Stresses from flip-chip assembly and underfill; measurements with the ATC4.1 assembly test chip and analysis by finite element method

The authors report the first measurements of in-situ flip-chip assembly mechanical stresses using a CMOS piezoresistive test chip repatterned with a fine pitch full area array. A special printed circuit board substrate was designed at Sandia and fabricated by the Hadco Corp. The flip-chip solder attach (FCA) and underfill was performed by a SEMATECH member company. The measured incremental stresses produced by the underfill are reported and discussed for several underfill materials used in this experiment. A FEM of a one-quarter section of the square assembly has been developed to compare with the measured as-assembled and underfill die surface stresses. The initial model utilized linear elastic constitutive models for the Si, solder, underfill, and PC board components. Detailed comparisons between theory and experiment are presented and discussed

Calculation and Validation of Thermomechanical Stresses in Flip Chip BGA Using the ATC4.2 Test Vehicle

We report the first in situ measurements of thermomechanical stresses in a 1000 I/O 250 {micro}m pitch piezoresistive flip chip test chip assembled to a 755 I/O 1.0 mm pitch 35 mm Ball Grid Array (BGA). The BGA substrates employed build-up dielectric layers containing micro-vias over conventional fiberglass laminate cores. Experimental data, which include in situ stress and die bending measurements, were correlated to closed form and Finite Element Method (FEM) calculations. Cracking and delamination were observed in some of the experimental groups undergoing temperature cycling. Through use of bounding conditions in the FEM simulations, these failures were associated with debonding of the underfill fillet from the die edge that caused stresses to shift to weaker areas of the package

Runaway Events Dominate the Heavy Tail of Citation Distributions

Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers form one of the best-known heavy tail distributions. Even in this case there is a considerable debate whether citation distribution follows the log-normal or power-law fit. The goal of our study is to solve this debate by measuring citation distribution for a very large and homogeneous data. We measured citation distribution for 418,438 Physics papers published in 1980-1989 and cited by 2008. While the log-normal fit deviates too strong from the data, the discrete power-law function with the exponent $\gamma=3.15$ does better and fits 99.955% of the data. However, the extreme tail of the distribution deviates upward even from the power-law fit and exhibits a dramatic "runaway" behavior. The onset of the runaway regime is revealed macroscopically as the paper garners 1000-1500 citations, however the microscopic measurements of autocorrelation in citation rates are able to predict this behavior in advance.Comment: 6 pages, 5 Figure

Turnover of passerine birds on islands in the Aegean Sea (Greece)

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73442/1/j.1365-2699.2007.01695.x.pd