Constitutive Response of Passivated Copper Films: Experiments and Analyses

2001 ◽  
Vol 695 ◽  
Author(s):  
Y.-L. Shen ◽  
U. Ramamurty
Keyword(s):  
Thermal Loading ◽  
Silicon Oxide ◽  
Kinematic Hardening ◽  
Copper Film ◽  
Temperature Response ◽  
Copper Interconnects ◽  
Constitutive Law ◽  
Copper Films ◽  
Rate Dependent ◽  
Constitutive Response

ABSTRACTThe constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.

An Analysis of the Two-Bar Ratcheting Behavior Using the Viscoplasticity Theory Based on Overstress (VBO)

1997 ◽  
Vol 119 (3) ◽  
pp. 306-312
Author(s):  
T. Nakamura ◽  
E. Krempl
Keyword(s):  
Thermal Loading ◽  
Kinematic Hardening ◽  
Strain Range ◽  
Constant Load ◽  
Material Models ◽  
Rate Dependent ◽  
Cyclic Temperature ◽  
The Mean ◽  
Number Of Cycles ◽  
Mean Strain

The ratcheting behavior of the “unsymmetric two-bar system” was investigated by numerical experiments. The two bars are restrained to the same length and are subjected to a constant load. One bar sees cyclic temperature variations, while the other bar is kept at constant temperature. The material models employed are rate independent plasticity (kinematic hardening) and the viscoplasticity theory based on overstress (VBO) matched to represent the cyclic neutral 6061 T6 aluminum alloy elastic and inelastic deformation behavior. For simplicity, temperature-independent material properties were assumed. Numerical analyses were performed to investigate the effects of rate of thermal loading and temperature range. Elastic-inelastic shake down is ultimately achieved due to work hardening. There is a strain range increase until it reaches a steady value. Kinematic hardening and VBO predict almost the same strain range, which, for the case of VBO, is nearly rate-independent. The behavior for both material models is very different for the mean strain. For VBO, the number of cycles to shakedown is rate-dependent and is considerably larger than for kinematic hardening. Finally, the steady-state mean strain and strain range are computed directly for VBO.

Analysis of large-strain shear in rate-dependent face-centred cubic polycrystals: correlation of micro- and macromechanics

1989 ◽  
Vol 328 (1600) ◽  
pp. 443-500 ◽  
Keyword(s):  
Strain Rate ◽  
Finite Strain ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Texture Evolution ◽  
Rate Sensitivity ◽  
Rate Dependent ◽  
Crystallographic Slip ◽  
Physically Based ◽  
Constitutive Response

Micro- and macroscopic aspects of large-strain deformation are examined through analyses of shear by using physical and phenomenological models. Past experiments and analyses are first reviewed to reveal current issues and put the present work in perspective. These issues are addressed by a complete set of simulations of large-strain shear with a finite-strain, rate-dependent polycrystal model. The model is based on a rigorous constitutive theory for crystallographic slip that accounts for the development of crystallographic texture and the effects of texture on constitutive response. The influences of strain hardening, latent hardening, strain-rate sensitivity, boundary constraints, and initial textures on texture evolution and constitutive response are studied. Coupled stress and strain effects such as axial elongation during unconstrained shear and the development of normal stresses during constrained shear are related to material properties, boundary constraint and texture. The formation of ideal textures and their role in determining polycrystalline behaviour is discussed in quantitative terms. Large-strain shear is also studied by using several phenomenological constitutive theories including J 2 -flow theory, J 2 -corner theory, and two versions of finite-strain kinematic hardening theory. The behaviours predicted by these phenomenological theories and the physically based polycrystal model are directly compared. A noteworthy outcome is the close correspondence found between the predictions of J 2 -corner theory and those of the micromechanically based physical model.

Analytical Solutions for Circular Bars Subjected to Large Strain Plastic Torsion

1990 ◽  
Vol 57 (2) ◽  
pp. 298-306 ◽  
Author(s):  
K. W. Neale ◽  
S. C. Shrivastava
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Large Strain ◽  
Kinematic Hardening ◽  
Flow Theory ◽  
Constitutive Laws ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Inelastic Behavior ◽  
Rate Dependent

The inelastic behavior of solid circular bars twisted to arbitrarily large strains is considered. Various phenomenological constitutive laws currently employed to model finite strain inelastic behavior are shown to lead to closed-form analytical solutions for torsion. These include rate-independent elastic-plastic isotropic hardening J2 flow theory of plasticity, various kinematic hardening models of flow theory, and both hypoelastic and hyperelastic formulations of J2 deformation theory. Certain rate-dependent inelastic laws, including creep and strain-rate sensitivity models, also permit the development of closed-form solutions. The derivation of these solutions is presented as well as numerous applications to a wide variety of time-independent and rate-dependent plastic constitutive laws.

Adhesion mechanisms of copper films deposited onto laser-irradiated alumina

1997 ◽  
Vol 12 (11) ◽  
pp. 3174-3181 ◽  
Author(s):  
Jae-Won Park ◽  
Anthony J. Pedraza ◽  
Douglas H. Lowndes ◽  
William R. Allen
Keyword(s):  
Laser Irradiation ◽  
Copper Film ◽  
Alumina Substrate ◽  
Interfacial Region ◽  
Transitional Region ◽  
Copper Films ◽  
High Adhesion ◽  
Strong Adhesion ◽  
Oxygen Excess ◽  
Higher Temperature

Strong adhesion between a deposited copper film and an alumina substrate takes place when the substrate is laser-irradiated prior to deposition. A post-deposition annealing is required to achieve the strong bonding. In this work, the interfacial region between the copper film and the alumina substrate was analyzed using Auger Electron Spectroscopy (AES). It was found that a transitional region is always present in couples that have a high adhesion strength, while little or no transitional region was found in weakly bonded couples. The transitional region depends on the laser irradiation atmosphere. In the case of laser irradiation in air, oxygen excess was found on the surface of the alumina substrate, and in the copper/alumina couple the transitional region consists of a copper oxide and a Cu–Al double oxide. When the laser irradiation was performed in a reducing atmosphere (Ar–4% H2), substoichiometric alumina and metallic aluminum were found on the surface of the substrate and also a reaction between copper and the substoichiometric aluminum oxide was detected in the subsurface. Although the substoichiometric alumina is formed on the surface irradiated in Ar–4% H2, a stable Al2O3 thin layer is formed on the outmost surface because the irradiated substrate is exposed to the atmosphere before deposition. This reoxidized layer remains whole at the interface of the couple upon low temperature (at least up to 300 °C) annealing, while it is ruptured upon higher temperature annealing (500 °C in this work). In the latter case, the copper film can contact and react with the substoichiometric alumina formed in the subsurface of the substrate irradiated in the Ar–4% H2 atmosphere. It is concluded that the Cu–Al–O interfacial compound formed in the transitional region causes the strong adhesion between the copper film and the alumina substrate.

A Kinematic Hardening Finite Elements Model to Evaluate Residual Stresses in Shot-Peened Parts, Local Measurements by X-Ray Diffraction

2006 ◽  
Vol 524-525 ◽  
pp. 161-166 ◽  
Author(s):  
Choumad Ould ◽  
Emmanuelle Rouhaud ◽  
Manuel François ◽  
Jean Louis Chaboche
Keyword(s):  
Finite Elements ◽  
Residual Stresses ◽  
Shot Peening ◽  
Kinematic Hardening ◽  
Constitutive Law ◽  
Loading Path ◽  
Isotropic Hardening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Local Measurements

Experimental analysis can be very costly and time consuming when searching for the optimal process parameters of a new shot-peening configuration (new material, new geometry of the part…). The prediction of compressive residual stresses in shot-peened parts has been an active field of research for the past fifteen years and several finite elements models have been proposed. These models, although they give interesting qualitative results, over-estimate, most of the time, the level of the maximal compressive stresses. A better comprehension of the phenomena and of the influence of the parameters used in the model can only carry a notable improvement to the prediction of the stresses. The fact that the loading path is cyclic and is not radial led us to think that a model including kinematic hardening would be better adapted for the modelling of shot peening. In this article we present the results of a simulation of a double impact for several constitutive laws. We study the effect of the chosen constitutive law on the level of residual stresses and, in particular, we show that kinematic hardening, even identified on the same tensile curve than isotropic hardening, leads to lower stress levels as compared with isotropic hardening. Furthermore, the overall shape of the stress distribution within the depth is significantly different for the two types of hardening behaviour. Further, in order to check the modelisations, local measurements were carried on with X-ray diffraction on a large size impact and correlated with the topography of the impact.

Thermomechanical Stresses in Copper Films at Elevated Temperature

2010 ◽  
Vol 2010 (HITEC) ◽  
pp. 000129-000135 ◽  
Author(s):  
Martin Lederer ◽  
Javad Zarbakhsh ◽  
Rui Huang ◽  
Thomas Detzel ◽  
Brigitte Weiss
Keyword(s):  
Elevated Temperature ◽  
Thermal Cycling ◽  
Copper Film ◽  
Film Stress ◽  
Elastic Response ◽  
Copper Films ◽  
Thermomechanical Stress ◽  
Wafer Curvature ◽  
Electronic Parts ◽  
Stoney Formula

Thermomechanical stresses in metallic films are a root cause for material fatigue which limits the lifetime of electronic devices. Since the yield stress of metals is temperature dependent, plastic deformations during thermal cycling are increased at elevated temperature. This effect reduces the reliability of electronic parts. In order to investigate this problem, a 20μm thick copper film was deposited on a silicon wafer. After annealing at 400°C, the sample was exposed to thermal cycles in the temperature range between room temperature and 600°C. The different values for the CTE of copper and silicon lead to a curvature of the sample. The wafer curvature was measured by a multi-laser beam method. On the basis of the experimental results, a new theoretical model was developed, which describes the stress evolution in the film during thermal cycling. In this investigation, the relation between wafer curvature and film stress is calculated by analogy to a model by Freund [1] which is an improvement to the well known Stoney formula. In addition to the elastic response, the new model considers plasticity of the copper film as well as temperature dependence of creep. It is demonstrated that the model can well describe the experiment and thus thermomechanical stress in copper films.

Room Temperature Self-Annealing of Electroplated and Sputtered Copper Films

1999 ◽  
Vol 562 ◽  
Author(s):  
Michelle Chen ◽  
Suraj Rengarajan ◽  
Peter Hey ◽  
Yezdi Dordi ◽  
Hong Zhang ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Room Temperature ◽  
Copper Film ◽  
Copper Films ◽  
Organic Additives ◽  
X Ray Diffraction ◽  
X Ray ◽  
Transmission Electron ◽  
Electroplated Copper ◽  
Effect Of Copper

ABSTRACTSelf-annealing properties of electroplated and sputtered copper films at room temperature were investigated in this study, in particular, the effect of copper film thickness, electrolyte systems used, as well as their level of organic additives for electroplating. Real-time grain growth was observed by transmission electron microscopy. Sheet resistance and X-ray diffraction measurements further confirmed the recrystallization of the electroplated copper film with time. The recrystallization of electroplated films was then compared with that of sputtered copper films.

Inelastic, Nonlinear Analysis of Stiffened Shells of Revolution by Numerical Integration

1974 ◽  
Vol 96 (2) ◽  
pp. 121-130 ◽  
Author(s):  
H. S. Levine ◽  
V. Svalbonas
Keyword(s):  
Numerical Integration ◽  
Cross Sections ◽  
Thermal Loading ◽  
Large Deflection ◽  
Kinematic Hardening ◽  
Integration Scheme ◽  
Shells Of Revolution ◽  
Stiffened Shells ◽  
Numerical Integration Scheme ◽  
Deflection Analysis

This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.

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