Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Xie, Yidan
Master of Science - MSc
University of British Columbia
Infrared reflectance and transmittance measurements of diamond-like carbon thin films grown by d.c. magnetron sputtering were performed at nearly normal incidence, using a Bruker IFS 1 13V Fourier-transform spectrometer. The project was a collaboration with Glenn Clarke, a Ph.D student under the supervision of Dr. R. Parsons. Glenn Clarke grew all of the films and extracted the absorption coefficient from the reflectivity and transmission data, using a matrix method. The spectral features were mainly the broad interference oscillations characteristic of thin films and the absorptions caused by excited vibrational modes. An interband-transition model of n and k, together with a dispersion model, which is a superposition of the background absorption and the vibrational resonances, was used to fit the experimental data and obtain some information about the chemical bonds in these films. It was found that the optical properties of the diamond-like carbon films were strongly dependent on the deposition pressure during the sputtering and any hydrogen incorporation.
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THE MEASUREMENTS OF THE OPTICAL PROPERTIES OF DIAMOND-LIKE CARBON THIN FILMS BY FOURIER-TRANSFORM INFRAREDSPECTROSCOPYbyYIDAN XIEB.So., Peking University, P.R.China, 1991A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standard1.1THE UNIVERSITY OF BRITISH COLUMBIAOctober 1994© Yldan Xie, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)____________________Department of PInisThe University of British ColumbiaVancouver, CanadaDate Oct. 12, 1994-DE-6 (2/88)AbstractInfrared reflectance and transmittance measurements of diamond-likecarbon thin films grown by d.c. magnetron sputtering were performed at nearlynormal incidence, using a Bruker IFS 1 13V Fourier-transform spectrometer. Theproject was a collaboration with Glenn Clarke, a Ph.D student under thesupervision of Dr. R. Parsons. Glenn Clarke grew all of the films and extracted theabsorption coefficient from the reflectivity and transmission data, using a matrixmethod. The spectral features were mainly the broad interference oscillationscharacteristic of thin films and the absorptions caused by excited vibrationalmodes. An interband-transition model of n and k, together with a dispersionmodel, which is a superposition of the background absorption and the vibrationalresonances, was used to fit the experimental data and obtain some informationabout the chemical bonds in these films. It was found that the optical properties ofthe diamond-like carbon films were strongly dependent on the deposition pressureduring the sputtering and any hydrogen incorporation.Table of ContentsAbstractTable of Contents iiiList of Tables viList of Figures viiAcknowledgment ixChapter 1 Introduction I1.1 Diamond-like Carbon Thin Films 11.1.1 Attractive Properties and Applications 11.1.2 Deposition Technology 31.1.3 Experimental Work on the Properties of DLC Films 61.1.3.1 Mechanical Properties 61.1.3.2 Electrical Properties 71.1.3.3 Optical Properties 81.2 Characterization Method for Optical Properties and Structures 121.2.1 Ellipsometry 121.2.2 lR Spectroscopy 121.2.3 Raman Spectroscopy 131.2.4 X-ray Photoelectron Spectroscopy (XPS) and AugerElectron Spectroscopy (AES) 131.3 Purpose and Outline of the Thesis 14Chapter 2 Experimental Method and Instrumentation 162.1 Fourier-transform Spectroscopy 162.1.1 Michelson Interferometer 17III2.1.2 Fourier Analysis 202.1.2.1 Fourier Transformation 202.1.2.2 Sampling Interval and Alising 232.1.2.3 Picket-fence Effect and Zero Filling 272.1.2.4 Leakage and Apodization 282.1.3 Resolution 302.1.4 Phase Correction 342.1.5 Comparison Between Grating and FT-IR spectrometer-Jacquinot and Fellgett Advantage 352.1.5.1 Jacquinot Advantage 352.1.5.2 Fellgett Advantage 362.2 Instrumentation 372.2.1 Bruker IFS 113V FT-IR spectrometer 372.2.2 Sources 422.2.3 Beamsplitters 422.2.4 Detectors 43Chapter 3 Measurements 453.1 Reflectance Measurements 453.1.1 Sample Chamber Arrangement 453.1.2 Measurement Procedure 453.2 Transmittance Measurements 493.2.1 Sample Chamber Arrangement 493.2.2 Measurement Procedure 493.3 Sample Preparation 52ivChapter 4 Reflection, Transmission and Absorption in AmorphousThin Films 544.1 Matrix Method for Reflectance and Transmittance Calculation 544.1.1 The Sample Boundary 544.1.2 Assembly of Thin Films 554.1.3 Coherent Films and Incoherent Substrate 594.2 Optical Model for Amorphous Solids in the Interband Region 614.2.1 Derivation of k(E) 614.2.2 Derivation of n(E) 634.3 Optical Model for Amorphous Solids in Long WavelengthRegion 64Chapter 5 Experiment Results and Discussion 675.1 Experiment Results 675.1.1 Far-infrared Results 675.1.2 Mid-infrared Results 685.1.3 Near-infrared Results 695.1.4 Absorption Coefficients and Bonding Configuration 695.2 Discussion 715.2.1 Optical Properties and Bonding Configuration 715.2.2 Effects of Hydrogen and Oxygen Incorporation 725.2.3 Effects of Deposition Pressure 73Chapter 6 Conclusion 93Bibliography 96VList of Tables2-1 Coefficients for Blackmann-Harris function 303-1 Optical Parameters in the Bruker IFS 1 iSV 473-2 Deposition Parameters for the Samples Tested 535-1 Fitting Parameters and Possible Bonding 92viUst of Figures1-1 Schematic of a planar magnetron sputtering system 52-1 Schematic of a basic Michelson interferometer 192-2 Examples of spectra and their corresponding interferograms 222-3 Continuous interferogram and its computed spectrum 252-4 Sampled interferogram and its computed spectrum 252-5 Apodization functions and their corresponding InstrumentalLineshapes 312-6 Optical system of the Bruker IFS 113V 393-1 Front channel optical arrangement in the Bruker IFS 113V 463-2 Sample holder for reflectance measurements 463-3 Back channel optical arrangement in the Bruker IFS 113V 503-4 Sample holder for transmittance measurements 504-1 Schematic of a pile of layers and coordinates 564-2 The transformations of the waves across the interface betweenlayers and through the inside of the layer 564-3 Schematic of layers in our samples 605-1 Far-infrared reflectance spectra of SI-GaAs and sample acapl8 775-2 Far-infrared transmittance spectra of SI-GaAs and sample acapi 8 785-3 Mid-infrared reflectance and transmittance spectra of SI-GaAs 795-4 Mid-infrared spectra of sample acjul 1 805-5 Mid-infrared spectra of sample acjul3 815-6 Mid-infrared spectra of sample acau07 825-7 Mid-infrared spectra of sample acjul7 B3vi’5-8 Mid-infrared spectra of sample acjl27 845-9 Near-infrared reflectance spectra of acau07 and acjul7, and theirbest fittings 855-10 Mid-infrared absorption coefficient spectrum of acjul 1 and its bestfitting 865-11 Mid-infrared absorption coefficient spectrum of acjul3 and its bestfitting- 875-12 Mid-infrared absorption coefficient spectrum of acjul7 and its bestfitting 885-13 Mid-infrared absorption coefficient spectrum of acjl27 and its bestfitting 895-14 Mid-infrared absorption coefficient spectrum of acauo7 and its bestfitting 905-15 Near-infrared kfor films of different deposition pressure and forfilms with and without impurity incorporations 91VIIIAcknowledgmentI would like to thank my supervisor, Dr. J. E. Eldridge, for his patient,knowledgeable and valuable instructions and supervision.All the samples were provided by Dr. Parson’s lab. I am very grateful toGlenn Clarke for growing the samples and the work of obtaining film thicknessesand optical constants. I also would like to thank him for his helpful suggestionsand discussions.This work was supported by grants # 5-85653 and # 5-81631 from theNatural Science and Engineering Research Council of Canada (NSERC).ixChapter 1INTRODUCTION1.1 Diamond-like Carbon Thin Films1.1.1 Attractive Properties and ApplicationsCarbon has two elementary forms: crystalline and amorphous. In itscrystalline form, it can exist as either diamond, a wide band semiconductor, orgraphite, a semimetal. The diamond crystal structure is face-centered cubic, inwhich each atom is covalently bonded to four other carbon atoms. These bondsare known as sp3 tetragonal bonds. The structure of graphite is described aslayers of carbon atoms with strong sp2 trigonal bonds in the plane, and the fourthatom in the outer shell forms a weak van der Waals type bond between planes [1].As a result, diamond has the properties of extreme hardness, chemical inertness,high electrical resistivity, high dielectric strength, excellent optical transparency inthe infrared, and high thermal conductivity, while graphite appears to be theopposite: softness, lubricity, good electrical conductivity, lower density and agrayish-black appearance. On the other hand, in its amorphous forms, carbon canbe regarded as degenerated or imperfect graphite structure, where only shortrange order exists and is responsible for the intermediate properties.Though diamond exhibits excellent mechanical and optical propertieswhich make it an ideal window material, it is not readily available. This led to thedevelopment of Diamond-like carbon (DLC) films. They were first produced byAisenberg and Chabot [2] and are characterized by extreme hardness and scratch1Chapter 1 Introduction 2resistance, high electrical resistance, high dielectric strength, chemical inertness,and transparency in the infrared region. The properties of DLC films are closer tothose of diamond than graphite. This may be explained by their structure andbonding network: the films are amorphous rather than crystalline, with all possiblecombinations of sp1, sp2, and sp3 bonds, which are typical for carbyne, graphite,and diamond, respectively [3]. It has been found that a significant fraction of thecarbon atoms is present as sp3 tetrahedrally coordinated sites in diamond-likecarbon films [4] [5].Arising from the extraordinary properties similar to diamond, the DLC filmshave drawn great attention and have been applied extensively, such as for wear-and corrosion-resistant coatings in sliding devices, antireflection coatings,protective coatings, dielectric p-n junctions, barrier coatings, passivation layers,and heat sinks in electrical devices [1]. The followings are some examples ofthese applications:•Overcoats on thin-film media for magnetic recordingSince head-disk contact occurs intermittently when the drive starts andstops, the overcoats on the thin-film media used in computer hard disks areessential for reliable memory storage. The overcoats should be as thin aspossible, resist wear by the head, have low static and dynamic friction coefficientswith the head, and protect the medium against corrosion. Thus, the hard DLC filmare widely used as wear resistant overcoats on thin film media [1].•Antireflection coatings on germaniumThe DLC film is smooth, hard, durable and optically transparent in theinfrared, thus it is a suitable coating for germanium, which is the most commonlyused window and lens material in this region but which is easily scratched byChapter 1 Introduction 3sand and chemically attacked by salt water. Furthermore, the refractive index of 4of germanium makes it reflect the incident light considerably. DLC films wereshown to be very good as antireflection coatings on germanium [6].•Protective coatings on front surface aluminum mirrorThe optical performance of front surface mirrors in thermal imagingsystems tends to deteriorate with time and with exposure to the atmosphere. DLCfilms have been demonstrated to be suitable protective coatings needed for thefront surface mirrors in the infrared region, since they overcome the shortcomingsof other types of coatings in this optical region [6].1.1.2 Deposition TechnologyDiamond-like carbon films can be generally divided into two categories:hydrogenated and non-hydrogenated. Hydrogenated DLC films are typicallyprepared by impact of hydrocarbon ions in the energy region from several tens to100eV. Direct deposition from hydrocarbon ion beams and by r.f. self-bias plasmaassisted chemical vapor deposition are the most commonly used methods, whichprovide much higher impact energy than other methods. Non-hydrogenated DLCfilms containing little hydrogen can be prepared by sputtering of carbon, by direction beam deposition from ion beams or by condensation of vaporized carbonatoms produced by laser evaporation . It is impractical to describe all of thesesystems, and so some typical ones have been chosen..Ion beam plating methodIon beam plating of hydrocarbons at an acceleration voltage has been used toprepare hydrogenated DLC films. Electrons, emitted from a hot tungstencathode and accelerated passing through an anode grid up to 200eV, ionizeChapter 1 Introduction 4the vapor or gas molecules which are introduced into the deposition chamberand create a plasma [7]. Ions generated are accelerated to the substrate whichis negatively biased. The ionization device is surrounded by a screen held at afloating potential. The hydrocarbon vapor used for film deposition are usuallymethane, ethane, butane, propane and benzene etc. [8].•r.f. plasma depositionr.f. plasma assisted chemical vapor deposition has the advantage of the abilityto grow smooth transparent hydrogenated DLC films with a high depositionrate on a large area. One of these deposition systems was described byA.Bubenzer [9] to grow hydrogenated hard carbon thin films in an r.f. glowdischarge sustained by a hydrocarbon gas. The system is first evacuated, thenAr discharge is started in order to sputter clean the substrate. A hydrocarbongas is subsequently leaked into the system. In the r.f. discharge, hydrocarbonsare partially ionized and cracked. Within the ion sheath region, the positivelycharged particles are accelerated toward the substrate and thereby form thecarbon film. Benzene is usually chosen because of the comparatively lowcoating stress and high deposition rate that it can give..Magnetron sputteringThis method is widely used to generate non-hydrogenated carbon films.Though the deposition rate is low, it can produce smooth, transparent DLCfilms under extremely good operational control with respect to uniformity andhomogeneity. Moreover, it can be used to grow multilayer films and has theability to scale to the larger sources and substrate areas necessary forindustrial application [10].Chapter 1 Introduction 5GROUNDSHIELDINERT REACTIVEGAS GASSUBSTRATEHOLDERSUBSTRATEHIGH VACUUM PUMP(A)Fig. 1-1: (A) Schematic of a planar magnetron sputtering system. (B) Schematic ofthe cathode assembly of the planar magnetron sputtering system.VACUUMCHAMBER/7 /777////“\ /TARGET))‘)MAGNETS/////yz_ // 7/ (B)Chapter 1 Introduction 6A d.c. planar magnetron sputtering system in Dr. Parson’s lab was used for oursamples and is shown in Fig. 1-1 [11]. The system was described in detail inGlenn Clarke’s M.A.S c thesis [11]. The pyrolytic graphite target is bombardedby energetic Ar ions and a portion of the ejected atoms then condense ontothe substrate, which is positioned between 4 to 12 cm from the target surface,producing a thin film. The application of the magnetron can increase thedeposition rate and overcome the film damage problem caused by thebombardment by highly energetic electrons [11].1.1.3 Experimental Work on the Properties of DLC FilmsDLC films have attracted considerable attention because of their unusualproperties and promising applications. A lot of work has been done to exploretheir structures, properties and it is clear that different deposition techniques andsystem configurations yield greatly variable film properties. Besides, a variety ofcharacterization techniques are employed for investigation of the properties andthe relationship between the properties and the preparation conditions. Thefollowing review is mainly extracted from reference [1].1.1.3.1 Mechanical PropertiesThe hydrogenated DLC films typically have mass densities ranging from1.4 to 2.0 g/cm3, with the least dense films found at the highest hydrogen content[4]. The densities of non-hydrogenated DLC films are usually higher than those ofthe hydrogenated ones. For the films prepared by the sputtering method, the filmdensity is found to be dependent on the d.c.. or r.f. sputtering power: withincreasing sputtering power, the density of the films decreases [10] [12].Chapter 1 Introduction 7Hardness measurements of DLC films grown by d.c. magnetron sputteringindicate that pressure also affects film density [13].Internal stresses and adhesion are important features since they determinethe stability of the coating/substrate composite and thus the lifetime of thecomponent. They may be affected by a number of processing parameters, suchas deposition rate, angle of incidence, deposition temperature, and incorporationof impurities [4]. The hydrogenated DLC films are usually found in a highcompressive stress state, the level of which increases with increasing hydrogencontent, and the addition of fluorine increases compressive stress while nitrogenreduces compressive stress.DLC films exhibit low values of friction coefficient [14]. Increasing humidlityis found to result in a increase in friction coefficient and a decrease in wear factor[15].1.1.3.2 Electrical PropertiesSince electrical resistivity is one of the crucial properties to characterizethe electronic structure of carbon, it has been studied by many people.In general, hydrogenated DLC films are characterized by high resistivity,and they have higher resistivities than non-hydrogenated films. The resistivity isincreased greatly by hydrogen due to the stabilization of four-fold sp3 bonds byhydrogen [16]. It has been suggested that amorphous DLC films consist of amixture of diamond and graphite bonds which act as the localized conductionstates [19]. Thus, electrical resistivity may be a sensitive tool to measure thedegree of amorphousness.Chapter 1 Introduction 8The resistivity of DLC films shows strong dependence on depositionconditions. The amorphous carbon films prepared by vacuum evaporationgenerally have a room temperature resistivity of between 10-1 and 1 cm [17],while the film prepared by d.c. magnetron sputtering at low power can have 10ccm [10]. The electrical measurements taken by N.Savvides [10] showedconsistence with Mott’s model, which is, the conduction in amorphous carbon iscaused by thermally activated hopping or tunneling of electrons between localizedstates which are associated with the it bonds of three-fold coordinated (graphitic)carbon atoms. For the d.c. magnetron sputtering method, It has also been foundthat conductivity varies with sputtering power, and the DLC film grown at lowpower possess insulating properties [10]. The spectra of the imaginary part of thecomplex dielectric function E2 is found to possess features typical of amorphoussemiconductors [18]. It also showed in [13] that there is an increase in resistivitywith increasing sputtering pressure, which cannot be explained simply in terms offilm microstructure, and seem to imply changes in the bonding coflfiguration of thecarbon atoms. As for other deposition methods, the resistivity of films is found torely on the deposition parameters such as r.f. power and substrate temperature inthe glow discharge deposition of hydrocarbons and bias voltages in ion plating orii decomposition of hydrocarbons [1].1.1.3.3 Optical PropertiesThe potential application of DLC films as protective windows has led to agreat deal of research on their optical properties. Furthermore, optical propertiesare closely related to the microstructures of the film, which determine the filmproperties.Chapter 1 Introduction 9Generally speaking, the optical properties of DLC films are closer to thoseof diamond, a large band gap semiconductor, than those of graphite, a semimetal.The optical constants n and k can be calculated from the reflectance andtransmittance measurements. The extinction coefficient k shows a rapid decreasewith increase of wavelength or decrease of photon energy in the visible region. Inthe infrared region, the absorptions are mainly associated with carbon, hydrogen,and oxygen vibrational modes. On the other hand, by increasing the hydrogenconcentration, the band gap is increased to a maximum value, thus causing thefilms to become more transparent.Optical properties in solids can be described in terms of the complexrefractive index N—n+ik or the complex dielectric function £=E1+k’2. The tworepresentations are related by:=n2—k£2 = 2nkAbsorption is characterized by the absorption coefficient x(v) = 4ivk where v isthe wavenumber..The visible absorption can be expressed by the Tauc formula:(aE)1”2=B(E—E0,where Eis the photon energy. The optical band gap E0, whichis an important parameter to characterize amorphous solids, can be deduced fromthe intercept of the extrapolated linear fit to a plot of (aE)1versus E [20] [1]. Thecorrelation of E0 with hydrogen content has been shown in [3] for rf-plasmadeposited films: with increasing bias voltage, the hydrogen content decreases andso does E0.The optical constants n and k vary with the preparation conditions. Forsputter-deposited non-hydrogenated DLC films, the refractive index n appears toChapter 1 Introduction 10increase with sputtering power, and shows minimum dispersion in infrared (lR)region for film deposited at less than 50W [10]. In most cases, n of hydrogenatedamorphous carbon films remains roughly constant in the visible (VIS) region [21].Details of the atomic arrangement and bonding structure can be derivedfrom the analysis of the IR absorption bands. For hydrogenated DLC films, in thecase of ion-plating-deposited layers [22], considerable absorption occurs only inthe wavenumber range v1 500 cnr1, which may be explained by the activation ofphonons in the carbon network. Absorption lines due to C-H bonds were notobserved. For microwave-deposited samples, strong absorption lines occur near2920 cm (sp3 C-H stretching vibrations), 1450 cm-i (deformation vibrations ofCH2 or CH3 groups), and around 1300 cm-’, 1600 cm-1, corresponding to sp2- orsp2-and sp3- hybridized carbon atoms. The bonding structure of tile hydrogenatedDLC films prepared by d.c. magnetron sputtering is given by S.Craig [20]. Theoptical studies done by O.Stenzel et al. on ion-plating-deposited samples showedthat the strong absorption lines occur at the region 750 crn1<v<1700 cm-1, and2800 c,w1<v<3200 cm-1, and there is the expected window between 1700-2800cm-1. In addition, a dispersion model combining polymer-like features withabsorption tendencies typical of amorphous solids was given, which was asuperposition of Lorenze lines for vibrational resonances and an Urbach tail forthe background absorption. J Ullmanri et at. studied the DLC films prepared byr.f. sputtering with target voltage as a parameter, and found that at low targetvoltage, the optical properties is similar to those of DLC films grown by d.c.plasma deposition and ion-plating deposition [24].Hydrogen incorporated in the amorphous DLC films may play a crucial rolein the bonding configuration of the carbon atoms. It is believed that hydrogen canChapter 1 Introduction 11help stabilize the tetrahedral coordination (sp3 bonding) of the carbon atomswhich is the origin of the diamond like properties of the hydrogenated DLC films[101. In order to understand the influence of hydrogen, the changes of C-Hbonding as determined by IR spectroscopy have been studied with heating, forthe films formed by ion beam processes [23]. It has been found that most of thecarbon atoms in the film which are attached to hydrogens have a tetrahedral (sp3)structure, and some sp2 even sp1 bonding also exist depending on the depositionconditions. On heating the films for 1 hour in 500°C range, the sp3 carbon losehydrogen forming sp2 bonds. On heating to 700 °C or more, the remaininghydrogen is lost and the films lose transparency which is proceeded by anincrease in the refractive index. The study indicates that the presence ofhydrogen is required to obtain carbon films that are transparent in the IR regionand have good mechanical properties as well. In another work of IR spectroscopy[20], the role of hydrogen in optical properties was concluded as altering the optoelectronic properties of the hydrogenated DLC film by modifying the distribution ofbonding and antibonding states of the basic singly bonded carbon network. Thisis indicated by the reduction in optical band gap resulting from 500°C bake-out ofthe hydrogen and an increase in C=C double bonding. However, afterinvestigating the properties of the non-hydrogenated DLC film prepared by d.c.magnetron sputtering of graphite, N.Sawides and B.Window suggested that thepresence of hydrogen is not strictly necessary for obtaining stable tetrahedralbonding in the amorphous carbon matrix, though the incorporation of hydrogendoes improve the overall diamondlike properties by reducing the refractive indexand increasing the IR optical transparency [10].Chapter 1 Introduction 121.2 CharacterizatIon Methods for Optical Properties and StructureA great number of characterization methods are available to studyamorphous DLC films. Among them, the most commonly used methods for opticalproperties are ellipsometry and IR spectroscopy. X-ray photoelectronspectroscopy and Auger electron spectroscopy are two of the most powerfulsurface composition analysis techniques. Some other techniques such as X-raydiffraction, transmission electron spectroscopy, laser Raman spectroscopy andelectron-energy-loss spectroscopy are also important tools for studying thin filmstructures.1.2.1 EllipsometryIn spectroscopic ellipsometry, a non-destructive optical probe, the changeof polarization of elliptivally polarized light due to reflection is measured andinterpreted in terms of properties of the reflecting surface [1]. There are twocharacteristic parameters measured in ellipsometry: the change of relativeamplitude and phase difference of two orthogonal components of light due toreflection. From these measured quantities, thickness and refractive index of atransparent film can be determined if the optical constants of the substrate areknown. The optical constants of DLC films were measured by ellipsometry in thevisible region [13] [25].I .2.2 IR SpectroscopySince ellipsometry is only efficient in the visible region, another method isnecessary for the longer wavelengths. IR spectroscopy is always employed in thiscase because the optical constants of the films can be calculated from theChapter 1 Introduction 13measured reflectance and transmittance spectra. Thus, the absorption behavior ofthe film can be obtained. The strong absorption lines in this region are mainly dueto the excitations of vibrational modes, therefore, the information of atomicbondings in the films can be obtained through analysis of the characteristicvibrational frequencies of chemical bonds. Most works on the optical propertiesintroduced in previous section were performed by this method.1.2.3 Raman SpectroscopyRaman spectra of solids result from inelastic scattering of optical photonsby vibration phonons and is a very useful technique for the characterization ofmaterial structures. Unilke IR spectroscopy, which is related to the change ofelectrical dipole moment, Raman spectroscopy is connected with a change in thepolarizability of the molecule during vibrations. Raman spectra are sensitive tochanges that disrupt the translational symmetry of the material and thus are usefulfor the study of disorder and crystallite formation in DLC films [1].1.2.4 X-ray Photoelectron Spectroscopy (XPS) and Auger ElectronSpectroscopy (AES)In XPS, x-rays are used to eject electrons by raising each electronic energylevel from its original value by the amount of the photon energy. The outstandingstrength of XPS is its ability to detect small chemical shifts in electron energylevel. However, it lacks of spatial resolution.The Auger process is easily understood by an analogy with X-ray emission,in which an incident electron ejects an atomic electron creating a core hole andChapter 1 Introduction 14initiates a de-excitation process. AES is useful because of the rapidity of datacollection owing to the high efficiency of the Auger process.Both XPS and AES can provide information on bonding between atoms andon core level binding energy, and thus can be used to distinguish both theelements and its chemical states [1].1.3 Purpose and Outline of the ThesisThe purpose of this thesis is to study the optical properties of amorphousDLC thin films deposited by the d.c. magnetron sputtering method, and obtain theinformation of atomic bondings in the films, by using a Fourier-transform infrared(FT-IR) spectrometer. This work was a cooperation between Dr. Parsons’s thinfilm lab and Dr. Eldridge’s FT-lR spectroscopy lab. The DLC films were all grownby Glenn Clarke in Dr. Parsons’s lab and then tested by FT-IR spectrometer in Dr.Eldridge’s lab. Glenn Clarke also developed programs to obtain the filmthicknesses and n,k results in the MIR region. Furthermore, we investigated thecorrelation between the deposition parameters and the film properties so that it ispossible to determine the optimum conditions for deposition of infraredtransparent DLC films in Dr. Parsons’s lab.In the second chapter of this thesis, the principles and advantages of aFourier-transform infrared spectrometer are described, together with the details ofthe Bruker 11 3V interferometer used for the experiments.In the third chapter, the details of reflectance and transmittancemeasurements are given. There is also a brief description of the samples tested.Chapter 1 Introduction 15The fourth chapter is the theory of the reflectance and transmittancecalculation, using the matrix method, as well as the optical absorption modelsapplied to interband and longer wavelengths regions.The fifth chapter contains the experiment results, which include thereflectance and transmittance spectra for 6 samples, the results of opticalconstants calculated from the reflectance and transmittance data, and the fittingsof the absorption coefficients using a dispersion model described in Chapter 4.Therefore, information about the chemical bonds can be obtained. Finally, bycomparing these samples, the effects of the deposition parameters on the filmproperties are discussed.The final chapter is the conclusion, a summary of the work and themeaning of the research.Chapter 2EXPERIMENTAL METHOD AND INSTRUMENTATION2.1 Fourier Transform SpectroscopyFourier-transform spectroscopy is one of the fundamental and importanttools for studying condensed matter, since it is simple yet powerful. Resulting fromits non-contact and non-destructive characteristics, it is most commonly used tostudy the optical properties of materials over a wide frequency range.Mainly due to the two-beam interferometer and the computer facilities used,Fourier-transform (FT) spectrometer has the following advantages [26] over thetraditional instruments such as diffraction grating monochromators:• It receives information from the entire spectral range during each time elementof a scan, while the grating instrument can just receive the information in a verynarrow band. This is known as Fellgett or multiplex advantage, which will bedescribed in detail later.• It can operate with small f numbers (i.e. with large solid angles at the sourceand detector), thus, it can collect a large amount of energy at high resolution.• It has a large resolving power as a result of the first two advantages.• It has high wavenumber accuracy achieved by the precise change in theinterference pattern, which is due to the laser interferogram used and theaccuracy of the laser frequency.• The stray or unwanted flux problem has been greatly reduced because of theinterference phenomena involved in the interferometer. The unwanted light16Chapter 2 Experimental Method and Instrumentation 17signals do not get modulated by the moving mirror, nor do they appear in theinterferogram.• By the means of rapid-scan technology, the measurement can be performedextremely fast and electrical filtering can be used. This advantage will bediscussed in detail later.These advantages, as well as some other additional ones, make FTspectroscopy widely used in many fields, especially in Physics and Chemistry. Formore information about the merits and applications, see the reference by Bell [26].In order to understand this technology better, it is necess&ry to review thebasic theories of the data collection and manipulation of the spectra. Therefore,the following sections will describe the Michelson interferometer, FT analysis, andother related data processing techniques.2.1.1. Michelson InterferometerThe main component of the spectrometer is the Michelson interferometer.Fig. 2-lA shows the basic Michelson interferometer with the sample in therecombined beams after the beamsplitter.The beam from the source S is chopped and collimated, then directed tothe beamsplitter, where half of it (beami) is reflected and goes to mirror Ml whilethe other half is transmitted and goes to mirror M2. Both of the two beams will bereflected back to the beamsplitter. After the beamsplitter, the transmitted part ofbeam 1 and the reflected part of beam2 will recombine with each other andinterfere, since they are spatially coherent.M2 is a fixed mirror. Suppose beam2 travels a distance L12 before hittingM2, then the total optical path of beam2 is L when it hits the beamsplitter again.Chapter 2 Experimental Method and Instrumentation 18Ml is a movable mirror which can be controlled to move back and force around112 by a distance xJ2. So the total optical path difference between the two beamsat the point they recombine is x. The intensity of the recombined beam, which ismeasured by the detector, is a function of x and called the interference pattern orinterferogram. For a monochromatic source with intensity 1(v) at wavenumber v(v=1IA in cm-i), the interferogram has the form:1(x) =I(1+ cos2itnx) (2.1)and is shown in Fig. 2-iC. For a polychromatic source, the interferogram is theintegral of the monochromatic interferogram over the frequency or wavenumberrange:1(x)= fmc!(v)(1+ cos27rvx)dv(2.2)= —I(O) +$“I(v)cos2itvxci2where 1(0) is the intensity at zero path difference, Vmjn vmax are the minimum andmaximum wavenumber generated by the polychromatic source. Fig. 2-1 B showsthe interferogram in this case. Though the detector usually detects theinterferogram from the polychromatic source, the interference pattern generatedby the monochromatic light, such as a He-Ne laser, is also very important,because it allows very precise tracking of the moveable mirror. Thus, it is used inall modem Fourier-transform infrared (FT-lR) spectrometers to control themovement of the moveable mirror and measure the change in the optical pathdifference.Fig. 2-iC shows how the lR interferogram is digitized precisely at the zerocrossings of the laser interferogram. Since the accuracy of the sample spacingbetween two zero crossings is determined by the precision of the known laserChapter 2 Experimental Method and Instrumentation 19wavelength, FT-JR spectrometers have a wavenumber calibration of highprecision. This advantage is known as Connes advantage [27].Ml___________xSBM2A3— --x‘I’llIIIliCFig.2-1: (A) Basic Michelson Interferometer. S: source. B: chopper. BS:beamsplitter. Ml: movable mirror. M2: fixed mirror. G: sample. D: detector. x:mirror displacement. (B) Signal measured by detector 0. This is interferogram of apolychromatic source. (C) Interference pattern of a laser source. Its zero crossingsdefine the positions where the interferogram is sampled (dashed lines)Chapter 2 Experimental Method and Instrumentation 202.1.2 Fourier Analysis2.1.2.1. Fourier TransformationThe interferogram is measured as a function of path difference x. In order toobtain the spectrum, which is a function of wavenumber (or frequency), theFourier-transform integral theorem must be applied.Mathematically, a function I(.’) can be written as1(x) = fI(v)exp(—i21rvx)dP (2.3)If we know I(.c) and want 1(v), it is given by1(v) = fI(x)exp(i2itvx)cfv (2.4)where the second integral is called the continuous Fourier transform and the firstone is called the inverse Fourier transform. However, experimentally, thewaveform (the interferogram) is discretely sampled at evenly spaced intervals.Suppose we have N consecutive sampled values, the discrete Fourier transform(DFT) can be defined to approximate the original Fourier transform:I(kAv) = I(nAx)exp(i27tnk IN) (2.5)where the continuous variables v have been replaced by discrete values Mxand kAy respectively. Thus, the DFT is acceptable for the purpose of digitalmachine computation. The spacing Av in the spectrum is related to AxbyAv=1I(NAx) (2.6)The DFT expresses a given function as a sum of sine and cosine functions.The resulting new function I(kAv) will form the spectrum. Alternatively, if the I(kAv)Chapter 2 Experimental Method and Instrumentation 21is known, the formula for the inverse DFT, which recovers the interferogramI(nAx), is:I(nAx)=EI(kAv)exp(—12,rnk /N) (2.7)Fig. 2-2 shows the spectrum with one or two monochromatic lines, a Lorentzianline, a polychromatic source, and their corresponding interferograrns.The general qualitative rule for an approximate description of thecorrespondence between I(niXx) and I(kbv) is that a finite spectral line width (as isalways present for real samples) is due to damping in the interferogram: Thebroader the line, the stronger the damping. This is illustrated in Fig. 2-2C and 2-2D. Another related rule can be seen by comparing the widths at half height(WWH) of I(nA and I(kzv): The WWH’s of a ‘hump-like” function and its FT areinversely proportional. Using this rule, one can explain why the interferogram inFig. 2-2D has a very sharp peak around the zero path difference position (x=O),while the wings of the interferogram, which contains most of the useful spectralinformation, has a very low amplitude.By examining Eq.(2.7), one can also see that when n=O, the intensity 1(0)measured at the interferogram centerburst actually is a measure of the averagespectral intensity.Eq.(2.5) is seldom used in practice, since it appears to be an order of N2process for N points. In fact, DTF can be computed in an order of Mog2Noperation with an algorithm called the fast Fourier transformation (FFT) so thatsubstantial computer time can be saved. There are a number of variations of thebasic FFT algorithm and the most famous and commonly used one is the CooleyTukey algorithm, in which N must be chosen as a power of 2. In this case,.theChapter 2 Experimental Method and Instrumentation 22spectra taken with a laser-controlled FT-IR spectrometer will show a samplespacing of Av=mlaser wavenumber/2N.Fig. 2-2: Examples of spectra (left) and their corresponding interferograms (right).(A) One monochromatic line. (B) Two monochromatic lines. (C) Lorentzian line.(D) Broadband spectrum of polychromatic source.AB4-- %4.CIL.P.2eWPYENUIIBERS C$4—1Chapter 2 Experimental Method and Instrumentation 232.1.2.2 Sampling Interval and AliasingIn order to understand ‘aliasing and other effects better, a very useful toolin modern scientific analysis should be introduced first: the convolution theorem.This theorem states that the Fourier transform (Fr) of the product of two functions,e.g., 1(x) and A(x), is the convolution of their individual Fourier transforms 1(v) andA(v), where the convolution is defined as:I(v)®A(v) = fA(u)I(v—u)du (2.8)The convolution theorem is used in Fig. 2-3 to illustrate how to determinethe Fourier transform of a sampled interferogram. In most practical situations, onlysamples of the continuous interferogram can be obtained. The sampledinterferogram can be related to the continuous interferogram by the shah function111(x):I(x) ffl(—-)I(x) (2.9)where 18(x) is the sampled interferogram, Ic,(x) is the continuous or the completeinterferogram, and zSx is the sampling interval. 111(x) is defined as:ffl(x)=6(x—n) (2.10)where 8(x-n) is the Dirac delta function and n is an integer. From Eqs. (2.10) and(2.9), we can see that lIl(x/Ax) will just allow in 15(x) those values of theinterferogram for which x=0, ±Ax, ±2zx After applying the convolution theoremand the properties of shah function [26], the FT of the sampled interferogram andthe complete interferogram has the following relationship:/(v)=I(v—niv) (2.11)Chapter 2 Experimental Method and Instrumentation 24where Av=-!_. (2.12)AxThat is, we obtain the complete spectrum every time v equals to nAy for allintegers n. In other words, the spectrum is periodic starting at nAy.Fig. 2-3A shows the ordinary interterogram and Fig. 2-3B gives its completespectrum, which include both positive and negative wavenumbers. The negativewavenumber part of the spectrum is actually just the mirror image of the positivewavenumber part of the spectrum, and is usually discarded. However, we cannotignore it here. Fig. 2-4A shows the sampled interferogram and Fig. 2-4B is thecomputed spectra from the sampled interferogram. The spectrum is completelysymmetric about v=O, ±v, ±2v The solid lines are the contributions from thepositive wavenumbers and the dashed lines are their mirror images. It is very clearthat if Av is big enough or Ax is small enough, the repeated spectra will notoverlap with each other. But if Av is too small, the original spectra of the positiveand negative wavenumber will overlap and the total spectrum will be the sum ofthe dashed lines and the solid lines, as shown in Fig. 2-4C, and one cannotseparate them. This phenomena is called aliasing. In this case, one could notdetermine the true spectrum from the spectrum which is computed from thesampled interferogram.As illustrated in Fig. 2-4C, the sampled spectra is symmetric about v=O, ±v,±2v. ..and is periodic with period of Av. Then the Nyquist wavenumber or foldingwavenumber is defined as:v,=jAv=2. (2.13)Chapter 2 Experimental Method and Instrumentation 25Fig. 2-3: (A) Interferogram. (B) Computed spectrumscan. It is a two-sided spectrum.I(x)txI,liii kfljIOriginFig. 2-4: (A) Sampled interferogram. (B) Computed spectral components from thesampled interferogram. The solid line represents the positive v spectra from Fig.2-3B and the dashed line represents the negative v spectra from Fig. 2-3B. (C)The total spectrum which is the sum of the spectral components in (B).Ic(X)L A-Origin/Vfrom a continuous, completeAKIs(V)VCOf 2AvChapter 2 Experimental Method and Instrumentation 26In order to avoid aliasing, Av must be big enough to avoid overlapping therepeated spectra. One method is to require that the spectrum is zero about amaximum wavenumber Vmax which is smaller than the Nyquist wavenumber vf:(2.14)or2vAmtn. (2.15)So the sampling interval must have an upper bound. In addition, Eq. (2.15) impliesthat one must sample twice in every cycle of the smallest wavelength variation inthe interferogram. From the previous section, we know that the sampling positionsare determined from the zero crossings of an He-Ne laser wave with a wavelength?. of 1/15800 cm. As a zero crossing occurs every 2J2, it samples twice in everycycle and the minimum possible sample spacing Ax,,, is 1/31600 cm, whichcorresponds to a Nyquist wavenumber of 15800 cm1, i.e., the maximumbandwidth which can be measured without overlap has a width of 15800 cm-1.When the investigated bandwidth is much smaller than 15800 crrr1, as in the caseof mid-infrared and far-infrared, Ax can be chosen to be an rn-fold multiple ofAx which leads to an rn-fold reduction of the interferogram size.If the spectrum has a lower limit of Vmin instead of zero, that is, it is zerobelow a lower band limit Vmjn and Vmjn is not zero as assumed before, one has[26]:Ax1(2.16)2(VipVmin) Vif and only ifChapter 2 Experimental Method and Instrumentation 27Vmin=Vmax (2.17)Based on the condition of Eq. (2.17) and the fact that V)( must be a naturalfraction of the He-Ne laser wavenumber, one can fill the previous empty spacefrom 0 to Vmjn with n-i further copies of the original spectrum. Thus, it is possibleto achieve greater reduction of the data size. This technology is calledundersampling.One advantage of an advanced FT-IR software package is that it can takecare of the proper sampling and undersampling automatically so that only theupper and lower limits of the interested spectral range need to be specified. Thusthe only thing one needs to do is to make sure that proper optical or electronicfilters have been inserted so that the spectrum outside the range Vmjn to Vmax Sreally zero.2.1.2.3 Picket-fence Effect and Zero FillingWhen the interterogram contains wavenumbers which are not coincidentwith the sampling wavenumber kAv=W(NAx), an erroneous signal reduction canoccur [27]. This is called the “picket-fenc& effect since one seems to be viewingthe true spectrum through a picket fence, therefore clipping those spectralcontributions lying between the sampling position kzv. The picket-fence effect canbe overcome by the method of zero filling, which is adding zeros to the end of theinterlerogram before applying DFT. As a result, the number of data points in theinterferogram N increases, and zV, which is 1/(Nx), becomes smaller. Thismeans that we will have more points to determine the spectral peaks. Thus, zerofilling has the effect of interpolating the spectrum and reducing the error. As abasic rule, the zero filling factor (ZFF) should be at least 2, that is, one shouldChapter 2 Experimental Method and Instrumentation 28always at least double the original interferogram size. Zero tilling is superior topolynomial interpolation techniques because it will not change the instrumentalline shape and no errors are introduced.2.1.2.4. Leakage and ApodizationThe leakage problem is caused by the truncation of the interferogram atfinite optical path difference. The basic Fourier-transform integrals have theinfinite optical path difference, however, in practice, the interferogram must beobtained over a limited range. In fact, the truncated interferogram I(x can beobtained by multiplying the infinite interferogram F(x) with the infinite optical pathdifference by a rectangular function rect(x), which isrect(x) =1 (lxi XM)(2.18)=0 (N>x1)where XM is the maximum optical path difference. According to the convolutiontheorem mentioned before, the Fourier transform (FT) of a product of twofunctions is the convolution of their individual Fourier transform. Thus, the actualspectrum, which is the FT of the finite interferogram, is:/(v) = F(v) ® ILS(v) (2.19)where F(v) is the FT of the infinite interferogram and ILS(x) is the FT of therectangular function, which is usually called the Instrumental Line Shape function(ILS) or spectral window. In the case of rectangular function, the ILS is the wellknown sinc function:ILS(v) = XM sin(2lwxM) (2.20)2ItVXMChapter 2 Experimental Method and Instrumentation 29which is plotted in Fig. 2-5A. We can see from the figure that ,apart from themaximum central line, there are a lot of side lobes which look like ‘feet” in thespectrum. These side lobes cause a ‘leakage’ of the spectral intensity [27], i.e.,the intensity is not strictly localized but contributes also to these side lobes. Theside lobes or feet of the sinG function drop 22% maximum below zero which islarge and unacceptable. Besides, the side lobes do not correspond to actuallymeasured information but rather represent artifacts due to the sharp sides of therectangular function. Therefore, it is necessary to use gentler functions instead ofabruptly truncating functions in order to decrease the side lobes. This process isknown as apodization, which means “ removal of the feet” (hence the name“apodization” is from Greek “podos” for foot.)There are many apodization functions for this purpose. The common onesare:Triangular (TR):TR(x)=1—1-.— (IXI<xM)(2.21)=0 (XM)Trapezoidal or Four-Point(FP):FP(x)=1 (j<BPC)(BPCIxIBPD) (2.22)=0 (N>BPD)This is a square window between 0 and breakpoint BPC, and then a triangularfunction between breakpoints BPC and BPD. In figure , we choose BPD—xM.Hamming or Happ-Genzel (HG):Chapter 2 Experimental Method and Instrumentation 30HG(x) = 0.54 + 0.46 cos(!) (lxi XM)(223)=0 (jXI>XM)Three- and four-term Blackmann-Harris (BH):BH(x) = A0 + Alcos() + A2 cos(!) + A3cos()+ A4 cos(4lrx)(224)XM XM XM XMThis set of windows is a generalization of the Happ-Genzel function. Thecoefficients have been chosen for optimum suppression of the side lobes [27]:Table 2-1 coefficients for Blackmann-Harris functionA0 Al A2 A43-term BH 0.42323 0.49755 0.07922 0.04-termBH 0.35875 0.48829 0.14128 0.01168Fig. 2-5 shows several apodization functions, including the rectangularfunction, and their ILS’s. It should be noticed that, in Fig. 2-5B to E, the negativelobes are absent, the sizes of the side lobes is smaller, and at the same time, themain lobes of all of the ILS’s are broader than that of the sinc function in Fig. 2-5A.The price paid for the leakage reduction is lower resolution.2.1.3. ResolutionThe resolution of the instrumental line, 6v, is originally defined as the fullwidth at half height (FWHH) of the ILS function. For the sinc ILS functioncorresponding to the rectangular truncation or no apodization, we can haveChapter 2 Experimental Method and InstrumentationAIoxcBTRJ AM C PRCTRRPZOJDRLDIAPP—GCNZt.N.CA31Figure 2-5: Several apodization functions (left) and the “Instrumental Lineshape”produced by them (right).Chapter 2 Experimental Method and Instrumentation 321.21(2.25)2XMAnd for the triangular apodization, the ILS function has the form of XM sinc2(ltvxM),then8v=°90 (2.26)XMOn the other hand, in terms of the separation of two close lines, theresolution can be defined by the Rayleigh criterion. The Rayleigh criterion statesthat two resonance (2 lines with equal intensity) in a spectrum are resolved if theyare separated such that the peak of one resonance falls at the first zero of thesecond one. Under this criterion, for the triangular apodized spectrum, öv isactually the distance between the peak frequency and the frequency at zerointensity:6v=-1- (2.27)XMIf the Rayleigh criterion is applied to two sine ILS functions, which is the case ofno apodization, we will have:(2.28)By comparing Eqs.(2.25) and (2.28), we can see that the full width at halfheight (FWHH) of the rectangular ILS function is l.2/xM and the Rayleighcriterion separates two equal rectangular ILS functions by lI2xM . Thus, thefrequency spreads 6v in these two criteria are equal to each other to within about20%. As for the triangular apodization, the two frequency spreads agree to withinabout 10%.Chapter 2 Experimental Method and Instrumentation 33From the above discussion, we can conclude that the resolution for theunapodized spectrum is higher than that for the apodized spectrum, and it isinversely proportional to the maximum optical path difference used to obtain theinterferogram. Therefore, the choice of particular apodization function depends onthe resolution required. Despite the fact that the Black-Harris function has nearlythe same resolution as the triangular- and Happ-Genzel functions, it is consideredto be the top performer among these three windows, because the highest sidelobe is the most suppressed and it is furthermore nearly zero at the interval ends(see Fig. 2-5).Resolution does not depend only on the maximum path difference andapodization function. It may also be restricted by the aperture size. In the previousdiscussion, we only considered a plane wave incident normally on. the mirror. Withany finite-sized aperture, the radiation from the off center points will be incident onthe mirror at some angle e and will cause a reduced optical path differencebetween the two arms of the interferometer. As a result, the effect of the entireaperture is to spread a monochromatic line at v1 into a range from v1 tovi-vicosemax, where 0max is the maximum incident angle. Furthermore,considering the resolution of two lines in the spectrum, we can arrive at the resultgiven by Jacquinot [26):(2.29)where 2 is the solid angle subtended by the aperture and R is resolving powerdefined by:(2.30).6vThus, the resolution is:Chapter 2 Experimental Method and Instrumentation 346v= (2.31)2,tSo, we can improve the resolution by reducing the aperture size, but the cost isthe reduction of the optical throughput.2.1.4 Phase CorrectionPhase correction is necessary because the FT of a measured interferogramgenerally generates a complex spectrum c(v) [27] from a double-sidedinterferogram rather than a real spectrum S(v), in order to eliminate phase errors.Phase errors are introduced when the symmetry about the zero optical pathdifference point O is lost. The main sources for this asymmetry are [27]:(1) None of the sampling positions is coincident exactly with the position of thezero path difference. This is the main cause and leads to a phase shift linear in v.(2) Only a one-sided interferogram is measured, i.e., only one side is recorded toits full extent.(3) The interferogram may be asymmetric due to poor optical alignment, and/orthe phase delay of either the optics, the detector/amplifier unit, or the electronicfilters.A complex spectrum C(v) can be expressed by the sum of the purely realpart R(v) and the imaginary part 1(v):C(v)=R(v) + iI(v) (2.32)or by the product of the true amplitude spectrum S(v) and the wavenumberdependent phase factor exp(A(v)) containing the phase errors:c(v)=S(v)exp(A(v)) (2.33)Since the power spectrum P(v)=C(v).C(v) is independent of phase errors, it isusually used to extract the amplitude spectrum S(v):Chapter 2 Experimental Method and Instrumentation 35S(v)=[C(v)• C*(v)]l2=[R2(v)+1)]1” (2.34)The process of correcting phase errors and extracting S(v) is known asphase correction. It also can be done by multiplying C(v) by the inverse of thephase exponential and taking the real part of the result:S(v)=Re[0(v)exp(-A(v))] (2.35)4(v) can be calculated from 0(v):•(v)=arctan[I(v)IR(v)] (2.36)This procedure (Eq.(2.35)) is called ‘multiplicative phase correction’ or the ‘Mertzmethod’.It should be noted that one-sided interferograms are extremely useful inorder to shorten overall scan time. With the help of an on-line computer, the phasecorrection can be quickly computed and the entire spectrum can then besymmetrized.2.1.5 Comparison Between Grating and FT-IR Spectrometer- Jacquinot andFellgett Advantages2.1.5.1 Jacquinot AdvantageIn a lossless optical system, the brightness of an object equals thebrightness of the image and therefore the flux throughput and brightness can beconsidered at any point [26]. Throughput is defined as the product of the solidangle subtended by the source and the projected area of the collimator, If there isno loss between the elements in the system of interferometer, the throughput isfound to be a constant for the instrument from the source to the detector. UsingChapter 2 Experimental Method and Instrumentation 36the solid angle-resolving power product which is given by Eq. (2.29), we canobtain the throughput of a Michelson interferometer:E=AP,,,,=2nA,,/RM (2.37)where EM stands for the throughput of Michelson interferometer, AM is the area ofthe collimator mirror and RM is the resolving power of the interferometer.For the grating spectrometer, the entrance slit limits the power through theinstrument. So the slit area defines the effective source area, and the slit subtendsthe solid angle from the collimating mirror. Assuming the same area and focallength for the collimators and the same resolving power, the ratio of theinterferometer and grating throughput is given by [26]:(2.38)where F is the focal length of the collimator and f is the slit length.Even for the best grating spectrometers, F/f is never less than 30. That is tosay, about 200 times more power can be put through the interferometer thanthrough the best grating spectrometer. In addition, the optical system for theinterferometer can be much smaller than that for the grating spectrometer. Thisthroughput advantage is also known as the Jacquinot advantage.2.1.5.2 Fellgett AdvantageThe Fellgett advantage, also called the multiplex advantage, is concernedwith the signal to noise ratio S/N.Suppose there is a broad spectrum band from the wavenumber v1 to v2.With resolution &v, the number of spectrum elements in the band is:M=1V2 .! (2.39)6v 6vChapter 2 Experimental Method and Instrumentation 37Let T be the total time required for a scan from v1 to v2, and assume the noise israndom and independent of the signal level. In the grating instrument, each smallband of width v is observed individually for a time TIM. Thus, the integratedsignal received in the band 6v is proportional to TIM and the noise is proportionalto (TIM)112.The signal to noise ratio SIN for a grating instrument will be [26]:(SI N)G Dc (TIM)112 (2.40)But for the interferometer, since it receives the entire signal from the sourcecontinously, the integrated signal in a small band 6v is proportional to T, and thesignal noise is proportional to 71/2• Therefore, the signal to noise ratio S/N for ainterferometer will be:(SIW),ocT112 (2.41)Comparing Eqs.(2.40) and (2.41), the multiplex or Felgett advantage is:“—M1’ (242)(SIN)GSince M is of the order of the resolving power, typically about iO order, Eq.(2.42)predicts that the interferogram has a much higher signal-to-noise ratio than thegrating or prism instruments.2.2 InstrumentationThe Bruker IFS 1 13V Fourier-transform infrared (FT-lR) spectrometer wasused in all the reflectance and transmittance measurements reported here.2.2.1 Bruker IFS 113V FT-IR SpectrometerBruker IFS 1 13V FT-IR spectrometer is a powerful and flexible vacuumbench research spectrometer which covers the entire wavenumber range from theChapter 2 Experimental Method and Instrumentation 38far infrared to the near infrared (-. lOcmt - 15800 on-ri). The maximum resolutionis 0.03 cm-1. The optical system of the IFS 113V is divided into four modules asshown in Fig. 2-6: source, interferometer, sample, and detector. The radiation fromthe source is directed into the interferometer chamber, where it is transmitted andreflected by the beamsplitter, then the recombined light travels to one of the twosample chambers and finally reaches the selected detector. The optical conditionsat the entrance and the exit of each module are identical and the samplecompartments can be vacuum isolated from the other modules. Rotatable mirrorsare used for beam switching.There are some important features that make this a popular spectrometer.They are summarized as follows:1. Focused BeamThe interferometer is of a modified Michelson type in which the infrared beamis focused at the beamsplitter so that the beamsplitter can be of a small size.As a result, the Hdrum hea& effect, which refers to the diffusion of the IR beamand resulting spectral noise due to the slight vibration of a big beamsplitter, isdecreased dramatically. Moreover, it is easier to produce small beamsplittersand consequently, the quality of the beamsplitter is improved. Since thebeamsplitter is small, six of them can be mounted in a rotatable automaticchanger.2. Low Angle of Incidence on the BeamsplitterThe angle of incidence of the lR beam on the beamsplltter is 14 degrees. Thislow angle compared with other interferometers leads to a higher lightthroughput and minimum polarization effects.Chapter 2 Experimental Method and Instrumentation 393. Double-sided Moving Interferometer MirrorThe moving mirror is supported on a dual gas bearing which uses drynitrogen and driven by a linear induction motor. Both sides of the moving mirrorare used. Therefore, for a given optical path difference, the mechanicalmovement of the mirror is just half of that in a conventional Michelsoninterferometer. This results in greater spectrometer stability and the capabilityof performing high resolution work.Fig. 2-6: Optical system of the Bruker IFS 113V. (I) Source chamber: a—near-,mid- or far-lR sources. b—automatic aperture. (U) Interferogram chamber: o—optical filter. d—beamsplitter. e—two-sided movable mirror. f—controlinterlerometer. g—reference laser, h—remote control alignment mirror. (Ill)Sample chamber: i—sample focus, i—reference focus. (IV) Detector chamber: k—Near-, mid- or far-IR detectors.Chapter 2 Experimental Method and Instrumentation 404. Vacuum OperationWorking under vacuum has several advantages: reducing atmosphericabsorptions; higher throughput; less consumables; and maximum stability. Theoptical bench of the IFS 113V consists of several compartments. Thus thesample area can be vacuum isolated and purged, or a compartment can bereplaced by a user-designed one for special experiments.5. Total AutomationThe IFS 11 3V offers computer controlled switching of up to three sources, fourapertures, four optical filters, six beamsplitters, two samplà chambers, sixdetectors and numerous external experimental setups. The ability to changespectral range and experimental settings without opening the optical benchi.e. without breaking the vacuum, preserves the stable environment requiredfor reproduceable measurements.6. Rapid-Scan TechniqueA rapid-scan technique is used for data collecting, with the steps of the movingmirror determined by the interference fringes of the He-Ne laser referenceinterferometer. White light is used in addition to determine the mirror positioncorresponding to zero path difference. The scan speed can be adjusted over awide range to meet the requirements of different detectors. For amonochromatic source of wavenumber v, the moving mirror with a velocity of vwill result in an alternating electronic signal with frequency f at the detector.The modulation frequency f imposed by the moving mirror is given by:f=4vv (2.43).Since this frequency is unique for each wavenumber, we can handle itelectrically to filter out radiation outside our range of interest [28]. Thus, low-Chapter 2 Experimental Method and Instrumentation 41pass and high-pass filters are used to determine the electronic cutoff settingsfor signal processing and we no longer need to rely on optical filters to avoid‘false energies’ or ‘alising”. Other advantages of the rapid-scan techniqueinclude: the improved signal to noise ratio since averaging many short scanscan achieve a better signal to noise ratio than taking one long scan; discarding‘bad” runs which have their zero path difference peaks displaced more than apreset amount; and reduced 1/f noise which is the largest noise source fromthe He cooled bolometer.Measurements in different spectral regions require different choice ofsources, filters, beamsplitters and detectors. A brief introduction on theseimportant components will be given in the following sections.2.2.2 SourcesIn general, wide-band sources of radiation in the infrared region are “hotbody” radiation, whose intensity falls off rapidly in the far-infrared as thewavelength gets longer. The energy of distribution is given by Plank’s equation[29].In the Bruker IFS 1 13V spectrometer, three types of sources are providedfor different spectral ranges. In the far-infrared region, the mercury lamp is usedfor the wavenumber from 10 to 700 cnv. This lamp has the advantage [32], ascompared with other hot body sources, that it radiates a greater proportion of itstotal energy at longer wavelength than shorter wavelength. For the mid-infraredregion, a globar source is used between 100 and 6,000 crrr. In the near-infraredregion, a tungsten source is good for the spectral range of 1,850 to 15,000 cm-1.All these sources are water cooled.Chapter 2 Experimental Method and Instrumentation 422.2.3. BeamsplittersThe beamsphtter is a crucial part of the interferometer. It transmits andreflects the incident radiation with the ideal reflectance and transmittance of 50%.The beamsplitters can be made of self-supporting dielectric sheets or made offilms on a substrate. Generally speaking, in the far-infrared region below 400 cm[26], self-supporting Mylar or polyethylene beamsplitters are usually used. Fromabout 400 to 3,800 cm-1, a Ge film on various transparent substrates can be used.From about 2,000 to 16,000 cnv1, iron oxide (Fe203)or Si on different substratesare good for beamsplitters.If the incident radiation beam has an intensity of 1 and the overallreflectance (power reflected) and transmittance (power transmitted) of thebeamsplitter are R0 and T0 respectively, the usable radiation has the intensity of2R0Tand the intensity returning to the source is R02 +T02. The relative intensity,which is defined as 2R0T over (2R0T)1,is usually used to describe theproperty of beamsplitter [26]. There are two main factors that will affect the relativeefficiency: polarization and the multiple reflection within the beamsplitter. Since inthe Bruker IFS 1 13V, the polarization effects have been minimized by the smallincident angle on the beamsplitter, the relative efficiency will vary withwavenumber and depends on the film thickness for a given index of refraction.In the Bruker IFS I 13V spectrometer, beamsplitters are made of four typesof materials. For the long wavelength region, self-supporting Mylar beamsplitterswith different thickness, 3 tm, 6 jim, l2jim, etc. are available. As the wavelengthbecomes shorter, it is necessary to make the beamsplitters thinner, and thus,supporting transparent substrates are needed. For the mid-infrared region fromChapter 2 Experimental Method and Instrumentation 43400 to 4000 cm-1, the useful beamsplitter is Ge film, whose index of refraction isabout 4, on a KBr substrate with the index of refraction of about 1.6. The effectiverange for the Ge film on CaF2 beamsplitter is from 2500 to 10,000 aw1 [26], so itis used for near-infrared measurements with the wavenumber of interest between2000 and 9000 cm-1. For wavenumber beyond 9000 cm-1, a quartz substrate witha Si film can be used. This type of beamsplitter is efficient from 5000 to 20,000cm-1.2.2.4. DetectorsThe function of detectors is to convert the infrared radiation into anelectronic signal. Basically, there are two types of detectors: thermal detectors andphoto detectors. Thermal detectors measure a change in electronic propertiescaused by a change in temperature due to the absorbed radiation, while photodetectors measure the change in electronic properties caused by excess electron-hole pairs, which are produced by the absorbed radiation.Noise always exists in the detectors. The main noise sources are [30]:Johnson noise, which is the limiting noise in all conductors; 1/f noise, which ispresent in all detectors containing semiconductor elements; noise due tofluctuations in the generation and recombination of charge carriers, and due to therandom arrival of photons from the background; temperature noise produced byfluctuations in the temperature of the surroundings and amplifier current andvoltage noise.There are four detectors installed in the Bruker IFS 11 3V spectrometer:DTGS, MCT, InSb and Si diode, and a He-cooled bolometer is available too.These detectors are now described below.Chapter 2 Experimental Method and Instrumentation 44Deute rated-triglycerine-suIfate (DTGS) pyroelectrical detectors are wide-band thermal detectors. They are exceptionally sensitive, fast, dependable, andhave practically indefinite life. The DTGS detectors in the Bruker IFS 113Voperate at room temperature (—300K). If a KBr window is used, the useful range ofthe detector is 400-7000 cm , and the main application is in mid-infrared. If apoly-ethylene window is used, the useful range will be 10-600 cnv1, and theprimary application will be in the far-infrared.Mercury-cadmium-telluride (MCT, Hg1..CdTe) detectors are photodetectors and can operate in either photoconductive or photovoltaic mode. Thisdetector has a fast response and the spectral ranges of response peaks dependon the alloy composition. In the Bruker 113V, this detector works in aphotoconductive mode at an operating temperature of 77K, and has the usefulrange of 400-5000 cnv1 with the KRS-5 window. Thus, it is always used for mid-infrared measurements.The InSb detector is a high-performance photo detector working on thephotovoltaic mode [31]. The detector is actually a PN junction. The photovoltaicprocess involves measuring an external voltage produced by the infrared photonscollecting at the PN junction. The operating temperature is 77K, and the effectiverange of this detector with a Sapphire window is in the near-infrared, from 1850 to10,000 cm1.The Si diode is a highly sensitive detector in the near-infrared regionbeyond 9000 cnv , working on the photovoltaic mode. The operating temperatureis room temperature (300K).In addition, a He-cooled bolometer may be substituted for the DTGSdetector if high sensitivity is desired in the far-infrared region.Chaper 3MEASUREMENTS3.1 Reflectance Measurement3.1.1 Sample Chamber ArrangementThe front sample compartment in the Bruker IFS 1 13V was used for thereflectance measurement, as shown in Fig. 3-1, which is viewed from the top [33].Infrared radiation from the interferometer chamber is focused on an adjustablerectangular aperture F, which is used to restrict the size of the focused beam. Thelight through the aperture will focus again on the plane of the sample A andreference B with an incident angle of about 15 degrees. The sample holder canbe moved from the outside in the horizontal direction M. Thus, we can put thereference or the sample into the beam alternatively. The vertical position of theimage can be adjusted by the 1St toroidal mirror Hi. The reflected radiation fromthe sample is collected by the 2nd toroidal mirror H2 and directed to the detector.The chopper I can be moved into the beam by the external rod J when the secondtoroidal mirror is to be aligned for maximum signal using a digital voltmeter.3.1.2 Measurement ProcedureIn all of these reflectance measurements, an aluminum mirror was used asthe reference.45Fig. 3-i: Optical arrangement in the front sample chamber of the Bruker IFS113V. A, B—mirror and sample. C—sample holder. E—rotateable polarizer. F—adjustable rectangular aperture. 0—plane mirrors. Hi, H2—toroidal mirrors. I—chopper with motor. J—external rod to move chopper into beam. K—extension tosample chamber. L—plexiglas lid. M—illustration of translational degree offreedom.(- _)Fig. 3-2: Sample holder for reflectance measurements: (A) front view. (B)back ofpart I of the sample holder. M: reference mirror. S: sample.Chapter 3 Measurements 46(A)I(B)Chapter 3 Measurements 47Before starting the measurements, it is important to make sure that themirror and the sample are clean, especially free of grease. This was achieved bycleaning the sample in an ultrasonic cleaner: the sample was first immersed in abeaker of acetone, then trichiorylethelyne, followed by methanol, finally, it wasrinsed in de-ionized water and blown dry with N2 gas.The cleaned mirror and samples were mounted on a sample holder asshown in Fig. 3-2. Grease was used to stick the mirror and the samples on theholding surface instead of copper clips at the back of the mirror and samples inorder to avoid any reflections from the clips. Moreover, a piece of black felt paperwas put behind the mirror and samples to absorb the transmitted radiation andprevent the transmitted radiation from being reflected by other components in thesample chamber.For measurements in different spectral regions, the optical settings shouldbe chosen to get the optimum results. Table 3-1 shows the optical parametersused in different regions:Table 3-1: Optical Parameters in the Bruker 11 3VOptic Parameters NIR MIR FIRSource Tungsten Globar Mercury LampBeamsplitter CaF2 GeIKBr Mylar 3.5i.tmOptical Filter Open Open BlueAperture 1.25mm 5.0mm 10.0mmDetector InSb MCT DTGSSpectral Range 2000-9000 cm1 500-5000 cm1 100-1000 cm1Scanner Velocity 0.333 cm/s 0.333 cm/s 0.099 cm/sChapter 3 Measurements 48Before each measurement, the appropriate optics were first selected, then thetungsten source, which emits visible radiation, was used to see the spot on therectangular aperture and thus adjust the position of the aperture so that a focusedimage could be formed at the plane of the sample. It was found that the position ofthe beam focus on the aperture depends on the beamsplitter used. Furthermore,the size of the aperture restricts the size of the focused beam, so it was alsoadjusted to suit the sample and to get optimum results. It has been found that thesmaller the size of the focused beam, the closer the reflectance of GaAs to theliterature value, due to the fact that all of the detectors have fairly small elements.However, the small size of the focused beam results in a low energy throughputand a large noise level in the spectrum. Thus one should be very careful to setthe size of the aperture. In the near-infrared and mid-infrared measurements donehere, the aperture size was set to about lxi mm2.Evacuating the system is the next step after putting the mirror and samplesinto the sample chamber and setting the proper optics. Vacuum is indispensableto reduce atmospheric absorption and gain higher throughput as well as themaximum thermal stability. The waiting time of approximately 0.5 to 2 hoursbefore starting the measurement was long enough to obtain stable signals. Sincethe reflectance chamber is designed such that the movement of the sample holderand the alignment of optics can be done externally while the spectrometer isunder vacuum, the stability is not a big problem.Before taking measurements and applying the Fourier-transformation, thealignment in the sample chamber was adjusted to obtain the maximum signal onthe detector. This was done by rotating the sample holder about the vertical axisand adjusting the second toroid mirror H2. An easier method than to maximize theChapter 3 Measurements 49interferogram peak is to maximize the a.c. output of the detector produced by thechopper which can be brought into the beam to produce an a.c. signal. Since thereference mirror and samples are held on the flat sample holder with grease, theymay not be in the same vertical plane even through the holding surface is verysmooth. Therefore, we maximized the signal from the mirror before applying thebackground measurement, and also maximized the sample signal before thesample measurement.For each background and sample measurement, several hundreds ofscans were performed and averaged to increase the signal to noise ratio. Thescanner velocity listed before was chosen according to the response time of thedetector. Typically, it takes about 4 minutes for a 256-scan measurement.Due to the imperfect surface of the aluminum mirror, the reflectancemeasured was always a little bit higher than the ideal one, which could be seenfrom the GaAs measurement. To solve this problem, a piece of GaAs whosereflectance is known was measured along with the other samples, then thereflectance of the samples were calibrated by the GaAs.3.2 Transmittance Measurements3.2.1 Sample Chamber ArrangementTransmittance measurements were performed in the back channel of theBruker IFS 1 13V. The settings in the sample chamber are relatively simple asshown in Fig. 3-3. An adjustable iris aperture is positioned at about the focus ofthe beam from the interferometer chamber. The sample stands on a sampleholder (Fig. 3-4) which is put behind the aperture without touching it. The sample1sornpe ho1cerFig. 3-4: Sample holder for transmittance measurements.Chapter 3 Measurements 50Fig. 3-3: Back channel optical arrangement. (A): Sample (B): Iris aperturesce ewChapter 3 Measurements 51holder can also be used in the brass cryostat for low temperature measurements.The radiation which transmits through the sample will travel to the detectorchamber.3.2.2 Measurement ProcedureSimilar to the reflectance measurements, after setting the proper optics inthe interferometer chamber, the tungsten source was first used to see the spot onthe iris aperture. The aperture could be moved so that it was at the focus of thebeam. The size of the aperture could be adjusted to restrict the focused beam onthe sample since the sample was placed right behind it. One reason for placingthe sample very close to the aperture is to obtain a well focused image, and theother reason is that if the sample is too far away from the aperture, the spreadspot on the sample may exceed the dimensions of the sample and some radiationmight leak around the edge of the sample to reach the detector. For the samereason introduced in the reflectance measurements, the size of the focused beamhas been found to affect the transmittance in the same way as the reflectance. So,the aperture size should be carefully chosen. Because the GaAs sample used forcalibration was very narrow, the aperture was set very small, with a diameterabout of 1mm.The reference spectrum was taken just before putting the sample into thechamber, i.e., only with the aperture in the sample chamber. Since atransmittance module which would allow the sample holder to be rotatedexternally has not yet been construted, the chamber had to be vented to put in thesample. To avoid changing the background which has been taken before thesample measurement, the sample was put in carefully without touching theChapter 3 Measurements 52aperture and as close to it as possible. After the sample measurement, thebackground was taken again to make sure that it had not changed.After evacuating the system, it was necessary to wait for the system tobecome stable before taking the measurements. The waiting-period was at least15 minutes.Several hundred scans were taken for each measurement just as in thereflectance measurements. The settings of the parameters were the same asthose in the reflectance measurement in a specific spectral region, except that theback channel was chosen.3.3 Sample PreparationThe diamond-like carbon thin film samples tested here were grown bymagnetron sputtering method by Glenn Clarke in Dr. Parsons’s lab, as part of hiscourse for Ph.D degree. Magnetron sputtering, which is a sputtering techniqueunder the application of a magnetic field parallel to the target surface [11], has theadvantages of surface smoothness, the ability to control film uniformity andthickness, and the ability to deposit over a large area.In Glenn Clarke’s M.A.Sc thesis [11], this deposition process has beendescribed: During the magnetron sputtering process, the material of interest fordeposition, called the target, is bombarded by energetic particles (ions) to ejecttarget atoms, a number of which will deposit onto the substrate. The system isworking in a vacuum chamber which is initially pumped down to a pressure of.1O6 Torr [11], then an inert argon gas is introduced to raise the pressure.Moreover, a reactive gas such as nitrogen or oxygen is sometimes also added togenerate a dielectric film. After the desired gas pressure is reached, a negativeChapter 3 Measurements 53potential is applied to the target to create a plasma discharge, while the chamberand part of the target assembly are usually grounded. Thus, the main depositionparameters are: deposition pressure, which is the total gas pressure in thechamber including argon and other gases; partial pressure of a particular gas;target voltage; target current; and the substrate voltage. The structure andproperties of the films are greatly dependent on these preparation parameters.Seven samples were studied here. Their deposition parameters are listedin Table 3-2:Table 3-2: Deposition parameters for the samples testedsample deposition H2 partial °2 partial target target substratepressure pressure pressure voltage current voltage(Pa) (Pa) (Pa) (V) (mA) (V)acapl8 8 0 0 —530 —190 --7acjull 8 0 0 532 190 7acjul3 4 0 0 555 181 17acjul7 1 0 0 618 163 25acjl27 1 0 0.1 623 161 25acau07 1 0.1 0 557 181 24Chapter 4REFLECTION, TRANSMISSION AND ABSORPTION IN AMORPHOUS ThINFILMS4.1 Matrix Method for Reflectance and Transmittance CalculationWhen an electromagnetic wave is incident on a solid media, it can bereflected, transmitted, and absorbed. The optical properties of this solid can beobtained by measuring the intensity of the reflected and transmitted light. Toachieve this, one of the most commonly used methods is the matrix method.4.1.1 The Simple BoundaryAn incident plane electromagnetic wave can be expressed as:E1(r,t)=E,exp[i(k. —xt)] (4.1)Assume that the media are isotropic and homogeneous, the opticalproperties of the media can be described by the complex index of refraction:N=n÷ik (4.2)where n is the real refractive index, or often simply refractive index, and k isknown as the extinction coefficient. k is a measure of the absorption in the media.It is related to the absorption coefficient by:a=4ikI=4,ckv (4.3)where v (=1/k) is the wavenumber in cm-1.Considering the simplest case where an plane electromagnetic wave isincident on a single boundary between two media, denoted by suffix 0 for theincident medium and suffix 1 for the exit medium, for normal incidence, the54Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 55Fresnel amplitude reflection and transmission coefficients are given by p and trespectively [34]:(44)E, 14+NE. 2N0 (45)E, N0+N1where E Er and E are the electric field amplitudes of the incident, reflected andtransmitted waves respectively, and N0 ,N1 are the complex refractive indices formedium 0 and 1 respectively.If I,, I,. and 4 are the intensities of the incident, reflected and transmittedlight, then the reflectance R and transmittance T are as follows for a non-absorbing incident media [34]:R—!.— *_(No—4)(!bO4l)* (46)T — —— 01 (4 7)1n0 (N0÷1)(+*where N0 is a real number.4.1.2 Assembly of Thin FilmsThe presence of two or more interfaces will produce successive reflectionsand transmissions. The summation of these beams will determine the propertiesof this assembly of thin films.As shown in Fig. 41, a plane wave E with electric field amplitude E. isincident normally on a pile of L parallel faced layers each of which is isotropicand homogeneous [35], then a reflected wave E1 and transmitted wave E exist.Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 562Fig. 4-1: The pile of layers and the coordinates used throughout the textzFig. 4-2: The transformation of the waves (E,Ej across the interface betweenlayer I-i and I and through the inside of layer Ixfrontcib(ack)ZL.1Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 57Considering the tangential components of the fields, the field in a layer I can bedescribed as the superposition of a positive-going wave and a negative-goingwave. In the case of s-polarized wave [35],+ - .0)E,(x,z, t) = [E, (z) + E, (z)]. exp[i(—xsina — 0)t)]C (4.8)= [E7 exp(i N,z)+ E exp(—iN,z)]. exp[i( xsincx — ot)]C C Cwhere + denotes the waves in the incident direction, - denotes the waves in theopposite direction and a is the angle of incidence. The transformations of waves(E,E) across layer us illustrated in Fig. 4-2:1. the transformation of the fields E and E across the interface between twolayers /and I-i:(EI+ =-i—.1 1 (4.9)E1) ‘r,,,_1 i%PIJ1 1 ) Ei)where PI,I and t are the Fresnel’s reflection and transmission coefficients:N-N 2Np= ‘‘, ‘r,, = ‘ (4.10)“ N, + N,, N, + N,1and N is the complex refractive index: N—n÷ik2. the transformation through the layer:IEfl o1E (4.11)where p, = exp(iN,d,) and d,is the thickness of layer I.Thus,Chapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 581E =1 1 ‘•‘-1.1 (4.12)0 0,) ;,1_1 Lp,,,_1 1 ) i.E1)For a pile of thin films (Fig. 4-1), the above two transfer operations have tobe applied successively. Consequently, the complete transfer from medium b tomedium a which is assumed vacuum here can be expressed as:(EI” (7, 72(E’1(413)Er)zz o — Ji T) owhere the matrix T is the product of L matrices of type (4.12) followed by thetransformation through the surface of this pile at ZL+1=O.With the definition of the reflection and transmission coefficients:Er(Z0) E(ZZ) (414E1(z=0) ‘ E,(z=O)Eq. (4.13) can be rewritten as(‘‘1 2’(tab (415)r)t71 72)iOjThen r and t, can be obtained!b=T2l/ll, t=1I71. (4.16)If considering the case that the light is incident on the back b and emerges at thefront a, we can have [35]:(°)=( .c2){d) (4.17)=2 ii;, t =(12 21)1 (4.18)Chapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 594.1.3 Coherent Films and Incoherent SubstrateThe definitions of the thin and thick films are based on the interferencephenomena [34]: The film is considered thin when the interference effects can bedetected i the reflectance and transmittance spectra, that is, when the opticalpath difference between the two beams is less than the coherence length of thelight, and the film is thick when the path difference is greater than the coherencelength. Usually, the films on the substrate can be treated as thin films and thesubstrate supporting the films can be treated as thick.If there is a system consisting of piles of thin films and substrate, such as:medium a/pile 1/substrate/pile 2/medium b [35], we can apply the procedures inthe above section and obtain the reflection and transmission coefficients frommedium a (front) to medium b (back):• • •r — r —LI4IL‘ab, A2LabA2‘sa’sb’Vs ‘sa’sb’VsIn the case of thick substrate, the waves reflected successively at the frontand back surfaces of the substrate add incoherently instead of coherently. Thus,taking the absolute values of the complex coefficients t, r and 0, coherence canbe turned off between the neighboring films. Therefore, for normal incidence andwhen medium a is the same as medium b, the reflectance and transmittance ofthis system with an incoherent substrate can be given by:IttrI2exp(—45.k8d)2(4.20)1—frr, exp(— 4—kd)Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 602 0)IttI exp(— 2—kd)mcohC (4.21)1IrrSL,Iexp( 4kd8)In the case of our samples, which is a carbon thin film layer on a GaAssubstrate, there are three boundary surfaces as shown in Fig. 4-3. Since thesubstrate is incoherent and non-absorbing, i.e., at normal incidence, Eqs.(4.20) and (4.21) can be simplified as:R = II2 + ItastSarsbl (4.22)1-IrsarsbI2T= 2 (4.23)1-Irr,!where rae, t, r and t are derived from Eqs. (4.12) to (4.18) and can be easilycalculated by computer program. Since there is just one boundary betweensubstrate and medium b, r and tsb are just Fresnel’s reflection and transmissioncoefficients through this boundary.medium a (vacuum)thin film fsubstrate smedium b (vacuum)Fig. 4-3: Layers in our samplesChapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 61Eqs. (4.22) and (4.23) were used for our samples.4.2 Optical Model for Amorphous Solids in the Interband RegionFrom the last section, we can see that when an electromagnetic waveinteracts with a solid medium, the reflectance and transmittance are determinedby the complex index of refraction N=n+ik, where n (refractive index) and k(extinction coefficient) are termed as optical constants. However, n and k are notconstant over the optical region. They depend on the photon energy E= hco, andexhibit structure in the interband region where bound electron transitions aredominant. Thus, the optical constants are presented as n(E), k(E). A.R.Forouhiand LBloomer gave a model for n(E) and k(E) in reference [36], which will bedescribed below.4.2.1 Derivation of k(E)Based on the quantum mechanical theory of absorption, an expression forthe extinction coefficient k can be deduced. In the fundamental optical region,interband transition of bound electrons are mainly responsible for opticalproperties. Using time-dependent perturbation theory, the rate, denoted as 1(ci),at which photon energy is absorbed from the incident beam can be derived fromthe probability that an electron transfers to an excited state. Furthermore, theabsorption coefficient x is proportional to 4(o), and thus, the extinctioncoefficient can be obtained. This method can be applied to amorphoussemiconductors and dielectrics, crystalline semiconductors and dielectrics, aswell as metals.Chapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 62From first order time-dependent perturbation theory, the rate of energyabsorbed, (co), in the frequency range 0) to .o-i-do, associated with an electrontransition between two arbitrary states Ia) and lb) where E,?EI,, is given by(co)=42h21(1)J2[— E )2 h22/4] (4.24)where e stands for electron charge, x is the electron position vector, (bixia) is thedipole matrix element between initial and final states, I, is the incident photonenergy, and ‘y is the reciprocal of the finite lifetime of the excited state. (o))reaches the maximum when ho) = EbUnder the assumption that there is only one peak in the optical constantsof amorphous semiconductors and dielectrics, taking Ia) and Ib) to be bondingstate Ia) and antibonding state la with associated energies E0 and E0., c1(co) foramorphous solids is4(o) =4e2&oI(a*lxla)I[(E—E0 — hco)2 +h2y/4)](4.25)Derived from Eq.(4.3), the extinction coefficient k is directly related to theabsorption coefficient a(o):k(co) =—-co) (4.26)2cox(co) is proportional to c1(w) and can be expressed ascL(0) = O(o)) /10 (4.27)where e represents the total number of ways that a photon of energy ho) can beremoved from the incident radiation, per unit volume in an infinitesimal layer ofthickness. 0 is proportional to the product of the number of occupied electronstates in the valence band in the energy range dE and the number ofunoccupied electron states in the conduction band. Let i(E), (E) stand forChapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 63the density of states in the valence band E and the conduction band Erespectively, and f(E) represents Fermi function, thus,0 + ho,)[1 — f(E + ho))]dE (4.28)In the case of amorphous solids, take the optical band gap as:Eg =E°°m—E7 (4.29)Then 0 can be written as0= const(ho —E9)2 (4.30)where const stands for a constant. From Eq.(4.26), (4.27), (4.25), and (4.30), k(co)can be derived for amorphous semiconductors and dielectrics:k(o) = constl(aIxJa)I(Ee — E ho)2 +h2o/41(h(1) E)2 (4.31)More compactly, it can be written ask(E)=EBC (4.32)with parameters:A= const(a*lxla)2y,8=2(Ea• — Es), C = (E0. —E0)2+h2y/44.2.2 Derivation of n(E)The refractive index n(E) is related to the extinction coefficient k(E) by theKramers-Kronig dispersion relations:n(E)—n(oo) lpj+k(E’)_k(oo)dE, (4.33)where n(oo) and k(oo) are the infinite limits of n(E) and k(E), and P is the Cauthy’sprinciple value integral.By evaluating Eq.(4.33), n(E) for amorphous semiconductors anddielectrics can be obtained:Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 64BaE+Ca (434)E2 BaE+CawhereBa =(_+EB_E92 C) (4.35)Ca =[(Eg2+C)_2EqC] (4.36)Q=(4C_B2)1’2 (437)k(E), n(E) can be fully and simultaneously determined by the parametersA, B, C, E and n(oo). E is simply the measured energy of which k(E) has itsabsolute minimum value. n(oe) is approximately equal to but always greater thanone. The value of B12 is approximate equal to the energy at which k(E) is amaximum. The parameter C depends on the energy difference betweendistinguishable states and the transition lifetime. The parameter A is associatedwith the square of the dipole matrix element and essentially gives the strength ofthe peak in k(E).k(E) and n(E) model is quite useful for determining the film thickness. Inthe case of our films, the near-infrared reflectance and transmittance features aredue to the interband transition, thus this model and matrix method can be used tofit the experimental data so that the film thickness can be obtained as a fittingparameter.4.3 Optical Model for Amorphous Solids in Long Wavelength RegionIn the interband optical region, the optical properties mainly depend onthe interband transitions of bound electrons. However, as the wavelength of theChapter 4 Reflection, Transmission andAbsorption in Amorphous Thin Films 65incident radiation becomes longer, i.e., the photon energy is away from the bandgap, the dominant optical processes in the medium are vibrational excitations. Inthe semiempirical dispersion model [7] used here for amorphous solids, thestrong absorptions in the long wavelength region are mainly due to excitedvibrational resonances, and the influence from the interband transition isconsidered to be an Urbach absorption tail. Therefore, the total absorption in thisregion will be the superposition of these two effects.The complex index of refraction is related to the complex dielectricfunction e(v) byN = n(v) + ik(v) = [e(v)]1’2 (4.38)and the absorption coefficient can be given by E(v):cz(v) = 4nk(v) = 4ivlm{[e(v)]1”2 (4.39)Even through amorphous solids do not have long-range order, theirvibrational behavior is very similar to that of the corresponding crystalline forms,except that the selection rules for transitions are relaxed (no k conservation) andsharp features in the density of vibrational modes are broadened. Thus, similar tothe Lorentz oscillator model used for crystalline materials, the dielectric functiondue to the vibrational resonances in the amorphous solids can be expressed asthe superposition of N Lorentz lines:Jr (4.40)7t1=voj—v—I Iwhere 4 A1, J,,, Vq and are constants. v0 is the resonance frequency, J is theintensity factor and 2T is the line width. The term 4+Av2 describes a weakbackground Sellmeier dispersion [37].The Urbach tail is presented in the form:Chapter 4 Reflection, Transmission and Absorption in Amorphous Thin Films 66= CL00 exp(v Iv0) (4.41)where cx and v are constants.Considering Urbach background absorption in the dielectric function,£(v) = {[E,(v)]”2+iau(v)}2(4.42)4ivFinally, from Eqs. (4.39), (4.38), we can haveN(v) = [(v)]1’2=[E,(V)]1’2+ .CL(v) (4.43)4,tvn(v) = Re{[e,(v)]112} (4.44)a(v) = 47rvIm{[E,(v)]’}+CL0( ) (4.45)Eq.(4.45) was used to fit the experimentally established absorption coefficientdata. More details will be given in the next chapter.Chapter 5EXPERIMENT RESULTS AND DISCUSSION5.1 Experiment ResultsThe samples are amorphous diamond-like carbon (DLC) thin films about 1tm thick on semi-insulating GaAs (SI-GaAs) substrate, named in chronologicalorder: acapl8, acjull, acjul3, acjul7, acjl27, acauO7, and acau24. Thedeposition parameters for these samples have already been described in Chapter3. Reflectance and transmittance measurements were performed at nearly normalincidence, using the Bruker 11 3V spectrometer.5.1.1 Far-infrared ResultsFigure 5-1 shows the far-infrared reflectance spectra of an amorphouscarbon thin film on SI-GaAs substrate, from 100 cm-’ to 700 cm-1, as well as thereflectance of the substrate. The sample was acapl8 grown under a depositionpressure of 8 Pa. Figure 5-2 is the transmittance spectra of sample acapl8 andSI-GaAs substrate. By comparing the spectra of sample acapi 8 with those of SI-GaAs, one can see that the spectra of the sample actually show the features ofSI-GaAs substrate. This is due to the small absorption of the carbon thin film inthis region. Thus, this region is not the one in which we are interested and wasnot investigated further.67Chapter 5 Experiment Results and Discussion 685.1.2 Mid-infrared ResultsIn the mid-infrared (MIR) region, from 800 cm-’ to 4000 cm-1, the extinctioncoefficient k of SI-GaAs is zero except at 1042 cm-1 [38], which is primarilyintrinsic due to multiphonon absorption. This means there is little absorption inthis region from SI-GaAs. As a result, SI-GaAs is a good substrate for studyingthe amorphous DLC thin films in this region. The MIR reflectance spectrum ofGaAs is shown in Fig. 5-3. However, the multiphonon absorption did not appear inFig. 5-3 for it might be too weak to see.The reflectance and transmittance spectra of the investigated samples areshown in Fig. 5-4 (A) to Fig 5-8 (A). The main features of these spectra are thewide interference oscillations characteristic of thin films, with dips indicatingabsorption from vibrational modes. Fig. 5-4 (B) to Fig. 5-8 (B) are the absorptancespectra, which are calculated from A=1-R-T, where A, R, T are the absorptance,reflectance, and transmittance respectively. The absorption behavior of the film ismuch clearer in the absorption spectra: Sample acjull, acjul3 and acau07 actsimilarly, showing the optical “window” between 1900 to 2700 cm-1, and strongabsorption bands around 1300 cm-1, 1600 cm-1,1700 cm-1 and 2900 cm-1. Sampleacjull and acjul3 also have absorption bands at around 3300 and 3500 cm-1.Sample acjul7 and acjJ27 are quite different from the others. They have verystrong absorption increasing with wavenumber after 1900 cm-1, which may due tothe interband absorption. Neither the flat transparent ‘window” nor the C-Habsorption bands from about 3000 to 3500 cm-’ have been observed in these twofilms.Chapter 5 Experiment Results and Discussion 695.1.3 Near-infrared ResultsReflectance measurements in the near-infrared (NIR) were performed inorder to determine the thickness of the thin film. An optical method to determinethe film thickness is better than a mechanical method since it is non-destructiveand more accurate. In the NIR region from 4000 to 9000 cm-1, the absorptionmechanism of the amorphous DLC film is the interband transition and novibrational modes have been observed. Thus, by fitting the experimental value ofthe reflectance using the optical constants model in the interband region, whichhas been introduced in Chapter 4, the film thickness can be obtained. In order toreduce the error, a reflectance measurement was also performed for the same filmon a glass substrate. As shown in Fig. 5-9, the model fits the experimental dataquite well. All of the data fitting in the NIR was performed by Glenn Clarke usinghis program, and thus he obtained the thicknesses of the films as one of the fittingparameters.5.1.4 Absorption Coefficients and Bonding ConfigurationsIn the MIR region, the absorption is mainly caused by the excitation ofvibrational resonances. Therefore, the optical constants model used in the NIRregion is not suitable anymore. However, based on the homogeneous film modelpresented in Fig. 4-3, n(v) and k(v) can be found from experimental values of thetransmittance T and reflectance R by means of the iteration method. Asintroduced in Chapter 4, R and T can be calculated by the matrix method, i.e.,Eqs. (4.22), (4.23), and then n(v) and k(v) may be solved from the equations:00Chapter 5 Experiment Results and Discussion 70In order to get the solutions of the nonlinear array of equations, the twodimensional Newton-Raphson iteration method was used [39]. Upon knowing k,the absorption coefficient as a function of wavenumber could be calculated. Theresults are shown in Fig. 5-10 to 5-14 with dotted lines. This work was also doneby Glenn Clarke, using programs written by him.The optical properties of the film rely on the atomic bonding configurationin the film. In order to get this information, a dispersion model, described inChapter 4 (Eqs. (4.40) to (4.45)), was used to fit the absorption coefficient dataobtained from the experimental reflectance and transmittance values. For sampleacjul 1, acjul 3, and acau07, an Urbach absorption tail was used as thebackground absorption, and czc, , v0 in Eq. (4.41) were obtained through fitting theMIR absorption coefficient data. Lorentz phonon lines were then successivelyadded. The strong absorption after 2700 crrr1 in sample acjul7 and acj127seemed to be interband transitions and to follow the Tauc law given by:(cE)”2= B(E—E0),where E is the photon energy, and B and E0 are constants. Tauc law thereforewas used first and then followed by an Urbach tail to fit the data of these twosamples. Lorentz lines below 1900 cm’ were also added to fit the vibrationalmodes in that region.The fitting results are the solid lines in Fig. 5-10 to Fig. 5-14. The fittingparameters used are listed in table 5-1, where v0, F, and J in Eq.(4.40) stand forresonance frequency, intensity factor and half line width, respectively.Chapter 5 Experiment Results and Discussion 715.2 Discussion5.2.1 Optical Properties and Bonding ConfigurationAs illustrated in the absorption coefficient spectra, Fig. 5-10 to Fig. 5-14,samples grown under high deposition pressure (acjul 1 and acjul3) and samplesgrown under low deposition pressure but with considerable hydrogen content(acau07), have similar MIR spectra, while samples prepared under low pressurewith or without oxygen incorporation (acjl27 and acjll7) are quite different.As for sample acjul 1, acjul 3 and acau07, the MIR region can beconveniently divided into 3 parts to describe the typical optical properties. Thefirst part is the C-C network and CH deformation region at v< 1700 cnr’. In thisregion, all of the 3 samples show strong absorption lines at about 1300 cm’, 1438cm-’, 1600 cm-’, and 1700 cm-’. The band at about 1700 cm-’ is known as C=Ostretch in C=O and HC=O while the one at about 1600 cm-’ is assigned to C=Cstretch [20]. The band at around 1438 cim’ is possibly due to C-H rock or CH2deformation [20], and the peak at 1300 cm-’ may be caused by sp2- and sp3-hybridized carbons [22]. Though the -CH3 symmetric bending at about 1375 cm-’[23] appear in the spectra of acjul 1 and acjul3, it does not show up in that ofacau07.The second region is the low absorption window between 1900 and 2700cm-’, which is of great interest for potential optical applications. Sample acjul 1and acauO7 exhibit better qualities than acjul3 which shows gradually increasingabsorption with wavenumber. The little peak at around 2100 cm’ may beassociated with nitrogen impurities (C-N bonds).Chapter 5 Experiment Results and Discussion 72The third region is the CH stretching vibration area after 2700 cm-’. Thestrong peak at about 2900 cm-1 in all of these 3 samples is the sp3C-H stretchingvibration [22]. Sample acau07 also shows a very weak absorption at about 3000cm-’, which might due to C-H stretch in =CH [20]. In stead of showing the peak at3000 cm-’, acjul 1 and acjul3 show strong absorptions at approximate 3300 cm’and 3500 cm-’. The former peak may be assigned to hydrogen bonded sp’hybridized carbon [23], and the latter is probably caused by 0-H stretchingmodes.Sample acjul7 and acjl27 are much more absorbing. The absorption whichincreases rapidly with wavenumber after 1900 cm-’ appears due to interbandtransitions, indicating a small optical band gap in these films. The broad bandfrom 1000 to 1700 cm-’ may be caused by overlapping vibrational resonances.From the data fitting, at least the resonances from C=C stretch at about 1600cm-’, CH2 deformation at 1438 cm-’ and sp2- ,sp3- hybridized carbon at around1300 cm-1 were found.5.2.2 Effects of Hydrogen and Oxygen IncorporationThe role of hydrogen in DLC film properties was examined by incorporatinghydrogen into the film instead of heating hydrogen out. Sample acjul7 andacauo7 were grown under the same deposition pressure (1 Pa), but acauo7 had ahydrogen partial pressure of 0.1 Pa. It is obvious that hydrogen changes the filmproperties. AcauO7 is more transparent and shows a low absorption windowbetween 1900 and 2800 cm-1. Thus, it indicates that hydrogen raises the opticalband gap of the film.Chapter 5 Experiment Results and Discussion 73Intentional incorporation of oxygen (sample acjl27) leads to an increase inabsorption. But there isn’t a C=O absorption band at about 1700 cm-’ observed inthis film. This may be due to that the C=O bond is weak and easily stripped off bybombardment from Ar neutrals and some other particles in the chamber. Besides,at this low pressure, hydrogen impurity is sputtered off thus little HC=O bond canbe formed. And it is also possible that the C=O absorption is widened and buriedby the strong interband absorption tail.5.2.3. Effects of Deposition PressureThe main deposition variable here is the deposition pressure. From aprevious study [13], the deposition pressure had a great effect on the propertiesof DLC films prepared by magnetron sputtering, such as hardness, resistivity andoptical constants in the visible region. It has been found that the higher thepressure, the softer the film, and the higher the optical constants in the visibleregion. So it is of interest to know the effect of deposition pressure on the infraredproperties.By comparing the spectra of sample acjul 1, acjul3 and aujul7, which weregrown under the pressure of 8 Pa, 4Pa and 1 Pa respectively, one can see thatthe higher the pressure, the more transparent the film appears to be. In the d.c.magnetron sputtering method used for these samples, the energetic working gasions, in this case Ar ions, bombard the target surface generating neutral targetatoms, neutralized sputtering Ar ions and secondary electrons. Under the appliedelectric and magnetic fields, the electrons are trapped by the Lorentz force andhave little effect on the film growth. In addition to the sputtered target neutrals, thebombardment from the Ar neutrals and Ar ions are the main factors in the filmChapter 5 Experiment Results and Discussion 74growth. Ar neutrals have the energies up to the target voltage in eVs and it hasbeen shown that Ar ions actually have little effect on the optical constants [13],thus, Ar neutrals seem to have the greatest effect on the film deposition. Themean freepath of a particle is inversely proportional to the pressure. Therefore, athigh pressure, the Ar neutrals have a relatively shorter mean free path, whichmeans they will endure more scattering and have lower energy when theybombard the growing film. In this case, some other impurities, such as hydrogenand oxygen, will then be easily incorporated into the film. And the hydrogenincorporated into the film can decrease the optical band gap and make the filmmore transparent. On the other hand, low pressure will result in long mean freepath and high bombardment energy, thus, hydrogen and oxygen impurities maybe sputtered off as a result of energetic impacts, while carbon atoms can stillaccumulate on substrate since C-C bond strength ( 607 KJ/mol) is greater thanthat of C-H bond (338 KJ/mol) and O=C bond (532 KJ/mol in O=CO) [40].However, C-N bond strength (754 KJ/mol) is even greater than C-C bond and thisis probably why the small C-N absorption peak always exists. With little C-Hbonding in the low pressure film acjul7, it appears to be very absorbing.Even though no hydrogen was deliberately introduced, there are stillconsiderable amounts of hydrogen in the films grown under high pressure (acjul 1and acjul3) as seen in the strong absorption band near 2900 cm due to the C-Hstretching mode, and it seems that the hydrogen makes the films moretransparent and like the hydrogenated film acauo7. So this indicates that thedeposition pressure may affect the film properties through incorporating hydrogenand other impurities into the film. This hydrogen can arise from a backgroundimpurity in the chamber or even from the carbon source since graphite stronglyChapter 5 Experiment Results and Discussion 75absorb H20. Furthermore, we should not assume that the films grown by d.c.magnetron sputtering are all hydrogen free since no hydrogen is intentionallyincorporated. These samples were grown under the lowest impurity levels that thesystem could reach, but we still can see that the C-H bonding at about 2900 cnY’exists in the high pressure films. Unfortunately, the system cannot do better thanthis, which means the hydrogen impurity cannot be totally removed from thesystem.Considering the C-H stretching absorption band at around 2900 cm-’,which has been used for quantitative analysis for chemically bound hydrogen [41]and used to evaluate hydrocarbon content in DLC films [42], it does not exist insample acjul7 and it is stronger and wider in acjull than in acjul3, indicatingmore hydrogen is bonded to carbon atoms in acjul 1 and there might be a largeramount of hydrocarbon. But it is hard to judge the total hydrogen content sincehydrogen can present in a bound and unbound form.From S.Craig and G.L.Harding’s report [20], the reduction in the opticalband gap is associated with a decrease in hydrogen content and an increase inC=C bonding. As for our samples, the absorption coefficient spectra (Fig. 5-10,Fig. 5-11 and Fig. 5-12) suggest that the higher the pressure, the larger theoptical band gap. This is consistent with S. Craig’s results because the higher thepressure, the more hydrogen atoms are bonded to carbon atoms. The backgroundabsorption is mainly due to the Urbach tail from interband tranitions, which isexpressed as an exponential function and indicates that the flatter the spectrumcurve, the larger the optical band gap. Then from the background shape, ft can bededuced that aejul 1 has the maximum optical band gap and acjul7 has theminimum. The statement by S.Craig about C=C bond seems to be true for acjul 1Chapter 5 Experiment Results and Discussion 76and acjul3 because C=C bonding increased in acjul3. But it is hard to say foracjul7 since the absorption band below 1700 cm-’ is so wide that it can consist ofmany overlapping resonances and it is difficult to extract accurate parameters forthis bond.As mentioned before, the study in the visible region found that the higherthe pressure, the lower the extinction coefficient k. This conclusion is supportedby our near-infrared (NIR) results. In the NIR region, reflectance measurements ofthe DLC film on both SI-GaAs and glass substrates were performed in order toreduce the error in k. As illustrated in Fig. 5-15, k increases with decreasingpressure.Chapter 5 Experiment Results and Discussion 77200 300 400 500 600wavenumber (cm—i)(A)700100908O70ci)C-)C 500C-)- 302010s001009080ci) 60U00 700(B)Fig. 5-1: (A):Far-infrared reflectance spectrum of SI-GaAs. (B) Far-infraredreflectance spectrum of sample acapi 8200 300 400 500 600wavenumber (cm—i)Chapter 5 Experiment Results and Discussion 78100908070605040302010s00 200 300 400 500 600wavenumber (cm—i)(A)700ci)cia-EC’,a-4J1009080s.— 70C-)0I.- 4000 700(B)Fig. 5-2: (A): Far-infrared transmittance spectrum of SI-GaAs. (B): Far-infraredtransmittance spectrum of sample acapl 8.200 300 400 500 600wavenumber (cm—1)Chapter 5 Experiment Results and Discussion 79SI—GaAs100go -reflectance80 - transmittanceN 70600’D 50C0)C)L 30-a)20100.1 • I • I .1.1.1 • I 1.1, I • I I • I • I •800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (c rn—i)Fig. 5-3: Reflectance and transmittance spectra of semi-insulating GaAs (SIGaAs)Chapter 5 Experiment Results and Discussionocjul 180ci.)C)C0--JC0C’)-o010090_____80706050403020100800 1200 1600 2000 2400 2800 3200wavenumber (cm—i)reflectancetransmittance4.—C)CC)C)C)C-8 PaNo impurityincorporation—_4___s•_ 4_s..VS. •43600 4000(A)acjul 15040302010800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm—1)(B)Fig. 5-4: (A): Mid-infrared reflectance and transmittance spectra of acjul 1. (B):Mid-infrared absorptance spectrum of acjul 1.Chapter 5 Experiment Results and Discussion 81U)CI.U)C-)L.U)0ci)C)Ca--JcL0U)aacjul 3reflectancetransmittance10090807060504030201008001 I • I • I4PoNo impurityincorporation1200 1600 2000 2400wavenumber(A)acaul 32800 3200 3600 4000(cm-i)1 —R—T4PoNo impurity incorporation504030201000 1200 1600 2000 2400 2800 3200wavenumber (cm—i)(B)Fig. 5-5: (A): MIR reflectance and transmittance spectra of acjul3. (B): MIRabsorptance spectrum of acjul 3.4000Chapter 5 Experiment Results and Discussion 82acauO7I I I I I Ireflectance- transmittanceI IiPa1009080706050 -403020100800-es.—a——H2 incorporationI • • I • I • I • I • I • I • • I • I • I • I • I • I1 200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm—1)(A)acauD7C)cCC)C-)C)5040C)(_) 3DCCD 200U)100(B)Fig.5-6: (A) MIR reflectance and transmittance spectra of acauO7. (B): MIRabsorptance spectrum of acauO7800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm—1)Chapter 5 Experiment Results and Discussionacjul 783100 • • •90reflectance80 transmittance7060 iPaNo impurity50 incorporation800 1200 1600 2000 2400 2800 3200 3600wavenumber (cm—i)(A)4000acjul 7C)0I.C)C)_______ci____cL5040G) 3DC)C0-200C,,•.0 1002400 2800 3200 3600 4000wavenumber (cm—i)• (B)Fig.5-7: (A) MIR reflectance and transmittance spectra of acjul7. (B): MIRabsorptance spectrum of acjul7800 1200 1600 2000Chapter 5 Experiment Results and DiscussionacjI271 600 2000 2400wavenumber84transmittancereflectanceiPa02 incorporation2800 3200 3600 4000(cm—i)(A)acjI27100 -90_____80Z’- 700) 60a, 0C 40C) 300) 200100 - -__ _800 120070—s. 600) 50C-)a-400C’,- 30a2(1200 1600 2000 2400wavenumber(B)Fig.5-8: (A) MIR reflectance and transmittance spectra of acjl27. (B): MIRabsorptance spectrum of acj1272800 3200(cm-i)4000Chapter 5 Experiment Results and Discussion 85ci)C)0C-)C.)C.)ci)C-)C0C-)C)4-ci)8000 9000rn-i)Fig. 5-9: Near-infrared reflectances of sample acauO7 and acjul 7. The dashed lineis experiment result and the solid line is data fillingNIR reflectancewavenumber (cm—i)0.80.70.60.50.40.30.20.1°4boo(A)NIR reflectance0.6 • •0.5 fittingexperiment0.4 acjul 7::—0.1°•4boo 5000 6000 7000wavenumber (c(B)EC)-4-,C.04-‘la)00C0L0(ri£1CacjullFig. 5-10: Absorption coefficient of acjul 1. The dotted line is from experimentsand the solid line is from data fittingChapter 5 Experiment Results and Discussion 86200018001600140012001000800600400200800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm1)Chapter 5 Experiment Results and Discussion 87EC)-4-,CU‘I9-1)0C)0-4-,L0U,-oC1 00800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm—i)Fig. 5-11: Absorption coefficient of acjul 3. The dotted line is from experiments,the solid line is from data fittingacjul3190017001 50013001100900700500300Chapter 5 Experiment Results and Discussion 88EC)Ca)04-9-a)00C0-I-)0L0U)-Daacjul7wavenumber (cm—i)Fig. 5-12: Absorption coefficient of sample acjul7. The dotted line is fromexperiments and the solid line is from data fitting900080007000600050004000300020001000800 1200 1600 2000 2400 2800 3200 3600 4000Chapter 5 Experiment Results and Discussion 89EC)C04-000C04JL0(I)-DCFig. 5-13: Absorption coefficient of sample acjl27. The doffed line is fromexperiments and the solid line is from data fittingacjI2J1100010000900080007000600050004000300020001000800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (c rn—i)Chapter 5 Experiment Resufts and Discussion 90Fig. 5-14: Absorption coefficient of sample acauO7. The dotted line is fromexperiments and the solid line is from data fittingacauO7F-’EUC0a)00C00L0(I)-Da1000900800700600500400300200100800 1200 1600 2000 2400 2800 3200 3600 4000wavenumber (cm—i)Chapter 5 Experiment Results and Discussion 91ocjul 1 (8 Paacjul 3(4 Paacjul 7(1 PaocauO7 .1--.---:—.——.0.040008[aI • I • I • I5000 6000 7000wavenumber (cm—i)8000(A)9000-0.4I.0)oQ.3‘4-0)000.20I.00.1-4Jx0)0.5C)C-)0.3a)0C)0C.)—x4000 9000Fig. 5-15: (A): Extinction coefficient k for films of different deposition pressure. (B):Extinction coefficient k for films of I Pa, with hydrogen and oxygen incorporation(acauO7 and aq127) and without any impurity incorporation (acjul 7)wavenumber (cm—i)(B)O.D‘-01CD I—D.ZC0CDC)Il<)-I4J.00—CO0CD0‘-CoU3Coca.1(.Cl)C’)33DCD 1—CDD.Doa--’(ax—.c)0-I0•CDCr‘.1D(0-o0)-‘0)3CDCD-ICl)Da.-o0C,)Cl)CD0DaCOI0)Q. Cl).C.)C,)Cl)9 -.QCl)3.-C-4--.-.•CoccCD0rCoCa).CD-4-CDCDCa).01C)0100-JCa)00001Ca)rz01—.L.4(D01CDCDCD.CDCDCDO..CD)1cDZ01CDOCD01ZM0001Ci)—‘r)-4 0r.Ca)-‘CD0)01-CD0(001rs30)CD(Ti010.40)Ci)Ci)0)Ca)LØ)0)99’PLCa)-CD(0(00)F’.)C)lr010CD-’-’-’-’--‘-‘r3rCi)Ci).0)r)o-’r’3ca).01-4-’CDCD-’.C)1or301CCCC-4.CD00CD01CC0-JCi)—.0)Cfl0F)-J-.40)0100CD(DC000C0100-’01-’-Lr3r’a)001Ci)-’r)1.p)0CD4)Ci)Ci)0)0Wr’.ZJO)QOOCO01rz0i-‘CD00D0)..4C0)L(CDI’)CD(D(71(0-.‘---.0)0.i01010C)ø(CDCD—..40CDC0CDJ.-.1‘)CDCa)0P!‘o.-JCDrz-‘0)Co1\)-Lra)0)0)01.o(71.L....L.L..LL0)LJ)(a).(7101rZF.)CD4CaZCoC00.01C31(0Ci)CDCD00—’J40-r’.0)0)CDCDCD-CD010)-4Ci)0)-J.CJ10).0)Ci)$a).bCDCO--a.-.L.CD(a).01010)0(DOC)-.j(fl.JOCi)..(0CD(O•Ci)..Ca)CD-(00010Z.-JCi)0Ci)OCi)o%J‘rzrC31-CD-’OCD-‘0)0)Z0)-’..r.COrz.01CDCD.0)-a.))Ci)0)01WJLCD4-’r)LCDCO(0.COCDCD0L4C0CDF)Chapter 6CONCLUSIONInfrared reflectance and transmittance measurements were performed onamorphous DLC films to study the optical properties of these films. The films weregrown on semi-insulating GaAs substrates and were deposited by a d.c.magnetron sputtering technique. Through analyzing the near-infrared (NIR)reflectance data, the film thicknesses were obtained. It has been found that theinterband transition model of optical constants fits the experimental data in thenear-infrared region fairly well. In the mid-infrared (MIR) region, a matrix methodwas used to calculate the reflectance and transmittance as a function of photonwavenumber. The real and imaginary parts of the complex refractive index weresolved by a two dimensional Newton-Raphson iteration method. Furthermore, theabsorption coefficient spectra were fitted by a dispersion model taking account ofthe Urbach background absorption and the excitation of vibrational resonances.Thus, information of chemical bonding was acquired. Even though this model canalso fit the experimental results very well, it should be noted that smalladjustments to the parameters used in the model or adding more lines wouldallow a better I it. However, general bonding configuration of the films were stillobtained.The properties of DLC films were found to be strongly dependent on thefilm deposition parameters. Films prepared under different deposition pressuresdisplayed different optical properties. The NIR results showed that the higher thepressure, the lower the extinction coefficient k and absorption. This is consistentwith the findings in the visible region. Films grown under high pressure also93Chapter 6 Conclusion 94showed a high optical band gap and a flat low absorption window between 1900and 2700 cm-1. Considering the bonding configuration, it is different from film tofilm. At low pressures, neither C-H stretching bond at about 2900 cm-1 nor theC=O bond at around 1700 cm-1 were visible. At high pressure, more vibrationalresonances were seen. One possible explanation is the short mean free path andlow bombardment energy of Ar neutrals under high pressure and the resultingincorporation of impurities. Thus it suggests that the deposition pressure has aneffect on film properties mainly through incorporating impurities into the film. Thelarge optidal band gap and low absorption feature in the film grown under highpressure may be due to the incorporated hydrogen in the film. The role ofhydrogen was studied by incorporating hydrogen into the film grown under lowpressure (1 Pa). We can see that ,under the same deposition pressure, the filmwithout hycirogen incorporation and the one with hydrogen incorporation are quitedifferent. The hydrogenated film appeared to be more transparent in both NIR andMIR region. This is consistent with other people’s reports [20]. The effect ofoxygen incorporation was also investigated and it was found that oxygenincreased the absorption.One objective of this study was to see whether it is possible to use d.c.magnetron sputtering to grow diamond-like hydrogen free carbon films, which donot possess the C-H stretching absorption at about 2900 cm-1 and thus have aresulting much wider low absorption window. Unfortunately, it seems impossiblefor the system used for our films. At low pressure, there is not this C-H resonancebut the optical band gap is too low and the film is too absorbing in the wholeregion. At high pressure, the film is much more transparent and displays the flatlow absorption “window”, but there exists the C-H stretching absorption band evenChapter 6 Conclusion 95if no hydrogen has been incorporated. Therefore, one should not assume that thefilm is hydrogen free just because no hydrogen is incorporated intentionally. Theimpurities should not be ignored. This study suggests that the optimum depositionconditions for a DLC film with good IR transparency may be a low depositionpressure with hydrogen incorporation, which may result in a more IR-transparentfilm, with lower non-hydrogen impurity absorption, compared with a high pressureand no hydrogen incorporation.It was also shown in this study that Fourier-transform infrared spectroscopyis a very important and effective tool for the characterization of thin films. It hasthe advantage of being non-contact, non-destructive and covering a wide spectralrange.Bibliography[1] Hsiao-chu Tsai and D. B. Bogy, J. Vac. Sd. Technol. A5 (6), 3287 (1987)[2] S. Aisenberg and R.Chabot, J. AppI. Phys. 42, 2953 (1971)[3] B.Dischler, A. Bubenzer and P. Koidl, Appi. Phys. Lett. 42 (8), 636 (1983)[4] J. C. Angus and Y. Wang, Diamond and Diamond-like Rims and Coatings,edited by R. E. Clausing, L. L. Horton, J. C. Angus and P. Koidl (Plenum Press,New York, 1991 ), p.173[5] N. Sawides, J. Appi. 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Thesis/Dissertation
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Physics
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Graduate
The measurements of the optical properties of diamond-like carbon thin films by fourier-transform infrared spectroscopy
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