An Investigation of Reliability of High Density Electronic Package-to-Board Interconnections from the Perspective of Solder Joint Metallurgy

The integration and miniaturization trend of the electronic packaging leads to much finer pitch of the device and package lead terminations. Several reliability concerns and issues that were previously not encountered are now surfacing. The objective of this thesis work is to investigate the reliability of the package-to-board interconnection from the perspective of solder joint metallurgy. It was carried out with several advanced packages such as CSP, WLCSP and leadless ceramic packages on organic laminate PWBs using tin-silver-copper based interconnection materials. The assemblies were subjected to several loading conditions and levels such as thermal, mechanical, and environmental stresses. As expected, the board level reliability (BLR) of electronic assemblies strongly depended on microstructure and morphology of the solder joints. Dispersion strengthening effect of the intermetallic compounds (IMCs), coarsening of the IMC particles, strain rate hardening, solder fatigue, and recrystallization of Sn grains in the highly stressed areas were observed. These were found to directly impact Pb-free solder joint reliability. Appropriate thermal aging can improve joint reliability up to 50% due to coarsening of the IMC particles. In addition, other factors such as dissolution of metals, interfacial reactions, IMC spalling, and cross interaction of surface materials on the two sides of the joints were also observed and discussed. The effects can be expressed as a series of interactive relationships: materials (pad surface materials and solder alloy composition) and/or soldering process lead to microstructure change in bulk solder and/or at interface, which in turn leads to joint reliability variation

Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement

Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used the method of lines to discretize the SRHD equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code {\sl enzo}. We discuss the coupling of the AMR framework with the relativistic solvers. Via various test problems, we emphasize the importance of resolution studies in relativistic flow simulations because extremely high resolution is required especially when shear flows are present in the problem. We also present the results of two 3d simulations of astrophysical jets: AGN jets and GRB jets. Resolution study of those two cases further highlights the need of high resolutions to calculate accurately relativistic flow problems.Comment: 14 pages, 23 figures. A section on 3D GRB jet simulation added. Accepted by ApJ

Diethyl 4-(4-cyano­phen­yl)-2,6-dimethyl-1,4-dihydro­pyridine-3,5-dicarboxyl­ate

In the title compound, C20H22N2O4, the dihedral angle between the roughly planar dihydro­pyridine ring (r.m.s. deviation = 0.092 Å) and the benzene ring is 87.09 (6)°. One of the eth­oxy side chains is disordered over two orientations in a 0.669 (14):0.331 (14) ratio. In the crystal, mol­ecules are linked by N—H⋯N hydrogen bonds, generating chains

Three-Dimensional Relativistic MHD Simulations of the Kelvin-Helmholtz Instability: Magnetic Field Amplification by a Turbulent Dynamo

Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Using conditions relevant for GRB internal shocks and late phases of GRB afterglow, we obtain amplification of the electromagnetic energy fraction to $\epsilon_B \sim 5 \times 10^{-3}$. This value decays slowly after the shear is dissipated and appears to be largely independent of the initial field strength. The conditions required for operation of the dynamo are the presence of velocity shear and some seed magnetization both of which are expected to be commonplace. We also find that the turbulent kinetic energy spectrum for the case studied obeys Kolmogorov's 5/3 law and that the electromagnetic energy spectrum is essentially flat with the bulk of the electromagnetic energy at small scales.Comment: accepted for publication in ApJL; high-resolution version available at http://cosmo.nyu.edu/~wqzhang/publications/kh.pdf; movies of simulations available at http://cosmo.nyu.edu/~wqzhang/movies

Connecting the vulcanization transition to percolation

The vulcanization transition is addressed via a minimal replica-field-theoretic model. The appropriate long-wave-length behavior of the two- and three-point vertex functions is considered diagrammatically, to all orders in perturbation theory, and identified with the corresponding quantities in the Houghton-Reeve-Wallace field-theoretic approach to the percolation critical phenomenon. Hence, it is shown that percolation theory correctly captures the critical phenomenology of the vulcanization transition associated with the liquid and critical states.Comment: 9 pages, 5 figure

Pathway Switching Explains the Sharp Response Characteristic of Hypoxia Response Network

Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks

Relativistic Flows Using Spatial And Temporal Adaptive Structured Mesh Refinement. I. Hydrodynamics

Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used method of lines to discrete SRHD equations spatially and used a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code enzo, which uses the Berger-Colella AMR algorithm and is parallel with dynamical load balancing using the widely available Message Passing Interface library. We discuss the coupling of the AMR framework with the relativistic solvers and show its performance on eleven test problems

Dynamics of Competitive Evolution on a Smooth Landscape

We study competitive DNA sequence evolution directed by {\it in vitro} protein binding. The steady-state dynamics of this process is well described by a shape-preserving pulse which decelerates and eventually reaches equilibrium. We explain this dynamical behavior within a continuum mean-field framework. Analytical results obtained on the motion of the pulse agree with simulations. Furthermore, finite population correction to the mean-field results are found to be insignificant.Comment: 4 pages, 2 figures, revised, to appear in Phys. Rev. Let