Treasure of the Past VII: Measurement of the Thickness and Refractive Index of Very Thin Films and the Optical Properties of Surfaces by Ellipsometry

The use of the ellipsometer for the measurement of the thickness and refractive index of very thin films is reviewed. The Poincaré sphere representation of the state of polarization of light is developed and used to describe the reflection process. Details of the operation of the ellipsometer are examined critically. A computational method is presented by which the thickness of a film of known refractive index on a reflecting substrate of known optical constants may be calculated directly from the ellipsometer readings. A method for computing both the refractive index and thickness of an unknown film is also developed. These methods have been applied to the determination of the thickness of an adsorbed water layer on chromium ferrotype plates and on gold surfaces. In the former case the thickness was 23 to 27 Å, and in the latter was 2 to 5 Å. The measurement of the thickness and refractive index of barium fluoride films evaporated on chromium ferrotype surfaces is used as an illustration of the simultaneous determination of these two quantities.     

Thickness of Adsorbed Polystyrene Layers by Ellipsometry,

The adsorption of polystyrene from cyclohexane below the theta temperature onto chrome ferrotype plate was studied by means of ellipsometry (polarization spectrometry). In this technique changes in the state of polarization of polarized light are measured upon reflection from a film-covered surface. The measurements were carried out in situ and permitted determination of the thickness and refractive index of the swollen polymer film at the solidsolution interface. A concentration range of 0.18 to 9.7 mg/ml was studied for polymer with a molecular weight of 76,000. The thickness of the adsorbed film increased with increasing solution concentration, reaching a plateau for most of the concentration range studied. The average thickness at this plateau was approximately 210 Å. The adsorbed film was highly swollen, consisting of about 12 g/100 ml of polymer for most of the concentration range. The amount adsorbed was determined to be approximately 2.25×10⁻⁴ mg/cm² at the plateau. Comparison of the radius of gyration of polystyrene in solvent is made to the results obtained.     

Oxide thickness measurements by infrared ellipsometry

Current interest' in anodized aluminum surfaces as substrates for adhesive bonding has created a need to measure the properties of the oxide layer in a non-contacting manner. Visible light ellipsometry is a very sensitive non-contacting technique for measuring the thickness of very thin films on smooth surfaces whose optical constants are known. However, the method is limited to film thicknesses which are generally less than 2000 Å and validity is lost when there is appreciable scattering caused by the roughness of the substrate and the structure of the oxide itself. These objections become much less severe if the operating wavelength is in the infrared region. Such an infrared ellipsometer has been developed to measure the thickness of oxides produced by anodization of aluminum with production-finished surfaces. The instrument operates with a 10.6 μm beam from a low power CO₂ laser and uses a 6328 Å beam from a He-Ne laser for alignment and location of the measurement region. The oxides were formed on unclad 7075 aluminum by anodization in an ammonium pentaborate solution at constant current to termination voltages of from 25 to 275 V in 25 V increments. The measured ellipsometric quantities Δ and ψ were used to compute the corresponding metal oxide film thicknesses using a complex refractive index N = 2.39?i41.36 for the substrate. The results for a film refractive index of 1.50 were in close agreement with those measured with a scanning electron microscope. Elemental concentration profiles for each surface were made by Auger electron spectroscopy.     

Use of artificial neural networks to predict thickness and optical constants of thin films from reflectance data

Artificial neural networks and the Levenberg–Marquardt algorithm are combined to calculate the thickness and refractive index of thin films from spectroscopic reflectometry data. Two examples will be discussed, the first is a measurement of thickness and index of transparent films on silicon, and the second is a measurement of three thicknesses and index of poly-silicon in a rough poly-silicon on oxide stack. A neural network is a set of simple, highly interconnected processing elements imitating the activity of the brain, which are capable of learning information presented to them. Reflectometry has been used by the semiconductor industry to measure thin film thickness for decades. Modeling the optical constants of a film in the visible region with a Cauchy dispersion model allows the determination of both thickness and refractive index of most transparent thin films from reflectance data. The use of an alloy interpolation model for the optical constants of poly-silicon allows the determination of thicknesses and poly optical constants. In this work artificial neural networks are used to obtain good initial estimates for thickness and dispersion model parameters, these estimates are then used as the starting point for the Levenberg–Marquardt algorithm which converges to the final solution in a few iterations. These measurement programs were implemented on a Nanometrics NanoSpec 8000XSE.     

Determination of film thickness and refractive index in one measurement of phase-modulated ellipsometry

Ellipsometry is often used to determine the refractive index and/or the thickness of a polymer layer on a substrate. However, simultaneous determination of these parameters from a single-wavelength single-angle measurement is not always possible. The present study determines the sensitivity of the method to errors of measurement for the case of phase modulated ellipsometry and identifies conditions for decoupling film thickness and refractive index. For a specific range of film thickness, both the thickness and the refractive index can be determined from a single measurement with high precision. This optimal range of the film thickness is determined for organic thin films, and the analysis is tested on hydrogel-like polymer films in air and in water.     

Measurement of the physical thickness and refractive index of thin epitaxial garnet films

A technique for the measurement of refractive index and physical film thickness of epitaxial garnet films is described which utilizes variable wavelength measurements. Experimental results are presented for gadolinium gallium garnet substrates and two different bubble domain film compositions. From these results, it is concluded that the technique is not applicable to wafers with films on both sides due to the differences in film thickness of the two films. For single sided wafers, the refractive index can be determined with an accuracy of ±0.3 percent.     

Transparent thin-film characterization by using differential optical sectioning interference microscopy

We propose an optical thin-film characterization technique, differential optical sectioning interference microscopy (DOSIM), for simultaneously measuring the refractive indices and thicknesses of transparent thin films with submicrometer lateral resolution. DOSIM obtains the depth and optical phase information of a thin film by using a dual-scan concept in differential optical sectioning microscopy combined with the Fabry-Perot interferometric effect and allows the solution of refractive index and thickness without the 2pi phase-wrapping ambiguity. Because DOSIM uses a microscope objective as the probe, its lateral resolution achieves the diffraction limit. As a demonstration, we measure the refractive indices and thicknesses of SiO2 thin films grown on Si substrate and indium-tin-oxide thin films grown on a glass substrate. We also compare the measurement results of DOSIM with those of a conventional ellipsometer and an atomic force microscope.     

Ellipsometry of Liquid Helium Films on Gold, Cesium, and Graphite

We have developed a modulated null ellipsometer with sub-monolayer resolution to measure adsorbed liquid helium thin films at temperatures below 4 K. Adsorption isotherms of ⁴He on gold, cesium, and graphite are presented. For Au and Cs substrates, the reflecting surface for our ellipsometric measurements is the metallic electrode of a quartz crystal microbalance(QCM). Performing both types of measurements simultaneously on the same substrate provides a direct method of converting the ellipsometric signal into an absolute film thickness without constructing a detailed model of the refractive index of the substrate. Isotherms on gold above and below T¸ show that the ellipsometric signal is unaffected by the superfluid transition; the ellipsometer measures the total film thickness independent of the superfluid fraction. Isotherms on cesium above the wetting temperature show a prewetting step. Isotherms on clean graphite show steps due to layering.     

PECVD法低温制备二氧化硅薄膜(英文)

针对金属层间介质以及MEMS等对氧化硅薄膜的需求,介绍了采用等离子增强型化学气相沉积(PECVD)技术,以SiH4和N2O为反应气体,低温制备SiO2薄膜的方法.利用椭偏仪和应力测试系统对制得的SiO2薄膜的厚度、折射率、均匀性以及应力等性能指标进行了测试,探讨了射频功率、反应腔室压力、气体流量比等关键工艺参数对SiO2薄膜性能的影响.结果表明:SiO2薄膜的折射率主要由N2O/SiH4的流量比决定,而薄膜均匀性主要受电极间距以及反应腔室压力的影响.通过优化工艺参数,在低温260℃下制备了折射率为1.45～1.52、均匀性为±0.64%、应力在-350～-16MPa可控的SiO2薄膜.采用该方法制备的SiO2薄膜均匀性好、结构致密、沉积速率快、沉积温度低且应力可控,可广泛应用于集成电路以及MEMS器件中.     

A note on the use of ellipsometry for studying the kinetics of formation of self-assembled monolayers

Ellipsometry is currently one of the most important techniques for characterization of the deposition and growth mode of ultra thin organic films. However, it is well known that for thicknesses normally encountered in organic monolayer films, as would occur for example in self-assembled monolayers, ellipsometry cannot be used to simultaneously determine the thickness and refractive index of the monolayer film. Current practice is to assume a reasonable value for the film refractive index and calculate an effective ‘ellipsometric thickness’. This communication seeks to show that the alternative approach of assuming a thickness for the monolayer (determined by the length of the molecule) and calculating the effective film refractive index lends itself to easier and more meaningful physical interpretation. The Lorentz-Lorenz formula is then used to transform the effective refractive index into a surface coverage and hence to an effective mass coverage. The methodology advanced is applied to the kinetics of formation of a self-assembled monolayer of a well-studied molecule, octadecanethiol on Au.     

Ellipsometric examination of the thermal oxidation process for plated chromium films

The process of thermal oxidation of ion-plated chromium films having the A15 structure deposited on the glass BK-7 and on quartz glass was investigated in air and in oxygen at 676 K. It has been stated that the optical constants of plated chromium films do not depend on the nature of the substrate; the substrate, however, does influence the rate and character of the process. The oxidation of chromium on quartz substrates proceeds according to the inverse logarithmic rule and on glass according to the parabolic rule. A layer of chromium oxide is always formed on chromium films irrespective of the atmospheric composition (oxygen or air); in air the layer of chromium oxide is thicker than in an atmosphere of pure oxygen. Ellipsometric measurements allow the determination of both the refractive index and the thickness of the chromium oxide formed on chromium films.     

Ellipsometric Study of Superfluid Onset in Thin Liquid 4Helium Films

We have developed a modulated null ellipsometer capable of measuring single layers of adsorbed ⁴He films at 1.4 K. The small optical index of liquid helium, the extreme sensitivity to temperature gradients, and the requirement of sub-monolayer stability over many hours presents significant experimental challenges, which will be briefly discussed. The main goal of our experiments is to independently measure the superfluid and normal coverage in thin adsorbed ⁴He films. This is a particularly important issue for helium films on intermediate strength substrates such as rubidium and thin cesium, where previous measurements indicate that prewetting and the Kosterlitz-Thouless transition interact strongly, and the K-T transition appears to have nonuniversal features. Independent determination of the superfluid and normal fraction can be accomplished by using the ellipsometer in conjunction with a quartz crystal micro balance (QCM). QCM measurements rely on viscous coupling of the fluid layers, and therefore respond only to the normal component of a ⁴He film. In contrast, the ellipsometer is sensitive to the total thickness, independent of the state (superfluid or normal) of the film. By combining the QCM and ellipsometric measurements we can determine the total coverage, the normal fluid component and thus the superfluid fraction.     

Far-infrared laser measurement of the refractive index of polypropylene

The refractive index of polypropylene in the far infrared (FIR) is measured by means of a suitably modified laser of a FIR spectrometer. When thin polypropylene films of 12.7-microm nominal thickness are introduced in the optical cavity of a laser at the Brewster angle, the radiation ceases because of the change in the optical path of the laser beam. This change is measured from the displacement of one of the laser mirrors, which is necessary to restore the laser resonance. The refractive index of polypropylene is deduced from this measurement and from the film thickness, as obtained from an independent measurement based in pycnometry. The value obtained for the refractive index is 1.492(15) for the wavelengths between 118.834 and 251.140 microm, for a polypropylene film of 12.71(2)-microm thickness and 0.9049(7) g/cm3 density.     

Tailoring the structural,electrical, and optical features of Erbium(III)-Tris(8-hydroxyquinolinato) nanostructured films for optical applications: effect of film thickness

This paper elaborates on the thickness-dependent structural, optical, and electrical properties of Erbium(III)-Tris-8-hydroxyquinolinato (ErQ3) films. The surface morphology reveals the grains that consolidate to make denser films with increasing film thickness. The ErQ3 grain sizes increased from 80 to 187 nm as the thickness increased from 80 to 190 nm. From XRD analysis, the ErQ3 films are partially crystallized with only one peak at 2θ?=?9.80° and a plateau in the range of 20–40°. Electrical measurement of ErQ3 films showed that the electrical conductivity had a strong dependence on film thickness. Transmittance and reflectance measurements showed that the films exhibited a 2.60 eV bandgap, and it does not depend on the thickness of the film. Also, the dispersion of the refractive index was analyzed to determine the essential parameters. The nonlinear optical parameters such as nonlinear refractive index and third-order nonlinear optical susceptibility were calculated by Miller's principles.

     

Two-dimensional thickness measurements based on internal reflection ellipsometry

An imaging ellipsometer technique on internal reflection geometry that can measure the thickness distribution of a thin film possessing an assumed refractive index is described. Because a prism is used for the internal reflection geometry, it was theoretically predicted that angular derivation from the normal incidence on the prism surface affects only the psi value by a factor of 0.97 at maximum. Measurements were carried out for an optical system of silica substrate-TiO2 layer-silica layer-protein film-air, with a thin-film array of dried protein as the sample film. Thickness of the protein films was two-dimensionally estimated only from the measured map of the delta value by use of the simulated relationship between the thickness and the delta value. The thickness map obtained was coincident on the whole with the results according to a mechanical scanning. The detection limit was approximately +/- 0.2 nm. These findings validate the optical effect of a high-index additional layer to improve the sensitivity and precision of thickness measurements of the sample film on transparent substrates.     

Further investigations on a poly(vinyl alcohol)- polyelectrolyte chemically selective optical film

The ionomer poly(vinylbenzyltrimethylammonium chloride) has been blended with cross-linked poly(vinyl alcohol) to form optically clear composites that can be covalently linked as thin films to oxide surfaces. Films are characterized using spectroscopic ellipsometry with refractive index (n) and extinction coefficient (k) data presented for wavelengths 300 to 1100 nm. A refractive index of 1.54 and average thickness of 709 nm are typical of an air dry film prepared by spin-coating. Dynamic in situ ellipsometry results for films exposed to 0.1 M KNO(3) and 1.0 mM Fe(CN)(6)(-3) are presented. Upon initial exposure to 0.1 M KNO(3), an air dry film expands by about 160% and stabilizes in size and refractive index at about 18 hours. Ion exchange of film cationic groups with ferricyanide is marked by slight film contraction, presumably due to electrostatic cross-linking by the multivalent anion. These films are useful in the spectroelectrochemical sensor with our newly developed fluorescence detection mode, as demonstrated by results of the reversible incorporation of the fluorescent anion fluorescein.     

Measurement of the refractive index and thickness of a transparent film from the shift of the interference pattern due to the sample rotation

A method is described for the simultaneous measurement of the refractive index and thickness of a transparent film. The method is based on the rotational shift of the interference pattern caused by the change of the light incidence angle. The refractive index is evaluated without any prior information about film thickness or about the substrate and its refractive index. In addition, the roughness of the interfaces and/or the presence of an unidentified thin layer are not important. In two experimental examples, the refractive index and thickness are measured for a GaN thin film and a cling-film.     

Determination of properties of wedged, nonuniformly thick, and absorbing thin films by using a new numerical method

Nonuniformity in the thickness of thin films can severely distort their transmission spectra as compared with those of flat, smooth films. Methods that extract properties such as refractive index, thickness, and extinction coefficient of such films can suffer inaccuracies when they are applied to wedged or nonuniformly thick films. To accurately extract optical properties of nonuniform films, we have developed a novel numerical method and efficient constitutive relations that can determine film properties from just the transmission spectrum for films that are locally smooth with negligible scattering loss. This optimum parameter extraction (OPE) method can accommodate films with two-dimensional thickness variation that would result in significant errors in the values of refractive index and film thickness if not considered. We show that for carefully chosen test cases and for actual pulsed-laser-deposition AlN thin films, properties such as refractive index, extinction coefficient, and film thickness were very accurately determined by using our OPE method. These results are compared with previous techniques to determine the properties of thin films, and the accuracy of and applicable conditions for all these methods are discussed.     

Calculation of film thickness for dip coated antireflective films

Antireflective films require an accurate film thickness to be able to perform optimally. The ideal thickness on most films is a quarter wavelength optical thickness (QWOT). The physical thickness of the QWOT film depends on the refractive index of the material that is being used. Each layer of the antireflective coating will have different optimal conditions for applying the film. When using the dip coating method, these conditions are withdrawal speed and concentration of solution.When using the currently accepted equations derived by Yang et al. to calculate the film thickness an error of 31.7% was noted when compared with the experimentally measured film thickness. Realising that the refractive index of the film plays a role in determining the thickness of the film, the equations were modified to take refractive index into account. Once this was taken into account, the calculated film thickness deviated from the measured film thickness by 8.7%. This error can be attributed to experimental errors which involve temperature and concentration fluctuations.