Multilevel schemes

Obviously, these two items are not strictly separated in contrast, the most fruitful approach is when they are simultaneously followed, so that they can mutually benefit from each other. In this chapter, we want to focus on the use of simulation methods as a design tool for gas-fluidized bed reactors, for which we consider gas-solid flows at four distinctive levels of modeling. However, before discussing the multilevel scheme, it is useful to first briefly consider the numerical modeling of the gas and solid phase separately. 

Although multilevel schemes are more complex than single layer systems, the former will probably grow in importance because high resolution capability can be reached in a very straightforward way. These systems often require tailor-made polymers and photosensitive materials, thus giving rise to a lot of research in this field. 

Tolbert L M etal., 2002, Charge Balance Control Schemes for Cascade Multilevel Converter in Hybrid Electric Vehicles. IEEE Transactions on Industrial Electronics, 49(5), 1058-1064. 

These control schemes are very effective for a certain class of processes but are not versatile and ineffective for, for example, multilevel-multilevel transitions we shall consider in this chapter. There exist several mathematical studies that investigate controllability of general quantum mechanical systems [11,12]. The theorem of controllability says that quantum mechanical systems with a discrete spectrum under certain conditions have complete controllability in the sense that an initial state can be guided to a chosen target state after some time. Although the theorem guarantees the existence of optimal fields, it does not tell us how to construct such a field for a given problem. 

One sees that the ZBR scheme is effective enough for random matrix systems that is, the optimal fields can be obtained even for this type of complicated problem of multilevel-multilevel transitions. However, it seems that the further analysis is difficult because the power spectra for the optimal fields, Figs, lb and 2b, are very complex that is, they contain many frequency components. ... 

Organosilicon polymers are becoming important in many aspects of device technology. Multilevel metallization schemes require the use of a thin dielectric barrier between successive metal layers (i). Often, these dielectric materials are silicon oxides that are deposited by low-temperature or plasma-enhanced chemical vapor deposition (CVD) techniques. Although conformal in nature, CVD films used as intermetal dielectrics frequently result in defects that arise fi om the high aspect ratios of the metal lines and other device topographies (2). Several planarization schemes have been proposed to alleviate these problems, some of which involve the use of organosilicon polymers (2-4). 

As mentioned in Chapter 1, the present state of CMP is the result of the semiconductor industry s needs to fabricate multilevel interconnections for increasingly complex, dense, and miniaturized devices and circuits. This need is related to improving the performance while adding more devices, functions, etc. to a circuit and chip. This chapter, therefore, discusses the impact of advanced metallization schemes on the performance and cost issues of the ICs. Our discussions start with the impact of reducing feature sizes on performance and the need of various schemes to counter the adverse effect of device shrinkage on the performance of interconnections. An impact of continued device shrinkage on circuit delay is discussed. Then the need of low resistivity metal, low dielectric constant ILD, and planarized surfaces is established leading to the discussion of CMP. Finally various planarization techniques are compared to show why CMP is the process that will satisfy the planarity requirements of the future. 

JM. Steigerwald, R. JGutmann, S. P. Murarica Electrochemical Effect in the Chemical Mechanical Polishing of Ct ipm and Titanium Thin Film Used For Multilevel Interconnect Schemes , Proc. of lEEE-VMIC (1993) P.205... 

N. Baker, M. Holst, and F. Wang, Adaptive multilevel finite element solution of the Poisson-Boltzmann equation 11 Refinement schemes based on solvent accessible surfaces, 1. Comp. Chem. 21 1343 (2000). 

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