes decrease again gradually for voltages V >> VBF . Clearly, the same effects as described insection 5.5 for 25◦C also take place at higher temperatures. It is apparent that for this materialVBF shifts to higher voltages (4.5V to 5V) with an increase in temperature. Therefore, comparedto the situation at room temperature, slightly higher voltages can be applied at higher temper-atures without the occurrence of backflow. If backflow does not occur for a certain voltage atroom temperature, backflow will also not occur at higher temperatures for the same voltage.Fig.6.1 shows that the turn on time decreases with increasing temperature, for all voltages. Thisis also represented in Fig.6.2, where the turn on time is shown as a function of temperature fordifferent voltages.

Although it was not possible to verify this experimentally, we expect that the same trends withtemperature are also applicable if temperatures below 25◦C are considered: VBF will be shiftedto lower voltages and higher switching times will be obtained if the temperature is decreased.

65

Figure 6.2: Experimental temperature-turn on time characteristic for different driving voltages (LC-A4.2µm sample).

As a conclusion, the display switches faster from the black state to the static transmission forincreasing temperatures. Although not very practical, energy efficient and still technologicallychallenging, heating up the display would thus lead to better performance. This can also beextracted easily from Eqn.2.12 and 2.13, taking into account that the value of the rotationalviscosity decreases with temperature.

6.3 Temperature dependency of ∆ε, γ and Kii

Datasheets of liquid crystal materials typically contain only (restricted) information on ∆ε, ∆n,γ, K11 and K33 at a single temperature. It is necessary to know the influence of temperatureon these material parameters in order to extend the simulation model presented in section 5.4to take temperature effects into account. Therefore, the influence of temperature on materialparameters such as ∆ε, γ and Kii must be measured or extracted to run accurate simulations.The estimates for the viscosity coefficients ηij at different temperatures immediately follow fromthe fitting procedure presented in subsection 5.4.3 as the order parameter S from Eqn.5.17already includes the temperature dependency.

6.3.1 Influence of T on ∆ε

As discussed in subsection 3.2.3, the values of ε|| and ε⊥ can be extracted by using the voltage-capacitance setup if the capacitance C0 of the empty cell (measured before filling with the liquidcrystal material) is known. C0 was measured as 0.1367nF. The temperature profile of ε|| and ε⊥can be extracted by inserting the VA sample in the hot stage and performing voltage-capacitance

66measurements at different temperatures. The experimental profiles of ε||, ε⊥ and ∆ε obtainedin this way are shown in Fig.6.3. The values of ε||, ε⊥ and ∆ε as a function of temperature arealso listed in Table 6.1 at the end of this section.

Figure 6.3: Experimentally obtained dielectric permittivities ε⊥, ε|| and ∆ε for LC-A as a function oftemperature.

It follows from Fig.6.3 that ∆ε is linearly dependent on temperature until about 85◦C. As canbe seen, this is because ε⊥ is linearly decreasing with temperature while ε|| is, in good approx-imation, temperature independent. Therefore, two measurements of ε⊥ and ε|| (e.g. at 25◦Cand Tc) are in good approximation sufficient to characterize the variations of ε⊥, ε|| and ∆ε withtemperature. These observations are in very good agreement with general trends observed forVA materials1.At T = 95◦C, ε|| = ε⊥ (∆ε = 0), indicating that the liquid crystal material has become isotropic.Taking the temperature step of ∆T = 5◦C into account, we conclude that the clearing temper-ature Tc is situated in the range 90◦C-95◦C. In what follows, we will use Tc = 95◦C whichcorresponds to the experimental value listed in Table 5.1. The deviation from the datasheetvalue of Tc = 90◦C can be caused by a possible difference between the temperature in the hotstage and the actual temperature inside the liquid crystal layer of the sample. Furthermore, itis possible that there is a deviation between the clearing temperature in the thin liquid crys-tal layer in the test cell and the clearing temperature in the bulk material (which is listed indatasheets).

6.3.2 Influence of T on Kii

The Frank elastic coefficients Kii(i = 1, 2, 3) decrease with temperature. According to [44], theKii are proportional to the order parameter squared:

Kii ∝ S2. (6.1)1From private discussion with the supplier of the liquid crystal materials

67Eqn.2.11 suggests that K33 can be extracted by measuring the threshold voltage Vth from astatic voltage-transmission measurement:

K33 = ε0|∆ε|(Vth

π

)2

. (6.2)

In this way, the proportionality relation in Eqn.6.1 can be verified for LC-A, taking the temper-ature dependency of ∆ε extracted in subsection 6.3.1 into account when applying Eqn.6.2. Thevoltage-transmission profiles were measured using the hot stage at different temperatures. Thethreshold voltages Vth were extracted using a matlab routine that calculated the intersectionpoint of the voltage axis and the tangent at the rising slope of the voltage-transmission curve.Using Eqn.6.2, K33 can be calculated as a function of temperature as shown in Fig.6.4(a). Al-ternatively, K33 can also be plotted as a function of S2 by using the relation from Eqn.5.17(Fig.6.4(b)).

Figure 6.4: Experimentally obtained values of K33 as a function of (a) temperature and (b) S2 for LC-A.The linear interpolations are calculated as: K33 = −0.18T +19 (a) resp. K33 = 42.2S2−6.74(b).

The red curves in Fig.6.4 show the result of linear fittings performed on the experimental data.Fig.6.4(a) shows that K33 is in good approximation decreasing linearly with temperature. Theproportionality relation from Eqn.6.1 is clearly also a good approximation (see Fig.6.4(b)). Us-ing the linear interpolation, the value of K33 at 20◦C can be estimated as 15.4pN. This value isin good agreement with the datasheet value of 14.8pN (4% error).

68It is much harder to extract K11 and K22 as a function of temperature. Therefore, we have tocome up with a fitting based on reasonable approximations. Eqn.6.1 suggests that all elasticitycoefficients show the same dependency on S2. However, it was pointed out by the supplier ofthe liquid crystal material that the proportionality relation from Eqn.6.1 is only for K33 in goodagreement with experimental results. We choose to make a fitting of K11 and K22 based on thelinear relationship between K33 and temperature observed in Fig.6.4(a). We propose a lineardecrease of K11 and K22 with temperature with the same relative slope as in the linear fittingfor K33. The equation of the curves can be determined using the known values K20◦C

11 resp.K20◦C

22 at 20◦C. In this way, following estimates for K11 and K22 are obtained:

K11 = − 0.18K20◦C

33

K20◦C11 (T − 20) +K20◦C

11

K22 = − 0.18K20◦C

33

K20◦C22 (T − 20) +K20◦C

22 . (6.3)

As no datasheet value is actually available for K22, K20◦C22 = 4.275pN is chosen in accordance to

the fitting procedure mentioned in subsection 5.4.2. As we assume a linear relationship betweenKii and temperature, two voltage-transmission measurements (at e.g. 25◦C and 75◦C) shouldbe approximately sufficient to calculate the variation of K33 with temperature. The slope ofthe resulting interpolated characteristic is then used to calculate the temperature dependencyof K11 and K22.The values for Kii that were obtained in this subsection are listed in Table 6.1 at the end of thissection.

6.3.3 Influence of T on γ

The strong temperature dependency of the rotational viscosity γ is well known. Many formulashave been presented to explain experimental data, [44]. A common used formula was derivedby Hess, [45]:

γ ∝ S2 exp(

E

kBT

), (6.4)

with S from Eqn.5.17 and E the activation energy of diffusion. Eqn.6.4 suggests that, if T isnot too close to the clearing temperature (S should stay close to unity), the value of γ decreasesexponentially with temperature.For liquid crystal materials with ∆ε < 0, measurement of γ(T ) is only possible with a magneticmethod ([46]). This method is however expensive, very time consuming and requires a precisetemperature control. Consequently, only a very limited amount of data on the temperatureprofile of γ is available for VA materials. However, Eqn.2.13 suggests that it is possible toextract γ by measuring the 90% turn-off time τoff . Indeed, from Eqns.2.13 and 2.11 it follows:

γ ∝π2τoffK33

d2. (6.5)

It is possible to measure τoff at different temperatures using the experimental setup with hotstage in time-transmission mode as described in section 3.2. To obtain τoff , the cell was switchedfrom 4V to the black state (0V) and the turn-off time was extracted from the time-transmissionprofile.To extract the values of γ as a function of temperature, the right hand side of Eqn.6.5 was firstcalculated at different temperatures, taking the temperature dependency of K33 estimated in

69subsection 6.3.2 into account. Next, a fitting of the form presented in Eqn.6.4 was calculatedfor the results from the previous step. The proportionality constant for the relation in Eqn.6.5was obtained by extrapolating the fitted curve to 20◦C and assuming that the value at thistemperature is equal to the datasheet value at 20◦C (listed in Table 5.1). The values of γ canfinally be calculated from Eqn.6.5 by using the obtained proportionality constant. Fig.6.5 showsthe resulting profile of the rotational viscosity as a function of temperature. The obtainedvariations of γ with temperature can be compared in Fig.6.5 to the rule of thumb2 for VAmaterials that the rotational viscosity decreases by 25% for every 5◦C decrease in temperature.

Figure 6.5: Experimental values and rule of thumb for the rotational viscosity γ of LC-A as a functionof temperature.

As can be seen, good agreement between the extracted values and the rule of thumb is found.The values of γ as a function of temperature obtained in this subsection are listed in Table 6.1.

6.3.4 Conclusion

Not much information is currently available on the temperature dependency of the materialparameters ∆ε, γ and Kii in the literature or datasheets as it is, even at room temperature,difficult or time consuming to measure these parameters with a high accuracy. To describethe effect of temperature on the liquid crystal material, it was therefore necessary to follow aheuristic path by using a combination of several measurements and fittings. In this way, thematerial parameters at different temperatures could be extracted indirectly. The fitting proce-dures presented are straightforward, but based on reasonable physical arguments. The resultsthat were obtained in this way agree well with theoretical expectations. Table 6.1 summarizes

2From private discussion with the supplier of the liquid crystal materials

70the obtained values for ε⊥, ε||, γ and Kii(i = 1, 2, 3) of LC-A at different temperatures in the25◦C-80◦C interval.

Table 6.1: Obtained values for ε⊥, ε||, γ and Kii(i = 1, 2, 3) as a function of temperature for LC-A.

T (degr.C) ε⊥ ε|| γ (Pa.s) K11 (pN) K22 (pN) K33 (pN)25.0 7.40 3.50 0.1428 12.9608 4.0150 14.890030.0 6.90 3.50 0.1050 12.1216 3.7551 12.740035.0 6.70 3.50 0.0868 11.2824 3.4951 11.970040.0 6.50 3.50 0.0606 10.4432 3.2351 11.260045.0 6.30 3.50 0.0550 9.6041 2.9752 10.580050.0 6.10 3.50 0.0405 8.7649 2.7152 9.380055.0 5.90 3.50 0.0342 7.9257 2.4552 8.940060.0 5.70 3.50 0.0289 7.0865 2.1953 8.040065.0 5.60 3.50 0.0214 6.2473 1.9353 7.220070.0 5.45 3.55 0.0176 5.4081 1.6753 5.980075.0 5.30 3.55 0.0137 4.5689 1.4154 5.350080.0 5.05 3.55 0.0094 3.7297 1.1554 3.9500

6.4 Simulating the effect of temperature on the switching in

VA-LCDs

6.4.1 Introduction

The simulation model introduced in section 5.4 can be extended to take temperature effects intoaccount by using the information extracted in section 6.3. Similar simulations as in subsection5.4.4 will be performed to find good agreements with the experimental results from Fig.6.1.We first choose to neglect the temperature dependency of the refractive indices ne and no here.The error on this approximation will be discussed in subsection 7.3.2.

6.4.2 The use of the default estimates for ηij

Now that the variations of the material parameters ε⊥, ε||, γ andKii(i = 1, 2, 3) with temperatureare known, only the viscosity coefficients ηij need to be generated before simulations can beperformed. This is done by using the estimation procedure discussed in subsection 5.4.3 with γaccording to Table 6.1. The resulting viscosity coefficients are shown as a function of temperaturein Fig.6.6. Note that the ηij coefficients at 25◦C are different from the values listed earlier inTable 5.3, as the values of Table 5.3 were obtained using the 20◦C datasheet value of therotational viscosity γ in the estimation procedure.

Fig.6.6 reveals that the viscosity coefficient η22 becomes negative in case the temperature exceeds25◦C. This is physically not possible as η22 is one of the principal viscosity coefficients (see section5.3), which remain always positive. Therefore, the estimation procedure needs to be modified toobtain more acceptable estimates for the viscosity coefficients for temperatures exceeding 25◦C.This will be considered in the next subsection.

71

Figure 6.6: Viscosity coefficients of LC-A as a function of temperature (values according to the estimationprocedure of subsection 5.4.3).

6.4.3 Methodology to obtain better estimates of ηij

Subsection 6.4.2 revealed that unphysical estimates for the η22 viscosity coefficient were obtainedby using the estimation procedure presented in subsection 5.4.3. To obtain more accuratevalues, we propose to do a fitting of η22 based on the experimental results presented in Fig.6.1.Therefore, it is necessary to analyze the influence of η22 on the switching behaviour. This will bedone by considering simulated switching profiles which were obtained for varying values of η22

while all other material parameters were kept fixed. Next, we will keep η22 fixed in a second seriesof simulations to also investigate the influence of the variation of the other material parameterswith temperature on the transmission behaviour. This will reveal how η22 needs to be adjustedwith temperature to obtain a better agreement between simulated and experimental results.

η22 and its influences on the switching behaviour

We will observe the effect of η22 on the switching behaviour of the cell by performing time-transmission simulations in which the value of η22 is varied.The values of η11 and η22 are linked to each other through Eqns.5.6 and 5.7. This relationshipshould be considered in the simulations where η22 is varied. From Eqn.5.6, the expression forη11 can be rewritten using Eqn.5.5 as:

η11 =12(−α2 + α4 + α5)

=12(γ − α3 + α4 + α5) (6.6)

72Using the expression for η22 in Eqn.5.7, α3 can be written as:

α3 = 2η22 − α4 − α6. (6.7)

Substituting the result into Eqn.6.6 leads to:

η11 =12(γ − 2η22 + 2α4 + α5 + α6). (6.8)

According to the Parodi relationship (Eqn.5.4), only 3 coefficients in the set {α2, α3, α5, α6}are independent. If we assume that η22 is known and {α4, α6} are obtained using Eqns.5.13and 5.15, α3 can be calculated from Eqn.6.7. In this case, α2 follows again from Eqn.5.20.Consequently, α5 must be calculated from Eqn.5.4 instead of Eqn.5.14 in order to satisfy theParodi relationship:

α5 = α6 − α2 − α3. (6.9)

Substituting the expression above into Eqn.6.8 leads to:

η11 =12(γ − 2η22 + 2α4 + 2α6 − α2 − α3). (6.10)

Using this result, η11 can be adjusted correctly depending on the value of η22. The η33 and η12

coefficients are independent from η22 and are calculated from Eqns.5.8 and 5.9 with α1 accordingto Eqn.5.18. The viscosity coefficients corresponding to η22 values of {0.005, 0.015, 0.030, 0.040}Pa.s are listed in Table 6.2.

Table 6.2: Modified viscosity coefficients for varying values of η22 at 25◦C.

η22 (Pa.s) η11 (Pa.s) η33 (Pa.s) η12 (Pa.s)0.005 0.1808 0.0383 -0.03320.015 0.1708 0.0383 -0.03320.030 0.1558 0.0383 -0.03320.040 0.1458 0.0383 -0.0332

Fig.6.7 shows the simulated time-transmission characteristics for switching between 0V-6V, ob-tained by correctly adjusting the viscosity coefficients to the varying value of η22 (Table 6.2)and keeping all other material parameters constant according to their 25◦C value (Table 6.1).

It follows from Fig.6.7 that η22 has a direct impact on the dynamic behaviour. Indeed, theswitching behaviour becomes much faster for increasing values of η22 because the double-peakedresponse becomes less pronounced. For high values of η22 (Fig.6.7(d)), even the monotonic in-creasing time-transmission characteristic is obtained. This leads to the important conclusionthat (for the same voltage step and fixed ε||, ε⊥, γ and Kii) less backflow occurs when η22 isincreased. Of course, if a fixed value of η22 is considered, the occurrence of backflow still mainlydepends on the amplitude of the voltage step, but VBF will be shifted to higher (resp. lower)voltages if η22 is increased (resp. decreased).

It was already described in section 5.5 that for voltages below the backflow threshold voltageVBF the material parameters K33, ∆ε and γ determine the switching behaviour (according toEqn.2.12). For voltages above VBF , it was pointed out that the switching times are mainlydependent on K22, as the twist deformation plays a dominant role in the switching mechanism.It has now become clear that for the range in between, the viscosity coefficient η22 plays animportant role in the switching behaviour as VBF is strongly dependent on this value.

73

Figure 6.7: Simulated time-transmission profiles for different values of η22 when a voltage step of 6Vamplitude is applied at t = 0ms (LC-A 4.2µm sample). Except for the ηij which varyaccording to Table 6.2, all other material parameters are kept constant (25◦C value in Table6.1).

The influence of the temperature variations of {Kii,∆ε, γ} on the switching behaviourfor a fixed value of η22

We present here the results of time-transmission simulations for different temperatures wherethe values of the material parameters follow the values listed in Table 6.1. However, the value ofη22 is kept constant to see the effect of the variations of the other parameters on the switchingbehaviour as a function of temperature.

A fitting of η22 was performed to choose a reasonable fixed value. This was done by tuningη22 until good agreement between the simulated and experimental VBF at 25◦C was found. Inthis way, η22 = 6.0mPa.s was obtained. For this fixed value, the other viscosity coefficientsfor temperatures different from 25◦C are calculated in the same way as in the first part of thissubsection. The resulting values are listed in Table 6.3.

Fig.6.8 shows the simulated switching turn on time graph obtained by using the material pa-rameters from Tables 6.1 and 6.3.

74

Table 6.3: Viscosity coefficients at different temperatures with η22 kept fixed.

T (degr.C) η11 (Pa.s) η22 (Pa.s) η33 (Pa.s) η12 (Pa.s)25.0 0.1798 0.0060 0.0383 -0.033235.0 0.1144 0.0060 0.0216 -0.028945.0 0.0761 0.0060 0.0125 -0.024455.0 0.0513 0.0060 0.0077 -0.019765.0 0.0348 0.0060 0.0052 -0.014875.0 0.0228 0.0060 0.0043 -0.0095

Figure 6.8: Simulated voltage-turn on time characteristic for different temperatures (LC-A 4.2µm sam-ple). The values of the material parameters used in the simulations are taken from Tables6.1 and 6.3.

By comparing Figs.6.8 and 6.1, it is clear that the obtained simulated characteristics are inqualitative agreement with the experimental results, as comparable trends can be observed inboth figures. First, for increasing temperatures, the switching turn on time decreases for allvoltages. Furthermore, the threshold voltage VBF is shifted to higher voltages for increasingtemperatures. However, the shift observed in the simulated characteristic for 75◦C (Fig.6.8) isalmost two times higher than observed in Fig.6.1.It is apparent that a very good agreement between experiments (Fig.6.1) and simulations(Fig.6.8) is obtained for the complete curve at 25◦C by only fitting η22 at this temperatureto obtain a good match in VBF . In general, the switching times obtained through simulationsin Fig.6.8 are in good agreement with experiments for low voltages (where no backflow occurs)while there is a deviation when higher voltages are considered (where backflow occurs).

75Conclusion: a fitting procedure for η22

If η22 is kept constant while variations of all other material parameters with temperature areconsidered (Table 6.1), already a good qualitative agreement is found between simulations andexperiments of the switching behaviour in VA-LCDs, except for the shift in backflow thresholdVBF which is too large at high temperatures. However, it appeared from the first part of thissubsection that, for a fixed set of material parameters, VBF is shifted to lower voltages if η22

is decreased. Therefore, the value of η22 can be fitted at higher temperatures by adjusting thisparameter until a good match for VBF is obtained between the simulated and experimentalresults. The viscosity coefficients η11, η33 and η12 are calculated according to Eqns.6.10, 5.8 and5.9, respectively.

6.4.4 Simulating the temperature dependency of the switching behaviour in

VA-LCDs

To simulate temperature effects on the switching behaviour of VA-LCDs, we use the variationsof the material parameters Kii,∆ε and γ according to Table 6.1 while the viscosity coefficientsare calculated according to the procedure sketched in subsection 6.4.3. To extract η22 as a func-tion of temperature, we choose to do another fitting of η22 at 75◦C and assume here a linearrelationship of η22 in the interval 25◦C-75◦C. The fitting procedure at 75◦C has lead to the valueη22 = 0.0040Pa.s. The viscosity coefficients that are finally obtained are listed in Table 6.4.

Table 6.4: Viscosity coefficients at different temperatures for linearly decreasing η22.

T (degr.C) η11 (Pa.s) η22 (Pa.s) η33 (Pa.s) η12 (Pa.s)25.0 0.1798 0.0060 0.0383 -0.033235.0 0.1148 0.0056 0.0216 -0.028945.0 0.0769 0.0052 0.0125 -0.024455.0 0.0525 0.0048 0.0077 -0.019765.0 0.0364 0.0044 0.0052 -0.014875.0 0.0248 0.0040 0.0043 -0.0095

Using the material parameters and viscosity coefficients listed in Tables 6.1 and 6.4, similarsimulations as in subsection 6.4.3 (see Fig.6.8) were performed. The resulting voltage-turn ontime characteristic is shown in Fig.6.9.

It is clear that the obtained characteristics in Fig.6.9 are in remarkable agreement with theexperimental results (see Fig.6.1). The approach to assume a linear relation of η22 with temper-ature between the values obtained by fitting this parameter at 25◦C and 75◦C clearly lead to agood modelling of the threshold voltages for the occurrence of backflow. To assess the model ina more quantitative way, the relative error on the turn on time τon is defined as:

relative error =τ simon − τ exp

on

τ expon

,

where τ simon and τ exp

on denote the turn on times obtained through simulations resp. experiments.The resulting relative error on τon as a function of voltage for different temperatures is plottedin Fig.6.10.

76

Figure 6.9: Simulated voltage-turn on time characteristic for different temperatures (LC-A 4.2µm sam-ple). The values of the material parameters used in the simulations are taken from Tables6.1 and 6.4.

Figure 6.10: Relative error on the simulated turn on time τon as a function of voltage for different tem-peratures (LC-A 4.2µm sample).

77Fig.6.10 shows under which conditions the simulation model is performing optimum. It is clearthat the error on the simulated turn on time is rather small (less than 25%) for voltages V < VBF ,for all temperatures. The error becomes larger for all temperatures when V ≈ VBF (the interval4.5V-5V, depending on the temperature). Although it was shown that the modelling of thebackflow threshold was in good qualitative agreement with the experiments, it follows that it ishowever hard to model this transition zone in a very accurate way. For V > VBF , there can bea quite large steady-state error on the estimate of the turn on time, depending on temperature.Once the temperature exceeds 50◦C, an error of about +50% is inevitable. We believe that thediscrepancy in case backflow occurs has two main causes, next to the approximation to neglectvariations of the refractive indices with temperature. First, the error can be linked to the in-accuracy in the estimate of K22. Indeed, K22 has a direct influence on the turn on time as theswitching time is determined by how fast the liquid crystal molecules twist back to the mostenergy favorable configuration (see section 5.5). As the simulated turn on times are too high,we expect that too low values of K22 were extracted (see Fig.6.7). Second, an error might beintroduced due to the fact that domaining can not be taken into account in the one-dimensionalsimulation model, as discussed in subsection 5.5.

Let us recall that the activation energy E from MBBA was used to calculate the viscosity coef-ficient α4 (see Eqn.5.13). As mentioned in subsection 5.4.3, the values of α4 could be adjustedat different temperatures to improve the similarity between the simulated and measured time-transmission profiles. The influence of α4 on the turn on times for V > VBF is very restrictedas this parameter has no influence on the twist deformation which determines the switchingon times in this zone. Taking the good agreement between simulations and measurements intoaccount that was already obtained for voltages V ≤ VBF , it does not seem to be necessary toadjust the value of E.

It can be concluded that the model can accurately simulate the switching dynamics for all tem-peratures in the complete voltage range which is of practical importance for display applications(i.e. V < VBF ). First, the model works fine over the whole temperature range 25◦C-75◦C topredict switching turn on times for voltages where no backflow appears. Second, also the thresh-old voltage where backflow occurs is modelled accurately for all temperatures, as can be seen bycomparing Figs.6.9 and 6.1 for 4.5V-5V. It is important to know at which voltage backflow oc-curs as, due to its dramatic effect, backflow should be avoided at any time, for all temperatures.Therefore, this threshold voltage VBF puts an upper limit on the voltage range that can be usedfor VA-LCDs to obtain an acceptable performance. The inaccuracy for the voltages V > VBF

is relatively not so important, as for practical applications these voltages should be avoided dueto the dramatic effect of backflow on the switching behaviour.

786.4.5 Verification of the model for a different LC

It is important to investigate if the model discussed above is widely applicable. Therefore, aVA cell with a cell gap of 3µm was filled with a different liquid crystal: LC-B. The importantdatasheet values of LC-B at 20◦C are listed in Table 6.5.

Table 6.5: Material parameters LC-B material (datasheet values at 20◦C). The clearing temperature Tc

indicated by an asterisk corresponds to the value measured experimentally (see Fig.6.12).

no ne ε|| ε⊥ K11(pN) K33(pN) γ (Pa.s) Tc(◦C) T ∗c (◦C)

1.4881 1.6042 3.4 6.7 15.5 16.3 0.152 95 105

The temperature dependency of the switching behaviour of the LC-B cell will be investigatedin the same way as for the LC-A cell with 4.2µm cell gap. First, various measurements will beperformed to investigate whether the same trends with temperature occur as observed for theLC-A cell. Next, the variations of the material parameters with temperature will be extracted.Finally, the switching behaviour of the cell will be simulated at different temperatures. Asthese three steps were already described extensively in the previous subsections, we restrict ourattention to a discussion of the results.

Experimental results

We investigated the temperature dependency of the LC-B cell in a similar way as done in section6.2. The results are shown in Fig.6.11.

Figure 6.11: Experimental voltage-turn on time characteristic for different temperatures (LC-B 3µm sam-ple).

79By comparing Fig.6.1 and Fig.6.11, it is immediately clear that both figures feature the sametrends with temperature: higher temperatures lead to lower switching times for a fixed voltage.Furthermore, the backflow threshold voltage VBF is shifted to higher voltages if the temperatureis increased. These observations confirm the results of section 6.2: the dynamic behaviour ofVA-LCDs is improved if the display is operating at higher temperatures.

Temperature dependency of ∆ε, γ and Kii

Comparable voltage-capacitance measurements as in subsection 6.3.1 were performed to extractε||, ε⊥ and ∆ε as a function of temperature. The results are shown in Fig.6.12.

Figure 6.12: Experimental dielectric permittivities ε⊥, ε|| and ∆ε of LC-B as a function of temperature.

Taking the datasheet values from Table 6.5 into account, reasonable values for the dielectricpermittivities at 25◦C are obtained. Taking the temperature step of ∆T = 5◦C into account,it can be concluded from Fig.6.12 that the clearing temperature Tc is situated in the range100◦C-105◦C. A 10% error deviation from the datasheet value Tc = 95◦C is observed. Justas for the LC-A material, this deviation might be due to a possible difference between thetemperature in the hot stage and the actual temperature inside the liquid crystal layer of thesample. Furthermore, the clearing temperature in the thin liquid crystal layer in the test cellmight differ from the clearing temperature in the bulk material (which is listed in datasheets).

Just as in subsection 6.3.2, voltage-transmission profiles were measured to extract the variationsof K33 with temperature. The resulting values are plotted in Fig.6.13. If again a linear variationof K33 with temperature is considered, it follows from Fig.6.13 that the value of K33 at 20◦Ccan be estimated as about 17pN. Just as with the estimate for LC-A, this value is in goodagreement with the datasheet value of 16.3pN (4% error). The variations of K11 and K22 withtemperatures are again obtained by assuming a linear decrease with temperature with the samerelative slope as for K33.

To extract variations of γ with temperature, the turn off times from a static transmission value(4V) to the black state were measured in the same way as described in subsection 6.3.3. Theresulting profile is shown in Fig.6.14.

80

Figure 6.13: Experimentally obtained values of K33 as a function of temperature and S2 for LC-B. Thelinear interpolations are calculated as: K33 = −0.173T + 20.4 resp. K33 = 47.7S2 − 8.38.

Figure 6.14: Experimental values and rule of thumb for the rotational viscosity γ of LC-B as a functionof temperature.

81Simulations of the effect of temperature on the switching behaviour

According to the strategy described in subsection 6.4.4, the effect of temperature on the switch-ing of the LC-B cell was simulated. The resulting voltage-turn on time characteristic is shownfor different temperatures in Fig.6.15. The quality of the simulated results can again be assessedquantitatively by plotting the relative turn on time error as a function of voltage, as shown inFig.6.16.

Figure 6.15: Simulated voltage-turn on time characteristic for different temperatures (LC-B 3µm sample).

For low voltages V < VBF , the simulated turn on times from Fig.6.15 decrease correctly withtemperature as in Fig.6.11, but the simulated turn on times are too low. We believe that thiserror is caused by inaccurate values of the rotational viscosity γ, which has a determining influ-ence on τon (see Eqn.2.12). We think that too low values of γ were extracted, as the simulatedturn on times are too low. Because the LC-B cell has a smaller cell thickness d and a lowerrotational viscosity than the LC-A cell, the LC-B cell switches faster as can be observed by com-paring the turn on times from Figs.6.1 and 6.11. Consequently, also the value of the measuredturn off times that were used for the extraction of γ are lower. For example, the turn off times(switching from 4V to 0V) at 25◦C for LC-A resp. LC-B were measured as 50.4ms resp. 17.1ms.Therefore, the (fixed) error on the extraction of the turn off times becomes relatively larger forfaster cells, which leads to a lower accuracy on the extracted values of γ. The rotational viscositydecreases at higher temperatures, leading to even smaller turn off times and further reducingthe accuracy of the extracted values of γ at higher temperatures. This explains the observationthat the relative error on τon increases with temperature, as observed in Fig.6.16.

82

Figure 6.16: Relative error on the simulated turn on time τon as a function of voltage for different tem-peratures (LC-B 3µm sample).

The temperature range in this series of simulations was limited to 55◦C because of a calculationinstability when simulations are performed with the material parameters obtained at temper-atures exceeding 55◦C. We believe that this is again due to too low values of the rotationalviscosity. This is also indicated by the fact that the calculations stabilize for temperaturesexceeding 55◦C if higher values of γ are used in the simulations. The lack of accuracy in theextraction of the rotational viscosity for faster cells is an important drawback of the relativelyeasy extraction procedure proposed in subsection 6.3.3. Therefore, more complex measurements(magnetic method, [46]) of the variation of γ with temperature could provide more accuratemeasurements. These setups were however not available to perform a comparison.

Fig.6.16 shows that there is a relative large error on τon for voltages V ≈ VBF (the range 5V-6V,depending on the temperature). Indeed, Fig.6.15 shows that the shift of VBF with temperatureis not modelled as accurately as for the LC-A cell (see Fig.6.9). We believe that this error isagain caused by less accurate values of the rotational viscosity. It was pointed out that lessaccurate values of γ have a direct negative impact on the simulated values of the turn on time.It is therefore easy to understand that also the accuracy of VBF will be very sensitive to theinaccuracy of the rotational viscosity.

For voltages V > VBF , a remarkable good agreement is found between simulations and mea-surements. However, keeping the inaccurate values of γ into account, care must be taken in theinterpretation as it was already pointed out in subsection 6.4.4 that the fitting of K22 probablylead to too low values of K22, which increase the simulated turn on times. This compensatesthe effect of the values of γ which lead to a decrease in simulated turn on times. The interplayof these two error phenomena accidentally leads to turn on times in the right value range.

836.4.6 Conclusion

The effect of temperature on the switching behaviour of VA-LCDs has been simulated accuratelyin this section for the LC-A material. This was done by using the material parameters listed inTable 6.1, as derived in the previous section. It has been pointed out that the viscosity estimationprocedure from subsection 5.4.3 leads to unphysical negative values for η22 at temperaturesexceeding 25◦C. It has been shown that η22 is an important coefficient as it has a direct influenceon the occurrence of backflow, so it should not be neglected. Therefore, a modification of theestimation procedure has been proposed: good results are obtained if a linear decrease of η22

with temperature is assumed. The η22 values at the boundaries of the temperature range arefitted to have a good match in voltage where backflow starts to occur. It was shown that goodquantitative results are obtained for all temperatures in the voltage range which is of practicalimportance for display applications (i.e. V < VBF ).

Performing similar measurements and simulations on a faster LC-B cell lead to partly satisfyingresults. First, it was observed that the experimental results confirmed the trends observedwith temperature for LC-A. Consequently, it can be concluded quite generally that a change intemperature mainly has two effects: the switching times decrease and the backflow thresholdvoltage VBF is shifted to higher values when the temperature is increased.The extraction of the temperature dependency for LC-B was however not so successful as for theLC-A material. Especially the limited accuracy on the extracted values of the rotational viscosityrestricted the ability to perform simulations over the complete temperature range. Furthermore,this also affected the validity of the obtained switching on times which were simulated as toolow and lead to a reduced accuracy on the modelling of the change of VBF with temperature.It is unfortunate that the extraction of γ with temperature severely limited the ability to assessthe validity of the temperature model itself for this material.

846.5 Conclusion of Chapter 6

It has been investigated in this chapter how the switching behaviour of VA-LCDs is influencedby temperature variations. It has been shown experimentally that the switching time decreaseswith temperature, and this for all voltages that were applied. Furthermore, it was observed thatthe voltage VBF where backflow starts to occur is shifted to higher values when the temperatureis increased. Consequently, it can be concluded that a better switching behaviour is obtainedwith increasing temperature.

In order to obtain a better understanding of the effect of temperature, it was investigated how thematerial parameters that govern the switching behaviour change with temperature. Because notmuch quantitative information is known about how these parameters change with temperature,various experiments were performed that allowed indirectly to extract these variations withtemperature.

Using the knowledge gained on the temperature dependency of various material parameters,simulations were performed to model the effect of temperature on the switching behaviour. Thishas not been straightforward, as not all the viscosity coefficients were estimated accurately usingthe estimation procedure discussed in chapter 5. The important effect of η22 on the occurrenceof backflow was pointed out and an important modification to estimate this parameter wasproposed. This finally resulted in an extension of the simulation model of chapter 5, leading tothe capability to simulate temperature effects accurately in the voltage range which is importantfor display applications (maximum error of 25% for V < VBF ). Accurate extraction of thevariations of ∆ε, K33 and especially γ with temperature is a necessary requirement to obtain agood agreement between the experimental and simulated characteristics.

Chapter 7

A temperature compensating

overdrive scheme for VA-LCDs

7.1 Introduction

For mobile and TV applications, optimum display performance is required to provide videocontent to the user. This should not only be achieved in a lab environment, but proper displayfunctioning has to be maintained over a wide range of conditions. For example, the display in acell phone should ideally achieve the same performance if the user is skiing in the Alps or lyingon a beach during summer. The effect of temperature on the switching behaviour of VA-LCDswas considered in chapter 6. This chapter considers how these temperature effects can be takeninto account in the driving scheme applied to the LCD.

The overdrive scheme is a common driving scheme to achieve fast(er) switching of the liquidcrystal molecules. The principles of this scheme will be shortly reviewed and it will be consideredhow such a driving scheme can be practically extracted. Furthermore, it will be investigated howthe display properties change with temperature if the conventional overdrive scheme is applied.In order to improve the display performance, it will be considered if it is possible to design anoverdrive scheme that actively compensates for temperature effects. The temperature modeldeveloped in the chapter 6 will show its practical importance for this purpose. To conclude thechapter, the practical applicability of such a temperature compensating overdrive scheme willbe investigated in an experimental way. The results will be assessed in both a qualitative andquantitative way in the last section.

7.2 The conventional LCD overdrive scheme

7.2.1 Introduction

The most straightforward approach to drive a single pixel of a LCD is to apply a voltage on theelectrodes which corresponds to the intended static transmission value. However, the switchingtime for such a transition can be too high for practical applications. For example, to displayvideo content on a display, the driving voltages corresponding to a new frame are providedevery 16ms (60Hz refresh rate). Of course, it is desirable that the intended transmission valueis shown as long as possible during the frame time of 16ms. Therefore, the transition accordingto switching from one grey scale to another should be kept as low as possible.

85

86The overdrive scheme is a conventional technique to obtain shorter switching times than thestraightforward static approach sketched above, [47]. The principle of this overdrive scheme isshown in Fig.7.1.

Figure 7.1: Principle of the overdrive scheme used to obtain shorter switching times in LCDs.

In the case of overdrive, the applied driving scheme is divided in two steps, each lasting oneframe time. The goal is to reach the intended static transmission after the first frame time. Ifthe voltage according to the final static transmission value is immediately applied, the transitioncan be too slow to fit into a single frame, as indicated by the blue line in Fig.7.1. The ideabehind overdrive is to apply a voltage which is higher (hence the name overdrive) than thevoltage corresponding to the intended static transmission during the first frame time. Thisoverdrive voltage is chosen carefully such that exactly the target transmission value is obtainedwhen the transition is cut after one frame time. When the voltage according to the intentedstatic transmission value is applied in the next frame, the target transmission is maintainedduring the whole frame time.

The scheme sketched above is applicable to obtain faster switching when switching from a lowerto a higher transmission value. A straightforward extension can be easily obtained to achievefaster switching from a higher to a lower transmission value. In this case an underdrive strategycan be applied where first a lower voltage is applied during the first frame, followed in the nextframe by the voltage corresponding to the intended final transmission value.

877.2.2 Extracting an overdrive scheme

To obtain a complete overdrive scheme, the transitions between all different grey scale levelsneed to be considered. In this way, a table can be constructed that indicates for every possibletransition which overdrive voltage needs to be applied. One possible way to extract the overdrivevoltage is to perform time-transmission measurements where, starting from the voltage thatcorresponds with the first grey scale level, all possible voltage steps in the applicable range (e.g.avoiding backflow) are applied. Afterwards, the transmission values after one frame time areextracted and the corresponding grey scales can be calculated. The drive voltage for whichthe transmission after one frame time matches the intended grey scale is finally tabulated forthe intended transition. The values corresponding to the intended static transmission can beimmediately extracted from a static voltage-transmission characteristic.Instead of using experimental results, also simulations can be used to extract the overdrive tablein a similar way. This approach does not require the manufacturing of various prototypes in theearly research phase. Once the necessary material parameters are known, the use of simulationscan be less time consuming and more practical than performing measurements for all possiblevoltage steps. To illustrate the procedure, an overdrive scheme for transitions between the blackstate and various grey scale levels at 25◦C will be created for the LC-A 4.2µm sample for atypical frame time of 16ms. Depending on the properties of the liquid crystal material and thepossibilities of the driver electronics also shorter frame times can be obtained (e.g. 8ms).

The first step in obtaining an overdrive scheme is to extract (for every voltage) the transmissionvalue at 16ms after the voltage step was applied. This is done by selecting the appropriatetransmission values from time-transmission simulations at 25◦C according to the model fromsubsection 6.4.4.In order to obtain a practical driving scheme, it is necessary to convert the transmission valuesinto grey scale levels. Indeed, in practical applications not a continuum of transmission valuescan be provided by the display, but the transmission range is quantized into different grey scalelevels. Therefore, the applicable voltage range that needs to be covered by the display driver is,instead of a continuum, restricted to a fixed number of values. This quantization is not uniformbut a gamma correction1 needs to be applied. Images for visual display are typically stored with8 bits for each red, green and blue subpixel, leading to 28 = 256 different grey scales. The greyscale value G according to a transmission value T is obtained in the following way:

G = 255(

T

Tmax

) 1γ

, (7.1)

where Tmax denotes the maximum transmission value reached in the static voltage-transmissioncurve and γ is the gamma correction factor. In what follows a gamma correction factor γ = 2.2will be applied.The graph presented in Fig.7.2(a) shows the obtained transmission values at 25◦C after oneframe time as a function of the amplitude of the voltage step (applied at t = 0ms). Parallel tothe simulations, comparable measurements at 25◦C were performed to verify the validity of thesimulated results. For comparison, the experimental voltage-transmission (after 16ms) charac-teristic is also shown in Fig.7.2(a).

1The main purpose of gamma correction in video, desktop graphics, prepress, JPEG, and MPEG is to code

intensity into a perceptually-uniform domain, so as to obtain the best perceptual performance from a limited

number of bits in each of the red, green and blue color components, [48].

88

Figure 7.2: Simulated and experimental voltage-transmission characteristics (LC-A 4.2µm sample): (a)shows the transmission values obtained at 16ms after the voltage step was applied, (b) showsthe static transmission (values at 1000ms after the voltage step was applied).

In order to extract the driving voltages corresponding to the intended static transmission values,also the static transmission values need to be known as a function of voltage. Therefore, staticvoltage-transmission measurements and simulations were performed. To measure the statictransmission values as a function voltage, the transmission was captured 1000ms after a voltagestep with varying amplitude was applied. The simulated and experimental results are shown inFig.7.2(b).

It was necessary to perform some corrections on the gathered data for comparing the simulatedand experimental results. The light leakage through the (not perfect) crossed polarizers causesa certain offset on the transmission values. To compensate for this effect (which is obviously nottaken into account in simulations), this offset value was subtracted from the measured trans-mission values. Also the difference in 100% transmission reference between simulations andmeasurements should be taken into account. In simulations, the transmission is calculated asthe ratio between the light intensity that is transmitted through the analyzer and the intensitythat was transmitted through the first polarizer. In the experimental setup however, the trans-mission is calculated as the ratio between the voltage provided by the photomultiplier duringthe measurement and a user-defined 100% reference value (set according to subsection 3.2.6).Therefore, it is necessary to scale the experimental results in order to compare the transmissionvalues obtained through measurements and simulations. This was done by assuming that themaxima of the simulated and measured voltage-static transmission characteristic should havethe same value. In this way, a scaling factor was calculated. All experimental results presentedin this chapter are compensated with the same scaling factor and offset transmission value.

89Fig.7.2(b) shows that the static voltage-transmission characteristic is correctly simulated. Itis clear from Fig.7.2(a) that the transmission values after 16ms are simulated accurately forvoltage amplitudes below 4.5V. For voltages above this value, there is a discrepancy betweenthe experimental and simulated results. It was pointed out in chapter 5 that backflow starts tooccur for voltage amplitudes V ≥ 4.5V which leads to a drastic change in the switching profile.Due to the more complex shape of the time-transmission characteristic, it can be understoodthat there can easily appear a difference between the transmission values after one frame timeobtained by measurements and simulations.The transmission values from Fig.7.2(a) corresponding to voltages exceeding the backflow thresh-old VBF (V > 4.5V, see section 5.2) are not useful for overdrive. Even when voltages V > VBF

are only applied during a single frame time, the twist deformation induced by backflow contin-ues until a stable static director configuration is reached. Therefore, the transmission will notremain stable during the second frame of overdrive where the static driving voltage is applied,so overdrive will not work. Therefore, the amplitude of the voltage steps applicable in practicaldisplay applications is ultimately limited by the threshold voltage VBF where backflow starts tooccur. Therefore, the discrepancy that appears for voltages V > VBF does not pose a problemas this voltage range is not of interest for practical driving schemes.

Using the simulated results shown in Fig.7.2, an overdrive scheme can be extracted easily. Asan illustration, such a scheme will be developed to drive the test sample from the black stateto the grey scale levels [75,125,175,225]. To extract the overdrive voltage for the first frame,the appropriate grey scale values are selected from the simulated curve from Fig.7.2(a) and thecorresponding driving voltage is extracted. The same procedure is repeated to extract the staticdriving voltage from the simulated curve from Fig.7.2(b). For the transitions from the blackstate to the [75,125,175,225] levels, this leads to the overdrive table shown in Table 7.1.

Table 7.1: Overdrive table at 25◦C for transition from the black state to different grey scale values. Thisscheme was extracted using solely the results of simulations. The asterisk denotes that thelisted value does not correspond to the optimum driving voltage.

75 125 175 225overdrive voltage (V) 3.5177 3.8993 4.2789 4.5∗

static drive voltage (V) 2.2384 2.4824 2.7937 3.3708

As denoted by the asterisk in Table 7.1, it is not possible to extract an overdrive voltage for thetransition to the 225 grey scale value from Fig.7.2(a), as clearly this value can not be reachedafter 16ms for any drive voltage. The only solution to reach the 225 grey scale as fast as possibleis to apply the highest possible driving voltage during the first overdrive stage. As mentionedbefore, this maximum value is limited by VBF (determined as 4.5V at 25◦C for this cell).

907.2.3 Experimental verification of the overdrive scheme

The overdrive scheme from Table 7.1 was tested experimentally to check its applicability. Fig.7.3shows the transmission profile upon switching to the different grey scales when the overdrivescheme is applied at 25◦C .

Figure 7.3: Experimental switching profiles at 25◦C obtained by applying the overdrive scheme fromTable 7.1 (LC-A 4.2µm sample). The different curves show the transition to different targetgrey scales (as denoted in the legend).

As can be seen in Fig.7.3, the presented overdrive scheme works very well for the transitionsto the 75, 125 and 175 grey scales: due to the applied overdrive, the transmission reachesits intended value after the first frame. Afterwards, the intended grey scale level is success-fully maintained during the second frame. In case no overdrive would be applied, much higherswitching times would be obtained (see Fig.5.3). As expected, the switching to the 225 greyscale value performs worse as it was not possible to obtain an optimum overdrive voltage. Inthis case, the intended value is reached after about three frame times.

It is clear from the discussion above that the overdrive scheme is very attractive for VA-LCDs asthe switching times can be reduced drastically. It is important to consider what happens if theoverdrive scheme for 25◦C is applied at different temperatures. The experimental results at vari-ous temperatures are shown in the plots of Fig.7.4. The grey scale values for these temperaturesare calculated from the normalized voltage-transmission curves, according to Eqn.7.1.

91

Figure 7.4: Experimental switching profiles at different temperatures obtained by applying the overdrivescheme from Table 7.1 (LC-A 4.2µm sample). The different curves show the transition todifferent target grey scales (as denoted in the legend).

92As can be seen from Fig.7.4, a change in temperature has a negative impact on the performanceof the overdrive scheme. First, the transmission value reached after one frame time is too high,which leads to an overshoot upon switching to the intended grey scale level. This overshootinterferes with the idea of overdrive as there is no smooth transition between the first and sec-ond overdrive frame which could lead to artefacts when video content is provided. Even worse,the overshoot leads to a drastic increase in switching time. Indeed, it is clear from the plots inFig.7.4 that the relaxation from the overshoot value to the intended static transmission typicallycan take two extra frames compared to the optimum transitions from Fig.7.3.Next to the overshoot on the transmission value after 16ms, also an error on the static trans-mission appears for higher temperatures (plots for 65◦C and 75◦C in Fig.7.4). This is due to achange in the static voltage-transmission curve for higher temperatures, as will be discussed insubsection 7.3.2. Therefore, the static transmission value according to a certain voltage at 25◦Cdiffers from the transmission value obtained at higher temperatures. This leads to an offset inthe obtained transmission values if the overdrive scheme optimized for 25◦C is applied at highertemperatures. It should be noted that the same offset error occurs in case the conventionalfixed static driving scheme is applied (because the same static driving voltages according to thesecond row of Table 7.1 are used).

The observed overshoot and offset error can both be assessed quantitatively by plotting the greyscale error of the 25◦C overdrive scheme as a function of temperature. This is done in Fig.7.5and 7.6 respectively. The static transmission values can fluctuate considerably due to noise inthe photomultiplier (see e.g. Figs.7.3 and 7.4). The maximum deviation on the measured greyscale value due to this noise contribution was measured as 3 grey scale units. To take this effectinto account in the quantitative assessment, error lines that denote the possible error on thepresented curves are drawn in Figs.7.5 and 7.6. This possible error should also be taken intoaccount in what follows. In order not to overload the graphs, the error lines will not be repeatedin all plots throughout this chapter.

Figs.7.5 and 7.6 confirm the qualitative observations made above. The transmission error after16ms is zero when the overdrive scheme is applied under its design conditions (T = 25◦C) forthe 75, 125 and 175 grey scale levels. As denoted by the arrow in Fig.7.5, there is a large errorfor the 225 level as no optimized overdrive was possible. If the overdrive scheme is applied athigher temperatures, the transmission error after the first frame time increases drastically whichleads to unacceptable performance. However, for the 225 grey scale level, the error is acceptable.While the extracted overdrive values from the 25◦C scheme lead to too high transmission valuesafter the first frame, the overdrive voltage for the 225 level (which was insufficient at 25◦C) leadsto an unintended better match at higher temperatures.Comparable conclusions can be made for the static transmission error (see Fig.7.6). For theintended grey scale levels {75, 125, 175}, there is a zero error at 25◦C. However, due to the shiftof the voltage-transmission characteristic, an unacceptable error starts to occur at about 65◦C.The error on the 225 grey scale level remains acceptable for the whole temperature range.

93

Figure 7.5: Transmission error after one frame time (16ms) as a function of temperature for the overdrivescheme from Table 7.1 (LC-A 4.2µm). The dashed lines show error limits on the curves dueto noise fluctuations.

Figure 7.6: Static transmission error for different grey scale levels as a function of temperature for theoverdrive scheme from Table 7.1 (LC-A 4.2µm). The dashed lines show error limits on thecurves due to noise fluctuations.

947.2.4 Conclusion

The general idea of applying an overdrive scheme to achieve faster grey scale transitions wasintroduced in this section. Such an overdrive scheme was extracted for the LC-A 4.2µm sampleat 25◦C by using the simulation model for VA-LCDs that was presented in chapter 6. It wasshown experimentally that the extracted overdrive scheme is capable of reducing switching timesto one frame time of 16ms, a drastic improvement in performance. However, it appeared thatthe performance of such a scheme is sensitive to temperature variations. In case the schemedesigned for 25◦C conditions is applied at higher temperatures, inaccurate grey scale transitionsare obtained. First, there appears an overshoot in transmission after the first frame which leadsto much higher switching times. Furthermore, also an offset on the intended static transmissionvalue occurs. Therefore, the transition to this intended grey scale will never be completed.Although the idea of applying an overdrive scheme in VA-LCDs looks promising from Fig.7.3,it is due to its strong temperature sensitivity not applicable in practical display applicationswhere proper operation over a large temperature range is required. As a consequence, still aconventional (single voltage) driving scheme has to be used in most of today’s VA-LCDs anda restricted faster switching can only be achieved by using special liquid crystal materials thatare optimized for this purpose.

957.3 Towards a temperature compensating overdrive scheme

7.3.1 Introduction

The strong temperature sensitivity of a single fixed overdrive scheme was shown subsection 7.2.3to be the limiting factor on the applicability of such a driving scheme. It will be considered inthis section how it is possible to take the effect of temperature into account in the overdrivescheme by using the simulation model presented in chapter 6.

7.3.2 Temperature dependency of ∆n

It is necessary to include the effect of temperature on the refractive indices in the simulationmodel in order to extract the transmission values accurately. Indeed, the transmission is de-termined by the retardation Γ from Eqn.2.10, which depends on the refractive indices ne andno. A change in ne and no with temperature will lead to a shift of the voltage-transmissioncharacteristic, as can be seen in Fig.7.7.

Figure 7.7: Experimental voltage-transmission characteristics at different temperatures (LC-A 4.2µmsample).

Fig.7.7 shows that the shift of the voltage-transmission characteristics stays limited in the range25◦C-50◦C, but a considerable shift is observed for temperatures exceeding 50◦C. Therefore, theapproximation in section 6.4 to neglect variations of the refractive indices with temperature willmainly have introduced an error on the simulated turn on times (determined by the slope of thevoltage-transmission characteristic) for temperatures T > 50◦C.

According to [49], the anisotropy in refractive index ∆n of liquid crystal materials is linearlyincreasing with the order parameter S (thus decreasing with temperature, see Eqn.5.17):

∆n ∝ S.

96Therefore, by assuming the datasheet value at 20◦C and requiring isotropy ∆n = 0 at the clearingtemperature Tc = 95◦C, the variation of ∆n with temperature can be calculated. Fig.7.8 showsthe resulting profile of the refractive index anisotropy as a function of the order parameter andtemperature, as it was included in the simulation model.

Figure 7.8: Modelling of the refractive index anisotropy ∆n as a function of temperature (left) and orderparameter (right).

The refractive indices ne and no are determined as:

ne = < n > +2∆n

3(7.2)

no = < n > −∆n3, (7.3)

where < n > denotes the average refractive index. According to [49], the average refractive index< n > decreases linearly with increasing temperature. This linear relationship was confirmedfor VA materials similar to LC-A 2 and a very comparable slope was observed for the consideredmaterials. Therefore, this slope was also assumed for LC-A to calculate the variation of < n >

with temperature. The values of ne and no as a function of temperature then follow fromEqns.7.2 and 7.3, by using the obtained values of < n > and ∆n (Fig.7.8).

2From private discussion with the supplier of the liquid crystal materials

977.3.3 Applying overdrive schemes at different temperatures

It will be investigated in this subsection if it is possible to extract functioning overdrive schemesoptimized for different temperatures by solely using the results of simulations. Therefore, asimilar extraction procedure as in subsection 7.2.2 will be performed on the simulated time-transmission characteristics for different temperatures obtained with the simulation model.As an illustration, Fig.7.9 shows the transmission curves required for extracting the overdrivescheme at 45◦C and 65◦C.

Figure 7.9: Simulated and experimental voltage-transmission characteristics at 45◦C and 65◦C. The leftresp. right plots show the transmission after one frame time resp. static transmission values(LC-A 4.2µm sample).

As apparent from Fig.7.9, the transmission values are both in the static case and after oneframe time simulated accurately. Similar satisfying results were also obtained for other tem-peratures in the interval 25◦C-75◦C. Using the simulated results, extra overdrive schemes wereextracted for {35◦C, 45◦C, 55◦C, 65◦C, 75◦C}. These overdrive schemes were tested experimen-tally under the temperature conditions for which they were designed. The results are shown inFig.7.10. The overdrive schemes work successfully as the intended transitions were achieved forall temperatures, as shown in Fig.7.10. This opens the road to make overdrive schemes appli-cable for VA-LCDs. Furthermore, it illustrates the power of the simulation model presented inChapter 6: simply by performing simulations according to this model, it is possible to extractvaluable overdrive schemes at any desired temperature.

98

Figure 7.10: Experimental switching profiles at various temperatures obtained by applying the appropri-ate overdrive schemes (LC-A 4.2µm sample). The different curves show the transition todifferent target grey scales (as denoted in the legend).

99If overdrive tables are stored for a limited number of temperatures, it is not possible to adjustthe overdrive schemes for every intermediate temperature. Instead, a stepwise strategy could beconsidered where, depending on the conditions, the most appropriate driving scheme is selectedfrom a set of fixed overdrive tables. It is important to consider the quantitative error on thetransmission as a function of temperature for such a modified overdrive scheme. An experimentwas performed where the most appropriate driving scheme from the set designed for {25◦C,35◦C, 45◦C, 55◦C, 65◦C, 75◦C} was chosen for every temperature in the range 25◦C-75◦C (steps∆T = 5◦C). There are two possibilities for temperatures that do not match the conditions ofthe fixed overdrive schemes. First, a backward scheme can be applied where the closest highertemperature scheme is chosen (e.g. apply the 55◦C scheme at 50◦C for which a specific schemedoes not exist). In a similar way, also a forward compensation scheme can be applied (applythe 45◦C scheme at 50◦C). Fig.7.11 shows the deviation from the intended grey scale for theforward compensation scheme after one frame time and for the static case.

Figure 7.11: Transmission error as a function of temperature for the forward compensating scheme:(a) error after 16ms, (b) static transmission error (LC-A 4.2µm sample).

As expected, Fig.7.11 shows that the grey scale error (both the static and the value after 16ms) isreduced to approximately zero in case an overdrive scheme can be used that matches the sampletemperature. For temperatures in between two schemes, a larger error appears. Although still aconsiderable error after the first frame time can appear, the static error can be kept below 15 greyscale levels for all temperatures. If these error values are compared to the errors of the fixed 25◦Coverdrive scheme in Figs.7.5 and 7.6 (maximum error of 150 grey scales after 16ms and a staticerror of 25 grey scales) and the conventional static driving scheme (same maximimum staticerror of 25 grey scale levels), a considerable increase in performance is observed. This illustratesthe potential of the presented temperature compensating overdrive scheme for application inVA-LCDs.

100To compare with the forward compensating scheme, also the backward compensating schemewas evaluated quantitatively. Similar to Fig.7.11, Fig.7.12 shows a quantitative transmissionerror analysis as a function of temperature for this scheme.

Figure 7.12: Transmission error as a function of temperature for the backward compensating scheme:(a)error after 16ms, (b) static transmission error (LC-A 4.2µm sample).

Fig.7.12 shows a comparable error profile as a function of temperature as presented in Fig.7.11.However, a few things are worth noting. First, if the transmission error is considered after 16ms,an undershoot error appears in general instead of an overshoot error (except for some cases).Furthermore, the absolute value of the error after 16ms is in general smaller than in the forwardscheme which also leads to smaller transition times (due to a smaller relaxation time requiredto reach the static value). However, when the static transmission error is considered, the errorvalue is in general larger, especially for temperatures exceeding 45◦C. Consequently, a trade-offwill have to be made between both schemes for practical applications.

Until now, the difference between the forward and backward scheme was quite arbitrarily, asonly a difference appeared between the schemes for values exactly in the middle between twooverdrive schemes (as otherwise the scheme closest to the sample temperature was chosen).However, a possible optimization could be to introduce a certain asymmetry for different greyscale values in this scheme. As an example, consider the error on the transmission values forthe 125 grey scale level around 50◦C for both the forward (Fig.7.11) and backward (Fig.7.12)compensating scheme. Although similar static errors are obtained for both schemes, it is clearthat the error after 16ms is smaller for the backward scheme, so this scheme is preferable. Forthe 225 grey scale however, the opposite is true: applying the forward scheme results in aboutthe same error after 16ms as in the backward scheme, but a much lower error on the statictransmission is obtained around 50◦C by applying the forward scheme. Such a differentiationfor switching to various grey scales will lead to a further increase in overall performance.

101In the temperature compensating schemes presented above, overdrive tables were extractedwith a temperature step ∆T = 10◦C. At a certain memory cost, a smaller step can be used (e.g.∆T = 5◦C) to further reduce the transmission errors.

It should be emphasized that all overdrive schemes used in experiments were extracted only byusing the results of simulations. In this way, satisfying results were obtained.

7.4 Conclusion of Chapter 7

The general idea of applying an overdrive scheme in VA-LCDs was introduced in this chapter.Although satisfying switching can be achieved for a small temperature range, it was shown thatthe performance of a conventional overdrive scheme is too sensitive to temperature variationsto be applicable for commercial display applications.Using the ability to include the effect of temperature on the switching behaviour in VA-LCDsin simulations as presented in Chapter 6, overdrive schemes were extracted for various temper-atures in the 25◦C-75◦C interval. By sensing the operation temperature and selecting the mostappropriate overdrive scheme, the highly temperature sensitive overdrive scheme introduced insection 7.2 could be extended to allow for temperature compensation. In this way, an overdrivescheme becomes applicable for VA-LCDs under all conditions. It was shown that the trans-mission error for such a scheme is considerably lower than for the conventional static drivingscheme used nowadays. Furthermore, much faster switching between different grey scales canbe achieved. Consequently, as the switching performance can be increased considerably by us-ing the temperature compensating overdrive scheme, such a scheme has a high potential forapplication in VA-LCDs.

Chapter 8

Conclusions

Vertically Aligned (VA) and In-Plane Switching (IPS) Liquid Crystal Displays (LCDs) have ahigh potential for wider use in mobile and television applications. Some aspects of the switchingbehaviour of VA and IPS-LCDs were investigated by means of experiments and simulations toobtain a better understanding of these technologies. This should ultimately lead to a progressionin performance of these technologies.

IPS samples with an electrode width varying between 4µm-8µm, electrode gap of 4µm to 20µmand an optimum cell thickness of 5µm were considered. It appeared from experiments andtwo-dimensional simulations that the sample with an electrode width of 6µm and electrode gapof 4µm shows the best performance. An investigation of the simulated transmission profile ofthis cell on micrometer scale pointed out that optimum performance was obtained due to aninterplay between both the Fringing-Field Switching (FFS) and IPS effect. Therefore, the cellconsidered can be referred to as having a hybrid FFS/IPS geometry. Comparison of this opti-mum cell geometry with an existing standard IPS design showed that the hybrid geometry isvery interesting as high transmission values are obtained both above and between the electrodes,in contrast to standard IPS cells where a low transmission is observed over the whole electrodearea. However, it appeared that an optimization of the liquid crystal material used in the hybridcell is required to get maximum performance for this cell. A further optimized design could leadto an increase in performance compared to conventional optimum IPS cells.

The switching time for reorientation of the liquid crystal molecules in VA-LCDs increases dras-tically if the amplitude of the driving voltage exceeds a certain threshold value VBF , becauseof the occurrence of the backflow phenomenon. The fluid flow created by the reorienting liquidcrystal molecules in the center of the cell forces the liquid crystal molecules in the upper partof the cell to reorient to a less energy favorable direction. A slow twist deformation is requiredto orient all liquid crystal molecules parallel to each other, as this is the most energy favorableorientation. This leads to a strong increase in switching time. The occurrence of backflow andits negative impact can be inhibited by reducing the amplitude of the applied voltage stepsbelow the threshold value VBF .It is necessary to include the hydrodynamic Leslie-Ericksen theory, which requires the knowledgeof four Miesowicz viscosity coefficients ηij , in simulations in order to model the backflow affectedswitching behaviour. In contrast to conventional simulations that use the MBBA viscosity co-efficients, material specific values obtained with a recent estimation procedure were included ina one-dimensional simulation model. In this way, a better agreement between experimental andsimulated switching profiles was obtained, even when backflow occured.

102

103The temperature range for which acceptable display performance is guaranteed puts a high re-quirement on LCDs for mobile applications. Therefore, it is important to know the effect oftemperature variations on the switching behaviour. An experimental study was performed forVA-LCDs to probe the effect of temperature on the switching properties. Two important obser-vations were made: first, the switching time decreases with temperature for all voltages. Second,the backflow threshold voltage VBF is shifted to higher voltages for higher temperatures. Thesetrends were confirmed by similar experiments on a different cell geometry filled with a anotherliquid crystal material. It can be concluded that a better switching behaviour of VA-LCDs isobtained at higher temperatures.In order to take temperature effects into account in simulations, the variations of the mate-rial parameters and viscosity coefficients with temperature need to be known. However, verylimited quantitative information on the effect of temperature on the liquid crystal material isknown, as it is very hard to measure these variations accurately. Therefore, an approach basedon a combination of fittings and relatively simple measurements (turn off time, transmission-voltage characteristic etc.) was developed, which allowed to extract material parameters suchas the anisotropy in dielectric permittivity ∆ε, the rotational viscosity γ and the Frank elasticconstants Kii(i = 1, 2, 3) indirectly. Such a heuristic approach is very interesting as valuableinformation can be extracted in a relative fast way with basic equipment present in a researchlab. It was shown that the presented approach provided accurate results, except for the rota-tional viscosity of faster liquid crystal materials. It became clear that the procedure to estimatethe viscosity leads to inaccurate results for the considered material at temperatures exceeding25◦C. Modifications to this procedure were introduced, leading to more accurate ηij coefficientsfor the whole 25◦C-80◦C temperature range. The simulations that were performed using theextracted material parameters and estimated viscosity coefficients lead to an accurate modellingof the switching behaviour for all temperatures, for the voltage range which is important forpractical display applications. Verification of the model for a different liquid crystal materialonly lead to partly satisfying results because the extraction of the temperature dependency ofthe material was not completely successful. The limited accuracy on the extracted value of γrestricted the ability to perform simulations over the whole temperature range. Furthermore,this also affected the validity of the obtained turn on times which were simulated as too lowand lead to a reduced accuracy on the modelling of the shift of the backflow threshold voltagewith temperature. Unfortunately, the low accuracy on γ severely limited the ability to assessthe validity of the temperature model itself.

The overdrive scheme is a common driving scheme to obtain faster grey scale transitions inLCDs. An overdrive scheme was extracted by using simulations for switching between the off-state and various grey scale values at 25◦C for a VA sample. It was shown experimentally thatit is possible to reduce the switching times to one frame time by applying this overdrive scheme,creating a considerable increase in performance. However, it was pointed out that such a schemeis too sensitive to temperature variations to be practically applicable in VA-LCDs as inaccurategrey scale transitions are obtained if the scheme is applied at higher temperatures. Indeed,an overshoot in transmission appears after the first overdrive frame, leading to unacceptableswitching times. Furthermore, also an offset error on the intended grey scale occurs. Inspiredby the good results if the overdrive scheme is applied under its design conditions, overdriveschemes were extracted for various temperatures in the interval 25◦C-75◦C, again using solelyresults obtained with the presented simulation model. It was shown experimentally that all

104driving schemes work properly in the appropriate temperature range. This illustrates the powerof the simulation model presented: simply by performing simulations according to this model,it is possible to extract overdrive schemes at any desired temperature. By sensing the opera-tion temperature and selecting the most appropriate overdrive scheme, the strong temperaturesensitivity can be eliminated and a temperature compensating overdrive scheme is obtained.Experimental results show that satisfying grey scale transitions are obtained with this schemefor the whole temperature range. First, the grey scale error of this scheme is considerably lowerthan for the conventional static driving scheme used in VA-LCDs used nowadays. Second, muchfaster switching between different grey scales can be achieved. As the switching performanceis clearly increased considerably by applying the temperature compensating overdrive scheme,such a scheme has a high potential for application in future VA-LCDs.

An extension to two or three-dimensional simulations (including flow) would definitely providean interesting follow-up on the VA part of this work. This would provide a better understandingof the influence of domaining on the switching behaviour and should lead to a further increasein accuracy of the modelling of the dynamic switching behaviour (including backflow effects) ofVA-LCDs. We presented a fitting procedure to extract η22 because the estimation procedurereported by Wang et al. lead to inaccurate estimates for the material we considered at tem-peratures exceeding 25◦C. It would be interesting from a theoretical point of view to furtherinvestigate if the fitting procedure could be extended to extract all viscosity coefficients as afunction of temperature. This could provide an interesting alternative for the (not always accu-rate) estimation procedure.The study on the effect of temperature on the switching behaviour could also be extended toother switching modes. In most cases it will be more easy to model the influence of temperaturein simulations (1D, 2D or 3D), as the switching characteristics will not be affected by backflow.The simulation results could also serve for these modes for the extraction of overdrive schemesat different temperatures.

Appendix A

Jones matrix implementation

A.1 Theory of the Jones matrix formalism

The electrical field of a polarized plane wave propagating along the z-axis in an isotropic mediumcan be written componentwise as:

Ex = Ax exp(jφx) exp[j(ωt− kz)] (A.1)

Ey = Ay exp(jφy) exp[j(ωt− kz)]. (A.2)

If the common phase factor is omitted, the information about the plane wave can be summarizedby a complex column matrix, called the Jones vector:[

Ex0

Ey0

]=

[Ax exp(jφx)Ay exp(jφy)

].

In anisotropic media, the longitudinal electrical field component Ez is not necessarily zero.However, it is sufficient in Jones calculus to know the complex components Ex and Ey becausethe longitudinal field component can be directly calculated from the wave intensity.As mentioned in subsection 2.2.4, the Jones matrix method can describe the optical transmissionthrough subsequent birefringent layers. The influence of one birefringent layer on the electricalfield (described by the Jones vector) can be represented by a Jones matrix J . This matrixrelates the field components of the incident field E0 and emerging field E of the layer under theassumption that all light is transmitted (reflections are not considered):

E = J.E0 (A.3)

⇒

[Ex

Ey

]=

[J11 J12

J21 J22

] [Ex0

Ey0

]

If an uniaxial material with thickness ∆z is considered with the extra-ordinary axis along thex-axis, the refractive indices of the eigenmodes are given by Eqns.2.8 and 2.9 where θ = π/2:n1 = no and n2 = ne. Consequently, the Jones matrix is found as:[

Ex

Ey

]=

[exp

(−j 2π

λ ne∆z)

00 exp

(−j 2π

λ no∆z)] [

Ex0

Ey0

]. (A.4)

105

106In the general case where the extra-ordinary axis lies in the xy-plane, a transformation of thecoordinates is necessary before the optical transmission can be calculated. If the azimuth anglebetween the optical axis and the x-axis is denoted by φ, the transformation consists of a simplerotation of the axes over an angle φ around the z-axis so that the optical axis coincides with thenew x-axis. The rotation matrix is given by R:

R =

[cosφ sinφ− sinφ cosφ

]. (A.5)

In this new coordinate system, the Jones matrix of the layer is identical to the Jones matrixas in Eqn.A.4. In order to go back to the original coordinate system, the inverse rotation R−1

is performed. The complete Jones matrix of the birefringent layer in the general case is thusfinally found as:[

Ex

Ey

]=

[cosφ − sinφsinφ cosφ

] [exp

(−j 2π

λ ne∆z)

00 exp

(−j 2π

λ no∆z)] [

cosφ sinφ− sinφ cosφ

] [Ex0

Ey0

].

In case there is also an inclination angle θ between the optical axis and the xy-plane, the samecalculation can be repeated, but the refractive index ne that was used in the previous case needsto be substituted by the complete expression for n2 in accordance to Eqn.2.9.By using the correct values for the azimuth and inclination angle, an expression can be put up forevery elementary liquid crystal layer. The Jones matrix description of the whole liquid crystallayer is found by multiplying the Jones matrices of the subsequent layers in the appropriateorder:

E = JN .JN−1. . . . .J2.J1.E0.

In this way, the electrical field (and so its polarization state) emerging from the liquid crystallayer can be described. The polarization ellipses can be drawn for every cross section by meansof a parametric plot of the real parts of [Ex,Ey], where ωt varies between 0 and 2π.

A.2 Implementation of the Jones matrix formalism in matlab

The main implementation of the Jones formalism is done in J sys.m. This function calculatesfor every cross section the Jones matrix of the subsequent layers using the information on thedirector profile as calculated by 2dimMOS.

J sys.m requires following input arguments:

• no: integer containing the ordinary refractive index of the liquid crystal used.

• ne: integer containing the extra-ordinary refractive index of the liquid crystal used.

• lambda: integer containing wavelength (in meters) of the light propagating through thelayer.

• slabThickness: integer containing the thickness (in meters) of a single liquid crystal slab(cell thickness divided by number of slabs).

• polAngle: integer containing the twist angle φ (in radians) of the bottom polarizer relativeto the conventional coordinate system as defined in Fig.2.2. The analyzer is implicitlyassumed to be oriented perpendicular to the first polarizer.

107• polOn: if the integer polOn is equal to one, the analyzer is included in the description of

the optical system. If polOn is different from one, this is not the case so the polarizationstate before the analyzer can be calculated afterwards.

• textfile: matlab string containing the name of the text file which contains the directorprofile as exported by 2dimMOS.

Four output arguments are assigned after executing J sys.m:

• T: vector containing the transmission profile along the cell.

• sys: cell (array of matrices) containing the Jones matrix description of every cross sectionalong the cell.

• tilt: matrix containing the tilt profile of every cross section along the cell.

• twist: matrix containing the twist profile of every cross section along the cell.

A code extract from J sys.m is given on the next page.

108

109As can be seen on code line 5, J sys.m uses the function importDataToFile to import data fromthe text file. This import function is described in the next section.

A.3 ImportDataFile.m

The function output=importDataToFile(data,type) used in J sys.m imports data from the textfile ’data’ into a variable with the desired name ’output’ in the matlab workspace. The argument’type’ indicates the formatting of the text file (number of headerlines and delimiter). Six differenttypes of text file formatting are supported:

• ’M time’: time-transmission characteristic formatting as exported by LabVIEW

• ’M volt’: voltage-transmission characteristic formatting as exported by LabVIEW

• ’S time’: time-transmission characteristic formatting as exported by DIMOS

• ’S volt’: voltage-transmission characteristic formatting as exported by DIMOS

• ’S volt 2D’: voltage-transmission characteristic formatting as exported by 2dimMOS

• ’S LC 2D’: director profile formatting as exported by 2dimMOS.

A code extract from importDataToFile.m is given on the next page.

110

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