A New Approach to Calculate Atomic Flux Divergence by Electromigration

1998 ◽  
Vol 120 (4) ◽  
pp. 360-366 ◽  
Author(s):  
K. Sasagawa ◽  
N. Nakamura ◽  
M. Saka ◽  
H. Abe´
Keyword(s):  
Current Density ◽  
Calculation Method ◽  
Void Formation ◽  
Experimental Result ◽  
Two Dimensional ◽  
Flux Divergence ◽  
New Approach ◽  
Line Structure ◽  
Atomic Flux

In this paper, a new calculation method of the atomic flux divergence used to predict the formation of electromigration-induced void is proposed by considering two-dimensional distributions of current density and temperature and also simply considering the line structure of not only polycrystalline, but also bamboo line. For the verification, electromigration phenomenon near the corner of an angled polycrystalline line, which results in two-dimensional distributions of current density and temperature, is treated as an example. The usefulness of the proposed method is discussed in the light of the comparison of prediction of void formation near the corner with the experimental result.

Threshold Current Density of Electromigration Damage in Angled Polycrystalline Line

2007 ◽  
Vol 353-358 ◽  
pp. 2958-2961
Author(s):  
K. Sasagawa ◽  
N. Yamaji ◽  
S. Fukushi
Keyword(s):  
Current Density ◽  
Line Shape ◽  
Threshold Current ◽  
Threshold Current Density ◽  
Experimental Result ◽  
Two Dimensional ◽  
Scale Down ◽  
Dimensional Shape ◽  
Metallic Interconnects ◽  
Electron Wind

As silicon ICs continue to scale down, several reliability issues have emerged. Electromigration- the transportation of metallic atoms by the electron wind- has been recognized as one of the key damage mechanisms in metallic interconnects. It is known that there is a threshold current density of electromigration damage in via-connected lines. The evaluation of the threshold current density is a matter of the great interest from the viewpoint of IC reliability. In this study, Al polycrystalline lines with two-dimensional shape, i.e. angled lines are experimentally treated for the evaluation. Comparing the experimental result with that of straight-shaped line, the effect of line-shape on the threshold current density of electromigration damage is discussed.

Analysis of Geometrical and Microstructural Effects on Void Formation in Metallization: Observation and Modelling

1996 ◽  
Vol 428 ◽  
Author(s):  
W. C. Shih ◽  
A. Ghiti ◽  
K. S. Low ◽  
A. L. Greer ◽  
A. G. O'Neill ◽  
...  
Keyword(s):  
Focused Ion Beam ◽  
Ion Beam ◽  
Void Formation ◽  
Grain Structure ◽  
Flux Divergence ◽  
Damage Development ◽  
Temperature Variations ◽  
Atomic Flux ◽  
Grain Structures ◽  
Microstructural Effects

AbstractThis paper reports the analysis of geometrical and microstructural effects on void formation in interconnects. Ion-beam machining is used to define segments for study at the cathode end of test lines. Scanning electron microscopy is used to observe damage development, focused ion beam microscopy to observe the corresponding grain structure. Finite-element calculations of self-consistent current density and temperature distributions in the conductor are used to predict damage locations both for a continuum material and for simulated grain structures. Cross-section changes in the line give temperature variations leading to divergences in atomic flux. Regions of high flux divergence are favoured for electromigration damage, but the precise sites of damage are determined by the grain structure, as shown both in the experiment and in the modelling.

Grain Boundary Grooving as the Mechanism of the Blech Electromigration in Interconnects

1995 ◽  
Vol 391 ◽  
Author(s):  
E.E. Glickman ◽  
L.M. Klinger
Keyword(s):  
Grain Boundary ◽  
Surface Diffusion ◽  
Current Density ◽  
High Current Density ◽  
Diffusion Flux ◽  
Stress Gradient ◽  
Displacement Velocity ◽  
Gradual Transition ◽  
Flux Divergence ◽  
New Approach

AbstractWe present a new approach to understand the mechanism of "homogeneous", or Blech electromigration (EM). This phenomenon describes macroscopically homogeneous displacement of the up-wind edge of thin film lines in microelectronic devices and is responsible for openings at contact windows, "vias" and other sites of perfect diffusion flux divergence.Our SEM, EPMA and EM drift velocity experiments have revealed the gradual transition from the microscopically homogeneous EM displacement to the highly nonhomogeneous mode wherein copious islands of residual material remain behind the drifting cathode edge of aluminum stripes. The transition is shown to occur due to an increase in either the current density, j, or in the stripe length, 1. The latter case suggests, that the transition results from the growth of the net grain boundary (GB) diffusion flux, I=le-Ib ,where Ie∝j and 1b∝1/1 are the EM flux and stress-gradient-driven back flux, respectively.Based upon recent progress in the theory of GB grooving under "external" GB fluxes, with surface diffusion acting as the healing mechanism, grooves' propagation along the line and their merging is considered to be the micromechanism of the "homogeneous" EM. In terms of the simple model described, the transition from the slow receding of the cathode butt edge slightly wrinkled by shallow grooves (A-regime of EM) to the fast extension and merging of slot -like grooves (B-regime) accounts for the transition observed in EM mode, while in both regimes the EM displacement velocity, V, is presumed to represent the groove propagation rate.The theory developed reduces to Blech formulae for V for the truly homogeneous A-regime and predicts quite different EM kinetics for the B-regime of microscopically nonhomogeneous EM. The latter is expected to dominate for films loaded by high current density with large grains and low surface diffusion.The dependence obtained for the residual mass left behind the drifted edge vs the displacement velocity, V, for unpassivated aluminum stripes of various lengths, loaded by j=2-106 A/cm2 at 548K provides a good evidence in support of a new approach.

scholarly journals Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime

2021 ◽  
Vol 154 (15) ◽  
pp. 154203
Author(s):  
Michael Woerner ◽  
Ahmed Ghalgaoui ◽  
Klaus Reimann ◽  
Thomas Elsaesser
Keyword(s):  
Terahertz Spectroscopy ◽  
Two Dimensional ◽  
New Approach ◽  
Even Order

Two-dimensional asynchronous spectrum with auxiliary cross peaks in probing intermolecular interactions

RSC Advances ◽  
2015 ◽  
Vol 5 (107) ◽  
pp. 87739-87749 ◽  
Author(s):  
Xiaopei Li ◽  
Anqi He ◽  
Kun Huang ◽  
Huizhou Liu ◽  
Ying Zhao ◽  
...  
Keyword(s):  
Intermolecular Interaction ◽  
Intermolecular Interactions ◽  
Two Dimensional ◽  
New Approach

A new approach called “asynchronous spectrum with auxiliary peaks (ASAP)” is proposed for generating a 2D asynchronous spectrum to investigate the intermolecular interaction between two solutes (P and Q) dissolved in the same solution.

Experiment and Numerical Simulation of Bubble Behaviors in Argon Gas Injection Into Lead-Bismuth Pool

2006 ◽  
Author(s):  
Yumi Yamada ◽  
Toyou Akashi ◽  
Minoru Takahashi
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Experimental Result ◽  
Feed Water ◽  
Force Model ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Argon Gas ◽  
Bubble Rising

In a lead-bismuth alloy (45%Pb-55%Bi) cooled direct contact boiling water fast reactor (PBWFR), steam can be produced by direct contact of feed water with primary Pb-Bi coolant in the upper core plenum, and Pb-Bi coolant can be circulated by buoyancy forces of steam bubbles. As a basic study to investigate the two-phase flow characteristics in the chimneys of PBWFR, a two-dimensional two-phase flow was simulated by injecting argon gas into Pb-Bi pool in a rectangular vessel (400mm in length, 1500mm in height, 50mm in width), and bubble behaviors were investigated experimentally. Bubble sizes, bubble rising velocities and void fractions were measured using void probes. Argon gas was injected through five nozzles of 4mm in diameter into Pb-Bi at two locations. The experimental conditions are the pressure of atmospheric pressure, Pb-Bi temperatures of 443K, and the flow rate of injection Ar gas is 10, 20, and 30 NL/min. The measured bubble rising velocities were distributed in the range from 1 to 3 m/s. The average velocity was about 0.6 m/s. The measured bubble chord lengths were distributed from 1mm up to 30mm. The average chord length was about 7mm. An analysis was performed by two-dimensional and two-fluid model. The experimental results were compared with the analytical results to evaluate the validity of the analytical model. Although large diameter bubbles were observed in the experiment, the drag force model for spherical bubbles performed better for simulation of the experimental result because of high surface tension force of Pb-Bi.

Half division two-dimensional method for simple sinusoidal quantities parameters accurate measurement

2021 ◽  
pp. 16-21
Author(s):  
Kirill Yu. Solomentsev ◽  
Vyacheslav I. Lachin ◽  
Aleksandr E. Pasenchuk
Keyword(s):  
Measuring Instruments ◽  
Measured Signal ◽  
Two Dimensional ◽  
Measuring Device ◽  
New Approach ◽  
Precision Measuring ◽  
Useful Signal ◽  
Midpoint Method ◽  
Order Of Magnitude ◽  
Current Measuring

Several variants of half division two-dimensional method are proposed, which is the basis of a fundamentally new approach for constructing measuring instruments for sinusoidal or periodic electrical quantities. These measuring instruments are used in the diagnosis of electric power facilities. The most general variant, called midpoint method, is considered. The proposed midpoint method allows you to measure much smaller than using widespread methods, alternating currents or voltages, especially when changing the amplitude of the measured signal in very wide ranges, by 1–2 orders of magnitude. It is shown that using the midpoint method it is possible to suppress sinusoidal or periodic interference in the measuring path, in particular, to measure small alternating current when sinusoidal or periodic interference is 1–2 orders of magnitude higher than the useful signal. Based on the results of comparative tests, it was found that the current measuring device implementing the midpoint method is an order of magnitude more sensitive than the currently used high-precision measuring instruments.

scholarly journals New approach to finite frequency Filter Design for two-dimensional T-S fuzzy systems

2021 ◽  
Vol 297 ◽  
pp. 01036
Author(s):  
Ben Meziane Khaddouj ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Fuzzy Systems ◽  
Filter Design ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Finite Frequency ◽  
New Approach ◽  
Filter Model ◽  
Error System ◽  
Non Linear Systems ◽  
Takagi Sugeno

This paper considers the problem of filter design for two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy mode. The problem to be solved in the paper is to find a H∞ filter model such that the filtering error system is asymptotically stable. A numerical example is employed to illustrate the validity of the proposed methods.

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