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Assuming AD, we show that all of the ordinals below
represented by descriptions (c.f. , but also defined below) are cardinals. Using this analysis we also get a simple representation for the cardinal structure below
. As an application, we compute the cofinalitites of all cardinals below
Processing and measurement of 200 biomedical samples has provided an opportunity to better understand the characteristics of accelerator mass spectrometry (AMS) analysis of such samples. We have utilized established procedures (Vogel 1992) and developed new methods for handling various biological samples. We have included secondary standards of known isotope ratio for all assays. A method of determining maximum precision for each unknown sample value is also reported. The presented data are an update of the ongoing radiocarbon AMS biomedical program at Purdue University.
We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal κ < ℵ ε0 in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).
High density thin film interconnects are expected to be widely used for multi-chip module application to accommodate next generation high I/O and high speed integrated circuits. These interconnects typically use polyimide as the dielectric, and aluminum or copper (with protective overcoat) as the conductor. The interconnects are typically built on silicon or alumina substrates. Large film stress occurs due to the high processing temperature required to cure polyimide and due to the mismatch in thermal coefficients of expansion (TCE) between the film materials and substrate materials. This work studies film stress for these materials.
An instrument which measures thin film stress in-situ at temperatures between 25 and 450°C was used to characterize the stress in polyimide, nickel, and copper films. Two substrate materials, silicon and sapphire, were used in order to extract the TCE and elastic modulus for each film material. Three polyimide materials were evaluated. One of the polyimides studied showed complete stress relaxation at temperatures above 300°C and was almost completely elastic upon heating and cooling between 25 and 300°C. The TCE was calculated to be 41×10−6/°C and the biaxial elastic modulus was 4.0×109 Pascal. The nickel had very low stress asplated, however, high tensile stress was observed after 350°C annealing as a result of TCE mismatch. After first annealing, the nickel was almost completely elastic upon cooling and repeated heating and cooling between 25 and 350°C. Copper, on the other hand, was not completely elastic under similar thermal treatments. High thermal stress caused plastic deformation to occur in copper films. The room temperature stress in copper film after 350°C annealing depended on yield strength instead of TCE mismatch. The stress in these materials and its effects on processing and reliability for high density interconnect will be reported.
Au-In eutectic bonding method which needs only a low process temperature (˜200°C) but produces high temperature (450°C) bonds is reported. In this study, multiple layers of Au and In are deposited directly on semiconductor wafers in one vacuum cycle to prevent indium oxidation and then bonded to substrates coated with Au. At 200°C the indium layer melts and dissolves the gold layers to form a mixture of liquid and solid. The diffusion process continues until the bond solidifies. Upon solidification, the bond has a melting temperature of 456.5°C. Scanning Acoustic Microscope was used to determine the excellent bonding quality before and after thermal shock tests and SEM with EDX capability is employed to determine the composition of the resulting bonds.
Let E be a coanalytic equivalence relation on a Polish space X and (An)n∈ω a sequence of analytic subsets of X. We prove that if lim supn∈kAn meets uncountably many E-equivalence classes for every K ∈ [ω]ω, then there exists K ∈ [ω]ω such that ∩n∈kAn contains a perfect set of pairwise E-inequivalent elements.