Half pitch

In order to obtain the relationship between S and the concentration C, a double logarithmic plot of S against C at each temperature was made as shown in fig. 4. It can be seen that log S is proportional to log C and, its slope n is an increasing function of temperature, characteristic of the specimens used. 

The extrapolated line of log S-log C crossed each other at a critical concentration Cq at which S stays constant and independent of temperature. These results suggest that the temperature dependence of the cholesteric pitch would inflect at the concentration higher than Cq This is analogous to the behavior of thermotropic liquid crystals composed of cholesteric solute and nematic solvent, where the sign of dS/dT reverses at a critical concentration. It is understood that the behavior of both thermotropic and lyotropic liquid crystals is comparable provided that the nematic substances of the former are substituted with the solvents of the latter. The critical concentration Cq is about 0.41 vol/vol and this value is very close to the concentration at which the side chains on neighboring molecules of the polymer come to contact each other ( refer to fig.5 ). From these results, it is expected that the origin or mechanism of twist would change at this concentration Cq. The 

It is convenient to use the reduced temperature T/T, where is the nematic temperature, instead of temperature T, in the temperature range near Fig. 6 shows the observed values of 1/S versus T/Tj, for PBDG in chloroform, at various concentrations. 

The slope B depends on the concentration, and it increases with concentration. If the cholesteric pitch was measured at constant concentration, the following equation holds  

As shown in the table, these values are clearly constant and independent of concentration. 

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A combination of tapered shaft diameter and increasing pitch is shown in Figure 10a. This allows a length-to-diameter ratio of about 6 1 instead of 3 1. A half pitch screw is used over the tapered diameter. This approach results in an exceUent mass flow pattern provided that the hopper to which it attaches is also designed for mass flow. 

Figure 7.4 Simplified macroscopic model for cholesteric (a) lateral and (b) top view of left-handed superhehx (photographs display a half-pitch length) composed of left-handed helical screws with pitch-to-diameter ratio much smaller than Jt. (Reprinted with permission of John Wiley Sons from Circular Dichroism—Principles and Applications, 2nd ed., N. Berova, K. Nakanishi, R. W. Woody, Eds., Copyright 2000.)...

The chiral pitch refers to the distance (along the director) over which the mesogens undergo a full 360° twist (the structure repeats itself every half pitch since the positive and negative directions along the director are equivalent). The pitch may be varied by adjusting temperature or adding other molecules to the LC fluid. For many types... 

In alternative embodiments the auxiliary electrode 30 and the corresponding structures on the substrate are not L-shaped but U-shaped. Two such arrays of detector elements SO and S2 can be arranged in parallel with each other and with the positions of the detector elements of the first array shifted relative to the second array by a half pitch of the element spacing. 

Figure 4.13. Scaling of transistor size. The top line indicates the technology node, whereas the bottom line indicates the physical size of the gate. It should be noted that the technology node no longer refers to physical dimensions of the transistor, but is rather an industry term related to a new fabrication process every 2 years, in accord with Moore s Law. By definition, the technology node refers to half the distance (half-pitch) between cells in a DRAM memory chip. It is noteworthy that the gate length, L, officially moved into the nanoregime in the year 2000. Reproduced with permission from Intel Corporation (http //www.intel.com).

The influence of temperature on magnitude of the side-chain LCICD was examined in dioxane. An independent measurement under a polarizing microscope showed that the cholesteric half-pitch in this solvent increased with temperature. Therefore the LCICD magnitude was expected to increase according to the theoretical... 

Fig. 12. Plots of the reciprocal half-pitch vs. temperature for PBLG liquid crystals (O) in m-cresol ( ) in benzyl alcohol...

A similar thermally-induced inversion of the cholesteric sense was observed for the PBLG liquid crystal in benzyl alcohol. In this solution, a gel-like opaque phase coexists with the cholesteric phase at lower temperatures. The opaque phase disappears around 70 °C, where endothermic peaks are observed in the differential scanning calorimetry curve. The value of S below 70 °C remains constant, and then changes with temperature above 70 °C. The compensation occurs at about 103 °C, and the transition from biphasic phase to the isotropic phase is observed above 150 °C in this case. The results are summarized in Fig. 12, where the reciprocal of the half-pitch is plotted against temperature. The sign of 1/S is taken as positive when the cholesteric sense is the right-handed. 

M. D. Austin et al., 6 nm half-pitch lines and 0.04 mm static random access memory patterns by nanoimprint lithography, Atonofec/moZogy, 16, 1058, 2005. 

Some of the leading edge memory device makers actually inserted ArF lithography into limited production runs at the 130 nm half pitch around 2002. 

Figure 15.11 Resolution SEM images of features ranging in size from 22-nm half-pitch (hp) to 90 nm (1 1.5 pitch), printed with maskless ion projection lithography system on 20-nm hydrosilesquixane resist, using 10-keV argon ions at an exposure dose of...

A. Conley, and I. Liu, Challenges of 29 nm half pitch patterning with 193 nm dry lithography... 

Figure 17.16 SEM cross section of 25-nm half-pitch lines patterned with LELE double-patterning technique. The line profiles were obtained after the final pattern transfer to the underlying substrate. The second-layer patterns after the second etch step are considerably longer than the first-layer patterns because they are capped with the second HM material. (Courtesy of S. Holmes.)...

Figure 17.20 SEM images of shallow trench isolation structures patterned with self-aligned double-patterning technique through various stages of the process flow, and ending in 22-nm half-pitch structures. The HM used is Applied Materials Corporation s advanced patterning film (APF). ...

C. Bencher, Y. Chen, H. Dai, W. Montgomery, and L. Huli, 22 nm half pitch patterning hy CVD spacer self ahgned double patterning, Proc. SPIE 6924, 69244E (2008). 

Figure 17.21 SEM images of 22-nm half-pitch gridded design structures patterned into silicon. The structures were fabricated with a SADP spacer HM scheme in conjunction with a cut mask. ...

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