Electromigration Failure Kinetics in Al Alloy Lines: A Microstructure-Based Constitutive Equation

1998 ◽  
Vol 516 ◽  
Author(s):  
S. H. Kang ◽  
J. W. Morris ◽  
C.-U. Kim
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Constitutive Equation ◽  
Line Width ◽  
Current Density ◽  
The Other ◽  
Al Alloy ◽  
Time To Failure ◽  
Line Geometry ◽  
Weakly Dependent

AbstractIn previous work we proposed a simple constitutive equation that describes the electromigration failure kinetics in naturally passivated Al(Cu) quasi-bamboo lines. The time to failure, tf obeys the relation, tf = t0 exp (−l/t0), where t0 and l0 are characteristic constants and l is the length of the polygranular segment that causes failure (which is ordinarily the longest polygranular segment in the line). The present paper gathers the data supporting this relation, which includes tests on lines as-patterned and annealed at low and high temperature, and examines the dependence of the factors t0 and l0 on current density, test temperature, line geometry, and Al2Cu precipitate distribution. The experimental data suggest that to varies geometrically with j, with exponent n ≈ 2.8, and exponentially with T−1, with activation energy of ∼0.69 eV. It also varies with the line width and the distribution of Al2Cu precipitates. On the other hand, l0 is only weakly dependent on current density and temperature, but may vary with the ratio of line width to grain size (w/G).

Electromigration in Submicron Wide Copper Lines

1996 ◽  
Vol 427 ◽  
Author(s):  
O. V. Kononenko ◽  
V. N. Matveev ◽  
Yu. I. Koval ◽  
S. V. Dubonos ◽  
V. T. Volkov
Keyword(s):  
Activation Energy ◽  
Current Density ◽  
Silicon Oxide ◽  
Parallel Line ◽  
Silicon Wafers ◽  
The Self ◽  
Copper Films ◽  
Time To Failure ◽  
Electron Lithography ◽  
A Current

AbstractCopper films were deposited onto oxidized silicon wafers by the self-ion assisted technique. A 0 and 6 kV bias was applied to the substrate during the deposition. The films were patterned into parallel line arrays of 20 lines 0.5 mm long, using electron lithography and dry etching. After patterning, the lines were covered by silicon oxide and annealed in vacuum for 1 hour at the temperature 450° C. Electromigration testing was performed in air in the temperature range from 280° to 350° C and at a current density 3.106 A/cm2.It was found that the resistivities of the films deposited at 6 kV and without bias were 1.7 and 2.0 μΩcm, respectively. The median times to failure are 398.6 and 240 h and the deviations in the time to failure are 0.8 and 0.54 for 6 kV lines and 0 kV lines, respectively. An electromigration activation energy of 0.89 eV was found for 0 kV films.

Prediction of Flow Stress for Superplastic Tension Deformation

2014 ◽  
Vol 941-944 ◽  
pp. 1501-1504
Author(s):  
Zhi Ping Guan ◽  
Ming Wen Ren ◽  
Pin Kui Ma ◽  
Po Zhao
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Flow Behavior ◽  
High Accuracy ◽  
Superplastic Flow ◽  
Al Alloy ◽  
Strain Rates ◽  
Good Reliability ◽  
Wide Range

With the development of numerical calculation and precision forming, constitutive equations are required to possess high accuracy and good reliability, rather than simplicity of mathematical form. Due to simple algorithm and constant parameters, the conventional constitutive models can not be suited to describing superplastic flow behavior which represents complex responses with a large strain. In this study, through surface fitting on experimental data from tension tests performed over a wide range of strain rates, tensile velocities and loads, an empirical approach was proposed to establish constitutive equation for complex superplastic behavior of Zn-5%Al alloy at 340 °C. The empirical constitutive equation not only represents the strain dependence and the strain rate dependence of stress, but also reflects the coupling effects of strain and strain rate on stress, which can not be achieved by traditional models. A comparison between the predicted flow stresses and the experimental data verified that the empirical constitutive equation has high accuracy and good reliability on modeling superplastic flow behavior of Zn-5%Al alloy at 340 °C in a wide range of strains 0~2.5 and strain rates 7.0×10-5~8.0×10-2s-1.

The Influence of Stress-Induced Voiding on the Electromigration Behavior of AlCu Interconnects

2000 ◽  
Vol 612 ◽  
Author(s):  
A.E. Zitzelsberger ◽  
A.H. Fischer
Keyword(s):  
Activation Energy ◽  
Median Time ◽  
Current Density ◽  
Life Time ◽  
Time To Failure ◽  
Small Decrease ◽  
Limited Life

AbstractThe influence of stress-induced voiding on the electromigration (EM) behavior has been investigated on narrow via-line structures. For this purpose the EM performance of metal lines containing stress-induced voids already before the electrical operation has been compared with samples without stress-induced voids. We found, that pre-existing stress voids in the metal lines do not affect the activation energy Ea and lead only to a small decrease of the EM median time to failure, but cause a relevant reduction of the current density exponent down to n = 1. As a consequence, a tremendous decrease of the electromigration limited life time is obtained.

Reaction Rate of Liquid-Quenchied Water-Floating Alloy

1994 ◽  
Vol 362 ◽  
Author(s):  
T. Aida ◽  
Y. Nishi
Keyword(s):  
Activation Energy ◽  
Specific Gravity ◽  
Apparent Activation Energy ◽  
Reaction Rate ◽  
Water Diffusion ◽  
Hydrogen Gas ◽  
The Other ◽  
Al Alloy ◽  
Other Hand ◽  
Early Reaction

AbstractWe investigate a reaction rate of Mg-Li Al alloy (specific gravity is 0.95) in water. The hydrogen gas is mainly generated as follows : Li + H2O → LiOH + 1/2 H2 ↑. Using the volume of hydrogen gas, the reaction rate is estimated. The apparent activation energy (E) is 4.63 kcal/mol for the early reaction period. It is approximately equal to that of the water diffusion. On the other hand, the E is 9 kcal/mol after the early reaction period at the 2 ml (the volume of hydrogen gas). Furthermore, we succeed to prevent the sample against the reaction by the use of coating paints.

Electromigration in Gold Line of GaAs IC

1998 ◽  
Author(s):  
A. Ohta ◽  
K. Yajima ◽  
N. Higashisaka ◽  
T. Heima ◽  
T. Hisaka ◽  
...  
Keyword(s):  
Activation Energy ◽  
Current Density ◽  
Electron Flow ◽  
Failure Mechanisms ◽  
Cathode Side ◽  
Time To Failure ◽  
Dc Bias ◽  
Molybdenum Surfaces ◽  
Mean Time ◽  
Test Current

Abstract This paper describes voids in a gold line, which is a new failure mechanisms of GaAs IC using gold line as interconnection. We have found voids in both first and second metal under DC bias test, current density of 0.67 to 1.27 106 A/cm2 in high temperature range of 230 °C to 260 °C. We have observed carefully the movement of voids during the test and found that voids moved toward a cathode, in the opposite direction of electron flow. The velocity of voids increased with the current density almost proportionally. The moving mechanisms of a void can be explained by assuming that gold atoms move toward an anode by electromigration. The activation energy of the void velocity was 0.84 eV at the cathode side. This was nearly equal to 0.6 eV - 0.9 eV reported on the velocity of the gold island on molybdenum surfaces [1]. The GaAs IC failed at the almost same time as the voids appeared. The activation energy of mean time to failure of the IC was 0.89 eV, which was nearly equal to that of the void velocity at the cathode edge of 0.84 eV.

Electromigration In Submicron Wide Copper Lines

1996 ◽  
Vol 428 ◽  
Author(s):  
O. V. Kononenko ◽  
V. N. Matveev ◽  
Yu. I. Koval ◽  
S. V. Dubonos ◽  
V. T. Volkov
Keyword(s):  
Activation Energy ◽  
Current Density ◽  
Silicon Oxide ◽  
Parallel Line ◽  
Silicon Wafers ◽  
The Self ◽  
Copper Films ◽  
Time To Failure ◽  
Electron Lithography ◽  
A Current

AbstractCopper films were deposited onto oxidized silicon wafers by the self-ion assisted technique. A 0 and 6 kV bias was applied to the substrate during the deposition. The films were patterned into parallel line arrays of 20 lines 0.5 mm long, using electron lithography and dry etching. After patterning, the lines were covered by silicon oxide and annealed in vacuum for 1 hour at the temperature 450° C. Electromigration testing was performed in air in the temperature range from 280° to 350° C and at a current density 3.106 A/cm2.It was found that the resistivities of the films deposited at 6 kV and without bias were 1.7 and 2.0 μΩ-cm, respectively. The median times to failure are 398.6 and 240 h and the deviations in the time to failure are 0.8 and 0.54 for 6 kV lines and 0 kV lines, respectively. An electromigration activation energy of 0.89 eV was found for 0 kV films.

Effect of ionizing radiation on the kinetics of hydrogenation on the Ni-MgO mixed catalyst

1982 ◽  
Vol 47 (7) ◽  
pp. 1780-1786 ◽  
Author(s):  
Rostislav Kudláček ◽  
Jan Lokoč
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Liquid Phase ◽  
Ionizing Radiation ◽  
Oxide Catalyst ◽  
Absorbed Dose ◽  
Hydrogenation Rate ◽  
Solution Composition ◽  
Mixed Catalyst ◽  
Kinetics Of

The effect of gamma pre-irradiation of the mixed nickel-magnesium oxide catalyst on the kinetics of hydrogenation of maleic acid in the liquid phase has been studied. The changes of the hydrogenation rate are compared with the changes of the adsorbed amount of the acid and with the changes of the solution composition, activation energy, and absorbed dose of the ionizing radiation. From this comparison and from the interpretation of the experimental data it can be deduced that two types of centers can be distinguished on the surface of the catalyst under study, namely the sorption centres for the acid and hydrogen and the reaction centres.

scholarly journals Two and three pseudoscalar production in e+e− annihilation and their contributions to (g − 2)μ

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Wen Qin ◽  
Ling-Yun Dai ◽  
Jorge Portolés
Keyword(s):  
Experimental Data ◽  
Theoretical Prediction ◽  
Pseudoscalar Meson ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Vacuum Polarization ◽  
Meson Production ◽  
The Other ◽  
Joint Analysis ◽  
The Standard Model

Abstract A coherent study of e+e− annihilation into two (π+π−, K+K−) and three (π+π−π0, π+π−η) pseudoscalar meson production is carried out within the framework of resonance chiral theory in energy region E ≲ 2 GeV. The work of [L.Y. Dai, J. Portolés, and O. Shekhovtsova, Phys. Rev. D88 (2013) 056001] is revisited with the latest experimental data and a joint analysis of two pseudoscalar meson production. Hence, we evaluate the lowest order hadronic vacuum polarization contributions of those two and three pseudoscalar processes to the anomalous magnetic moment of the muon. We also estimate some higher-order additions led by the same hadronic vacuum polarization. Combined with the other contributions from the standard model, the theoretical prediction differs still by (21.6 ± 7.4) × 10−10 (2.9σ) from the experimental value.

scholarly journals The Effect of α-Al(MnCr)Si Dispersoids on Activation Energy and Workability of Al-Mg-Si-Cu Alloys during Hot Deformation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xiaoguo Wang ◽  
Jian Qin ◽  
Hiromi Nagaumi ◽  
Ruirui Wu ◽  
Qiushu Li
Keyword(s):  
Activation Energy ◽  
Aluminum Alloys ◽  
Constitutive Equation ◽  
Hot Deformation ◽  
Flow Instability ◽  
Void Formation ◽  
Activation Energies ◽  
Compression Tests ◽  
Softening Mechanism ◽  
Dynamic Softening

The hot deformation behaviors of homogenized direct-chill (DC) casting 6061 aluminum alloys and Mn/Cr-containing aluminum alloys denoted as WQ1 were studied systematically by uniaxial compression tests at various deformation temperatures and strain rates. Hot deformation behavior of WQ1 alloy was remarkably changed compared to that of 6061 alloy with the presence of α-Al(MnCr)Si dispersoids. The hyperbolic-sine constitutive equation was employed to determine the materials constants and activation energies of both studied alloys. The evolution of the activation energies of two alloys was investigated on a revised Sellars’ constitutive equation. The processing maps and activation energy maps of both alloys were also constructed to reveal deformation stable domains and optimize deformation parameters, respectively. Under the influence of α dispersoids, WQ1 alloy presented a higher activation energy, around 40 kJ/mol greater than 6061 alloy’s at the same deformation conditions. Dynamic recrystallization (DRX) is main dynamic softening mechanism in safe processing domain of 6061 alloy, while dynamic recovery (DRV) was main dynamic softening mechanism in WQ1 alloy due to pinning effect of α-Al(MnCr)Si dispersoids. α dispersoids can not only resist DRX but also increase power required for deformation of WQ1 alloy. The microstructure analysis revealed that the flow instability was attributed to the void formation and intermetallic cracking during hot deformation of both alloys.

scholarly journals Kinetics and thermodynamic properties related to the drying of 'Cabacinha' pepper fruits

2016 ◽  
Vol 20 (2) ◽  
pp. 174-180 ◽  
Author(s):  
Hellismar W. da Silva ◽  
Renato S. Rodovalho ◽  
Marya F. Velasco ◽  
Camila F. Silva ◽  
Luís S. R. Vale
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Gibbs Free Energy ◽  
Removal Rate ◽  
Effective Diffusion ◽  
Drying Time ◽  
Three Samples ◽  
Different Temperatures

ABSTRACT The objective of this study was to determine and model the drying kinetics of 'Cabacinha' pepper fruits at different temperatures of the drying air, as well as obtain the thermodynamic properties involved in the drying process of the product. Drying was carried out under controlled conductions of temperature (60, 70, 80, 90 and 100 °C) using three samples of 130 g of fruit, which were weighed periodically until constant mass. The experimental data were adjusted to different mathematical models often used in the representation of fruit drying. Effective diffusion coefficients, calculated from the mathematical model of liquid diffusion, were used to obtain activation energy, enthalpy, entropy and Gibbs free energy. The Midilli model showed the best fit to the experimental data of drying of 'Cabacinha' pepper fruits. The increase in drying temperature promoted an increase in water removal rate, effective diffusion coefficient and Gibbs free energy, besides a reduction in fruit drying time and in the values of entropy and enthalpy. The activation energy for the drying of pepper fruits was 36.09 kJ mol-1.

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