On Failure Mechanisms in Flip Chip Assembly—Part 2: Optimal Underfill and Interconnecting Materials

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Yoonchan Oh ◽  
C. Steve Suh ◽  
Hung-Jue Sue
Keyword(s):  
Time Scale ◽  
Flip Chip ◽  
Thermal Stresses ◽  
Failure Modes ◽  
Scale Effects ◽  
Short Time Scale ◽  
Long Time ◽  
Solder Joint Fatigue ◽  
Scale Properties ◽  
Short Time

The physics explored in this investigation enables short-time scale dynamic phenomenon to be correlated with package failure modes such as solder ball cracking and interlayer debond. It is found that although epoxy-based underfills with nanofillers are shown to be effective in alleviating thermal stresses and improving solder joint fatigue performance in thermal cycling tests of long-time scale, underfill material viscoelasticity is ineffective in attenuating short-time scale propagating shock waves. In addition, the inclusion of Cu interconnecting layers in flip chip area arrays is found to perform significantly better than Al layers in suppressing short-time scale effects. Results reported herein suggest that, if improved flip chip reliability is to be achieved, the compositions of all packaging constituent materials need be formulated to have well-defined short-time scale and long-time scale properties. Chip level circuit design layout also needs be optimized to either discourage or negate short-time wave propagation. The knowledge base established is generally applicable to high performance package configurations of small footprint and high clock speed. The approach along with the numerical procedures developed for the investigation can be a practical tool for realizing better device reliability and thus high manufacturing yield.

On Failure Mechanisms in Flip Chip Assembly—Part 1: Short-Time Scale Wave Motion

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Yoonchan Oh ◽  
C. Steve Suh ◽  
Hung-Jue Sue
Keyword(s):  
Time Scale ◽  
Wave Motion ◽  
Flip Chip ◽  
Thermal Stresses ◽  
Failure Modes ◽  
Coefficient Of Thermal Expansion ◽  
Short Time Scale ◽  
Time Frequency ◽  
Thermal Transients ◽  
Short Time

The demand for higher clock speed and larger current magnitude in high-performance flip chip packaging configurations of small footprint has raised the concern over rapid thermal transients and large thermal spatial gradients that could severely compromise package performance. This paper explores coupled electrical-thermal-mechanical multiphysics to evaluate the concern and to establish the knowledge base necessary for improving flip chip reliability. It is found that within the first few hundreds of nanoseconds after power-on, there are fast-attenuating, dispersive stress waves of extremely high frequency propagating in the package. The concepts of high cycle fatigue, power density, and joint time-frequency analysis are employed to characterize the waves along with the various damage modes resulting from the propagation of these short-lived dynamical disturbances in bulk materials and along bimaterial interfaces. A qualitative measure for failure is developed to evaluate the extent of damage inflicted by short-time wave motion. Damages identified in this study are in agreement with physical failure modes commonly seen in industry, thus implying that micron scale cracks or interfacial adhesion flaws initiated at the short-time scale would be further propagated by the coefficient of thermal expansion induced thermal stresses at the long-time scale and result in eventual electrical disruptions.

scholarly journals Stratified Flows over and around Long Dynamically Tall Mountain Ridges

2019 ◽  
Vol 76 (5) ◽  
pp. 1265-1287 ◽  
Author(s):  
Arjun Jagannathan ◽  
Kraig Winters ◽  
Laurence Armi
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Stratified Flows ◽  
Half Width ◽  
Short Time Scale ◽  
Late Time ◽  
Low Level ◽  
Long Time ◽  
Flow Splitting ◽  
Short Time

Abstract Uniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layerwise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. On the short time scale, upstream blocking is established quickly and the flow is well described as a purely infinite-ridge overflow. Over the long time scale associated with flow splitting, low-level flow escapes around the sides, but the overflow continues to be hydraulically controlled and streamwise asymmetric in the neighborhood of the crest. We quantify this late-time overflow by estimating its volumetric transport and then briefly demonstrate how this approach can be extended to predict the overflow across nonuniform ridge shapes.

scholarly journals Mathematical modelling and application of frog choruses as an autonomous distributed communication system

2019 ◽  
Vol 6 (1) ◽  
pp. 181117 ◽  
Author(s):  
Ikkyu Aihara ◽  
Daichi Kominami ◽  
Yasuharu Hirano ◽  
Masayuki Murata
Keyword(s):  
Mathematical Model ◽  
Wireless Sensor Network ◽  
Mathematical Modelling ◽  
Sensor Network ◽  
Time Scale ◽  
Wireless Sensor ◽  
Multiple Time Scales ◽  
Short Time Scale ◽  
Long Time ◽  
Short Time

Interactions using various sensory cues produce sophisticated behaviour in animal swarms, e.g. the foraging behaviour of ants and the flocking of birds and fish. Here, we investigate the behavioural mechanisms of frog choruses from the viewpoints of mathematical modelling and its application. Empirical data on male Japanese tree frogs demonstrate that (1) neighbouring male frogs avoid call overlaps with each other over a short time scale and (2) they collectively switch between the calling state and the silent state over a long time scale. To reproduce these features, we propose a mathematical model in which separate dynamical models spontaneously switch due to a stochastic process depending on the internal dynamics of respective frogs and also the interactions among the frogs. Next, the mathematical model is applied to the control of a wireless sensor network in which multiple sensor nodes send a data packet towards their neighbours so as to deliver the packet to a gateway node by multi-hop communication. Numerical simulation demonstrates that (1) neighbouring nodes can avoid a packet collision over a short time scale by alternating the timing of data transmission and (2) all the nodes collectively switch their states over a long time scale, establishing high network connectivity while reducing network power consumption. Consequently, this study highlights the unique dynamics of frog choruses over multiple time scales and also provides a novel bio-inspired technology that is applicable to the control of a wireless sensor network.

scholarly journals Sliding of spherical ball on solid lubricating coating combined with wear process

2021 ◽  
Vol 93 (1) ◽  
pp. 39-50
Author(s):  
Marcin Białas ◽  
Jan Maciejewski ◽  
Stanisław Kucharski
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Contact Region ◽  
Short Time Scale ◽  
Steady State Condition ◽  
Wear Process ◽  
Spherical Ball ◽  
Long Time ◽  
Short Time ◽  
Solid Lubricating Coating

In present paper we show results of ball-on-disk wear experiment of MoS2 film deposited on Ti6Al4V substrate. The ball materials is aluminum oxide. The tests are performed for different surrounding temperature conditions: 20 oC, 200 oC and 350 oC. It is shown that depth of the wear groove increases with increasing surrounding temperature. A finite element modeling approach is next developed to mimic the experimental observations of ball-on-disk wear process. It is based on the assumption of steady state condition developed during short time scale at contact region. The steady state results can next be applied to long time scale in which wear process is numerically simulated. Model results are compared with experimentally obtained wear groove and show satisfactory agreement.

scholarly journals The Mathematical Analysis On The Effect Of Strong Nonlinearity On Steady-State Self-Focusing And Filamentation Of Whistlers In A Plasma

2016 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Ghanshyam Rai
Keyword(s):  
Time Scale ◽  
High Frequency ◽  
Small Scale ◽  
Nonuniform Heating ◽  
Short Time Scale ◽  
Strong Nonlinearity ◽  
Self Focusing ◽  
Long Time ◽  
Short Time ◽  
Very High

<div><p><em>A high-power Gaussian Whistler propagating in a magnatoplasma becomes self-focused because of (i) ponderomotive force and (ii) nonuniform heating nonlinearities (i) being dominant for t &lt;&lt; T and (ii) being dominant for t &gt; t<sub>E</sub>. On short time scale (t &lt;&lt; t<sub>E</sub> ) whistlers of all frequencies can be focused (the self – focusing length is very large for ω= </em><em> /2 and decreases rapidly on both sides), whereas on the long time scale (t &gt; t<sub>E</sub>) only high frequency whistlers (ω&gt; </em><em> /2) are focused. At very high powers the plasma is depleted almost completely from the axial region and self-focusing does not occur, rather, defocusing takes place. </em></p><p><em>            A plane uniform whistler of high intensity is seen to be unstable for small scale fluctuations, i.e., it must break up into filaments in course of it propagation. The growth rate increases with decreasing scale length of perturbation and is seen to be a saturating function of power density of the beam. </em></p></div>

scholarly journals Antipersistent dynamics in short time scale variability of self-potential signals

2000 ◽  
Vol 43 (2) ◽  
Author(s):  
V. Cuomo ◽  
M. Lanfredi ◽  
V. Lapenna ◽  
M. Macchiato ◽  
M. Ragosta ◽  
...  
Keyword(s):  
Time Scale ◽  
Order Structure ◽  
Short Time Scale ◽  
Spatial And Temporal Variability ◽  
Scale Invariant ◽  
Geophysical Monitoring ◽  
Scale Properties ◽  
Short Time ◽  
Self Potential

Time scale properties of self-potential signals are investigated through the analysis of the second order structure function (variogram), a powerful tool to investigate the spatial and temporal variability of observational data. In this work we analyse two sequences of self-potential values measured by means of a geophysical monitoring array located in a seismically active area of Southern Italy. The range of scales investigated goes from a few minutes to several days. It is shown that signal fluctuations are characterised by two time scale ranges in which self-potential variability appears to follow slightly different dynamical behaviours. Results point to the presence of fractal, non stationary features expressing a long term correlation with scaling coefficients which are the clue of stabilising mechanisms. In the scale ranges in which the series show scale invariant behaviour, self-potentials evolve like fractional Brownian motions with anticorrelated increments typical of processes regulated by negative feedback mechanisms (antipersistence). On scales below about 6 h the strength of such an antipersistence appears to be slightly greater than that observed on larger time scales where the fluctuations are less efficiently stabilised.

scholarly journals Four-Types of IIT-Induced Group Integrity of Plecoglossus altivelis

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 726
Author(s):  
Takayuki Niizato ◽  
Kotaro Sakamoto ◽  
Yoh-ichi Mototake ◽  
Hisashi Murakami ◽  
Takenori Tomaru ◽  
...  
Keyword(s):  
Time Scale ◽  
Brain Network ◽  
Collective Behaviour ◽  
Short Time Scale ◽  
Plecoglossus Altivelis ◽  
Global Parameter ◽  
Fish Schools ◽  
Long Time ◽  
Spatio Temporal ◽  
Short Time

Integrated information theory (IIT) was initially proposed to describe human consciousness in terms of intrinsic-causal brain network structures. Particularly, IIT 3.0 targets the system’s cause–effect structure from spatio-temporal grain and reveals the system’s irreducibility. In a previous study, we tried to apply IIT 3.0 to an actual collective behaviour in Plecoglossus altivelis. We found that IIT 3.0 exhibits qualitative discontinuity between three and four schools of fish in terms of Φ value distributions. Other measures did not show similar characteristics. In this study, we followed up on our previous findings and introduced two new factors. First, we defined the global parameter settings to determine a different kind of group integrity. Second, we set several timescales (from Δ t = 5 / 120 to Δ t = 120 / 120 s). The results showed that we succeeded in classifying fish schools according to their group sizes and the degree of group integrity around the reaction time scale of the fish, despite the small group sizes. Compared with the short time scale, the interaction heterogeneity observed in the long time scale seems to diminish. Finally, we discuss one of the longstanding paradoxes in collective behaviour, known as the heap paradox, for which two tentative answers could be provided through our IIT 3.0 analysis.

scholarly journals Microlensing variability in FBQ 0951+2635: short-time-scale events or a long-time-scale fluctuation?

2009 ◽  
Vol 397 (4) ◽  
pp. 1982-1989 ◽  
Author(s):  
V. N. Shalyapin ◽  
L. J. Goicoechea ◽  
E. Koptelova ◽  
B. P. Artamonov ◽  
A. V. Sergeyev ◽  
...  
Keyword(s):  
Time Scale ◽  
Short Time Scale ◽  
Scale Fluctuation ◽  
Long Time ◽  
Short Time

ENTANGLEMENT EVOLUTION OF A PAIR OF TWO-LEVEL SYSTEMS IN NON-MARKOVIAN ENVIRONMENT

2009 ◽  
Vol 07 (01) ◽  
pp. 385-393 ◽  
Author(s):  
X. L. HUANG ◽  
L. C. WANG ◽  
X. X. YI
Keyword(s):  
Sudden Death ◽  
Time Scale ◽  
Mutual Interaction ◽  
Short Time Scale ◽  
Entanglement Sudden Death ◽  
Initial State ◽  
Entanglement Evolution ◽  
Long Time ◽  
Two Level Systems ◽  
Short Time

The entanglement evolution of a pair of two-level systems is studied in this paper. The two systems without mutual interaction are independently coupled to different two-band non-Markovian environments. By comparing our results to others in the literature, we find that taking one of the Bell states as the initial state, certain non-Markovian effect protects the entanglement in short time scale, while on long time scale it leads to the entanglement sudden death (ESD), which never occurs for this initial state in the Markovian case. Finally, by analyzing the parameters in our model, a relation between disentanglement and decoherence is established and discussed.

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