High current density induced damage mechanisms in electronic solder joints: a state-of-the-art review

High current density induced damages such as electromigration in the on-chip interconnection /metallization of Al or Cu has been the subject of intense study over the last 40 years. Recently, because of the increasing trend of miniaturization of the electronic packaging that encloses the chip, electromigration as well as other high current density induced damages are becoming a growing concern for off-chip interconnection where low melting point solder joints are commonly used. Before long, a huge number of publications have been explored on the electromigration issue of solder joints. However, a wide spectrum of findings might confuse electronic companies/designers. Thus, a review of the high current induced damages in solder joints is timely right this moment. We have selected 6 major phenomena to review in this paper. They are (i) electromigration (mass transfer due electron bombardment), (ii) thermomigration (mass transfer due to thermal gradient), (iii) enhanced intermetallic compound growth, (iv) enhanced current crowding, (v) enhanced under bump metallisation dissolution and (vi) high Joule heating and (vii) solder melting. the damage mechanisms under high current stressing in the tiny solder joint, mentioned in the review article, are significant roadblocks to further miniaturization of electronics. Without through understanding of these failure mechanisms by experiments coupled with mathematical modeling work, further miniaturization in electronics will be jeopardize

ZnZ_n elliptic Gaudin model with open boundaries

The $Z_n$ elliptic Gaudin model with integrable boundaries specified by generic non-diagonal K-matrices with $n+1$ free boundary parameters is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained.Comment: 21 pages, Latex fil

Developmental morphology of the small intestine in Yangzhou goslings

The objective of this study was to investigate the development of the weight and the morphological development of the small intestine in Yangzhou geese. The weight, length and perimeter of the small intestine, height and width of the villi, depth of the crypts were measured when geese were 1, 14, 28, 42, 56 and 70 days of age. The results revealed that the weight of the duodenum, jejunum, and ileum (relative to the BW) increased, peaked on day 14 and tended to decline thereafter with age. The weight of the duodenum, jejunum, and ileum (relative to the BW) kept steady-going on 56, 42, 42 days, respectively. A 3-fold increase in length and 2-fold increase in perimeter for the three segments during the period were obtained. The duodenum increased little in length, whereas both jejunum and ileum increased 2 and 3-folds from 1 to 70 days examined. The increase in perimeter of the duodenum, jejunum and ileum was greater from day 1 to 14 than from day 14 to 28. The length and perimeter of the intestinal segments of the gastro-intestinal of Yangzhou geese (relative to the BW) peaked on day 1, then decreased with age and kept steady-going on 42 days, except the relative perimeter of the duodenum. The villus height, surface area and crypt depth in the small intestine were positively correlated with the age of the geese. The ratio of the villus height to the crypt depth (V/C) differed among the segments of the small intestine and at the different time points. The V/C in the ileum increased from day 1 to 70, whereas in the duodenum the ratio first decreased, then rose and descended. However, in the jejunum the ratio increased first, then dropped and rose again, and descended eventually.Key words: Geese, small intestine, morphology

Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems

We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system, in the presence of weak disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The interplay between the two is investigated by treating the long-range Coulomb interaction and the random disorder potential in a self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength.Comment: 4 pages, revtex, 4 figures, to be published in Phys. Rev. B as a Rapid Communicatio

Determinant Representations of Correlation Functions for the Supersymmetric t-J Model

Working in the $F$-basis provided by the factorizing $F$-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions for the model.Comment: Latex File, 41 pages, no figure; V2: minor typos corrected, V3: This version will appear in Commun. Math. Phy

Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.Comment: Latex file, 25 page

Energy relaxation of an excited electron gas in quantum wires: many-body electron LO-phonon coupling

We theoretically study energy relaxation via LO-phonon emission in an excited one-dimensional electron gas confined in a GaAs quantum wire structure. We find that the inclusion of phonon renormalization effects in the theory extends the LO-phonon dominated loss regime down to substantially lower temperatures. We show that a simple plasmon-pole approximation works well for this problem, and discuss implications of our results for low temperature electron heating experiments in quantum wires.Comment: 10 pages, RevTex, 4 figures included. Also available at http://www-cmg.physics.umd.edu/~lzheng

The sintering, sintered microstructure and mechanical properties of Ti-Fe-Si Alloys

A systematic study has been conducted of the sintering, sintered microstructure and tensile properties of a range of lower cost Ti-Fe-Si alloys, including Ti-3Fe-(0-4)Si, Ti-(3-6)Fe-0.5Si, and Ti-(3-6)Fe-1Si (in wt pct throughout). Small additions of Si (≤1 pct) noticeably improve the as-sintered tensile properties of Ti-3Fe alloy, including the ductility, with fine titanium silicides (TiSi) being dispersed in both the α and β phases. Conversely, additions of >1 pct Si produce coarse and/or networked TiSi silicides along the grain boundaries leading to predominantly intergranular fracture and, hence, poor ductility, although the tensile strength continues to increase because of the reinforcement by TiSi. Increasing the Fe content in the Ti-xFe-0.5/ 1.0Si alloys above 3 pct markedly increases the average grain size and changes the morphology of the α-phase phase to much thinner and more acicular laths. Consequently, the ductility drops t

Interplay between edge states and simple bulk defects in graphene nanoribbons

We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eigenfunctions, as well the dependence of the local density of states (LDOS) on energy and position. We note that roughly half of the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize with the impurity state, and the corresponding eigenvalues are shifted with respect to their unperturbed values. The maximum shift and hybridization occur for a state whose energy is inverse proportional to the impurity potential; this energy is that of the impurity peak in the DOS spectrum. We find that the interference between the impurity and the edge gives rise to peculiar modifications of the LDOS of the nanoribbon, in particular to oscillations of the edge LDOS. These effects depend on the size of the system, and decay with the distance between the edge and the impurity.Comment: 10 pages, 15 figures, revtex

Direct Measurements of the Branching Fractions for D0→K−e+νeD^0 \to K^-e^+\nu_e and D0→π−e+νeD^0 \to \pi^-e^+\nu_e and Determinations of the Form Factors f+K(0)f_{+}^{K}(0) and f+π(0)f^{\pi}_{+}(0)

The absolute branching fractions for the decays $D^0 \to K^-e ^+\nu_e$ and $D^0 \to \pi^-e^+\nu_e$ are determined using $7584\pm 198 \pm 341$ singly tagged $\bar D^0$ sample from the data collected around 3.773 GeV with the BES-II detector at the BEPC. In the system recoiling against the singly tagged $\bar D^0$ meson, $104.0\pm 10.9$ events for $D^0 \to K^-e ^+\nu_e$ and $9.0 \pm 3.6$ events for $D^0 \to \pi^-e^+\nu_e$ decays are observed. Those yield the absolute branching fractions to be $BF(D^0 \to K^-e^+\nu_e)=(3.82 \pm 0.40\pm 0.27)$ and $BF(D^0 \to \pi^-e^+\nu_e)=(0.33 \pm 0.13\pm 0.03)$. The vector form factors are determined to be $|f^K_+(0)| = 0.78 \pm 0.04 \pm 0.03$ and $|f^{\pi}_+(0)| = 0.73 \pm 0.14 \pm 0.06$. The ratio of the two form factors is measured to be $|f^{\pi}_+(0)/f^K_+(0)|= 0.93 \pm 0.19 \pm 0.07$.Comment: 6 pages, 5 figure