Films thickness

The thickness of thin film layers separated by uniform, parallel interfaces can be determined from optical interference patterns that result. These measurements can be made from about 400 nm out through the visible spectrum and on into the near-infrared (NIR) region. Since film thickness measurements rely not on the absolnte magnitude of the reflected light, but on the variation of that signal with wavelength, the choice of nnits is less important. Typically %R is used, but in some cases raw intensity is also satisfactory. We will treat thickness determinations in more detail in the applications section of this chapter. 

Instrumentation for UV-vis process analysis falls into four categories scanning instruments, diode-array instruments, photometers, and fiber-optic diode-array and CCD instruments. The former two are more typically encountered in at-line or near-line applications, whereas the latter two are better suited to actual on-line analyses. 

Diode-array spectrophotometers have no moving parts, or at most a shutter that moves thus they are more suited to locations near the process. However, these instruments still require the introduction of the sample into the instrument s sample cavity, as well as the necessity for a separate reference measurement. These instruments are usually only found in a single-beam configuration. 

Photometers are relatively simple devices that make use of a light source and one or more filters to present a narrow band of wavelengths to a sample and then to a photodetector. 

or even three wavelength analyses are possible with these devices. In addition, photometers are designed for location on-line, with samples generally plumbed into a sample cavity in the analyzer. 

Primer should be applied at a thickness of 10 3 pm and the top coat should be applied at a thickness of 12 5 pm. Coating thicknesses should not exceed 15 pm for primer, 20 pm for top coat. 

The third parameter comes into play when considering film-covered surfaces. The reason for calling it a forgotten parameter is that it cannot be measured directly by intensity-reflection methods and so it is too often ignored completely. 

The problem of predicting the outcome of this kind of interaction was solved by Drude, whose equations (see Appendix) form the basis of the interpretation of ellipsometric results from film-covered surfaces. 

There are two basic kinds of ellipsometer nulling and intensity modulating. The nulling ellipsometer is historically the first to be invented and was the only kind available until the late sixties. The working principle is to 

With a strong light source, the null can be detected by eye. Sensitivity is increased by using a photomultiplier detector and the sensitivity is then limited by that of the divided circles in which the optics are mounted. However, finding repeated nulls is a laborious process, because it involves iterative approach to the null by successive adjustments to two divided circles. It is also very time-consuming, so that dynamic measurements, except on a very long time scale, are impossible. The process can now be automated, however, making it feasible to record several points per second. 

This method has the usual advantages of null techniques, i.e. immunity to noise and potentially very high precision. The presence of a quarter-wave 

Comparative tests have shown that industrial atmosphere is more severe than marine atmosphere, because there are more or less abrasive dust particles and gaseous pollutants such as sulphur dioxide (SO2) [24]. The minimal thickness must be 20 p.m for industrial and marine atmospheres [25]. 

An annual decrease in thickness of 0.4-0.6 p.m in marine atmosphere and of 0.7-0.9 p,m in industrial atmosphere has been reported in outdoor testing stations testing samples with an anodic coating thickness of 15 p.m [27]. This decrease in thickness probably results from a chemical attack or erosion by abrasive dust particles. Such a decrease in thickness is never observed in buildings, even after service times as long as 20 years or more [28]. It is generally estimated that the decrease in thickness of an oxide layer varies from 0 to 0.03 p,m per year [29]. 

The properties of wrought products for buildings are the subject of several French and international standards [30]. The NF A 91-450 standard (AFNOR) defines the anodisation 

The resistance of electrolytic coloration does not differ significantly from that of sulphuric colourless anodisation, if properly sealed. However, in the absence of regular maintenance, the dark bronze C34 and black C35 from the EURAS palette show a marked tendency to chalking and pitting [33]. 

Class Average minimum thickness (p.m) Local minimum thickness (p.m) 

Internal diameter (mm) Linear carrier gas velocity Flow rate  

The variation in the film thickness at a given internal diameter and column length gives the user the possibility for optimization of special separation tasks. As a rule, thick films are used for volatile compounds and thin films for high-boilers and trace analysis. 

For the analysis of polar compounds it needs to be considered that thicker films provide higher inertness and less residual column activity by better shielding from any polar remaining free glass silanol groups. 

The Relationship between Film Thickness and Internal Diameter 

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The problem of film flow is formulated on the assumption that the film thickness h is much smaller than the length 1 (in our case h/1 10 ). In Cartesian coordinates with transversal axis y and longitudinal one z we can write the equation for a film flow as follows ... 

Now days the devices operating in the radiowave range are designed and they used for oil film thickness measurements and for the oil spills volume evaluation. The device operating on the frequencies from 37,5 to 10,7 begHz provides the measurements of the film thickness in the range from 100 to 6 — 7 pm. It means that all accident happening on the seas surface may be estimated. 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

In a study of tarnishing the parabolic law, Eq. VII-30, is obeyed, with kj = 0. The film thickness y, measured after a given constant elapsed time, is determined in a... 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Fig. XI-3. Ellipsometric film thickness as a function of number of layers of methyl 23-(trichlorosilyl)tricosanoate on silicon wafers (Ref. 33).

Electrolyte adsorption on metals is important in electrochemistry [167,168]. One study reports the adsorption of various anions an Ag, Au, Rh, and Ni electrodes using ellipsometry. Adsorbed film thicknesses now also depend on applied potential. 

Calculate the film thickness for the Marongoni instability shown in Fig. Xlll-2 using the relationship in Eq. XIIl-3, assuming that the interfacial tension is 20 mN/m. 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

The existence of a characteristic isotherm (or of a r-plot) gives a very important piece of information about the adsorption potential, at least for polar solids for which the observation holds. The direct implication is that film thickness f, or alternatively n/n is determined by P/I independent of the nature of the adsorbent. We can thus write... 

This may be based on Eq. XVI-2 [232] or on related equations with film thickness given by some version of the Frenkel-Halsey-Hill equation (Eq. XVII-79) [233,234],... 

Figure Bl.19.27. AFM topographic images (7x7 pm ) of 20 epitaxial Ag films on mica prepared at five substrate temperatures (75, 135, 200, 275, and 350 °C) and four film thicknesses (50, 110, 200, and 300 mn)...

Figure Bl.26.14. Plot of A versus K, the imaginary part of the refractive index. (B) MEASUREMENT OF FILM THICKNESS AND OPTICAL PROPERTIES...

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

The growth according to this equation is self-limiting as the field strength F is lowered (at constant voltage) with an increasing film thickness x. 

Ultra-high vacuum (UHV) surface science methods allow preparation and characterization of perfectly clean, well ordered surfaces of single crystalline materials. By preparing pairs of such surfaces it is possible to fonn interfaces under highly controlled conditions. Furthennore, thin films of adsorbed species can be produced and characterized using a wide variety of methods. Surface science methods have been coupled with UHV measurements of macroscopic friction forces. Such measurements have demonstrated that adsorbate film thicknesses of a few monolayers are sufficient to lubricate metal surfaces [12, 181. 

A possible explanation of the hysteresis could be the non-equilibrium of the DNA hydration. In that case the value of hysteresis has to depend on the size of the experimental sample. However, such a dependence is not observed in the wide range of DNA film thicknesses (0.05-0.2 fmi) [14], [12]. Thus, hysteresis cannot be a macroscopic phenomenon and does reflect the molecular interaction of water and the biopolymer. 

The gas permeability constant is the amount of gas expressed in cubic centimeters passed in 1 s through a 1-cm area of film when the pressure across a film thickness of 1 cm is 1 cmHg and the temperature is 25°C. All tabulated values are multiplied by 10 and are in units of seconds" (centimeters of Hg) k Other temperatures are indicated by exponents and are expressed in degrees Celsius. 

Volumes in mm (liquid) radii and film thicknesses in A area in m g . The remainder of the standard columns ([1] to [9]) may be built up from Tabic 3.2A an alternative table, based on regular intervals of r, may be built up from Table 3.2B. 

For each group of pores, the pore volume 6v is related to the core volume by means of a model, either the cylinder or the parallel-sided slit as the case may be. Allowance is made for the succession of film thicknesses corresponding to the progressive thinning of the multilayer in each pore, as desorption proceeds. Thus for group i, with radius rf when the film thickness is tj j > i) and the core volume is the pore volume 6vf will be given by... 

It will be noted that the first suffix of Q j refers to the pore radius of the group, and the second to the film thickness. 

When the relative pressure falls to P2/p°, corresponding to r = 80 A, the second group of pores will have given up a volume of adsorbate equal to dv 22-But since the film thickness has now diminished to t2, there will have been an additional loss from the walls of group 1 the total loss from group 1 is therefore so that the total loss from both groups is... 

Another important characteristic of a gas chromatographic column is the thickness of the stationary phase. As shown in equation 12.25, separation efficiency improves with thinner films. The most common film thickness is 0.25 pm. Thicker films are used for highly volatile solutes, such as gases, because they have a greater capacity for retaining such solutes. Thinner films are used when separating solutes of low volatility, such as steroids. 

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