The ever increasing requirements for electrical performance of on-chip wiring has driven three major technological advances in recent years. First, copper has replaced Aluminum as the new interconnect metal of choice, forcing also the introduction of damascene processing. Second, alternatives for SiO2 with a lower dielectric constant are being developed and introduced in main stream processing. The many new resulting materials needs to be classified in terms of their materials characteristics, evaluated in terms of their properties, and tested for process compatibility. Third, in an attempt to lower the dielectric constant even more, porosity is being introduced into these new materials. The study of processes such as plasma interactions and swelling in liquid media now becomes critical. Furthermore, pore sealing and the deposition of a thin continuous copper diffusion barrier on a porous dielectric are of prime importance. This review is an attempt to give an overview of the classification, the character...

Low dielectric constant materials for microelectronics

http://www.eng.usf.edu/~volinsky/VolinskyActaMatReview2002.pdf

Interfacial toughness measurements for thin films on substrates

I. Fundamental concepts and examples.- 1. Hyperbolicity, genuine nonlinearity, and entropies.- 2. Shock formation and weak solutions.- 3. Singular limits and the entropy inequality.- 4. Examples of diffusive-dispersive models.- 5. Kinetic relations and traveling waves.- 1. Scalar Conservation Laws.- II. The Riemann problem.- 1. Entropy conditions.- 2. Classical Riemann solver.- 3. Entropy dissipation function.- 4. Nonclassical Riemann solver for concave-convex flux.- 5. Nonclassical Riemann solver for convex-concave flux.- III. Diffusive-dispersive traveling waves.- 1. Diffusive traveling waves.- 2. Kinetic functions for the cubic flux.- 3. Kinetic functions for general flux.- 4. Traveling waves for a given speed.- 5. Traveling waves for a given diffusion-dispersion ratio.- IV. Existence theory for the Cauchy problem.- 1. Classical entropy solutions for convex flux.- 2. Classical entropy solutions for general flux.- 3. Nonclassical entropy solutions.- 4. Refined estimates.- V. Continuous dependence of solutions.- 1. A class of linear hyperbolic equations.- 2. L1 continuous dependence estimate.- 3. Sharp version of the continuous dependence estimate.- 4. Generalizations.- 2. Systems of Conservation Laws.- VI. The Riemann problem.- 1. Shock and rarefaction waves.- 2. Classical Riemann solver.- 3. Entropy dissipation and wave sets.- 4. Kinetic relation and nonclassical Riemann solver.- VII. Classical entropy solutions of the Cauchy problem.- 1. Glimm interaction estimates.- 2. Existence theory.- 3. Uniform estimates.- 4. Pointwise regularity properties.- VIII. Nonclassical entropy solutions of the Cauchy problem.- 1. A generalized total variation functional.- 2. A generalized weighted interaction potential.- 3. Existence theory.- 4. Pointwise regularity properties.- IX. Continuous dependence of solutions.- 1. A class of linear hyperbolic systems.- 2. L1 continuous dependence estimate.- 3. Sharp version of the continuous dependence estimate.- 4. Generalizations.- X. Uniqueness of entropy solutions.- 1. Admissible entropy solutions.- 2. Tangency property.- 3. Uniqueness theory.- 4. Applications.

Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves

Recent experiments have shown the 'size effects' in micro/nano scale. But the classical plasticity theories can not predict these size dependent deformation behaviors because their constitutive models have no characteristic material length scale. The Mechanism - based Strain Gradient(MSG) plasticity is proposed to analyze the non-uniform deformation behavior in micro/nano scale. The MSG plasticity is a multi-scale analysis connecting macro-scale deformation of the Statistically Stored Dislocation(SSD) and Geometrically Necessary Dislocation(GND) to the meso-scale deformation using the strain gradient. In this research we present a study of nano-indentation by the MSG plasticity. Using W. D. Nix and H. Gao’s model, the analytic solution(including depth dependence of hardness) is obtained for the nano indentation , and furthermore it validated by the experiments.

Mechanism-based Strain Gradient Plasticity 를 이용한 나노 인덴테이션의 해석

A relationship between the adhesion of a Cu conductor to its surrounding medium, the electromigration drift velocity, and lifetime in a conventional electromigration test has been demonstrated. Lifetime measurements demonstrate that the drift velocity and the activation energy for mass transport along an interface correlate with the measured adhesion energy of the interface as determined by a four-point bending test. The results indicate that a linear relationship is expected between the electromigration activation energy and the intrinsic work of adhesion, which is consistent with a simple model relating the two. The data indicate that interfacial cleanliness and bond character at the interface (i.e., metal/dielectric versus metal/metal bonding) have a significant impact on all measured parameters.

Relationship between interfacial adhesion and electromigration in Cu metallization

The effects of plasticity in thin copper layers on the interface fracture resistance in thin-film interconnect structures were explored using experiments and multiscale simulations. Particular attention was given to the relationship between the intrinsic work of adhesion, Go, and the measured macroscopic fracture energy, Gc. Specifically, the TaN/SiO2 interface fracture energy was measured in thin-film Cu/TaN/SiO2 structures in which the Cu layer was varied over a wide range of thickness. A continuum/FEM model with cohesive surface elements was employed to calculate the macroscopic fracture energy of the layered structure. Published yield properties together with a plastic flow model for the metal layers were used to predict the plasticity contribution to interface fracture resistance where the film thickness (0.25–2.5 μm) dominated deformation behavior. For thicker metal layers, a transition region was identified in which the plastic deformation and associated plastic energy contributions to Gc were no longer dominated by the film thickness. The effects of other salient interface parameters including peak cohesive stress and Go are explored.

Plasticity contributions to interface adhesion in thin-film interconnect structures

Martensitic phase transitions are often modeled by mixed-type hyperbolic-elliptic systems. Such systems lead to ill-posed initial-value problems unless they are supplemented by an additional kinetic relation. In this paper we explicitly compute an appropriate closing relation by replacing the continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or a physically motivated account of underlying discrete microstructure. We model phase boundaries by traveling wave solutions of a fully inertial discrete model for a bi-stable lattice with harmonic long-range interactions. Although the microscopic model is Hamiltonian, it generates macroscopic dissipation which can be specified in the form of a relation between the velocity of the discontinuity and the conjugate configurational force. This kinetic relation respects entropy inequality but is not a consequence of the usual Rankine--Hugoniot jump conditions. According to the constructed solution, the dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality of the lattice model may be responsible for the multivaluedness of the kinetic relation and can quantitatively affect kinetics in the near-sonic region. Direct numerical simulations of the transient dynamics suggest stability of at least some of the computed traveling waves.

/pdf/kinetics-of-martensitic-phase-transitions-lattice-model-3wy5k7t3hr.pdf

Kinetics of martensitic phase transitions: lattice model*

A typical stress-strain relation for martensitic materials exhibits a mismatch between the nucleation and propagation thresholds leading to the formation of the nucleation peak. We develop an analytical model of this phenomenon and obtain specific relations between the macroscopic parameters of the peak and the microscopic characteristics of the material. Although the nucleation peak appears in the model as an interplay between discreteness and nonlocality, it does not disappear in the continuum limit. We verify the quantitative predictions of the model by comparison with experimental data for cubic to monoclinic phase transformation in NiTi.

http://www.math.pitt.edu/~annav/papers/JMPS_preprint.pdf

The origin of nucleation peak in transformational plasticity

We consider a one-dimensional chain of phase-transforming springs with harmonic long-range interactions. The nearest-neighbor interactions are assumed to be trilinear, with a spinodal region separating two material phases. We derive the traveling wave solutions governing the motion of an isolated phase boundary through the chain and obtain the functional relation between the driving force and the velocity of a phase boundary which can be used as the closing kinetic relation for the classical continuum theory. We show that a sufficiently wide spinodal region substantially alters the phase boundary kinetics at low velocities and results in a richer solution structure, with phase boundaries emitting short-length lattice waves in both direction. Numerical simulations suggest that solutions of the Riemann problem for the discrete system converge to the obtained traveling waves near the phase boundary.

The role of spinodal region in the kinetics of lattice phase transitions

We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of a diatomic Toda lattice. Results of numerical integration of the full diatomic Toda lattice equations confirm the formation of these genuinely localized wave structures at special values of the mass ratio that are close to the analytical predictions when the ratio is sufficiently small.

Anna Vainchtein

Papers

Plasticity contributions to interface adhesion in thin-film interconnect structures

Kinetics of martensitic phase transitions: lattice model*

The origin of nucleation peak in transformational plasticity

The role of spinodal region in the kinetics of lattice phase transitions

Solitary waves in diatomic chains.