Projected linewidths

Fig. 5. (a) Two-dimensional 1SN- H dipolar/chemical shift spectrum obtained from [lSN]acetylvaline showing the dipolar and chemical shift projections. Linewidths are typically 50-150 Hz for the dipolar and 0.5-1.0 ppm for the chemical shift dimension. vR = 1.07 kHz. (b) Dipolar cross-sections taken from the 2D spectrum. Each trace runs parallel to ivh through a particular rotational sideband in u>2. (i) Experimental i5N-H spectra from [15N]acetylvaline, vR = 1.07 kHz. The two simulations (ii and iii) assume two different orientations of the dipolar and shielding tensors, (ftD = 22°, D = 0°) and (Ai = 17°, aD = 0°), respectively, and illustrate the subtle differences in orientation which can be detected in the spectra. 

After consideration of all factors which limit resolution such as exposure hardware, resist systems, registration, alignment, and linewidth control, there is a general consensus that the useful resolution limit of photolithography may lie somewhere between 0.4 and 0.8 /im and depends on such factors as the implementation of short wavelength UV and the ability to accurately place images from a projection tool onto a silicon wafer. 

The projection in F2 corresponds to H- CCP/MASNMR spectrum ensuring site resolution the projections in F corresponds to H wide lines the linewidth can be correlated with molecular mobility of a particular site... 

Scanning the frequency of the dissociation laser and collecting the total OH fluorescence, while the state-selection and probe frequencies are kept fixed on specific transitions, produces a PHOFEX spectrum an example is displayed in the right-hand panel of Fig. 10. The lines correspond to specific resonance states with rotational quantum number J and projection quantum number if = 2 in vibrational state (6,0,0). If the individual lines are broader than the resolution of the laser system, one can determine the width from fitting the spectrum and thus determine the state-specific dissociation rate. If the true linewidth caused by dissociation is smaller than the resolution of the laser system, the rates can be extracted from time-resolved measurements. All three laser frequencies are fixed, and the OH probe laser used to detect a particular state of OH is delayed with respect to the dissociation laser. In this way one can monitor the appearance of the OH products as function of the delay time, in the same way as described above for N02- In contrast to NO2, however, the rate is a state-specific rate rather than an average rate, because of the high selectivity of the overtone... 

More generally, in Eq. (8) At = l/v, where u is a characteristic rate of measurements. With this definition, Eq. (8) holds both for ideal and nonideal (realistic) measurements. Relation (8) comes about since measurements (projections) dephase level e), analogously to phase randomization by collisions, which induce a linewidth that is equal to the collision rate v. 

Berger and J.M. Gibson, New approach to projection electron lithography with demon strated 0.1 p,m linewidth, Appl. Phys. Lett. 57, 153 (1990) S.D. Berger, J.M. Gibson,... 

In a three-dimensional experiment it is quite likely that the nuclei evolving in ti and 2 have different spin-spin relaxation times T2 and. This means that a response in the S FiJ 2) plane may have very different natural linewidths in the two frequency dimensions. With a skew sfice through evolution space at an angle a, Fourier transformation generates a projected response with a Lorentzian width given by... 

One example of the NMR reconstraction problem employs the reversible-jump Markov chain Monte-Carlo method [16]. It assumes that the model spectram S Fi,F2) is made up of a limited number m of two-dimensional Gaussian resonance lines. Then m, the linewidths, intensities, and frequency co-ordinates are varied until the Markov chain reaches convergence. The allowed transitions between the current map M and the new map M comprise movement, merging or splitting of resonance lines, and birth or death of component responses. Compatibility with the experimental traces is checked by projecting M at the appropriate angles. The procedure has been found to be stable and reproducible [16]. 

Nmr relaxation measurements allow the molecular motions of the segments of a polymer molecule to be investigated. The spectral line width, which is proportional to I/T2 (i.e. the reciprocal of the spin-spin relaxation time of proton nmr) is a direct measure of segment mobility. It would be anticipated that the anchor segments in the trains attached to the surface of the adsorbent particle would display low mobility. On the other hand, those segments in loops and tails that project into the continuous phase should possess much higher mobility. Two distinct linewidths would therefore be expected for the two different types of segments. 

Experimentally this has been found in dhcp Pr (Houmann et al. 1979, Jensen 1976) and PrAlj (Purwins et al. 1976). Various theoretical methods have been used to describe mixed-mode excitations pseudospon techniques, (Elliott et al. 1972), diagrammatic methods (Thalmeier and Fulde 1975) and equation of motion techniques (Morin et al. 1980b, Aksenov et al. 1981). In the RPA all these methods lead to mixed excitations of infinite lifetime. Lifetime effects can be included in a phenomenological manner, see, e.g., Becker et al. (1981). For a microscopic treatment of linewidth effects beyond RPA the projection operator technique is more suitable (Huggins et al. 1984). 

It is clear that the progress in VLSI technology is closely linked to lithographic techniques, as the size of the circuit decreases, the speed and the power consmnption decreases. These techniques are dependent on the photochemistry and the resists. The minimum linewidth permitted is already around 0.1 pm or less with sources like electron-beam, X-rays or the 193 nm excimer laser. No doubt these limits will progress and one already speaks of 157 nm projection lithography. The requirements placed on photoresists will probably increase in the near future. 

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