In previous work, we have formalized the notions of "planarization length" and "planarization response function" as key parameters that characterize a given CMP consumable set and process. Once extracted through experiments using carefully designed characterization mask sets, these parameters can be used to predict polish performance in CMP for arbitrary product layouts. The methodology has proven effective at predicting oxide interlevel dielectric planarization results.In this work, we discuss extensions of layout pattern dependent CMP modeling. These improvements include integrated up and down area polish modeling; this is needed to account for both density dependent effects, and step height limits or step height perturbations on the density model. Second, we discuss applications of the model to process optimization, process control (e.g. feedback compensation of equipment drifts), and shallow trench isolation (STI) polish. Third, we propose a framework for the modeling of pattern dependent effects in copper CMP. The framework includes "removal rate diagrams" which concisely capture dishing height and step height dependencies in dual material polish processes. I. MOTIVATION: PATTERN DEPENDENT CMP CONCERNSThe motivation for this work is the presence of substantial pattern dependencies in CMP. As illustrated in Fig. 1, these concerns arise in a variety of key CMP process applications. In oxide or interlevel dielectric (ILD) CMP, the global planarity or oxide thickness differences in different regions across the chip is a key concern. In addition, the remaining local step height (or height differences in the oxide over patterned features and between patterned features) may also be of concern, although such local step heights are typically small compared to the global nonplanarity across the chip resulting from pattern density dependent planarization. In shallow trench isolation (STI), one is typically concerned about dishing within oxide features resulting from over-polish, as well as the erosion of supporting nitride and in some cases the details of the corner rounding near active areas. In metal polishing (such as in copper damascene), one is concerned also with dishing into metal lines, as well as the erosion of supporting oxide or dielectric spaces in arrays between lines.In this paper, we begin by reviewing previous work on characterization and modeling of oxide CMP pattern dependencies. In Section II, we review the density-dependent oxide CMP model, as well as the important determination of "effective density" based upon a planarization length or planarization response function determination. In Section III, we also review a recent advance in oxide modeling, through which a step height dependent model (proposed elsewhere) has been integrated with the effective density model to produce an integrated time-evolution model for improved accuracy in step height and down area polish prediction. In Section IV we present example applications of the oxide characterization and modeling methodology. These inclu...

Hexavalent chromium, Cr(VI), is toxic to living systems. Widespread contamination of water and soil by Cr(VI) present a serious public health problem. Chromium-resistant bacteria can reduce and detoxify Cr(VI). Twelve bacteria resistant to high concentrations of Cr(VI) were isolated from soil enrichment cultures. Environmental parameters and kinetic parameters of Cr(VI) bioreduction by one monoculture isolate, identified by 16S rRNA gene sequence as Bacillus sp. PB2, were studied. The optimal temperature for growth and Cr(VI) reduction was 35 degrees C. The isolate grew luxuriantly and substantially reduced Cr(VI) at initial pH 7.5 to 9. Maximal Cr(VI) bioreduction occurred at initial pH 8.0. Substantial Cr(VI) bioreduction was observed in salt media, but removal efficiency was inversely related to salt concentration (1-9%). Michaelis-Menten hyperbolic equation and the Lineweaver-Burk double reciprocal plot were comparatively employed to determine the k (m) and V (max) of Cr(VI) bioreduction. A k (m) of 82.5 microg mL(-1) and V (max) of 7.78 microg mL(-1) h(-1) were calculated by nonlinear regression analysis of the hyperbola curve. Linear regression analysis of the double reciprocal plot revealed k (m) and V (max) of 80.9 microg mL(-1) and 10.6 microg mL(-1) h(-1), respectively. Time course studies displayed about 90% reduction of Cr(VI) at an initial concentration of 8,000 microg L(-1) in 8 h, with an estimated t (1/2) of 4 h. Data from time course analysis of the rate of Cr(VI) bioreduction fitted zero-order model, and the kinetic constant k was calculated to be 840 microg L(-1) h(-1). The monoculture isolate, Bacillus sp. PB2, strongly reduces Cr(VI) and could be used for bioremediation of Cr(VI)-contaminated aquatic and terrestrial environments.

Chemical mechanical polishing (CMP) has become the preferred planarization method for multilevel interconnect technology due to its ability to achieve a high degree of feature level planarity. However, methods are needed to understand and model both wafer level and die level uniformity in interlevel dielectric (oxide) polishing. This paper examines the variation of die level planarity across the wafer and at different process conditions. Substantial dependency of planarization length, a characteristic length which determines die level planarity, on table speed and down pressure is found, varying from 6.2 to 7.8 mm in the experiments considered here. In addition, a dependence of planarization length on die position within the wafer is found, varying by ϳ0.5 mm across the wafer resulting in a difference of ϳ300 Å total indicated range from one die to the next. Some die are impacted even more strongly resulting in much smaller planarization lengths (near 5.0 mm in some cases) due to wafer edge effects. We conclude that accurate modeling and optimization of within-die variation depends on accurate modeling and measurement of not only wafer scale removal rate variation but also wafer scale planarization length variation.