ELECTRICAL BEHAVIOUR LANGMUIR FILMS A REVIEW,

Electrocomponent Science and Technology1975, Vol. 2 pp. 1-31

(C) Gordon and Breach Science Publishers Ltd.Printed in Great Britain

ELECTRICAL BEHAVIOUR OF LANGMUIR FILMS"A REVIEW, PART I

V. K. AGARWALf

International Centre for Theoretical Physics, Trieste, ltaly.

(Received July 1, 1974; in final form August 22, 1974)

The electrical behaviour of thin films obtained by a variety of processes, e.g. thermal evaporation in vacuum, havebeen extensively studied. However, the study of organic mono- and multilayer films obtained by theBlodgett-Langmuir technique (commonly referred to as Langmuir films) has gained considerable momentum onlyduring the past decades. Unlike evaporated films, the striking features of these organic films are their controllablethicknesses down to one monolayer (,-, 25 A) and the possibility of obtaining them free from holes and conductingimperfections. The aim of this paper is to describe the film deposition techniques, some of the properties of thefilms so obtained and to review their electrical behaviour. It is also intended to make this review a comprehensiveand up-to-date source of information for those who are either already engaged in this field or are planning to makeLangmuir films the subject for future investigations.

In this survey, emphasis is put on problems worth further study to obtain greater insight into the basic propertiesof these films. Further, since they possess some interesting electrical properties, this paper may prove useful in theassessment of our depth of knowledge about them and in reducing the existing gap between basic research andtechnological applications. Thus their potential usefulness in the development of devices is also discussed.

The survey is divided into two parts. Part is concerned with deposition techniques, the physical properties ofLangmuir films and certain electrical properties, namely dielectric behaviour and electrical conduction phenomena.Part II, which will appear in the next issue, will be concerned with electrical breakdown behaviour, voltageinduced changes in electrical behaviour (forming) and ionic transport phenomena in the films and will finish withsuggestions as to future trends in work with such films together with a summary of possible applications.

To assist the reader, the two parts have been numbered consecutively with regard to sections of the text, figuresand references.

1. Introduction 2

Film Deposition Techniques 42.1 Blodgett-Langmuir Technique 4

2.1.1 List of precautions 52.l.2 Selection of substrate and cleaning procedure 6

2.2 Evaporation method 6

Physical Properties of Langmuir Films 73.1 Nature and Orientation 73.2 Uniformity and Thickness 73.3 Film Structure 83.4 Defect Nature 83.5 Skeletonization Process 9

Dielectric Properties 104.1 Early Measurements 104.2 Recent Measurements 124.3 Theoretical Work 15

4.3.1 Monomolecular films 164.3.2 Multimolecular films 16

4.4 Dielectric Loss Measurements 17

Present address: Research Institute of Electronics, Shizuoka University, Hamamatsu-432, Japan.

2 V.K. AGARWAL

Electrical Conduction Properties5.1 DC Conduction Theories in Thin Films

5.1.1 Fowler-Nordheim type tunnelling5.1.2 Richardson-Schottky effect5.1.3 Space charge limited currents5.1.4 Poole-Frenkel effect

5.2 Conduction Mechanisms in Langmuir Films5.3 High Field Conduction Characteristics

References

1919202020212126

29

KEY:

e dielectric constantC capacitanced monolayer thicknessN no. of monolayers transferredA area of the film capacitorn number of carbon atoms in the molecular chain1 currentV voltagek Boltzmann’s constantT absolute temperature

work functionj"= frequencyJ current densitye electronic chargen Planck’s constantm electronic mass

electron mobilityq potential barrier heightxi work function of the insulatorXm work function of the metal

INTRODUCTION

Insulating thin films in the thickness range 100 A to20,000 A have been of interest to the scientificcommunity because of their potential applied signifi-cance for developing optical, magnetic and electronicdevices. Some of the unusual electrical propertiespossessed by thin films, which are unlike those ofbulk materials, led to ideas about their technologicalapplications and consequently interest in thin filmstudies grew rapidly. Earlier studies were not veryinspiring because the films obtained always had pin-holes, stacking faults and other impurities, and hencethe results were not reproducible. In the last fewdecades, however, many sophisticated methods havebecome available for the production and examinationof thin films, and greater reproducibility can beachieved. Nevertheless, the unknown nature of in-herent defects in a wide variety of thin film systemsstill complicates the interpretation of many experi-mental data and thus limits their use in devices.

In a recent bibliographical survey on breakdownconduction in thin films, the author found that themajor subject of investigation have been films pre-

pared by thermal evaporation in vacuum. Langmuirfilms have remained less known among workers inthis field. In fact, films formed by oil on watersurfaces were known as early as 1774 when BenjaminFranklin reported their presence. Lord Rayleigh2 wasthe first to propose that these films were only onemolecule thick. Rayleigh’s hypothesis of mono-molecular spreading thus gave birth to a new branchof science involving the study of the physics andchemistry of surfaces3. Subsequently, Langmuir4

introduced the simple technique of transferring thesemonolayers onto a substrate by moving the latteracross the film-covered surface. This technique oftransferring the monolayers onto the solid surface bya repeated dipping and withdrawal process was latermodified by Blodgett and Langmuir5,6 and hasbecome the basis of a new field of thin filminvestigations. This novel technique of "building-up"mono- and multilayer films is commonly known asthe Blodgett-Langmuir (henceforth B-L) technique,and the films thus formed are often referred to asLangmuir films.’

Using this simple technique, it is now possible toobtain monomolecular spreading of a number oforganic substances, such as fatty acids and theirsoaps, branched and unsaturated fatty acids, esters,dyes and many proteins.

It appears that this is the only technique by whichit is possible to deposit films on smooth substrateswhich are uniform, structurally oriented and whosethicknesses are accurately known and controllable. Itis now well established that films which are largelyfree from defects and other conducting imperfectionscan be obtained, and a wide range of electricalcharacteristics can be studied in a variety of organicmaterials in thin film form. However, we shall here beconcerned only with "solid" monolayers in which themolecules are closely packed, and which can bedeposited on solid surfaces. Among the many sub-stances which form a stable monolayer, the straight

-These films are also quoted as ’L.B. films’ and thetechnique as the Langmuir-Blodgett (L. B.) technique’ in theliterature elsewhere.

ELECTRICAL BEHAVIOUR OF LANGMUIR FILMS 3

chain fatty acids and their metal soaps are used formost electrical measurements. This is probablybecause the fatty acids precipitated by calcium orbarium ions in the solvent were used initially4,5,6and the technique was perfected for them.

Although in principle any substance forming aninsoluble, stable and condensed monolayer can beused for building up multilayers, in practice this isnot necessarily so. For example, the moleculescontaining a hydrophilic group such as-OH or-COOH at one end of the chain and a hydrophobicgroup such as CH3 at the other have been found toform good monolayers, the molecules being arrangedalmost vertically on the water surface and becomingclosdy packed when the monolayer is compressed.But not all such substances behave this way. If themolecule is too short, the Van der Waals forces alongtheir lengths will be insufficient to hold them togetheras a "solid" film and with long molecules, the bucklingof the molecules themselves may give rise to acrumpled film on compression. Therefore, onlymolecules of intermediate chain length can be used toobtain an oriented, close-packed, solid monolayer onthe water surface. However, there are no clear cutcriteria for the choice of substances forming goodLangmuir films. Reference should be made to theexcellent text of Gains7 for the choice of material,and a recent review by Srivastavas is a comprehensivesource of information for beginners in this field. Inaddition, the reader is referred to several morereviews and texts 9-14 that have appeared.

Langmuir films were successfully prepared as earlyas 1935 but study of their dielectric properties at thattime did not yield reproducible results. Renewedattempts were made in the sixties but it was not untillate sixties that reliable results were obtained. Thiswas because many further advances in the originalB-L technique were made during the last decade toobtain a good film for reliable electrical measure-ments. A handful of experimental data on electricalbehaviour of Langrnuir films during the last few yearshas yielded some very interesting electrical charac-teristics which will be discussed exhaustively in thispaper. There is no other useful survey available in theliterature giving an up-to-date account of their elec-trical behaviour. Even books and reviews publishedrecently or in the past covering the whole subject ofthin films do not mention work on Langmuir films.The one review devoted to Langmuir filmss containsonly limited information about their electrical charac-teristics.

Essentially, the two crucial factors governing thinfilm properties are their uniformity of thickness and

structural perfection. Particularly, all the electricalproperties are very sensitive to these parameters andthus, for a judicious experimental study, one requiresfilms of accurately known thickness and free fromgross defects. Langmuir films are known to fulfillthese requirements to a far greater extent than othertypes of thin films. For instance, Mann and Kuhn s

have recently shown through their electrical studiesthat the films obtained by the modified B-L tech-nique were free from any holes and conductingimperfections. Secondly, the uniform thicknesses ofthese films are accurately known, as measured bystandard optical methods like Tolansky’s multiplebeam interferometry,16,17 and may be controlledand reproduced successfully to as little as onemolecule thick (about 25 A). In addition to manyother features described in the text of the paper,these two constitute a sound basis for studying thesefilms. Control of these two parameters in other filmsystems is notoriously difficult to achieve.

To fulfill the aim of this paper, the film depositiontechnique of Blodgett and Langmuirs,6 will bediscussed in detail. The recently proposed evapor-ation technique18 to obtain such organic films downto one molecule thick and with better purity than theevaporant, will also be described. The physical prop-erties of these films, which are relevant in thecontext of their electrical behaviour, are described inthe next section. Each of the following sections covera particular aspect of the electrical behaviour andincludes a detailed account of experimental andtheoretical work. To make this survey more sub-stantial, it has been thought desirable to discussbriefly the existing theories about conductionmechanisms, breakdown behaviour, etc., in theappropriate sections. This will certainly prove usefulfor the better understanding of the subject and mayfurther help the researchers to select suitable prob-lems for their studies on Langmuir films.

As many reviews and books have already beenpublished on the whole range of electrical measure-ments in thin films, this paper is devoted to Langmuirfilms only. However, to adopt a broad viewpoint,some pertinent references have been cited to makecomparisons between the results on Langmuir filmsand on other film systems. To make the survey anup-to-date source of information, all possible ref-erences since 1937 (when the earliest work on elec-trical properties was reported) have been provided.

Finally, some space has been reserved to discussbriefly the future potential of these films in thedevelopment of devices. In spite of the fact thatfurther electrical studies on Langmuir films would

4 V.K. AGARWAL

prove useful for a better understanding of the under-lying electrical phenomenon in thin films, it is alsovery likely that the use of such ordered film systemsin developing devices could lead to a major break-through in the advancement of thin film technology.

2 FILM DEPOSITION TECHNIQUES

2.1 Blodgett-Langmuir TechniqueThis technique requires a very simple apparatus con-sisting of a long narrow trough T (Figure 1) usually

(b) (c) (d)

FIGURE Diagrammatic representation of the apparatusfor building up the Langmuir films [modified after Lang-muir 1.

made of inert materials such as teflon, perspex, etc.Metals such as copper or aluminium are not usedbecause they may contaminate the solution withmetallic ions whose presence would stop the de-position. The inside of the trough is heavily waxed;’this waxing is necessary in order to obtain a higherwater level at the edges, which ensures that there isno leakage of the monolayer past the barriers. Thebarriers, rectangular in shape, such as glass slides,must also be waxed all around to render them hydro-phobic. The trough is first levelled and then filled tothe brim with doubly distilled or deionized water(specific resistance 6 x 10 fZ cm), having a lowconcentration of barium by adding 3 x 10 -s Mbarium chloride or the like. For easier deposition, thepH of the solution is adjusted to greater than 6 by theaddition of a specific quantity of an alkaline sub-stance. For example, KHCO3 at a concentration of4 x 10-4M holds the pH at 7.2. This results insmooth deposition of Y-type films. The surface of theliquid is now thoroughly cleaned by sweeping thewaxed barrier B across the long edges of the troughand finally leaving it resting on the trough end(Figure la). Another barrier, A, rests at the other endof the trough which is used to hold the waxed silk

+In the case of teflon trough, the waxing is not required.

thread S placed upon the water surface as shownbetween A and B. The thread is waxed so that it doesnot wet and sink into the water, and is carefully madeto touch the water surface at every point to avoid anypossibility of leakage of the spread monolayer. Thetechnique here is specifically for barium stearatefilms, but is similar for all other potential Langmuirfilms.

Stearic acid (or other material to be deposited)dissolved in benzene (concentration 3 x 10 -4 byweight) is placed by the micrometer syringe on thewater surface near D in the form of a small dropletwhich spreads spontaneously and pushes the threadoutwards to take the shape as shown in Figure lb. (Ifthe first drop does not spread quickly, it is anindication that the surface is not perfectly clean.) Assoon as the spreading is complete, the thread isfastened to the trough edges by two small clips C2. Atthis stage the divalent barium ions present in thesolution undergo surface reaction with stearic acidmolecules to form the barium stearate soap, and thesolvent (benzene) slowly evaporates, leaving behind amonolayer on the surface, its boundary being con-fined by the thread. If a second drop is put near Dafter the spreading is complete, it would not spreadbut remain as a residue, which is an indication thatthe available surface has been covered with themonolayer. The stearate molecules at this stageremain standing upright with their reactive carboxylgroups touching the water surface, but some of themalso tend to bend over the water surface due to therelatively large space available for them. A small dropof oleic acid called "piston oil" is now placed on thesurface at P which thus exerts a constant lateralcompression of 30 dyn/cm on the spread mono-layer. It has been found that this value of surfacepressure (’-30 dyn/cm) is sufficient to compress amono-layer of stearic acid into a solid phase with themolecules relatively closely packed. The threadboundary now separates the whole surface area be-tween barriers A and B into two regions, with astearic acid monolayer on one side of the thread andoleic acid on the other, these pressing each other togive an equilibrium shape to the thread (shown inFigure c). The transfer of the monolayer onto the"conditioned" slide may now be accomplished bymoving the dipper near D up and down repeatedlyacross the monolayer covered surface. "Conditioning"here means that the slide has been made hydro-phobic. This is achieved simply by rubbing the slidesurface with a waxy solid, e.g. ferric stearate. It hasbeen found that a pure aluminium or silver filmdeposited on the cleaned slide by thermal evaporation

ELECTRICAL BEHAVIOUR OF LANGMUIR FILMS

also behaves as a hydrophobic surface for goodmultilayer deposition.

The monolayer is thus transferred onto the"conditioned" slide on both its downward and upwardjourney, and the process may be continued until thethread S moves forward through an area to attain theshape shown in Figure d. Every time the threadmoves forward through an area equal to that of theslide on which the film is deposited, the threadmotion takes place because of the constant com-pression provided by the "piston oil." This visiblemotion of the thread is a very clear cut indicationthat the layers are being transferred on to the slideevery time it is dipped or withdrawn. The film thusbuilt up is termed "Y-type", and contains an evennumber of layers. Film thickness can then be accu-rately calculated by counting repeatedly the numberof monolayers, and multiplying it by the knownmonolayer thickness. To obtain an odd number ofmonolayers outside the water surface, it is necessaryfirst to dip the slide in the solution and then tospread the stearic acid- as shown in Figure lb. Inthis case, the first layer will be transferred when theslide is moved upwards, and finally an odd number oflayers will be obtained. Even to obtain one mono-layer, this process has been found satisfactory by theauthor in his studies of these films. To obtain X typefilms, it is necessary to make the solution morestrongly alkaline (pH 9) and then the transfer willoccur only during the downward movements of theslide. It is necessary to maintain the ambient temper-ature at 20-22C during experimentation, and thesubstrate should be raised or dipped across themonolayer very slowly and smoothly. To obtain alarge number of layers on a solid substrate i.e.thicker films, the author has found that use of atrough of large dimensions, and thus a large surfacearea for monolayer spreading, is not effective becausethe perfect cleaning of the surface becomes moredifficult, and the molecules develop a tendency tocollapse. More satisfactory results have been obtainedby using a trough of smaller dimensions (say29 x 20 x 6 cm, as used by Nathoo19) and using afresh solution after every deposition cycle is com-pleted. It is also advisable to prepare the solution allat once in a large quantity to avoid any possiblechanges in its pH value, which may affect the natureof monolayer deposition.

The technique described above appears attractivelysimple in principle. However, it requires experimentalskill to obtain structurally stable and smooth films. Itis therefore necessary to mention some of theimportant precautions to be taken during film pre-

paration. For further details reference should furtherbe made to the text book of Gains7 and to theoriginal papers of Blodgett and Langmuirs,6,2 o Onecan also make use of commercially available highlysophisticated film balances 13 for film deposition.

2.1.1 List of Precautions1) The wax and chemicals used in the experi-

mentation must be of highest quality and of extremepurity. For still higher purity, the solvents (benzene,etc.) should be fractionally distilled.

2) The water used should have good conductivity.For best results deionized water should be treatedwith KMnO4 (10-3 M) and NaOH (10-2 M) and afterheating it for about 10 hours at 70C, it must bedoubly distilled in a quartz apparatus. It must beremarked here that deionized water, if used directly,may contain some organic impurities.

3) Greatest care must be taken against dust con-tamination as the introduction of any foreignmaterial from the outside may cause disruptionof the film structure. It is thus necessary to cover thewhole experimental set-up with a suitable transparentshield box and to design it in a way that all theoperations needed during experimentation, e.g. themovement of the dipper, be operative from outside.

4) Any sort of mechanical vibrations or otherdisturbances during deposition may result in cracks inthe deposited film giving rise to voids and inhomo-geneities in the film. For this, the experiment shouldpreferably be performed on a rigid foundation or, if atable is used, anti vibration mountings must be used.

5) The required pH value must be maintainedaccurately by adding the specified concentrations ofthe substances. Any change in its pH may markedlyaffect the nature of the deposited film. Specifically,the barium ion concentration should be properlymaintained to avoid the presence of free stearic acidmolecules in the deposited film.

6) Since the hands of the workers are themselvesthe most likely source of greasy contamination, it isnecessary to clean them as thoroughly as possible.Specific attention is also required to avoid anysurface active contamination.

7) Film transfer should be accomplished under ashigh a lateral compression as possible. The higher thesurface pressure, the more compact will be the film.The use of oleic acid as "piston oil" ensures a satis-factory film deposition without voids.

8) The first monolayer should be transferred asslowly as possible to obtain a smooth surface, because

6 V.K. AGARWAL

it acts as the foundation for building-up the multi-layers. It is also essential that the slide be completelydry before each immersion.

Since the whole phenomenon is on a molecularlevel, even small concentrations of impurities orcontamination in any form may affect the resultsmarkedly. Therefore, the key-words in the prepara-tion of Langmuir films are the purity and cleanlinessof all the components used. For greater details oneshould refer to the recent work of Nathoo 19 who hasdescribed at length the preparation of Langmuir filmsfor electrical studies. One novel feature which hasbeen introduced by Nathoo 19 is the use of a deviceto raise and lower the substrate across the mono-layer-covered surface. The PTFE piston used for thedevice is pulled upwards by the suction of a pumpand falls under gravity when the suction is reduced.This device can control the speed of the dipper in therange 0.1 mm/s to mm/s.

2.1.2 Selection of substrate and cleaning pro-cedure Obviously, one of the major factorsgoverning the degree of uniformity of the depositedfilm in the above process is the smoothness of thesubstrate used. Therefore, considerable attentionmust be paid to the selection of a substrate withsmooth surfaces, and subsequent thorough cleaningto minimize the appreciable variations in the elec-trical properties which can occur. Microglass slideshaving no scratches are first selected and rinsedthoroughly with deionized distilled water. Theplaneness and smoothness of the selected slides arethen checked by the standard method of matchingtheir surfaces with a master optical flat21. On properillumination, the formation of reasonably straight,equidistant, parallel and smooth fringes show that theslide surfaces do not have much curvature and arealmost plane22. The smoothness of such selectedmicroglass slides can be of a much higher degree thanthat of the usual optical flatz . This is, for example,revealed by the absence of "wriggle" in the fringes ofequal chromatic order (FECO) in extensive filmthickness measurements on a 4-layer barium stearatefilm 16 using "Gold Seal" microslides. The authorhimself has used "Gold Seal" microslides in electricalmeasurements and found them satisfactory forobtaining uniform Langmuir films.

The selected microglass slides are then treated withchromic sulphuric acid (cold saturated), rinsed withdoubly distilled water and immersed in caustic sodasolution for several hours. Finally, they arethoroughly washed using a strong jet of doublydistilled witer and dried by a current of warm air.

Ultrasonic cleaning with Ultrax cleaning fluid, andwashing with distilled water also gives satisfactorycleaning. Both of these methods are used by Biicheret al3 in their work in building-up monolayers ofarachidic acid. The degree of cleanliness of a slidemay then be checked by immersing it through acleaned water surface covered with a small amount oftalcum powder, lycopodium or such like. Thepresence of any greasy contamination on the slide willbe detected by the grains of talcum being pushedaway when the slide is immersed. This simple test wasdevised by Langmuir’ and may also be applied tocontrol the cleanliness of all glass components usedfor the experiment. Absence of any "breath figures"on the slide after breathing on it is also a good test ofthe cleanliness.

2.2 Evaporation Method

The recent attempt by Baker18 to deposit thin films(of the order of one monolayer thick) of organicsolids by thermal evaporation in vacuum opens up anew field. It was reported by Luff and White thatthermal degradation of high molecular weightmaterials takes place during vacuum evaporation,whereas thermal effects are much lower in the case oflower molecular weight solids. Thus it was realizedthat thermal decomposition of stable compounds isless likely to occur. Making use of these arguments,Baker was successful in depositing thin films ofstearic acid (tool. wt 284.5)and melissic acid(mol. wt 466.8) by thermal evaporation in vacuum.The unchanged composition of both the evaporatedfilms and the evaporant residue are evidence for theabsence of thermal degradation in this case. Bakerobtained very thin fihns of the order of one mono-layer in thickness by maintaining a slow controlledrate of evaporation and other experimental require-ments. It has also been pointed out by him that thepurity of the remaining evaporant and evaporatedfilms was slightly higher than the acid salts originallyused, and has ascribed it to be due to the "outgassing"of the acid prior to deposition. Whereas thistechnique is of particular interest in the field oftribology because of the possibility of producinga monolayer film of boundary lubricant, the authorfeels that it is of equal importance for the physiciststo study the electrical characteristics of such evapo-rated films. Although Baker has not mentionedexplicitly the defect nature of these evaporatedorganic films, the absence of thermal decompositonand reported better purity are the two importantfeatures.


3 PHYSICAL PROPERTIES OF LANGMUIRFILMS

Many interesting physical properties of Langmuirfihns have been investigated and these have beenreviewed well in the existing literature 8. In thissection, only those properties which have relevance tothe electrical behaviour are discussed briefly.

3.1 Nature and Orientation

The nature and orientation of the deposited film ismainly governed by the angle of contact between themonolayer-covered solution and the solid surface;hence the condensed monlayers may be obtained, atwill, with different molecular orientation. Thesemonolayers are characterized as X, Y or Z types, andtheir molecular arrangements are shown in Figure 2.

& iCHTpe film

e COOH

y-Type film z-Type film

tb) (c)

FIGURE 2 The molecular orientation of built-upLangmuir films. (a) X type (b) Y type; and (c) Z type.

The molecules in the case of X and Z type films areoriented in the same direction and thus the surface ofthe film will be composed of carboxyl and methylgroups, respectively. On the other hand, in a Y typefilm, the molecules in adjacent layers are oriented inopposite directions, and the film surface is composedof methyl groups. Of these three types of films, theone which has been studied is the Y type in which themonolayer transfer takes place both ways, i.e. oneach dipping and withdrawal of the slide across thesurface. On the other hand, in X films, transfer takesplace only when the slide is being dipped and for Ztype, it takes place only when the slide is withdrawn.The orientation is termed "exotropic" when themethyl groups touch the solid surface and thecarboxyl groups remain away from it in the firstmonolayer. If the orientation of these two groups isreversed, the monolayer is termed "endotropic".

Thus, an X type film is made up of a series ofexotropic layers; the Y type is made up of a series ofalternating exotropic and endotropic layers, and theZ type is made up of a series of endotropic layers.However, it must be pointed out that Z type films arerather uncommon.

3.2 Uniformity and Thickness

Two crucial factors for making satisfactory electricalmeasurements on films are their uniformity andaccurate knowledge of their thickness. Both of theserequirements are fulfilled to a greater extent ifLangmuir films are used. The thickness of severalfatty acid monolayers has been measured using thebest known optical methods. For example, a sig-nificant contribution in this context has been due toSrivastava and Vermal 6,2 6. They16 have employedTolansky’s standard multiple beam interferometrictechnique with fringes of equal chromatic order(FECO), which ensured absence of any error in theirmeasurements due to surface irregularities. They thusobtained extremely sharp and smooth fringes, anddetermined thicknesses with higher accuracy. Sub-sequently, "C" spacings of these illms were alsomeasured by the same workers26 using the micro-focus X-ray technique and excellent agreement wasfound between C spacing values and those obtainedby interferometry. Recently, Scott and Sirhata 7

have used the above technique with some modi-fications. They employed a protective collodion layerin measuring thicknesses, which improved the qualityof the fringes and hence the precision of themeasurements. Use of the protective layer thusavoided damage of the monolayer in vacuum, whichis expected to have a marked influence on theovercoating deposited. In fact, it was indicated27,28

that over 60% of stearic acid film is removed byexposure to vacuum for 30 minutes.

As far as the uniformity of these films is con-cerned, it has already been stressed that the selectionof the substrate must be made carefully. However, ithas been shown by Holt29 that increasing the numberof monolayers increases the degree of uniformity ofthe film. To achieve the required uniformity thedeposition of the first monolayer is very important,since any voids or imperfections in it may lead tomajor disruption of the subsequent layers. Therefore,one must make sure that the slide emerging from thesolution is completely dry before being re-immersed.

Whereas films of barium copper stearate could bebuilt up containing as many as 3000 layers simply byrepeated dipping and withdrawal processes 5,6, some

8 V.K. AGARWAL

problems were encountered when thick multilayers ofother fatty acid salts were deposited. Blodgett andLangmuir6 noticed a "fogged" appearance for thickerbarium stearate films (300 layers) and also observedthe "cracking" tendency of these films, which in-creased with thickness. They then indicated that theaddition of copper ions (2xl0-6M) to thesolution avoided both these difficulties and facili-tated film deposition. Another factor which crops upduring deposition is the gradual crumpling orcollapse of the stearate monolayers. Henkeaavoided this simply by spreading a fresh monolayerover the solution after every forty or fifty dippings.This has already been recommended in the filmdeposition technique for obtaining a large number ofmonolayers. However, the collapse of stearate monoolayers is very unlikely to occur. Otherwise their use incommercially available step gauges, (cf. Ref. 7)which are based on the known and controllablethicknesses of the monolayer, would be impossible.

3.3 Film Structure

The obvious choice for investigating detailed filmstructure is the well-known electron diffractiontechnique. Germer and Storks31, particularly,investigated the molecular arrangement of depositedmono- and multilayer films of fatty acids and theirsoaps using this powerful technique. In their studiesin transmission as well as in reflection, by depositingfilms on thin supporting organic foils of Resoglaz andon a clean metal surface, the molecules were found tostand almost perpendicularly to the solid surface inthe first monolayer. Barium stearate moleules had amore precise normal alignment than the stearic acidmolecules. The hydrocarbon chains of stearatemolecules in the first monolayer were close packed,but irregularly arranged on a clean metal surface,whereas regular arrangement was observed in layerson top of the first one in the case of films onResoglaz foils. Thus, the layered structure of thesestearate films was shown to form simple hexagonalcrystals with the symmetry axis perpendicular to thefilm. The stearic acid molecules were found to formmonoclinic crystals, with their chain axis nearly inthe plane containing the surface normal and thedipping direction. In earlier studiess,6, it has beenshown that these films consist of superposed sheets oforiented molecules, and form positive uniaxial bire-fringent crystals with the optic axis perpendicular tothe plane of the film. However, some structuralchanges due to thermal disorientation of the mole-cules, or to evaporation were noticed at relatively

high temperatures when the temperature was raised inelectron diffraction studiesa- 3 s. This may be pos-sible, because the soap multilayer films are relativelysoft and have low melting points. On the other hand,in recent investigations by Holt29 the remarkablethermal stability of such films has been reported. Infact, these films could be heated at 90C in damp airover prolonged periods (the melting point or stearicacid is 69C) without any damage. Further, Holtobserved no change in the electrical properties eventhough the films were repeatedly and rapidly cycledfrom liquid nitrogen temperature at 50C in air.

Based on the above structural informationobtained by electron diffraction, these films wereknown to be monocrystalline in nature and thus wereregarded as a special case of a layer-by-layer mech-anical growth forming almost "two-dimensional"crystals. There is, however, evidence that bariumbehenate multilayers do, in fact, show an absence ofcrystallinity which has been demonstrated by elect-ron micrographic studies36. It has also been reportedby Knott et al. 7 that some time may be requiredafter multilayer formation for the formation ofcrystallinity, and no crystallinity was observed until30-60 minutes passed. Marc and Messier8 haveattributed the two absorption peaks, observed at-100C and -30C, to dipole movements in theamorphous and crystalline regions of the behenatelayers respectively. In fact, they had no clear cutevidence for amorphous zones in the monolayers andthe qualitative interpretation offered by them wasbased merely on the assumption of disorganizedstructures. Therefore, the author would like to stresshere that in future investigations one must be carefulin the interpretation of the electrical data in terms ofthe film structure. Renewed structural investigationswould also be desirable to make sure of the presenceof amorphous regions in these films.

3.4 Defect NatureMany of the earlier workers have reported thatorganic films obtained by the classical process ofmonolayer transfer always contained holes, cracks orother imperfections. For instance, Epstein39

demonstrated in his electron microscopic studies thatthe deposited films are discontinuous, and consist ofclumps of molecules, when the transfer was accom-plished at low surface pressures. Similarly, Ries andKimball4 observed discontinuous circular "islands" oraggregates in the stearic acid monolayer transferred at10 dyn/cm. These observations were not surprisingbecause the higher the surface pressure, the more


compact will be the film formed. In fact the mono-layers have been shown to be continuous and homo-geneous at higher pressures4t Nevertheless, it wouldbe an oversimplification to regard the film transferredat high surface pressure as perfectly uniform,coherent and defect free. Artifacts are introduced ifproper care has not been taken either during thetransfer process and the subsequent thermal evapo-ration of metal electrodes over the film may disturbthe film structure. In some radioautographic studies,the presence of spots, striations and other irreg-ularities such as "folded over" regions in thedeposited barium stearate monolayer wasdemonstrated in the earlier work of Roberts andGains27. On the other hand, Handy and Scala42 alsocarried out radioautographic studies and have shownthat these layers are generally uniform with noapparent gross defects. One reason for the presence ofsuch defects in the films as demonstrated by theseearly workers is that the original technique of B-Lhad not then been perfected. Many of the recentmodifications in this technique have made it possibleto obtain films largely free from gross defects orimperfections.

The one study giving quantitative proof of theabsence of any number of holes and conductingimperfections in such monolayers is that of Mann andKuhnis. They had employed a modified B-Ltechnique2a, and took other precautions. In theirstudies on breakdown phenomenon of Langmuirfilms (described later) Agarwal and Srivastava havealso indirectly shown the absence of "weak spots",and thus they inferred that the films are free fromgross defects. The development of striations in thedeposited film was ascribed to the irregularity of thedipping and withdrawal motion of the substrate27.Recently, Nathoo19 has introduced a novel techniquefor this, and has succeeded in obtaining acceptableand reproducible devices for electrical measurementsusing this technique and the other precautions dis-cussed above.

In spite of the fact that structural perfection maybe achieved by using Langmuir mono- and multi-layers, great attention must still be paid to identifyingthe defect structure of the films. Reliability andinterpretation of electrical data very much dependupon the nature of the defects and therefore specialcare must be taken.

3.5 Skeletonization Process

It is an established fact that films of metal salts offatty acids may contain free acid molecules, apparen-

fly in the solid solution if the metallic ion concentra-tion is low; their proportion depends upon the pH ofthe solutions,6. These free acid molecules can bedissolved out of the multilayers by soaking the filmfor a short time in benzene to which 1% of 90% ethylalcohol is added. This process is termed "skele-tonization", and the film thus obtained is said to be"skeletonized’’6, containing voids or holes in theplaces previously occupied by the acid molecules.Optical studies have shown that the films remainoptically clear even after this treatment if the amountof acid molecules contained is not more than 60%,but a striking change is observed in the interferencecolours reflected by the film. Further, it has beenshown that this change in colour is due to a change ofrefractive index and not to a change of thickness. Ifhalf of the acid content is dissolved, there is found tobe a change of less than 1% in the film thickness. Thestability of such a skeleton film is not affected, asindicated by its extraordinary rigidity even when itcontains up to 40% voids. The fact that the skele-tonized film does not collapse was checked by Raceand Reynolds43 who restored the original opticalthickness by refilling the free spaces with somenon-polar oil. In fact, these holes and voids in theskeleton films may be refilled with substances likepetrolatum, or other hydrocarbons; subsequently, ifrequired, these substances can be dissolved in benzenegiving again the same skeletonized films. This methodhas already been used to obtain films with variousrefractive indices between 1.18 and 1.512 o. However,not much attention has been paid to the study of theelectrical behaviour of such skeleton t’rims carryingforeign impurities like hydrocarbons. The author feelsthat the method is very attractive for obtainingdoped-like organic dielectrics and further explorationof their electrical properties would be worthwhile.Race and Reynolds4a have made an attempt to studythe electrical behaviour of such skeletonized films,and found the expected lowering of dielectric strengthby skeletonization. The physical concept, that theremaining soap and air (or any hydrocarbon substi-tuted) remain electrically in parallel, was found tohold true in their measurements.

As discussed above, the removal of free acid fromthe deposited films may also take place during theirtreatment in vacuum for elctrode evaporation. Thisprocess is known as "vacuum skeletonization". Infact, Roberts and Gains27,28 have noticed removal ofstearic acid from monolayers deposited on varioussubstrates. Evidently, the presence of voids or holes asreported by many workers may be an effect ofvacuum skeletonization. Many workers have failed to

10 V.K. AGARWAL

obtain useful devices for electrical measurements, andthis is presumably because the spaces previouslyoccupied by the free acid molecules may have beenfilled with the metal during thermal treatment invacuum, thus shorting the device. Because of this, it isoften stressed in the literature that Langmuir filmsmust be treated carefully in vacuum, particularlywhen electrical measurements have to be made.However, great care must have been taken in the firstplace to hold the required pH of the solution, becausethe degree of conversion to soap depends upon thepH. Since the soap or metal salts of long chain fattyacids are ionic substances forming stable monolayers(cf. Ref. 7, p. 193) it is possible that some ions arepresent in the deposited monolayer which may betransferred during deposition. It has been shown44

that with some cations, the ion composition of thedeposited film is very different from that on thewater surface, but much is unknown about the natureof such ions. The presence of such ions and theirmotion under an applied electrical field has recentlybeen pointed out by Barraud and cworkers4s intheir studies of thermally stimulated currents on MIMstructures using Langmuir films.

4 DIELECTRIC PROPERTIES

Interest in the dielectric studies of Langmuir films offatty acids and their metal salts grew rapidly in theperiod just after the advent of the B-L depositiontechnique. Such studies were taken up again onlyafter a gap of more than two decades when it wasrealized that Langmuir films could be uniform inthickness, and act as good insulators. In this sectionthe experimental measurements on resistance, capaci-tance and dielectric constant of these film systems aredescribed. These measurements have been dividedinto two parts; the first describes the work carriedout in the late forties and the second covers recentexperimental work. The dielectric loss measurementsand the theory for calculating the static dielectricconstant are discussed.

4.1 Earlier Measurements on Capacitance,Resistance and Dielectric Constant

The earliest work of Porter and Wyman (PW)46reported measurements on the impedance of filmsand related phenomena which they carried out onfilms of Cu-Ba stearate and Ca stearate using both Xand Y type films. Initially, mercury droplets wereused for small area probe measurements and an acbridge was used for impedance measurements. The

resistance of the films through the thickness wasfound to be very low (< f2) with high signalvoltages, whereas it was of the order of M f2 withsignals of or 2 V. Measurements at frequencies ofMHz and 0.244 MHz, and for films containing 7 to

141 monolayers gave dielectric constant valuesranging between 1.9 and 3.5 with an average value of2.5. Considerable variations in the results obtained onthe same film with different drops, or with the samedrop in different places, were due apparently todifferences in the droplet size, or in the exact area ofcontact between the drop and film at different places.No significant difference was found in the capaci-tance or resistance values between X and Y films. Inboth types of films the capacity decreased withthickness, as was expected from the relation used bythem for capacity determination, i.e.

C Ae/4rNd, (4.1)

in which e denotes the dielectric constant, N thenumber of layers, d the layer thickness and A the areaof contact between drop and film. On the other hand,the values of the resistance per layer showed adefinite increase with the thickness of the film. Thespecific resistance of films, thus determined fromtheir values of the resistance per layer, was about1013 2/cm2. Some dc resistance measurements werealso made by them using a drop of tap water in placeof a Hg drop and a striking difference between theresults was found. With mercury drops the filmruptured permanently when a breakdown voltage of106 V cm -1 was exceeded and the resistance waslow. No such rupture was observed with water drops.It was concluded that the different affinities of thetwo liquids for the film surface may have beenresponsible for the observed difference, and that thewater molecules were probably able to penetrate thefilms. Another conclusion arrived at was evidenceof power absorption in the films, increasing withfrequency over the range studied. This was concludedbecause the resistance of the films measured at bothfrequencies (1 and 0.244 MHz) was far less than thatdetermined from their dc measurements.

Race and Reynolds (RR)43 in 1935 made somepreliminary attempts to measure the dielectricproperties of barium stearate films, and found someexperimental limitations. For instance, the bridgeequipment used was not sensitive; the area of contactof mercury droplets was not accurately measured anddust contamination could not be avoided. Never-theless these results encouraged them to develop asophisticated experimental set-up and the necessarybridge equipment47. Multilayer films were deposited


on a clean polished chromium slide and mercurydroplets were used as the counter-electrode. All themeasurements were made over a frequency rangefrom 40 to 106 Hz using comparatively thickmultilayers (of both X and Y types) of variousstearates and arachidates. The results obtained bythem were:

1) The dielectric constant of various multilayerswas 22.55, with standard variation of 3%. Thevariation was attributed to the pH of the solution andtherefore the degree of conversion of acid to soap.

2) The dielectric constant was found to beindependent of thickness as well as of frequency inthe range studied.

Further, these workers4 3 measured the dielectricparameters of films which were soaked for from oneto ten seconds in a solvent such as benzene. Thebenzene dissolved the free acid leaving the soap filmas a skeleton with air filling the spaces previouslyoccupied by the acid. For calculating the dielectricconstant of such a skeletonized film, the remainingsoap and the air spaces were considered in parallel.The relation used was

el e0 + a 1- (4.2)

where eo and el are respective dielectric constants ofthe unskeletonized and skeletonized film; ea isthat of air and dl/do is the ratio of the densities ofthe skeletonized and unskeletonized films. Theirresults on unskeletonized (0) and skeletonized (1) filmsof cadmium arachidate are given in Table I. In thetable, to and tl refer to the apparent opticalthicknesses before and after skeletonization as deter-mined by Blodgett4 8. To check the collapse behaviourof the skeletonized films, the air space was refilled byallowing a drop of oil to run over the film, and thedielectric constant was measured again and calculatedusing Eq. (4.2) by substituting the dielectric constantof oil for Ca. RR used non-polar oil as well as a polarliquid (tetrachlorodiphenyl) to refill the air spaces inthe skeleton. The corresponding values of the di-electric constant have been represented by e2 and e3,respectively, in Table I.

As is evident from Table I, the agreement betweenmeasured and calculated values of e is sufficientlyclose. Obviously, the dielectric constant of the film(e2) increased as expected, when the air spaces in theskeletonized film were refilled with a non-polar oil(columns 8 and 9) having a dielectric constant of2.15. This was interpreted as a check on thestructural conception of a skeletonized film, i.e. theassumption that the remaining soap and air areelectrically in parallel (columns 6 and 7). However,

TABLEElectrical data on unskeletonized (0)and skeletonized (1)films of cadmium arachidate. [After Race and Reynolds .]

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)

Film Optical Filled with Filled with tetra-samples thickness non-polar oil chlorodiphenyl

to t (t,/to) (d/do)

A 75 53 0.707 0.574 2.48 1.69 1.85 2.29 2.342.48 1.74 2.202.47 1.71 2.192.49 1.87

1.73B 61 43 0.705 0.571 2.44 1.62 1.82 2.25 2.31 3.04 3.63

2.43 1.68 3.252.47 1.69

C 61 51 0.837 0.764 2.50 1.96 2.15 2.32 2.422.50 1.94 2.382.50 2.02

1.97D 59 51 0.86 0.797 2.49 2.10 2.18

Measd. Measd. Calcd. Measd. Calcd. Measd. Calcd.

12 V.K. AGARWAL

considerably higher calculated values of e3 than themeasured one (columns 10 and 11) are found with apolar liquid (dielectric constant 5.22), which wereinterpreted as indicating a reduction of the polarorientation of the liquid within the matrix ofcadmium arachidate molecules.

Buckwald, Zahl and co-workers49,s also becameinterested in measurements of the resistance andcapacity of alkali stearates consisting of varyingnumbers of layers, and deposited on metal surfaces.Preliminary measurements were made on bariumstearate f’flms49, and later calcium stearate films. Aspecial cell was designed, consisting of a cylindricalglass vessel partially filled with calcium chloridesolution. Two metal electrodes were immersed in thissolution and the films to be studied were depositeddirectly at the electrode surfaces. Using a slightlymodified conventional ac Wheatstone bridge network,a number of readings for films (1-41 layers)indicated the decrease in capacitance with increasingthickness for one set of their measurements. How-ever, in another set of measurements, an increase to amaximum of three layers was observed after whichcapacitance started decreasing. The latter data hasbeen attributed to the presence of serious imperfec-tions in the films. An average value of the dielectricconstant (23.7) for 41 layers was thus calculatedfrom the observed capacitance values (10 -6 F).Two-fold variation was found in the apparent dielec-tric constant, and several orders of magnitudevariation in the resistance in the thickness rangestudied. Further, both the capacitance and resistancewere found to be dependent on the nature andconcentration of the electrolyte. From the studiesusing copper sulphate as an electrolyte of varyingconcentrations, they inferred that the significantvariation of the electrical (and presumably thestructural) properties of the film may be due to thepresence of the copper ion, because these valuesdiffered widely from those taken wiflt Ca CI as anelectrolyte. Finally, these workers emphasised thatthe stearate films may be electrically modified bysimply varying the water content in the electrolyticsolution. It was further stated that the mercurydroplet method of RR43 has many advantages overthat used in their own work.

4.2 Recent Measurements on Capacitance,Resistance and Dielectric Constant

Handy and Scala 2 (HS) after more than two decadesrealized that mono-molecular layers obtained by theB-L technique satisfy all the conditions required for

reliable electrical measurements. For instance, suchorganic layers are thin, homogeneous, uniform inthickness and excellent insulators. In their detailedinvestigations, they tried to obtain a more compactfilm to minimize the presence of voids or holes in theorganic multilayer, and used evaporated metal elect-rodes. Figure 3 shows the results of capacity measure-

FIGURE 3 Reciprocal capacity 1/C vs. predicted numberof layers Nv. The heavy dashed line corresponds to the bulkvalue (e 2.5) and the dotted lines represent the experi-mental values of e 2.1 and 4.2. The cluster of points shownin the figure fall on top of each other and are slightlymisplotted to the left or right to show the density distri-bution of data. [After Handy and Scala42.]

ments on some 75 samples in which reciprocalcapacity (l/C) is plotted as a function of predictednumber of layers (N,). The capacitance measure-ments thus performed on stearate films (1-10 layers)led to e values between 2.1 to 4.2 with a bulk valueof e 2.5. These results agreed well with thoseobtained by PW using liquid contacts. Figure 4 showsa typical graph of capacity as a function of frequency(uppercurve) over the frequency range0.1- 20 KHz. On the basis of this curve, HS pre-dicted a slight dependence of e on frequency (a dropof about 5% over the range studied). The lower curveof Figure 4 shows the variation of the imaginary partof complex dielectric constant (proportional toC x D, D being the dissipation factor) with frequency.Evidently, there is a slight maximum near 700 Hzwhich has been taken to be indicative of the presenceof a weak polar absorption mechanism with a


characteristic relaxation time (1/2 r fm) of 0.23 m sec.The measurement uncertainty in the dissipationfactor D becomes comparable to the observed valuestowards the high frequency region (>10 KHz) (seethe lower curve of Figure 4).

FIGURE 4 Capacity C vs. frequency f (upper curve) andcapacity x dissipation factor (CXD) vs. frequency f flowercurve). [After Handy and Scala4 2.

The contribution of the oxide layer formedbetween the lower metal electrode and the organicfilm was neglected in presenting capacity measure-ments in view of its small resistivity compared withthat of the organic layers measured. In the ohmicconduction region (50mV), a wide range ofvariation of resistivity for the same film thickness wasobserved which supported the contention of a porousstructure in these films. HS42 thus concluded thatthe resistivity obtained for smaller thicknesses ischaracteristic of the oxide film, and its upper limitfor a given film thickness corresponds to the filmpossessing the smallest fraction of voids. The impor-tant conclusions arrived at were that the poorreproducibility of the characteristics is due to voidsand inhomogeneities in the film, and a reactive andhence oxidized surface is necessary for the formationand retention of low porosity layers. HS also foundthat the physicochemical nature of the substrateinfluenced the adhesion of more than the firstmonolayer, and that the porosity alone was con-sidered unlikely for such long-range effects. Positiveion adsorption, as described by Goranson andZisman , has been suggested as a possible alternativeand was shown to be consistent with some aspects ofthe electrical measurements. Becks2 has reportedmeasurements on capacitance for fatty acid mono-layers of different chain lengths sandwiched betweenA1 electrodes, and found capacitances reproducible

to within 3%, unlike HS who found a variation of50% in capacitance.

Drexhage and Kuhn 3 have measured the capaci-tance of cadmium arachidate and cadmium stearatefilms sandwiched between aluminium electrodes.Astonishingly, they found this method suitable forthe determination of film thickness even for a singlemonolayer, the capacitance C being given byEq. (4.1). As expected, a linear dependence of 1/Cwith the number of monolayers (N)was found.Evidently this means that e is independent ofthickness. The slopes of the straight lines in a plotI/C vs N yielded a value of d 26.6 A for cadmiumstearate by using e 2.40 (obtained simply by thesquare of the refractive index of barium stearate asdetermined earlier6). Holt29, using Langmuir mono-and multilayer films as thin film dielectricss4 carriedout preliminary measurements on stearic acid andstearate films sandwiched between metal electrodes.The standard deviation of C/A in each device was aslow as 3%, which he suggested to be of the order ofaccuracy of producing and measuring the areas of thebase and counter-electrodes. No significant variationof C and hence e with frequency were found. Theinteresting properties thus predicted by Holt, i.e.thermal stability and uniformity of organic films,have already been discussed. Another importantsuggestion made by him is that the dielectric constantcan be varied by altering the metal stearate pro-portions in the multi-monohyers.

In many of the measurements discussed above, theorganic film was sandwiched between evaporatedaluminium electrodes. The fact that a natural oxidelayer grows on the base aluminium electrode wasrealized, but its effect on the capacitance values ofthe device was neglected42, since the resistivity of theoxide f’flm is small compared with the resistivity ofthe organic layers. In the work of Mann and Kuhn(MK) xs the presence of such a thin oxide layerbetween metal electrodes and fatty acids is con-sidered; the relation used by them is

1---=(earl)-1C ,eox(dx+NJ) (4.3)

where dox and %x are the thickness and dielectricconstant of the oxide layer, ea is a dielectric constantof air, and all the other symbols have the usualmeaning. For calculating e values, they plotted 1/C asa function of superimposed layers (N) and, from theslope of straight lines thus obtained, the die valueswere determined. A plot of 1/C vs N is given in

14 V.K. AGAI,WA L

FIGU RE 5

,5 7N

Redprocal capacity 1/C vs. number of layers Nfor cadmium stearate (n 20) and cadmium behenate(n 22). [After Mann and Kuhn s.]

Figure 5 for stearate and behenate films which showsthe same y intercept in both cases. The capacitance,and hence the e values were determined by MK15 fora series of fatty acid monolayers of Cd salts. Forinstance, the values for stearic acid e 2.71 +- 0.17and for arachidic acid e 2.52 +-- 0.07 determined bythem were found to be comparable with respectivevalues e 2.59 0.08 and e 2.49 +_ 0.06 determinedearlier by RR4 3. However, their calculations 15 showan increasing e with decreasing chain length, which isqualitatively explainable due to the influence of thehighly polarizable cadmium carboxylate groups,which increases with. decreasing fatty acid chainlength.

Recent measurements of capacitance by Leger etal. have also shown a linear dependence of l/Cwithrespect to the number of transferred monolayers.They made use of this simple method for measuringthe thicknesses of organic films and found that it

yielded satisfactory results. A change of less than 10%in the capacitance of stearic acid films, increasingslightly towards the low-frequency region, has beenreported in the frequency region 10 -4 to 100 Hz byNathool 9.

More systematic investigation have recently beenmade by Khanna and Srivastavas6 (KS) on thecapacitance and hence dielectric constant of a fewfatty acid salts. In their measurements, sandwichstructures of the type Al-film-A1 were employed andthe capacity values were determined initially withoutconsidering the effect of the oxide layers6 For allthe film systems, measurements were made on 8 and110 layers using a universal bridge. The capacitance aswell as the dielectric constant values were found to bedistinctly different in the two cases. However, allthese results were in good agreement with theirtheoretically calculated values of e. The valuesobtained by KS, experimentally as well as theoretic-ally, are tabulated in Table II. A slight variation inthese values arises because their theoretical formula-tion sT,s8 is based on an ideal structure of the filmwhich is difficult to achieve in practice. Subse-quently, Khanna 9 calculated the e values consideringthe effect of the oxide layer, because this can beelectrically insulating and can contribute significantlyto the capacitance of the sandwich structure. Forthis, the expression already employed by Mann andKuhn. Eq. (4.3), was used, and the values for

dox 30 A and eox= 8 were taken. The e values thusobtained have also been given in Table II. Evidently,the effect of the oxide layer is more significant in thecase of a monolayer as compared with that formultilayers.To explain the significant difference of e values for

monolayers and multilayers obtained theoretically aswell as experimentally, Khanna59 carried out a

TABLE IICalculated and measured values of dielectric constant of a few long chain fatty acid Langmuir films. [After Khanna and Srivastava56’59.

(I) (2) (3) (4) (5) (6)

ecalc" (from theory)

ecalc" (from experimentaldata when oxide layereffect was inclusive).

monolayer for for for forfilm substance thickness monolayer multilayers monolayer ll0-1ayers

ecalc" (when oxidelayer effect excluded).

Capacitance per unitarea uF cm

for for for formonolayer multilayers monolayer multilayer

Ba-palmitate 23.25 1.65 2.90Ba-margarate 24.05 1.63 2.70Ba-stearate 25.75 1.67 3.10Ba-behenate 30.05 1.50 2.00

1.67 0.12 2.85 +/- 0.20 2.291.65-+ 0.07 2.59 +- 0.02 2.091.62 0.08 2.72 +- 0.07 2.101.60-+ 0.10 2.25 0.02 2.01.

2.88 0.636 0.009882.77 0.582 0.008662.63 0.554 0.006422.27 0.470 0.00604


systematic and detailed study of the thickness depen-dence of the dielectric constant from to 80monolayers. It was observed that the dielectricconstant increased slowly with thickness initially, butsaturated at a particular thickness (-1000 A) for alltypes of Langmuir films. A typical graph is shown inFigure 6, in which the dielectric constant e is plotted asa function of film thickness d for barium stearate films.

400 600 800 1000 1200 1400 ICO 1800 2000

FIGURE 6 Dielectric constant e vs. film thickness d ofbarium stearate film. (A) without oxide layer effect, (B) withoxide layer effect. [After Khanna .]

The upper curve (B) represents the variation of e whenoxide layer effects were taken into account, and thelower curve (A) shows when no such effects wereconsidered. This unusual behaviour has not beenreported in the earlier works, and the constancy of thedielectric constant with respect to thickness has beenshown 5,4 2,5 3,5 5. However, Khanna 9 has explainedher results qualitatively as given below. The observeddependence has been attributed to the porosity of filmsin the lower thickness range which decreases withincreasing thickness. In fact, an exactly similarthickness dependence of the dielectric constant hasbeen observed in evaporated ZnS films6 which hasbeen interpreted in terms of decreasing porosity orincreasing continuity of films with increasing thick-ness. The saturation of the dielectric constant athigher thickness ranges has also been observed forevaporated ZnS films. To explain why other workersfailed to obtain such a dependence, it has beensuggested that the films obtained by them were morecompact. For example, in the present work, the filmtransfer was accomplished at a surface pressure-30 dyn/cm, whereas in the work of Handy andScala4 2, a high surface pressure of 39 dyn/cm wasused. Ries eta/. 61,62 have already shown that voids

in the monolayer are inevitable if the transfer isaccomplished at a surface pressure significantly belowthe collapse pressure (42 dyn/cm in the case of stearicacid films). Further, the thickness of about 1000 A atwhich the e value saturates has been predicted as arough estimate of the range of electrostatic inter-action in Langmuir fatty acid soaps.

The author feels, however, that the explanationoffered above is in no way sufficient to explain thisunusual behaviour of the dielectric constant. Presum-ably the influence of highly polarizable metal carb-oxylate groups, which increases with increasingvolume ratio, would be a better explanation forincreasing e with decreasing chain length for a givennumber of layersis. For e saturating after firstincreasing with. thickness, the qualitative explanationmay be that dielectric losses are significantly less athigher film thicknesses, and therefore the dielectricconstant does not change. The magnitude ofdielectric losses has been related to the compactnessof the monolayers in recent measurements of Marcand Messier38 and it has been shown that there is adecrease with increasing compactness. Nevertheless,rigorous experimental work is required to investigatethe r61e of structural defects like voids, holes orinhomogeneities on the dielectric constant ofLangmuir fihns. Also, the observed increase of e maybe understandable in terms of the increasing polar-ization with increasing number of monolayers. This,in fact, has already been shown by Tanguy and Hestoexperimentally63, but it requires some structuralchanges inside the film which, in itself, is a problemyet to be studied.

4. 3 Theoretical Work

Unfortunately, not much attention has been paid todeveloping the theoretical formulation of dielectricparameters of Langmuir films. The only attempt inthis direction has been due to Khanna and co-workerssT,s8 who developed a theory for calculatingthe static dielectric constant of Langmuir films. Theirtheory is based on the layered structure of Langmuirfilms constituting a simple hexagonal, array, with themolecules oriented normal to the supporting surfaceand separated by a distance 4.85 .31 M011er’sassumption for calculating the Lorentz field for asimple hexagonal lattice64 could not be applied herebecause the molecular size (-25 N)is large comparedwith the lateral intermolecular distance (4.85 ). Thelocal field has been calculated by summing up theexternally applied field and the field due to all otherdipoles within the specimen. A reasonable assumption

16 V.K. AGARWAL

made for this purpose is that each molecule is dividedinto small CH groups separated by 1.27 b. along thechain axis (and, of course, the end carboxylategroup). Further, all the dipoles are assumed to bepoint dipoles, parallel to each other, with their axistaken to be the external field direction (Z axis)

4.3.1 Monomolecular films Following Salem’sassumption65 that D, the mutual distance betweentwo parallel linear chains, can be as small as about4 h if the basic units (in the present calculations,CH groups are the basic units) are bonds of averagelength 1.5 A, an expression for the contribution dueto intermolecular interaction between two molecularhydrocarbon chains was obtained 7

_N N 2k2X2 D2

E: p + 22 )5/2 (N x)

x:(D + X(4.4)

where p is the moment of the basic CHz unit(p ot]oc), ct is the electronic polarizability of theCH2 group (1.84 x 10-24 cma, cf. Ref. 66), ? is thedistance between the two CH2 groups along the chainaxis (1.27 A) and N is the number ofCH2 groups alongthe molecular chain. The electronic polarizabilityhere is assumed to be isotropic, and the two chains offatty soap molecule are considered to be coincident.For calculating the effect of the end carboxylategroup (unit), the relation derived was

E(end)=Pend --- 2Xi2 D2+ Z(D2 + Xi2)s/z

2Xi2+ p Z(D + Xi)s/z

(4.5)

where Pend is the moment of the end unit and Xi isthe distance of the ah CHz unit from the end unitalong the Z direction.

For calculating the intramolecular contribution tothe local field, the interaction between the units ofthe same molecule was calculated using the expres-sion

g , 2pi

Zi3, (4.6)

where Pi is the moment of the th unit and Z is thedistance between the reference and the different unitalong the Z direction.

4.3.2 Multimolecular films In the case of multi-molecular films, the molecules are considered to becontinuously distributed in all the layers except inthe one in which the reference molecule is situated.Thus, following Mailer’s treatment64 for layer lattices.the contribution of the continuous distribution to thelocal field is 4rP, (P is the polarization) and that ofthe reference layer is that calculated for a monolayerthe one by the above method. The density of soapfilms is taken here to be equal to that of the bulkwhich is, however, not a very good approximation.

For calculating the dipole moment, the totalpolarizability has been taken as the sum of electronicand atomic polarizabilities of all the groups, and theorientational polarizabilities of the polar end group.However, the atomic polarizabilities, being small, areneglected. The contribution due to metallic ionpresence in the end group has also been neglected inthe calculation of orientational polarizabilities, andthe end group is assumed equivalent to the- COOHpolar group, its dipole moment being 1.8 D (ef.Ref. 67). Finally, the static dielectric constant esalong the field direction (the symmetry hexagonalaxis), which is one of the principal axes of thedielectric tensor, is calculated using

es 1 + (4.7)E

Using this theoretical approach, Khanna andco-workers first calculated es for barium stearatemono- and multilayers and found these values to be1.6 and 3.0, respectively. 57 Later they reportedcorrected values of es for barium stearate as 1.7 and3.1, respectively, for a monolayer and multilayer, a

Here another assumption was introduced that abarium stearate molecule is equivalent to two"effective molecules", each consisting of one hydro-carbon chain and half of the end carboxylate group.These "effective molecules" were thought to form ahexagonal array with their axes normal to thesupporting surface. Their previous assumption57 thattwo hydrocarbon chains are coincident was notconsistent with the film structure reported by Germerand Storks31 Further calculations of es for a fewother fatty acid soaps were carried out56 and theseare given in Table II. All these calculations are doneonly up to seven nearest neighbours, and short-rangeinteractions, being small, have been neglected. Thesurface effects have already been considered in thecalculations on monomolecular films, and these areassumed to be insignificant for multimolecular(sufficiently thick) films.


It is evident from the above review of dielectricproperties that our knowledge about them hasadvanced somewhat through experimental measure-ments, but theoretical understanding is still lacking. Itis therefore necessary to attach special attention tomore rigorous theoretical work. The theoreticalformulation of Khanna et al. sT,s8 described abovehas been based on a simple classical approach, and anumber of the assumptions made do not hold underactual experimental conditions. For example, MiJller’streatment for layer lattices, which has been followedfor multimolecular films, no longer holds if themacroscopic volume of the sphere is large enough topermit the molecules to remain embedded in acontinuous medium with the same dielectric con-stant. The interaction of the sphere with its surround-ings thus requires electrostatic calculation whichshould be included in future work. Metal ions such asCa++ have been shown to reduce the mobility of thepolar groups by linking one molecule with another38

The contribution of such ions in the calculation ofelectronic polarizability of the end carboxylate group[such as (COO)2 Ba] has been neglected in the abovecalculations. Many more assumptions in the approachof Khanna and co-workers require attention. Moreinteresting would be the extension of this work totime-dependent fields, which obviously would involvethe complex dielectric constant of the system, and eswould become a special case of such a formulation.Both the real and imaginary parts of the complexdielectric constant would be frequency-dependent,and the imaginary part would be of more relevance toaccount for the dielectric losses. A quantum-mechanical approach would be even more difficult,and a description is beyond the scope of the presentpaper. For interested workers, reference should bemade to the monograph by Frohlich68 which is acomprehensive treatise on the theory of dielectrics.

4.4 Dielectric Loss Measurements

Some preliminary dielectric loss measurements werecarried out in the late forties by RR.4 They foundthat the dielectric loss neither depends upon thefrequency, in the range from 40 to 106 Hz, nor is itaffected by the film constitution. The dielectric lossesthus determined by RR were low, their order ofmagnitude being lower by a factor of 10 -a than thatobtained by Buckwald et al. 49 Similarly, Holt29 alsoobtained some information that the tangent loss angle(tan 6) drops from 0.02 at 225 A to 0.006 at 3700 A.The variation of tan 6 with frequency was predictedto follow normal thin film behaviour. However, these

measurements did not furnish any useful informationexcept the order of magnitude of tan 6, since thestandard deviation was 25%.A systematic study of dielectric losses in Langmuir

films of calcium stearate and behenate was reportedrecently by Marc and Messier38 (MM). The structureused was Al-film-A1 and the measurements wereperformed in the temperature range (-170 C to+50C) and over the frequency region(100 Hz-50KHz). All measurements were made after24 hours degassing under vacuum, since the dielectriclosses decreased rapidly by a factor of 2 during thefirst few hours of degassing. The results thus obtainedwere analysed by means of the equivalent circuitshown in Figure 7, where Cm and Rm refer to the

R

FIGURE

CmL Rm

Equivalent electrical circuit of a metal-Langmuir film-metal structures. [After Marc and Messier .]

capacitance/area and resistance of the organic mono-layer, and Co and Ro to that of the aluminium oxide

layer, respectively. R is the series resistance of severalohms due to the metal electrodes, which introduceseries losses of the form 2rRf; f denoting thefrequency. Since the loss angle of the structure (tan;) varied as f at high frequencies, they subtracted theseries losses -_JCco and considered the followingquantity:

tan i RCoPs C wRoCo 2 + wRmCm 2

(4.8)

where C (Co + Cm)-l.

18 V.K. AGARWAL

Evidently the quantity Ps is proportional to thelosses per unit area in the alumina and the mono-layers. Further, it was assumed that all N m.onolayersare equivalent, and therefore can be represented by Nimpedances in series. Calling dm the thickness, fn therelative dielectric constant and Prn the resistivity ofeach of the monolayers, Ps may be given by

dmPs oaRo Co 2 + N. (4.9)9e2 (erm)2 Pm

tanm. 103

[CH tCH}=,oC:O2Ca’’+ 1KHz

||=44dyn/,

-5o -oo -5 o ,50

FIGURE 8 Loss angle of behenate layers tan 6 m vs.temperature 0 measured at f KHz and at a surface pressurerr of 44 dyn/cm. [After Marc and Messier .]

Thus Ps depends linearly on N. Figure 8 shows thevariation of the loss angle of a behenate film (tan 6rn)measured at KHz as a function of temperature. Thecurves have been plotted for films consisting of 7, 13and 25 monolayers which were transferred at asurface pressure of 44dyn/cm. Evidently, twoabsorption peaks are observed around -100C and-30C. The peak around-100C is present in allthree films studied, whereas the other appears only inthick structures (N 13 and 25) which are known tocrystallize more easily. In a separate measurement,they found that the latter peak disappears when thestructure of the film is disorganized (see curve b ofFigure 9). Curves (a) and (b) in Figure 9 representdielectric loss plot’ted against temperature measuredat two different points of the same film. Curve (a)corresponds to a point in the middle of the filmwhere the molecules are well organized, and curve (b)to a point near the edge of the substrate where thelayer might get disturbed due to dipping or with-drawal.

The results obtained in the work of MN aresummarized below:

2,5

FIGURE 9 Comparison of dielectric losses with respect totemperature (a) corresponding to a point in the middle of thebehenate film, well organized structure, and (b)at a pointnear the edge, disorganized structure. Data reported forN "---25, r =44 dyn/cm and f= KHz. The lowest curverepresents losses due to oxide layer. [After Marc andMessier 38 .]

1) The losses per unit area increase linearly withincreasing film thickness, thus suggesting the move-ment of dipoles linked to the organic molecules. Thisis in accordance with the expression showing therelation ofPs and N (Eq. 4.9).

2) The losses due to the oxide layer are muchhigher than those due to the organic films, andparticularly those due to a monolayer.

3) The tan 6m curve does not change much withfrequency. The rise in the measurement frequencymerely causes a slight displacement of the tan 6mcurve towards higher temperatures.

4) The dielectric losses are much. greater when thestructure of the monolayer is disorganized (seeFigure 9). However, the order of magnitude of tan6m is 10 -3 for a compact monolayer which is smallerthan expected. To explain this, these workers suggestthat the Ca** ions considerably reduce the mobilityof the polar groups by linking the molecules, and therotation of a dipole around the molecular axisintroduces fewer losses.

5) The two absorption peaks observed at-100Cand -30C have been related to the degree oforganization of the monolayers. Finally, based onsimilar peaks in several other types of organicsubstances, (in polyethylene a peak similar to that at-100C; in stearon and nonapentacontanone a peaksimilar to that at-30C) these peaks have beeninterpreted in terms of dipole movements. Therespective peaks are thus thought to be due to the


movement of the dipoles in the amorphous region ofthe monolayers, and due to the molecular rotationaround the long axes in the crystalline parts of thelayers.

The interpretation in terms of the movement ofdipoles in these layers is not convincing because themeasurements are carried out under homogeneousapplied fields. In fact, motion of dipoles is possibleonly when non-homogeneous fields are applied. Sincethe soaps or metal salts of long chain fatty acids areknown to be ionic substances forming stable mono-layers (cf. Ref. 7, p. 193) there may be some ioncontent present in the deposited monolayers. There-fore, it appears to the author that the observed peaksmay be attributed to the motion of these ions ratherthan the dipoles. The existence of amorphous regionsin such organic monolayers, which these workers havesuggested, has not yet been verified in any otherexperimental work. Nevertheless, this is the onlysystematic work on loss angle measurements whichdistinguishes between the various kinds of losses, andwhich has thus led to an estimate of the loss angle dueto the Langmuir monolayers themselves. In presentingtheir measurements, MM were able to exclude thedielectric losses due to the natural oxide layer whosecapacity was determined to be 920 nF/cm2

It is interesting to point out the recent studies ontan by Nathoo19 for a 23 layer film of stearic acidat room temperature over the frequency region 10 -4

to 100 Hz. Under these experimental conditions, nopeaks were observed and the dielectric losses werefound to decrease by an order of magnitude withincreasing frequency in the range studied.

5 ELECTRICAL CONDUCTION PROPERTIES

Great emphasis was laid on studying electricalconduction through thin dielectric films, particularlyin the period following the second World War. It wasrealized that the conductive properties of filmsshould play an important role in the development ofdevices. Most of the earlier work on conductionbehaviour has been done, however, using either vacuumdeposited films or thermally grown oxide films onbase metal electrodes. Electrical conduction in filmshas already been widely treated in the literature inrecent years. The readers are advised to refer to therecent book by O’Dwyer69 who has given a compre-hensive picture of the subject.

Because of the defect nature of the films, it is notpossible to provide interpretation of experimentaldata using only one of the earlier concepts, such as

field emission from a free-electron metal by Fowlerand NordheimT, metal-vacuum-metal junctions byFrenke171, or metal-insulator-metal junctions bySommerfeld and Bethe72, etc. In fact, the con-duction process has been recognized to be an involvedprocess, and many co-operative phenomena such asspace charge modulation (due to trapped carriers) or,say, the Poole-Frenkel effect or Schottky effect havebeen found to occur. In the context of this paper,basic theories of conduction phenomena in thininsulating films are discussed briefly just to remindthe reader of the underlying basic concept. Thesimplest expressions used for the interpretation ofexperimental data are also given.

5.1 DC Conduction Theories in Thin Films

All the theories discussed here will apply to metal-insulator-metal systems, and the insulator in questionmay contain a significant proportion of impurities. Ingeneral the electron transport at a metal-insulatorinterface depends upon the nature of the contacts,and the conduction processes, in turn, are distin-guished as follows:

1) If the contacts are ohmic (m i, where mand i are the work functions of the metal andinsulator respectively) the conduction in the system islimited by the rate of electrons flowing through thebulk of the insulator, rather than the rate at whichthe electrons are supplied by the electrode. Theprocess is then termed "bulk limited".

2) In the case of blocking contacts (rn > i), therate of electrons flowing through the system islimited by the rate of electrons flowing over theinterracial barrier and the process is referred to as"electrode limited".

3) If the contacts are neutral, i.e. m i, thereis no necessity of charge transfer between theelectrode and insulator. This situation corresponds toa transition between an ohmic and blocking contact.Under special circumstances, neutral contacts alsooccur if rn i and the trap level is positionedmore than eV above the Fermi level. Traps ininsulating films arise because of the grain boundarydefects or because of the large stresses, particularly invacuum deposited films. These traps are an"extrinsic" property of the amorphous insulator,and their concentration may be as high as 1019

-3cm

However, if the system is subjected to sufficientlyhigh voltages, transition from bulk limited to elec-

20 V.K. AGARWAL

trode limited processes, or vice versa, may occurdepending upon the nature of contacts. We shall beconcerned here with several distinct conductionmechanisms only, and the discussion of theories willbe limited to three voltage ranges: low, intermediateand high. The process is electrode limited for low andintermediate voltages and is bulk limited in the highervoltage region. In practice, however, many moreco-operative phenomena may occur, because no dearcut criteria may be assigned to distinguish these threevoltage regions. For greater details, reference should bemade to a recent monograph73 on the subject.

5.1.1 Fowler-Nordheim type tunnelling Thisprocess requires that the system be subjected to highvoltage biases so as to lower the barrier thickness atthe negatively biased Fermi level to less than 50 A.The well-aaown expression of Fowler-Nordheim typeof tunnelling7 is then given by

exp (5.1)

where J is the current density, F is the applied fieldand is the mean potential barrier height above theFermi level of the cathode. This expression is trueonly if the ratio of the insulator effective mass to thefree-electron mass (m*) is unity. Otherwise theexponent of equation would become

( -0"69(m*)3)FThis process is electrode limited.

5.1.2 Richardson-Schottky effect The currentflow through the insulator in this process is governedby the rate at which the electrons are thermallyexcited over the interfacial potential barrier into theinsulator conduction band. Thus, the current flowingin the system is determined by Richardson’s therm-ionic equation

J=AT2 exp(-- k-), (5.2)

where A is the well-known Richardson constant((4mnek)/ha 120 if J is expressed in A cm-) ando is the interfacial barrier height. However, when theapplied field interacts with the attendant electrodeimage potential, it lowers the barrier height fromand permits more current to flow over the barrierwith increasing applied voltage. This effect is knownas the Schottky effect74, and the barrier lowering is

given by As =/3s F’/2 The current is then determinedby the Richardson-Schottky equation

J:AT2exp exp kT (5.3)

where s is a constant (= e3/(4zre*eo)’/2), and e* is thehigh frequency dielectric constant of the material. Forsufficiently high fields across the interface, tunnellingmay be the dominant conduction mechanism, and it is

then governed by a suitably modified form of Eq. (5.1)in which the image force has been included.

5.1.3 Space charge limited currents In both ofthe processes discussed above, space charge effectswere not considered. However, traps exist in most ofthe film systems used, and thus it is necessary toaccount for their contribution. First, the situationwill be discussed for a trap-free insulator. In the caseof ohmic contacts, a negative space charge regionexists on the surface of the insulator, and an equaland opposite (positive) surface charge on the elect-rodes. When the field is applied, the space charge inthe insulator increases and its redistribution takesplace, depending upon the nature of voltage bias.After this redistribution, if the positive charge existson the cathode, i.e. the cathode region acts as acharge reservoir to supply the required charge to theanode, the process is called "space charge limited"(SCL). For trap-free insulators, the expression derivedby Mott and Gurney7s to calculate the currentdensity is given by

19pee0) V2J8d

(5.4)

where d is the insulator thickness. However, inpractice, much lower currents have been observed,and they are found to be temperature sensitive, whichcould not be explained with the above equation.Rose76 then pointed out that when the insulatorcontains traps, a large fraction of the injected spacecharge condenses into the traps. Thus, it was suggest-ed to multiply the right-hand side of Eq. (5.4) by aquantity 0 (Nc/Nt) exp (-Et/kT), where N is thetrap density, E is the depth of the trap below thebottom of the conduction band, and Nc is theeffective density of states in the conduction band.Thus Eq. (5.4) may be expressed as:

19UeeO]v2 (5.5)J !


Since 0 is independent of V, the proportionalityJ V2 as in the case of trap-free insulator, stillholds.

5.1.4 Poole-Frenkel effect When the appliedfield is high, the coulombic potential barrier of adonor centre or trap is lowered by an amount7 7

AbpF tiP F FV2 (5.6)which is twice the attenuation of the barrier heightdue to the attendant image forces in the case of theSchottky effect. This occurs because the potentialenergy of an electron in a coulombic field is fourtimes that due to the image force effects./3p v is thus

(5.7)

This, in turn, amounts to the lowering of theionization potential, Eg, of the donors in a solid. Thebulk current density is then determined by thewell-known Poole-Frenkel equation

(5.8)J Jo expl 2 kT ]

where Jo e/aNcF exp (-Eg/2kT) and is the. lowfield current density. Traps having a coulombic typeof barrier would experience the PF effect at highfields, which results in the increase of the escapeprobability of immobile electrons therein 7s. Theexpression for insulators with shallow traps is givenby:

,kT l

The reader is reminded that the coulombic barrierexists not only between a donor centre and itselectron but also between a charged trap and anelectron. A charged trap is a trap which is chargedwhen empty and neutral when full. Furthermore,Simmons73 has discussed another situation where theinsulator contained both donor centres (lying belowthe Fermi level)and shallow neutral traps. The expres-sion for the bulk I-V characteristic of the film is thengiven by

J=Jo* exp (PFF1/2\2kT ]

(5.10)

where

Fexp2 kT

(5.11)

The suffixes d and ts here refer to the donor andshallow traps, respectively. This equation holds evenif there exists a range of trap and donor levels, andone of the trap levels is more dominant than theothers.

5.2 Conduction Mechanisms in Langmuir Films

Of all the conduction mechanisms that are discussedabove, the dominant one in Langmuir films seems tobe tunnelling. Obviously, for measuring tunnellingcurrents, one needs to separate two metal electrodesby a barrier of 20 )k- 100 A in thickness which mustbe uniform, homogeneous and an excellent insulator.Thin oxide films grown on base metal electrodes wereemployed for such studies by Giaver79 and Nicol etal.,8 because of their compactness and uniformity.The fact that Langmuir films of several organicmaterials may fulfill all these requirements for study-ing tunnelling was recognized by Miles andMcMahon.81 These workers employed a monolayerof barium stearate (25 A) as an insulating barrierbetween tin-lead and tin-indium evaporated filmpairs. The experiments, however, did not proveuseful, because an irreproducible and strongly time-dependent resistance of the device was observed inthese studies. This is not surprising, because themonolayer transfer technique was in its infancy andonly a handful of electrical measurements had beenperformed prior to this work. It was also not knownwhether voids, defects or inhomogeneities in thesefilms could be reduced to permit the construction oftunnel sandwiches. However, the studies of Miles andMcMahon81 provoked the interest of many others inthe conduction behaviour of Langmuir films.

Handy and Scala42 subsequently tried to obtainnew information on the conduction behaviour ofLangmuir multilayers and considerable efforts weremade by them to deposit compact films for theirstudies. In their extensive studies on Ba or Ca stearatefilms (1-10 monolayers) with counter-evaporatedelectrodes of Sn, Cu, Ag and Pb (and also using Hg asthe counter-electrode in a few cases), the conductioncharacteristics were found to be highly non-linear andstrongly temperature dependent. Figure 10 shows thetypical behaviour of a symmetric Sn-3 layer calciumstearate-Sn sandwich (-1 mmz area) at 0.1 Hz and at

22 V.K. AGARWAL

-0.6 -O.4

FIGURE 10 Current-voltage characteristics at 0.1 Hz ofSn 3 layer calcium stearate-Sn sandwich of lmm area atroom and liquid nitrogen temperatures. Polarity is that oforganic coated tin base layer. [After Handy and Scala42 .]

10.9

10-1o40 0 -40 -80 -120 -160 -200 -240

Temperature C

FIGURE 11 Plot of current vs. temperature at constantvoltage tbr -3 layer thick film (uppermost curve)and tbr 5layer thick film (three lower curves). Polarity of test voltageis organic coated base electrode positive. [After Handy andScala42.]

room and liquid nitrogen temperatures. HS furtherstudied the behaviour of a 3-layer and a 5-layer thickfilm at constant voltages for two junctions as shownin Figure 11. Detailed analysis of the temperaturedependence of conduction for a 3-layer sandwich ledthem to believe that the electron tunnelling is theconduction mechanism at low temperatures(<-100C) and small thickness, and thermionicemission at high temperatures (> 40C) and largerthicknesses. A superposition of both of these mechan-isms has, however, been assumed by them at anintermediate temperature range. Handy and Scala alsodetermined the zero voltage thermal activation energyb as 0.25 < b < 0.30 eV by plotting the thermioniccontribution to the current on a Schottky plot oflog((/-/)/T2) vs. 1/T as shown in Figure 12. In anattempt to analyse their results using theoreticalexpression derived by Stratton82 and Simmons,8a

they failed to obtain a satisfactory fit of the observeddata. Consequently no satisfactory explanation couldbe given for the observed temperature dependence. Infact, they have shown that the fatty acid films are

promising for electron tunnelling, and the low valuesof Ob could be due to the defects and impuritieswithin the film. One of the important conclusions isthe necessity of a reactive and hence oxidized surfacefor the formation and retention of low porositylayers. If noble metals (e.g. Ag or Au)were used asthe first electrode, the junction resistance was foundto be less than 2, and none of the gold-basedsamples were successful for electrical studies.

Horiuchi et al. 84 employed calcium stearate filmssandwiched between asymmetric electrodes of tin andaluminium to study the voltage and temperaturedependence of the current. As is shown in Figure 13athe observed current Ii was found to be stronglytemperature dependent above 200K and nearlyindependent below this temperature. This was thesituation when the lower tin electrode wasnegatively biased. Conversely, when the upper alu-minium electrode was negatively biased, the current12 was observed to be temperature independent in thetemperature range studied. This type of behaviour ofMIM junctions suggested that more than one mechan-


’:7 0 -50 -75 -150 -’;53 -175

_V-O.S rees Centigrde (1.6

0.7 -6 .4

i.

0.5’

0.3 ag’X 0.60.50,2[ %L_. 0,49 I0 11 12

1000/oK,

FIGURE 12 Plot of log (I/T2) vs. (l/T) and log ((I-I’)/T2) vs. (lIT) for 3 layer sandwich, where totalcurrent, I’ low temperature current in amperes and T absolute temperature. [After Handy and Scala* .]

10-7

] ’ eA NEGATIV’=

I10Ai{ZA 4 Xl0"2crn

0 0.5 1.0 1.5 2.0

V(VOLTS)

(a)

10-7r-

FIGURE 13 (a) Plot of 11 and I: vs. V at fixed temperature for Sn 3 layer Ca stearate-A1 junctions; and (b) plotof 11 and I vs. 1/T at fixed voltage for Sn-Ca stearate junctions. Black dots and white circles represent 12 and 11respectively. [After Horiuchi et al .]

24 V.K. AGARWAL

ism of electron transfer is operative (see Figure 13b).Horiuchi et al. analysed their V-I characteristics usingthe trapezoidal energy barrier model ofSimmons83,ss and Pollack et a/. 86,87 and thusdetermined barrier heights Cb at the two interfaces;bb 1.3 eV (for stearate-aluminium) and bt 0.8 eV(stearate-tin). This indicated that the work functionof tin is lower by 0.5 eV than that of aluminium,which is in contradiction to the known difference of1.5 eV. This discrepancy, however, could not beresolved by these workers even when they studiedsymmetric junctions of tin electrodes and took thenatural oxide layer into consideration.

From their detailed analysis it was shown that thetemperature and voltage dependence of the currentsatisfies the Schottky emission mechanism, whereastunnelling has been predicted from the voltagedependence of the low temperature current. Altern-atively, the two mechanisms have been found to beoperative for the negatively biased lower Sn electrodeand the upper A1 electrode, respectively. To resolvethe difference in the barrier height determined from

FIGURE 14 jN vs. V for A1-Cd stearate-Hg devices whenA1 electrode positively biased. The dashed curve N 5 to 21;

Ji (impurity dependent current), proportional to V and1/N. Full curve N 1; =it +Ji (it tunnelling current). Jtsurplus over Ji is given by dashed curve. [After Mann andKuhn s.]

the two operative mechanisms, they have assumed thepresence of some conductive patches in the filmswhich would let the tunnel current pass through themreadily. This seems reasonable, as tunnelling emissionwas found to be more strongly dependent on thebarrier height than the Schottky emission. From theirstudies of the I-V characteristics, which weresymmetrical with respect to the polarity of appliedvoltage, the dominant conduction mechanism hasbeen suggested to be barrier limited because thecharacteristic was dependent on electrode material.To avoid the formation of oxide layers, efforts weremade to study gold based devices, but measurementscould not be carried out because the samplesprepared showed ohmic characteristics with verysmall resistance.

Unlike the measurements of previous work-ers42,81,84, Mann and co-workers15,88 succeeded ingiving a quantitative proof of the tunnelling theory intheir measurements of dc conductance through Lang-muir films of a few fatty acid salts. The success oftheir measurements lies in the fact that film depositedby using a modified B-L technique23 did not possessany holes and conducting imperfections. Analysis ofthe experimental data was made in accordance with.the concept of quantum-mechanical tunnellingproposed by Sommerfeld and Bethe.72

To determine the conductivity, Bethe’s relation7for small values of applied voltages.was used, which isexpressed as:

(2mb)l/2exp [-(-)(2mq) ](5.12)

where b is the difference between the work functionof the metal and the electron affinity of the insulator.All other symbols have their usual significance. Thisequation refers to equal metals and, if the metalelectrodes are different, should be replaced by

tl 2 (5.13)

where ql and 2 are the values for the respectivemetal electrodes. Since each insulator is expected tohave some impurity-dependent conductivity oi inde-pendent of d, besides the tunnelling conductivity ot,

Mann et al have analysed the results by separating outthese two contributions from the experimental totalconductivity o( o + Or).


Mann and Kuhn investigated many samples inthe thickness range containing 5 to 21 layers with alower A1 electrode biased both positively andnegatively. The measurements of dc conductance at20C and -35C, with various upper electrodematerials, indicated that the logarithm of the currentdensity j is proportional to V and inversely propor-tional to d, as is expected. Figure 14 is a typical plotof N/versus V of cadmium arachidate film, where Nrefers to the number of layers. The dotted linerepresents the current due to impurities ]i and theother curve for N gives the total current j which isa sum of h and Jt (tunnelling current). In Figure 15,

-12

;n--19

" n 20

25 26 27 28 29

d(A)

FIGURE 15 Logarithm of a (jtd/V) V 0 (atunnelling conductivity) vs. d for A1-Cd salt of CH(CH2)n_2COOH-Hg devices at 20C and-35C withn 18 21. [After Mann and Kuhn .]

log Ot(O (l- Oi) is plotted against thickness d forfour types of cadmium salts of the fatty acids CHa(CH2)n-2 coon with n 18-21. Evidently, theexperimental points for both 20 and -35C are onthe same straight line in accordance with Bethe’sequation. This exponential decrease of conductivitywith increasing thickness of the insulating barrier dverifies the tunnelling theory. The vacuum work

functions of A1 and Hg determined in their worktheoretically were found to be in good agreementwith the known values.

Further experiments were performed to measurethe photocurrent in the sandwich assemblies betweensimilar and dissimilar electrodes. From these measure-ments, the vacuum work functions of A1 and Hgwere determined independently, and the excellentagreement between theoretical and experimentalvalues led to the belief that large imperfections wereabsent in the monolayer structures. Absence of evensmall numbers of holes and conducting imperfections,which strongly influence the resistance of the devices,have been verified quantitatively. These workers88 hadalso verified the tunnelling theory in a previous workon photographic sensitization. Fatty acid layers wereused as "distance keepers" in the sensitizers todistinguish between an energy transfer mechanismand an electron injection mechanism. The dye wasstill found to be sensitized, which led to theconclusion that the sensitization is due to the energytransfer mechanism, since the electron tunnellingthrough fatty acid monolayers was extremelyimprobable.89

Strong evidence for tunnelling at low voltage hasbeen presented by Leger et al. ss, who studiedelectronic transport through organic films of cyaninewith two grafted stearic chains (St2 Cy). A typicalI-V characteristic at 1.5K is shown in Figure 16 fora sample Al-cyanine-Pb for different voltageranges. The curve (B) is quadratic for voltages lessthan 0.1 V and exponential at higher voltages. Suchbehaviour is clearly not compatible with a conduct-ance dominated by pinholes in the organic film andtunnelling through the natural oxide layer. In anothercurve (A), the energy gap of superconducting lead(Apb) is clearly visible. Another striking feature ofthe characteristic is its non-linear behaviour forvoltages> 50mV which, together with the aboveobservations, led to the conclusion that tunnelling isthe dominant conduction mechanism at low voltages.However, contradictory results have been obtained insimilar work on Langmuir films of stearic acidcontaining 5 layers 19. Figure 17 shows a plot of log Iversus V/2 at room temperature which fits well anexpression of the form/c exp V’/2 with/3= 1.8 x lO(Vm)/. Predicted theoretical values of / arep= 4.7 x l0 (Vmf/2 for Poole-Frenkel conduc-tion and s 2.3 x l0 (Vmf/2 for Schottky con-duction. From such a comparison it was concludedthat the latter is the dominant mechanism in stearicacid films. Dominance of Schottky conductionmechanism in Langmuir films in the range of 1-10

26 V.K. AGARWAL

(’O’A) , -Cyanine P.b

0 100 200 300 400 500

1010

10:

05 07 09 11 13 I5 17

FIGURE 16 Plot of current vs. voltage for A l-cyanine-Pbdevice of area --1 mm at a temperature of 1.5K (curve A).Both the curves (A) and (B) are plotted to show thebehaviour in different voltage ranges. The appearance of thesuperconducting lead gap Apb is marked in the curve (A).

Vv

(volts/)FIGURE 17 Current-voltage characteristic for a 5 layerthick stearic acid film at room temperature plotted as logvs. VV2. [After Nathoo’ 9.]

monolayers has also been proposed by Srivastava,9

based on experimental studies of the thicknessdependence of the breakdown field (described later indetail).

All the conduction studies, described above, havebeen carried out in the low thickness range ofLangmuir films (1-10 monolayers)and differentconduction processes have been found operativeunder different conditions. However, careful examin-ation of existing data shows that the tunnellingmechanism is dominant even though there are someindications of Schottky conduction. In fact, tunnell-ing has been found to be the dominant conductionmechanism in many other types of film systems inthe comparable thickness range. On the other hand, ithas been indicated7 a that Schottky barriers in thinfilms are much more easily investigated using the actechnique. Nevertheless, to make sure that tunnellingis the operative conduction mechanism in Langmuirfilms, more experiments are required.

Since tunnelling currents are known to have only aslight temperature dependence, and the Schottkycurrents depend strongly on temperature, such

temperature-dependent studies may prove useful forthe choice of the conduction mechanism in thesefilms. Unfortunately, most of the data have beeninterpreted without considering the nature ofcontacts, which have a lot of influence on theunderlying conduction process. It is essential toexamine the nature of contacts in future studies onthese films. The presence of a space charge region inMIM structures has also not been accounted for inany of the measurements up to now, and this isperhaps the reason that some workers have indicatedmore than one conduction process to be operative,but failed to determine what exactly it is. Due to thelack of any judicious study which accounts well forall the factors influencing the conduction process,and in the light of the existing contradictory experi-mental evidence, it is premature to conclude anythingabout the conduction process in Langmuir films.

5.3 High FieM Conduction Characteristics

Multimolecular films of stearic acid were chosen forhigh field conduction studies because of their ordered

ELECTRICAL BEHAVIOUR OF LANGMUIR FILMS

structure and because such films had been used bymany workers in the study of tunnelling phenomena.Nathoo and Jonscher91 studied the behaviour ofthese films under high applied (ac and dc) fields toget more information about their dielectric proper-ties. A sandwich structure of the type A 1-film-A1was used, and the measurements were made byplacing the device in vacuum, since exposure toair caused reversible increases of the dc conductivityby an order of magnitude. A thickness range of 6-40monolayers was chosen.

The response of the metal-film device to a stepvoltage was characterised by an initial surge followedby a gradual decay which lasted for hours, andsometimes for several days in thicker films. At roomtemperature the current was time dependent follow-ing the relation I c to.7. On removal of a steady biasand shorting of the sample, a corresponding dischargecurrent was observed. Figure 18 shows a typical

27

/h’,2s. At fields in excess of l0 V cm- thecharacteristic, however, was found to obey Poole’slaw92 of the form

I cexp I-] (5.14)

where 2S is the distance between donor-like Poolecentres,93 i.e. neutral when occupied by the charge inquestion. To determine the value of 2S, Nathoo andJonscher obtained the I-V characteristics for a filmcontaining 11 layers at four different temperaturesand found that each of the characteristics obeysPoole’s law. At temperatures between 198K-295K,the values of 2S varied between 33 and 40 A. It isexpected that the donor-like centres should beseparated by an integral, multiple of the molecularlength of the fatty acid film under investigation. Inthe present case, they91 expected that the donor-like

FIGURE 18 Recorder tracing of the current after switching on a steady field for A1-8 layers thick stearic acidfilm-A1. The insert is a corresponding log log plot giving a slope of -0.7. [After Nathoo and Jonscher 1..]

recorder tracing of the decay current after switchingon adc field for an 8 layer thick film, which followsthe I c tn behaviour with t -0.7. The dccharacteristic shown here was obtained by subtractingthe discharge current from the charging current.Further, the current was slightly non-linear atfields < 10 V cm -1 varying according to

centres are probably located at th more reactiveCOOH end group of the molecules which separatethem by twice the molecular length (-50 A). Sincethe observed values of 2S were found to lie betweenone and two molecular lengths, the discrepancy canbe explained by assuming an effective carrier temper-ature Tc in excess of the ambient lattice temper-

28 V.K. AGARWAL

ature94. Subsequently, these authors measured "lowfield" ac conductance r(o0) at peak amplitudes < 10V cm -t and observed a relatively weak temperaturedependence of the absolute magnitude of o(o).Figure 19 is a plot of o(o) as a function of the

their suggestion is that these could be electrons orprotons, and much less likely heavier ions. Later,Jonscher9s has justified the observed behaviour of rin these ordered systems. He explained that even aperfectly ordered system in which all "hops" hadequal probability distribution, the actual delay timeswould vary over a certain range, which could give riseto the observed dependence.

Further measurements were made by these work-ers96 in the "high field" regime, extending upto2 x 106 V cm -t for a wide range of frequencies. Inparticular, their interest was to get information onwhether or not the time-and frequency-dependenceof the response was a function of the amplitude ofthe electric field. All the measurements were made ona 5-layer thick stearic acid film sandwiched betweenaluminium electrodes. Figure 20 shows the frequencydomain measurements on two areas of the same filmfor a wide range of field amplitudes. Curve (a) showsthat the results are different only in the lower

e105 K295 K

= 338 K362 K373 K

10"* 10"a

FIGURE 19 The ac conductivity a(o) vs. frequency forII layer thick film with the specben area ~lmm Theconductance scale refers to the lowest temperature, highertemperature characteristics being successively displaced byone decade for clarity. [After Nathoo and J onscher

frequency for a stearic acid film (11 layers thick) atdifferent temperatures. Evidently, all the character-istics may be represented by the power law depend-ent on frequency of the form

o() =n, (5.15)where n is temperature dependent and varies between0.5 < n < 1 at high and low temperatures, respect-ively. Similar behaviour of a(oo) was observed inmany other hopping systems, but these were mostlydisordered or amorphous. From the fact that organicfilms, which are known to be largely ordered, havealso shown a similar behaviour, they concluded thatthe frequency dependence of o is a general feature ofhopping systems and not restricted to disorderedsolids. Regarding the nature of the hopping charges,

-9Iog(/E)

V/cm-I0 x 1

AV.m.1 I=1 0.5=0.1

-1 o 1-d subtracted

o,o

FIGURE 20

-3 -2 -I 0 1 2

log (Hz)

Frequency domain measurements on twoareas (a) and (b) of the same device, A1-5 layer stearic acidfilm-A1, for a range of electric fields at room temperature.The dashed line for sample (b) represents the "true ac" dataafer deduction of the dc. Data for sample (b) are displaceddownwards by two orders of magnitude for clarity. Thecurves represent log-log plots of (I/E)vs. f where is thecurrent per cm and E is the field in V]cm. [After Jonscherand Nathoo96.]


frequency region (<0.1 Hz) which is due to theincreasing level of dc conduction and is stronglynon-linear for fields over 10SV cm -1 Curve (b)represents a similar characteristic taken at x 106 V-cm-1 when the dc level was subtracted from the totalcurrent. On extrapolation of the high frequency line,the exponent of Eq.(5.15) n0.8 was found.Obviously, the entire characteristic at a field of2 x 106 V cm -1 shifts upwards by a factor of about2.5 in the frequency region studied, but its slope doesnot change much. Thus it has been suggested that theonset of the frequency dependence of the character-istic does not change significantly because of theonset of ac non-linearity.

Time domain measurements were made on adifferent area of the same film, and the plots ofcharge currents (after subtracting the steady dccurrent) and discharge currents versus time are shownin Figure 21. The data give a dependence of the type-I c t-n which, in the linear regime, gives the conduct-ivity dependence of the type given by Eq. (5.15). Theslope of discharge currents increases from 0.74 at the"low fields" (2.25 x 105V cm -) to 0.87 at the

Dischargeogel.8 106v/era

(A) o x 1.35cO.9

--11 \ 0.45oi\ \o .0.2 25O e Charge (all fields)

"e o

-13 o+ X

-42 3 4

log (s)

FIGURE 21 Time domain measurements of the dischargecurrents (symbols indicated) and charge currents (opendrcles) for a different area of the same film as in Figure 20,for different charging fields. Charge currents have dc sub-tracted. The curves are log-log plots of vs. (time). [AfterJonscher and Nathoo96 .]

"high fields" (1.8 x 106V cm-1). The discrepancybetween the field-dependent slopes in the timedomain and in the frequency domain is attributedmore to the inapplicability of the Fourier transform-ation in the non-linear regime. Even the theoreticalsuggestion97 that the effect of a high field on thestep function response be represented to a firstapproximation by a change of the amplitude ofresponse without a change of time dependence, couldnot be strictly applicable in the present measure-ments. However, it has been used to explain theresults as a reasonable first approximation, whichthen permits Fourier transformation in the non-linearregime. Validity of such an approximation is furthersupported by the fact that a small but definiteincrease of capacitance with increasing field has beenobserved in both the time and frequency domainmeasurements. Such behaviour has also been reportedin measurements on silicon oxide98 and is alsoexpected theoretically.9 7

The whole range of data has been considered asevidence for a small but definite effect of high fieldson the time dependence of step function responsewhich is more pronounced in the time domain than inthe frequency domain. Such a definite trend couldnot be determined in the frequency domain measure-ments on silicon oxide.98 Although the results havebeen interpreted qualitatively by the authors91,96,no conclusion has been reached regarding the trans-ient behaviour of such films under high applied fields(dc) or about their ac conductivity. Nevertheless,they have opened up a new series of measurements,and further measurements along these lines wouldyield many more facts about the high field conduc-tion characteristics of Langmuir rllms. Most interest-ing would be to discover the nature of the hoppingcharges by studying the field assisted hoppingmechanism between closely spaced donor-like centresin several other organic compounds.

REFERENCES

1. V. K. Agarwal, Thin Solid Films 24, 55 (1974).2. Lord Rayleigh, Phil Mag., 48,321 (1899).3. N. K Adam, The Physics and Chemistry of Surfaces (3rd

ed., Oxford University Press, London, 1941) Chap. 2.4. I. Langmuir, Trans. Faraday Soc. 15, 62 (1920).5. K. B Blodgett, J. Am. Chem. Soc. 57; 1007 (1935).6. K.B. Blodgett, and I. Langmuir, Phys. Rev. 51, 964

(1937).7. G. L. Gains, Jr., Insoluble Monolayers at Liquid-Gas

Interfaces (Wiley, New York, 1966).8. V. K. Srivastava, Physics of Thin #Tlms (Academic Press,

New York, 1974) 7, 311.9. W. D. Harkins, Physical Chemistry ofSurface Films (Van

Nostrand-Reinhold, Princeton, 1954).

30 V.K. AGARWAL

10. A. W. Adamson, The Physical Chemistry of Surfaces,(Wiley, New York, 1960).

11. A. E. Alexander Rep. Prog. Phys. 9, 158 (1942).12. W. J. Popiel. Sci. Prog. 58,237 (1970).13. H. Ek Ries, Jr., Encyclopaedia of Science and Tech-

nology, (3rd ed., McGraw-Hill, New York, 1971).14. T. J. Davies and E. K. Rideal, Interracial Phenomena

(Academic Press, New York, 1961).15. B. Mann, and H. Kuhn, J. Appl. Phys. 42, 4398 (1971).16. V. K. Srivastava, and A. R. Verma, Proc. Phys. Soc. 80,

222 (1962).17. R. Sirhatta. and G.D. Scott, Appl. Opt., 10, 2192

(1971).18. M. A. Baker, Thin Solid Films 8, R13 (1971).19. M. H. Nathoo Thin Solid Films 16,215 (1973).20. I. Langmuir Proc. R. Soc. A 170, (1939).21. S. Tolansky. An Introduction to Interferometry,

(Longmans Green, London, 1955) 65.22. J. Strong, Modern Physical Laboratory Practice (Blackie,

London, 1940).23. H. BiJcher, O. V. Eisner, D. Mbbius, P. Tillmann and

J. Wiegand, Z. Phys. Chem. 65,152 (1969).24. I. Langmuir,J. Ant. Chem. Soc. 39, 1860 (1917).25. P. P. Luffand M. White, Vacuum 18,437 (1968).26. V. K. Srivastava, and A. R. Verma, Solid State Commun.

4, 367 (1966).27. R. W. Roberts and G. L Gains, Jr., Trans. Ninth Natl.

Vacuum Symp., Am. Vacuum Soc., 1962, 515.28. G. L. Gains, Jr. and R. W: Roberts, Nature 197, 787

(1963).29. L. Holt, Nature 214, 1105 (1967).30. B. L Henke, Adv. X-ray Anal. 7,460 (1964).31. 1.. H. Germer, and K. H. Storks, J. Chem. Phys. 6, 280

(1938).32. K. Tanaka, Mem. Coll. Sci. Univ. Kyoto A22, 377

(1939).33. K. G. Brummage,Proc. R. Soc. A 191,243 (1947).34. J. M. Cowley, Trans. Faradv Soc. 44, 60 (1948).35. J. W. Menter and D. Tabor, Proc. R. Soc. A. 204,514

(1950).36. H.J. Trurnit and G. Schidlovsky, Proc. European

Regional ConJ Electron Microscopy 1960, 2, 721(1961).

37. G. Knott, J. H. Sctiulman and A. 1:. Wells, Proc. R. Soc.A. 176. 534 (1940).

38. (;. Marc and J. Messier, J. Appl. i’hys. 45, 2832 (1974).39. H.T. Epstein. J. Phys. Colloid 67em. 54, 11)53 (1950).40. H.E. Ries, Jr. and W. A. Kimball,,/. Phys. (Ttem. 59, 94

(19553.41. H.E Ries, Jr.,Sci. Am. 204,152 (1961).42. R. M Handy and 1.. (’ Scala, J. Electrochem. Soc. 113,

109 (1966).43. H.H. Race and S. I. Reynolds, J. Am. Chem. Soc. 61,

1425 (1939).44. tt Sobotka, M l)emeny and J. I). (’hauley, J. Colloid

Sci. 13, 565 (1958).45. A. Barraud, J. Messier, A. Rosillo and J. Tanguy,

blloque A VISEM, Versailles (Sept. 1971 ).46. E.F. Porter and J. Wyman, Jr., .I. Am. Chem. Soc. 60,

1083 (1938).47. S.I. Reynolds and H.H. Race, G.E. Rev. 41, 529

(1938).48. K B. Blodgett, Use oflnter.[erence to Extinguish Reflec-

tion of Light from (;lass (unpublished).49. (’. E. Buckwald, D.M. Gallagher, (’. P. Haskins, E.M.

Thatcher and P. A. Zahl, Proc. Natl. Acad. Sci. 24,204(1938).

50. P A. Zahl, C.P. Haskins, D.M. Gallagher and C.E.Buckwald, Trans. Faraday Soc. 35,308 (1939).

51. R. W Goranson and W.A. Zisman, J. Chem. Phys. 7,492 (1939).

52. K.H. Beck. Ph. D. Thesis, University of Marburg, W.Germany, 1966 (unpublished).

53. K.H. Drexhage and H. Kuhn, Basic Problems in ThinbTlm Physics, (Gttingen, Vandenhoeck and Ruprecht,1966) 339.

54. P.L. Hawkes, Thin b1m Integrated Circuits, (AEIEngineering) 5, 304 (1965).

55. A Leger. J. Klein, M. Belin and D. Defourneau, ThinSolid Films 8, R51 (1971 ).

56. U. Khanna and. V. K. Srivastava, Thin Solid Films 12,S25 (1972).

57. U. Khanna, V.K. Srivastava and V.K. Agarwal, ThinFilms 2, 83 1971).

58. U. Khanna, and V. K. Srivastava, Thin Films 2, 167 (1972).59. U. Khanna, Ph.D. Thesis, University of Roorkee, India,

1973 (unpublished).60. K.I. Chopra,J. Appl. Phys. 36,655 (1963).61. H. E. Ries, Jr. and D. C, Walker, .L Colloid Sci. 16,361

(1961).62. H.E. Ries, Jr. and W.A. Kimball, Nature 181. 901

(1958).63. J. Tanguy and P. Hesto, Thin Solid Films 21,129 (1974)64. H. MOiler, Phys. Rev. 50, 547 (1936).65. L. Salem,J. Chetn. Phys. 37, 2100 (1962).66. K. G. Denbigh, Trans. braday Soc. 36,936 (1940).67. C.P. Smyth, Dielectric Constant and Molecular Struc-

ture, (Chem. Catalog., New York, 1931).68. H. FriShlich, Theory of Dielectrics (Oxford Univ. Press,

1958) 2nd Ed.69. J.J. O’Dwyer, The Theory o]’Electrical Conduction and

Breakdown in SolM Dielectrics, (Clarendon Press,Oxford, 1973).

70. R. H. Fowler and I.. Nordheim,Proc. R. Soc. A 119, 173(1928).

71. J. Frenkel,Phys. Rev. 36, 1604 (1930).72. A. Sommerfeld and H. Bethe, ltandbueh der Physik,

XXIV, Pt. 2, (Julius Springer, Berlin, 1933) 133.73. J.G. Simmons, D.C. Conduction in Thin Films, (Mills

and Boon, London, 1971).74. W. Schottky Ph.ys. Z. 15,872 (1914).75. N. Mott and R. W. Gurney, Electronic Processes in Solids

(Oxford University Press, London, 1948).76. A Rose, Phys. Rev. 97, 1538 (1955).77. J. Frenkel, Tech. Phys. USSR 5, 68 (1938); Phys. Rev.

54, 647 (1938).78. C. A. Mead, Phys. Rev. 128, 2088 (1962).79. J. Giaver, Phys. Rev. Lett. 5, 147 (1960); 5,464 (1960).80..I. Nicol, S. Shapiro and P. Smith, Phys. Rev. Lett. 5, 4.61

(1960).81. J. L. Miles, and H. O. McMahon, J. Appl. Phys. 32, 1176

(1961).82. R. Stratton,J. Phys. & 67tern. Sol. 23, 1177 (1962).83. J.G. Simmons, J. Appl. Phys. 34, 1793 (1963); 34, 2581

(1963).84. S. Horiuchi. J. Yamaguchi and K. Naito, J. Electrochem.

Soc. 115,634 (1968).85. J.G. Simmons,& Appl. Phys. 35, 2472 (1964).86. S.R. Pollack and (’. E. Morris, J. Appl. Phys. 35, 1503

(1964).


87. W.E. Flannery and S R. Pollack, J. Appl. Phys. 37,4417 (1966).

88. B. Mann. H. Kuhn and L.v. Szentpaly, Chem. Phys. Lett.8, 82 (1971).

89. L. v. Szentpaly, D. Mbbius and H. Kuhn, J. Chem. Phys.52, 4618 (1970).

90. V. K. Srivastava, Phys. Rev. Lett. 30, 1046 (1973).91. M.H. Nathoo and A. K. Jonscher, J. Phys. C 4, L301

(1971).

92. R. M. Hill,Phil. Mag. 23, 59 (1971).93. A. K. Jonscher, J. Vac. Sci & Technol. 8, 135 (1971).94. A. K. Jonscher,Phil. Mag. 23,205 (1971).95. A. K. Jonscher, J. Noncryst. Solids 8- 10, 293 (1972).96. A.K. Jonscher /nd M. H. Nathoo, Thin Solid Films 12,

S15 (1972).97. A K. Jonscher, J. Electrochem. Soc. (To be published).98. E.J. Le Sueur and A. K. Jonscher, Thin Solid Films 12,

59 (1972).

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


ELECTRICAL BEHAVIOUR LANGMUIR FILMS A REVIEW,

Documents

Transcript of ELECTRICAL BEHAVIOUR LANGMUIR FILMS A REVIEW,