Interference in thin films

The practical realization of two coherent light sources is very difficult (it can be achieved, for instance, with the use of lasers). However, there is a relatively simple way to carry out an interference. It consists of splitting a single light beam into two components by reflection from a pair of mirrors and then superposing them in a single point they will interfere, thus 

Since co = 2nlT and u = cin, the expression in square brackets is equal to A p = (2nlc 7 )(6 2n2- i i) = i2n/XJ S2n2-S ni). The product of the path traveled S and refraction index n is referred to as optical path length denoted by A. Keeping in mind that cT = Aq (Aq being the wavelength in vacuum). 

This expression joins the phase differences and the optical length traveled in the splintered wave. A(p defines the interference effects. Indeed, cos Aq = 1 corresponds to the maximum intensity since Acp = (2izlA A = 2nm. From this, the condition of the intensity maximum can be derived  

It is easy to see that the summation of waves described above with fourfold enhancement of intensity corresponds to the displacement of the two parts of the splintered wave from each other by the difference in lengths equal to the integer wavelengths (or, accordingly, to the phase difference Acp = 2nm). The complete extinction of the wave s intensity is observed at the displacement of the two wave parts on the wavelength half (on an odd number of the wavelength half, i.e., Acp = (2m + )n). 

Since the refraction index depends on the wavelength (see Section 6.5), the interference conditions are qualitatively different. Therefore, the film will decompose falling light in a spectrum, i.e., in falling white light the thin film always looks as if it has been painted. We all have met examples of this observing multicolored soap bubbles or an oil stain on the surface of water. 

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On the other hand, AR is a technique that eliminates the surface reflections by optical interference in thin films. It is used in optical lens and glasses by coating the surface with a multilayer of compounds with different refractive index by sputtering or vapor deposition. There was the basic research in our company, but in order to offer a timely solution to our customer s problem, we started a joint development with the American OCLI company and mass-produced the large size (500 mm x 1 m) AR polarizer, which was a big breakthrough at that time. 

For thin-film samples, abrupt changes in refractive indices at interfrees give rise to several complicated multiple reflection effects. Baselines become distorted into complex, sinusoidal, fringing patterns, and the intensities of absorption bands can be distorted by multiple reflections of the probe beam. These artifacts are difficult to model realistically and at present are probably the greatest limiters for quantitative work in thin films. Note, however, that these interferences are functions of the complex refractive index, thickness, and morphology of the layers. Thus, properly analyzed, useful information beyond that of chemical bonding potentially may be extracted from the FTIR speara. 

NAA cannot be used for some important elements, such as aluminum (in a Si or Si02 matrix) and boron. The radioactivity produced from silicon directly interferes with that ftom aluminum, while boron does not produce any radioisotope following neutron irradiation. (However, an in-beam neutron method known as neutron depth profiling C3J be used to obtain boron depth profiles in thin films. ) Another limitation of NAA is the long turn-around time necessary to complete the experiment. A typical survey measurement of all impurities in a sample may take 2-4 weeks. 

One of the more important uses of OM is the study of crystallization growth rates. K. Cermak constructed an interference microscope with which measurements can be taken to 50° (Ref 31). This app allows for study of the decompn of the solution concentrated in close proximity to the growing crystal of material such as Amm nitrate or K chlorate. In connection with this technique, Stein and Powers (Ref 30) derived equations for growth rate data which allow for correct prediction of the effects of surface nucleation, surface truncation in thin films, and truncation by neighboring spherulites... 

This very useful method also has the advantage that the equations do not contain anything about the material or diffraction conditions other than the Bragg angle and geometry. The independence from material parameters arises because the refractive index for X-rays is very close to unity. The equations are, of course, similar to those for optical interference from thin films, since the physics is the same, but in the optical case we do need to know the refractive index. 

These compounds tend to be hydroscopic and must be stored in tightly closed containers. High humidity will interfere with cure, particularly in thin films. The slow cure can be overcome by the addition of bisphenol A, which acts as an acid accelerator. 

It is possible to decolorize by adsorption techniques using materials like the activated carbons, or combinations of the carbons and clays, but only in relatively dilute solutions where the viscosity of the gum arabic will not interfere with the adsorption of color. With most adsorbants, when the gum arabic is dilute enough so that the color is adsorbed, some of the gum arabic is also adsorbed. There is then the problem of concentration without processing the gum arabic at such a temperature that some of the color is restored. The gum can be bleached or decolorized in dilute solution, but then the concentrate must be boiled the concentration, other than at very low vacuum, of the colloidal solutions is a problem without the intooduc-tion of further amounts of color, particularly on surfaces of tubes or in thin films. An attempt is made to get the darker colored materials out by visual selection at an early stage. If it is processed in dilute solution, color comes back when it is concentrated. 

The importance, feasibility, and value of in situ investigations of thin-film deposition from the gas phase by PVD and CVD methods have been demonstrated using two selected techniques. In both cases, the measurement conditions ensure a direct relationship between the obtained data and thin-film deposition. Special efforts are made to avoid any interference of the processes from the measurements and vice versa. TOF-MS with laser ionization is applied to detect intermediate gas-phase species involved in thin-film formation. Deflection of two probe laser beams induced by reflection from a curved substrate is used to determine the direction and amount of mechanical stress in the growing layer. 

One final procedure for minimizing substrate Raman scattering interference in thin polycrystalline films deposited on silica is based upon the polarization properties of the scattered light (16). Inherent molecular disorder present in vitreous silica substrates results in marked polarization anisotropy of the Raman-scattered light from the substrate. Raman scattering from a deposited polycrystalline film is isotropic since the individual randomly-oriented grains act to scramble the... 

Various methods have been developed for Raman characterization of very thin films and amorphous phase films that exploit the optical properties of the film to enhance the intensity of the Raman scattered radiation. Such techniques involve the lateral transmission of light in thin films, interference phenomena upon reflection at interfaces, or direct absorption of the probe radiation by the thin film. Raman scattering experiments based on these phenomena exhibit an increase in sensitivity from one to several orders of magnitude and allow molecular characterization of very thin films. 

ESA leads to an obstruction, for example, the ovens, Knudsen cells, etc. needed for deposition of thin films prevent a direct view of the substrate. This is one reason why RHEED is in rather widespread use in thin-film deposition systems—the electron gun and screen are remote and grazing incidence does not interfere with film deposition. Therefore, in many cases RHEED is a real in situ technique. By comparison, the conventional front view LEED system blocks essentially the full space and the rear view system blocks half of the space available. In this respect MEIS and RBS are also remote systems that do not take much space around the substrate or target. In some systems transport is installed as a solution (it is the only solution when adding STM to the tool box). 

In reality materials have a partial segregation of the vacancies, so that the solid contains alternating La-rich and La-poor layers. This means that Li conductivity is more akin to a two-dimensional process. Moreover, the segregation of the vacancies leads to microdomain formation and the presence of antiphase boundaries in the material, which may interfere with ionic conductivity, although in thin films of Lij Laj/j. TiOj it has been found that that these structural features have only a small influence on the magnitude of the Li ion conductivity. 

Typical for the visible reduction process of the sample surface is a reduction front travelling over the entire surface and leading to apparently metallic copper (video pictures). The lifetime of the reduced state is very short ( 1 s). Shortly after the metallic state, a progressing surface re-oxidation coiild be followed by eye as a succession of various colours due to light interference in thin CuaO films of increasing thickness. The maximal surface layer thickness can be estimated by the interference colours [24, 25] of at least 300 monolayers CU2O. 

The microstructure observed for thick films shows fibrils, about 4-10 nm in diameter for polystyrene, in agreement with SAXS measurements on the crazes in the bulk polymer. Very thin films of polystyrene (100 nm) show modification in the craze structure as there is no plastic restraint normal to the film [397]. Deformation zones have also been studied in polycarbonate, polystyrene-acrylonitrile and other polymers [398]. Crazes in thermosets can be studied in thin films spun onto NaCl substrates which can be washed away when the film has been cured. Mass thickness measurements are difficult to make in radiation sensitive materials that is why most TEM work has been done on polystyrene and least on PMMA. After developing the techniques described above for TEM Donald and Kramer [398] applied similar methods in optical microscopy to study radiation sensitive materials and the kinetics and growth of deformation zones. Thin films were strained on grids in situ in a reflecting OM. Change of interference color, which depends on the film thickness, was a very sensitive method for observing film deformation. 

The spectral distribution of returned light can also be altered by interference and diffraction. Interference colors are commonly seen in thin films of oil resting on water digital recording disks now provide a corrrmon example of spectral dispersion by diflractiorr... 

Finally, the stmcture formation of block copolymer in thin films is determined by two factors (1) the surface drives either the orientation of the bulk morphology or the stabilization of a different one, and (2) the film thickness can be varied by interference and confinement effects, so that the stability regions between different phases are bridged. ... 

As a point of interest, it is possible to form very thin films or membranes in water, that is, to have the water-film-water system. Thus a solution of lipid can be stretched on an underwater wire frame and, on thinning, the film goes through a succession of interference colors and may end up as a black film of 60-90 A thickness [109]. The situation is reminiscent of soap films in air (see Section XIV-9) it also represents a potentially important modeling of biological membranes. A theoretical model has been discussed by Good [110]. 

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