Ellipsometric thickness

Figure 5 Plot of positive CF3 secondary ion intensity versus ellipsometric thickness from a set of perfluoropolyether standards.

Figure 2.29 Plot of catalytic current for layer-by-layer self-assembled GOx and PAH-Os at 0.55 V in 60mM glucose for increasing film ellipsometric thickness. Lines indicate limiting cases I and II. Taken from Ref [147].

Table 2 Contact angle measurements, XPS analysis, Gantrez/4th Generation PAMAM dendrimer composites and ellipsometric thickness of ...

One of the drawbacks of ellipsometry is that the raw data cannot be directly converted from the reciprocal space into the direct space. Rather, in order to obtain an accurate ellipsometric thickness measurement, one needs to guess a reasonable dielectric constant profile inside the sample, calculate A and and compare them to the experimentally measured A and values (note that the dielectric profile is related to the index of refraction profile, which in turn bears information about the concentration of the present species). This procedure is repeated until satisfactory agreement between the modeled and the experimental values is found. However, this trial-and-error process is complicated by an ambiguity in determining the true dielectric constant profiles that mimic the experimentally measured values. In what follows we will analyze the data qualitatively and point out trends that can be observed from the experimental measurements. We will demonstrate that this... 

Almost linear OVPD calibration curves of the typical dopant rubrene for a variety of source flows up to 10 seem and up to 50 seem are presented in Fig. 9.9, which shows that the deposition rate can be precisely adjusted from 0.06 to 1.6 A s-1. Both curves are an ideal fit and reveal a linear relationship between deposition rate and source flow they were collected with two mass-flow controllers of different capacity ranges (10 seem and 50 seem). Ellipsometric thickness analysis confirmed for both experiments a deposition rate of 0.3564 and 0.3582 A s-1, which is a relative error of only 0.48% and is identical with our prediction of dopant controllability (Table 9.1). Using a standard OVPD deposition rate of 10 A s-1 for a hosts the doping range of rubrene can be very precisely adjusted in the range of 0-16%. 

Fig. 21. Ellipsometric thickness as a function of chain length plotted on a log-log scale. The points (squares and crosses) are the data of Takahashi et al. (1980) for PS adsorbing onto chrome from cyclohexane or CC14. Curves A and B are calculated using the SCF in Eqs. (71) and (72) curves C-F utilize the SCF of Eq. (70). Curves A-D result from the matched asymptotic solution, while curves E and F are groundstate solutions. Other parameters include y, = 1 and

The analysis is carried out using the Drude equations this leads to a combination of the ellipsometric thickness and the refractive index Increment. These characteristics of the adsorbate cannot be unambiguously separated. Conversion of the refractive index increment into the composition of the adsorbate layer is usually done by assuming drt/dx to be the same as in a fluid of composition x for 0 not too high this is usually allowed, but problems may arise when the adsorbate differs substantially from the solution, for Instance because of alignment of adsorbed chain molecules. The result obtained is not unique, in the sense that different profiles may lead to the same pair of ellipsometric parameters. Therefore, normally totally adsorbed amounts are presented. For accurate measurements a good optical contrast between adsorbate and solution is mandatory. 

Ellipsometric data are usually interpreted in terms of one equivalent homogeneous film with a refractive index n and an ellipsometric thickness d . This homogeneous layer is defined as a layer that gives the same reflected intensity and phase shift as the actual polymer layer with a z-dependent concentration. The parameters n " and can be extracted from the experimental data using the Drude equations (sec. 1.7.10b) usually, a numerical iteration is required. 

The principles of ellipsometry have been set forth in sec. 1.7.10b. For the ellipsometric thickness of an interlayer over which the index of refraction n changes with position we gave the following Drude equation... 

Fig. 3.7 Adsorption of fibrinogen on an EG2/EG6 gradient at pH 7.4. The incremental changes in ellipsometric thickness (filled circles) and the integrated area of the amide I peak obtained by FTIR-spectroscopy (open circles) are displayed...

Table 4.1 Advancing and receding water contact angles ((6) and (0)), and ellipsometric thicknesses (nm) of TPEDA SAMs of Library 1 and Library 2...

Adsorbed amount r as a function of ageing time as determined by ellip-sometry is plotted in Figure 4. Especially at pH 3 glycinin adsorbed very fast. After 1 minute, T was about 2.2 and 1.2 mg m 2 at pH 3 and 7.6, respectively. The adsorbed amount became about the same for both pHs after 1-2 hours. The ellipsometric thickness after 2 hours ageing was somewhat larger at pH 6.7 than at pH 3, i.e. about 12 and 8 nm, respectively.18... 

Figure 3. SPM topography images (2x2 microns) of three different islandlike PS brushes prepared by grafting-to method, effective ellipsometric thickness of PS layer 7.5M).5 nm.

The equation above builds on a shear model that assumes that all material in the distance range O-dgcM oscillates with the crystal and thus contributes fully to the tme sensed mass, whereas the material located further away from the surface does not oscillate with the crystal and does not contribute to the sensed mass. This is clearly a simplification, as are the optical models used for evaluating the ellipsometric thickness. It has been shown that the QCM thickness and the ellipsometric thickness are similar for relatively compact and homogeneous layers [28]. We do not expect this to be the case for more diffuse polymer layers since the ellipsometric thickness is directly influenced by the segment density profile [29], whereas the QCM thickness is influenced by the amount of water that oscillates with the crystal, and tlus quantity is at present an unknown function of the segment density profile. 

The time scale for the configurational rearrangement process is hours. When the sample was placed in the vacuum desiccator after equilibration at ambient humidity, more than 4 h were required for equilibration. Consequently, as long as the ellipsometric thickness measurements are done within about 4 h of dip coating, the PFOM film remains isotropic, and the ellipsometry provides an accurate value for the film thickness. 

Ellipsometric Thicknesses. The thicknesses of the monolayers were measured with a Rudolph Research Auto EL III ellipsometer equipped with a He-Ne laser (632.8 nm) at an incident angle of 70° from the surface normal. A refractive index of 1.45 was assumed for all films. For a given sample, the data were averaged over three separate slides using three spots per slide. 

Figure 2b shows the ellipsometric thicknesses of SAMs from Series 2. In this series, the thicknesses of the films generated fi om F(CF2)io(CH2)ySH with y = 2-6, 11, and 17 increase linearly as the number of CH2 groups increases (ca, 1.18 A per CH2), again reflecting the increase in thickness that accompanies the adsorption of progressively longer molecules [13]. 

Figure 2. Average ellipsometric thickness of (a) SAMs from Series 1, (b) SAMs from Series 2, and (c) SAMs from Series 3. All measured thicknesses were reproducible within 2 A of the reported average value.

The confrontation of this elegant prediction by experiment has taken many years to complete because all experimental techniques available at that time did not have the proper spatial resolution. Spectroscopic methods such as EPR, NMR, IR are only sensitive to the fraction of monomers attached to the wall. Ellipsometry measures the first moment of the monomer distribution and vields an average length called the ellipsometric thickness Hydrodynamic methods, based on flow restric-tion in capillaries covered by the adsorbed layer, yield another average length related to the maximum extension of the adsorbed layer To study concentration profiles at the solid-liquid interface, one has thus to devise special tools. 

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