Anisotropic imaging

For the isotropic structure (Figure la) the rose plot is almost a circle (Figure 3c) whereas for the anisotropic image, a gradual variation of the slope with direction gives rise to noncircular patterns (Figure 3d). 

Kaneko, T., Nishioka, H., Nishi, T., and Jinnai, H. (2005). Reduction of anisotropic image resolution in transmission election miciotomography by use of quadrangular prism-shaped section. J. Electron Micros. 54(5), 437-444. 

Figure C2.17.5. Transmission electron micrograph of a field of anisotropic gold nanocrystals. In tliis example, a lower magnification image of gold nanocrystals reveals tlieir anisotropic shapes and faceted surfaces [36],...

Figure 4.14 STM images of 1 L of oxygen exposed to Pt(lll) at the temperatures indicated, emphasising the anisotropic growth of oxygen islands. The scale bar of the image at 160K is 30 A that at all other temperatures is 50 A. (Reproduced from Ref. 25).

In contrast, a real challenge is the analysis of scattering images from anisotropic materials, and in this subarea many scientists surrender and resort to the interpretation of peak positions and peak widths in raw data (cf. citation of P. Debye on p. 1). So after having advanced by learning how to analyze curves, in the field of anisotropic materials we are now in a similar situation as science has been in 1931 in respect to isotropic data. 

A shortcut solution for the analysis of anisotropic data is found by mapping scattering images to scattering curves as has been devised by Bonart in 1966 [16]. Founded on Fourier transformation theory he has clarified that information on the structure in a chosen direction is not related to an intensity curve sliced from the pattern, but to a projection (cf. p. 23) of the pattern on the direction of interest. 

CDFs are computed from scattering data which are anisotropic and complete in reciprocal space. Thus the minimum requirement is a 2D SAXS pattern of a material with fiber symmetry taken in normal transmission geometry (cf. p. 37, Fig. 4.1). Required pre-evaluation of the image is described in Chap. 7. 

Transferred to the observation that the reflections in moderately anisotropic scattering images are found on ellipses3, it appears reasonable to parameterize such images in elliptical coordinates ( , v). The transformation relations are [266]... 

Figure 4.9 illustrates time-gated imaging of rotational correlation time. Briefly, excitation by linearly polarized radiation will excite fluorophores with dipole components parallel to the excitation polarization axis and so the fluorescence emission will be anisotropically polarized immediately after excitation, with more emission polarized parallel than perpendicular to the polarization axis (r0). Subsequently, however, collisions with solvent molecules will tend to randomize the fluorophore orientations and the emission anistropy will decrease with time (r(t)). The characteristic timescale over which the fluorescence anisotropy decreases can be described (in the simplest case of a spherical molecule) by an exponential decay with a time constant, 6, which is the rotational correlation time and is approximately proportional to the local solvent viscosity and to the size of the fluorophore. Provided that... 

Besides the remarkable directionality of the motion, the images also demonstrate a periodic variation of the cluster from an elongated to a circular shape (Fig. 39). The diagrams in Fig. 39 depict the time dependence of the displacement and the cluster size. Until the cluster was finally trapped, the speed remained fairly constant as can be seen from the constant slope in Fig. 39 a. The oscillatory variation of the cluster shape is shown in Fig. 39b. Although a coarse model for the motion has been presented in Fig. 39, the actual cause of the motion remains unknown. The ratchet model proposed by J. Frost requires a non-equiUb-rium variation in the energetic potential to bias the Brownian motion of a molecule or particle under anisotropic boundary conditions [177]. Such local perturbations of the molecular structure are believed to be caused by the mechanical contact with the scaiming tip. A detailed and systematic study of this question is still in progress. 

Figure 13a shows the resist in a three-layer Al-RIE-PCM system by Havas et al. The dry etching conditions were similar to those of plasma etching. Therefore, an undercut was produced under the Al PCM to facilitate lift-off. Figure 13b shows the resist image in a three-layer siloxane RIE PCM system. The dry etching process was sufficiently anisotropic to eliminate the undercut. 

Both the deep-UV-and the RIE PCM-delineated resist structures can be used for electroplating which was successfully demonstrated by Satini and Viswanathan 45) as shown in Figure 22 for the deep-UV PCM case. In this case the control of the image in the planarizing layer is critical. Because of the unique anisotropic characteristics of RIE, this control should also be feasible for RIE PCM. In such cases linewidth variations include the contribution from the planarizing layer as well as top layers. The consideration of resist removal after plating is similar to the case for lift-off. 

---