Multilevel

Figure Al.6.24. Schematic representation of a photon echo in an isolated, multilevel molecule, (a) The initial pulse prepares a superposition of ground- and excited-state amplitude, (b) The subsequent motion on the ground and excited electronic states. The ground-state amplitude is shown as stationary (which in general it will not be for strong pulses), while the excited-state amplitude is non-stationary. (c) The second pulse exchanges ground- and excited-state amplitude, (d) Subsequent evolution of the wavepackets on the ground and excited electronic states. Wlien they overlap, an echo occurs (after [40]).

Fundamentally, the conditions for lasing are detemiined unambiguously once the populations and coherences of the system density matrix are known. Yet, we have been unable to find in the literature any simple criterion for lasing in multilevel systems in temis of the system density matrix alone. Our conjecture is that entropy, as... 

Tannor D J and Rice S A 1987 Photon echoes in multilevel systems Understanding Molecular Properties ed J Avery et al (Dordrecht Reidel) p 205... 

Jean J M, Fleming G and Friesner R 1992 Application of a multilevel redfield theory to electron transfer in condensed... 

Tokmakoff A, Kwok A S, Urdahl R S, Franois R S and Fayer M D 1995 Multilevel vibrational dephasing and vibrational... 

However, by constructing a nested sequence of successively larger discrete spaces and approximations therein we hope to end up with some approximation of a unique invariant measure, which is then implicitly defined via the constructed sequence of subspaces. An expression of this mathematical consideration is the multilevel structure of the suggested algorithm - details see below (Section 3.2). In physical terms, we hope that the perturbations introduced by discretization induce a unique and smooth invariant measure but are so weak that they do not destroy the essential physical structure of the problem. 

J. Wary, R. A. Olson, and W. F. Beach, 2nd International Dielectricsfor VESI/ UESI Multilevel Insulation Conference (DUMIC), Santa Clara, Cal., Feb. 

Fig. 13. Examples of pipe gas distributors (a) simple sparger, (b) details of the pipe, (c) wagon wheel, and (d) multilevel distributor.

Oxidation of Silicon. Silicon dioxide [7631-86-9] Si02, is a basic component of IC fabrication. Si02 layers are commonly used as selective masks against the implantation or diffusion of dopants into silicon. Si02 is also used to isolate one device from another. It is a component of MOS devices, and provides electrical isolation of multilevel metalliza tion stmctures (12). A comparison of Si and Si02 properties is shown in Table 1. 

Polysilicon. Polysihcon is used as the gate electrode material in MOS devices, as a conducting material for multilevel metallization, and as contact material for devices having shallow junctions. It is prepared by pyrolyzing silane, SiH, at 575—650°C in a low pressure reactor. The temperature of the process affects the properties of the final film. Higher process temperatures increase the deposition rate, but degrade the uniformity of the layer. Lower temperatures may improve the uniformity, but reduce the throughput to an impractical level. 

S. R. Wilson, C. J. Tracy, and J. Freeman, eds.. Handbook of Multilevel Metallisationsfor Integrated Circuits, Noyes Data Corp., Park Ridge, N.J., 1993. 

Figure 12-88. Simplified multilevel refrigeration process an example of three different composition streams entering a single multiwheel case. Also see Figure 12-40C. (Used by permission Peters, K. L. Hydrocarbon Processing, V. 60, No. 5, p. 171, 1981. Gulf Publishing Company. All rights reserved.)...

HANDBOOKOF MULTILEVEL METALLIZATION FOR INTEGRATED CIRCUITS edited by Syd R. Wilson, Clarence J. Tracy, and Jchn L. Freeman, Jr. 

This reaction proceeds at a much faster rate than the hydrogen reduction of WFg. The result is erosion of the silicon substrate causing encroachment and tunnel defects. The use of a different precursor, such as tungsten carbonyl, W(CO)g, may solve this problem. CVD tungsten is presently limited mostly to multilevel-via-fill applications. 

Smith, P. M., et al., Chemical Vapor Deposition of Ternary Refractory Nitrides for Difiusion Barrier Applications, Proc. 13th. Int. Conf. on VLSI Multilevel Interconnections, Sandia National Labs., Albuquerque, NM (1996)... 

FIGURE 4.15 Cross-section of multilevel interconnections for advanced bipolar devices. Fourteen separate layers are laid down in the fabrication of interconnections such as the one shown. The precise orientation and composition of these layers are controlled by chemical process steps. Copyright 1982 by the International Business Machines Corporation. Reprinted with permission. 

The system of equations, including the Reynolds, him thickness, load balance, viscosity-pressure, and viscosity modih-cation equations, is simultaneously solved with the help of a multilevel technique described by Venner and Lubrecht with modihcations to take account of the variation in viscosity. The invariant parameters used in the computation are Z = 0.67, = 226 GPa, o = 0.04 Pa s, p j = 0.46 GPa, R... 

Lubrecht, A. A. and loaimides, E. A., Fast Solution of the Dry Contact Problem and Associated Surface Stress Field, Using Multilevel Techniques, ASME7. Tribal, Vol. 113, 1991, PP-128-133. 

Zhang, R, Busnaina, A. A., Reng, J., and Rury, M. A., Particle Adhesion Force in CMP and Subsequent Cleaning Processes," Proceedings, 4th International Chemical-Mechanical Planarization for ULSI Multilevel Interconnection Conference, Santa Clara, CA, Reb. 11-12,1999, pp. 61-64. 

A Russian expert system, PASS (prediction of activity spectra for substances) [84], uses substructural descriptors called multilevel neighborhoods of atoms [85] to predict over 900 different pharmacological activities from molecular structure. These activities include a number of toxicity end points such as carcinogenicity, mutagenicity, teratogenicity, and embryotoxicity. The accuracy of prediction has been shown [86] to range from about 85% to over 90%. One-off predictions can be obtained free of charge on the PASS website [84]. 

Filimonov DA, Poroikov VV, Borodina Y, Gloriozova T. Chemical similarity assessment through multilevel neighborhoods of atoms definition and comparison with the other descriptors. J Chem Inf Comput Sci 1999 39 666-70. 

We hope to have convinced the reader by now that the tunneling centers in glasses are complicated objects that would have to be described using an enormously big Hilbert space, currently beyond our computational capacity. This multilevel character can be anticipated coming from the low-temperature perspective in Lubchenko and Wolynes [4]. Indeed, if a defect has at least two alternative states between which it can tunnel, this system is at least as complex as a double-well potential—clearly a multilevel system, reducing to a TLS at the lowest temperatures. Deviations from a simple two-level behavior have been seen directly in single-molecule experiments [105]. In order to predict the energies at which this multilevel behavior would be exhibited, we first estimate the domain wall mass. Obviously, the total mass of all the atoms in the droplet... 

According to the quantum transition state theory [108], and ignoring damping, at a temperature T h(S) /Inks — a/ i )To/2n, the wall motion will typically be classically activated. This temperature lies within the plateau in thermal conductivity [19]. This estimate will be lowered if damping, which becomes considerable also at these temperatures, is included in the treatment. Indeed, as shown later in this section, interaction with phonons results in the usual phenomena of frequency shift and level broadening in an internal resonance. Also, activated motion necessarily implies that the system is multilevel. While a complete characterization of all the states does not seem realistic at present, we can extract at least the spectrum of their important subset, namely, those that correspond to the vibrational excitations of the mosaic, whose spectraFspatial density will turn out to be sufficiently high to account for the existence of the boson peak. 

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