This paper provides an overview of two topics. First, it presents a unified approach to various techniques addressing the non-uniqueness of the solution of the inverse gravimetric problem; alternative, simple proofs of some known results are also given. Second, it summarizes in a concise and self-contained way a particular multiscale regularization technique involving scaling functions and wavelets. 0266-5611/08/045019+25$30.00

A new type of slurry, in which much surfactant was added into aconventional CeO,slurty, was developed for Si0,chemical mechanical polishing (CMP). The new slurry has unique characteristics. Because the polishing rate drops as planadzation progresses, polishing can stop automatically. Therefore, it is easy to control the remaining thickness. Moreover, it is possible to planarize a surface without any dishing, even at a wide depressed pottiin (4 mm). Therefore, the global planatization within a chip can be obtained without any stopoing layer or design limitations.surfactant which was used forthis experiment is a polymer of the anion group.A commercial single-head polisher was used. Pad conditioning was applied after each wafer was polished. The process conditions are summarized in Table 1.The slurry performance was evaluated by measuring the remaining step in patterned 200 mm wafers coated with P-SiO,films, wherein the line and space (L&S) widths ranged from 10 pm to 4 mm. Uniformity was calculated as 3-sigma divided by the average (indicated as a percentage)for 17 points measured in the cross direction on the wafer. Results and dlscusslon IntroductionCMP, which is maintains the wafer planarity throughout the process, is the key to achieving a large process windowat quarter micron design rules. However, with the conventional CMP technique, in the case where there is a wide depressed portion between AI wiring, the center of the portion has priority over other portions in polishing, thus causing so-called dishing. Therefore, it is difficult to obtain the global planarization within a chip. Furthermore, it is very difficult to control the remaining thickness, because the polishing rate differs from wafer to wafer.To overcome these problems, several techniques have been suggested, forming astopping layer made of a material such as Si , N, , using a lower polishing rate SiO, film'), limiting the design rule" and developing of an end point monitoring technique3?This paper presents a new slurry for polishing the desired protruding portion superiorly without dishing and for controlling the remaining thickness of the polishing film in consideration of the above problems. ExperimentIn order to study the effect of the surfactant added to the slurry, the relationship between the concentration of the surfactant and the polishing rate was examined. The Figure 1 shows the relationship between the concentration of the surfactant and the polishing rate The polishing rate for the depressed portion (Rs polishing rate on the 4 "space) was redused almost to zero at a point of 2.2 weight % or higher, whereas the polishing rate for the protruding portion (RL : polishing rate on the 500 pm line) was abruptly decreased at a point close to 1 .O weight YO, and was redused almost to zero at a point of 5.0 weight % or higher. In short, with a region from 2.2 tO 4.5 weight O h . it is possible to control dishing. A. Effect of SurfactantIn addition, it is shown that the selectivity of the polishing rate (RL/Rs) reached amaximum at apoint of 2.5 ...