Shape changes of voids in bamboo lines: A new electromigration failure mechanism

The behaviour of electromigration-induced voids in narrow, unpassivated aluminium interconnects is examined. Failure voids are categorized in two different types: extended wedge-shaped voids and narrow slit-like voids. The occurrence of slits is found to increase with decreasing current density and line width. It is observed that shape changes of voids lead to the formation of the slit-like voids. These shape changes may consume a major part of the lifetime of a conductor line. A model to describe the evolution of the void shape is presented.     

Electromigration in layered Al lines studied by in-situ ultra-high voltage electron microscopy

In-situ side-view transmission electron microscopy (TEM) observations of electromigration in Al-on-TiN lines with a drift velocity measurement structure have been carried out using an ultrahigh voltage (2 MV) electron microscope. Thick chips as-diced from silicon substrates served as TEM samples. The observations revealed the dynamic behavior of electromigration-induced voids and hillocks during forward and reverse current feeding through the Al lines. The results include vertical growth of voids bounded by faceted Al, refilling of voids, void growth in a hillock upon current reversal, and whisker growth.     

ANALYSIS OF FAILURE MECHANISMS IN THE INTERCONNECT LINES OF MICROELECTRONIC CIRCUITS

Interconnect lines are thin wires inside microelectronic circuits. The material in an interconnect line is subjected to severe mechanical and electrical loading, which causes voids to nucleate and propagate in the line: microelectronic circuits often fail because an interconnect is severed by a crack. Many of the mechanisms of failure are believed to be associated with diffusion of material through the line; driven by variations in elastic strain energy and stress in the solid, by the flow of electric current, and by variations in the free energy of the solid itself. With a view to modelling interconnect failures, we have developed a finite element method that may be used to compute the effects of diffusion and deformation in an electrically conducting, deformable solid. Our analysis accounts for large changes in the shape of the solid due to surface diffusion, grain boundary diffusion, and elastic or inelastic deformation within the grains. The methods of analysis is reviewed in this paper, and selected examples are used to illustrate the capabilities of the method. We compute the rate of growth of a void in an interconnect by coupled grain boundary diffusion and creep; we investigate void migration and evolution by electromigration-induced surface diffusion; we study the influence of electromigration and stress on hillock formation in unpassivated interconnects, and compute the distribution of stress and plastic strain induced by electromigration in a passivated, polycrystalline interconnect line.     

Analysis of wave motion at the boundary surface of orthotropic thermoelastic material with voids and isotropic elastic half-space

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of orthotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived on the basis of the developed mathematical model under the boundary conditions for welded and smooth contacts. The dispersion curves giving the phase velocity and attenuation coefficient versus the wave number enable one to reveal the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction, normal stress, and temperature change for welded contact are obtained and presented graphically for a particular model showing the voids and anisotropy effects. Some special cases are also deduced.     

Grain boundary and vacancy diffusion model for electromigration-induced damage in thin film conductors

A theoretical model is proposed to explain the formation of both voids and hillocks in electromigration-induced damage. In this model, grain boundary mass transport is assumed to be responsible for the depletion and accumulation of diffusing atoms.The previously observed high compressive stresses generated in regions of atom accumulation can be explained using this model. In regions of atom depletion, vacancies are created but the expected tensile stresses are not observed because of efficient stress relaxation by the rapid diffusion of the vacancies into the neighboring lattice. The annihilation of these diffusing vacancies at film surfaces causes local film thinning which leads to the formation of electromigration-induced through-voids at grain boundaries.     

Electric Current-induced Failure of 200-nm-thick Gold Interconnects

200-nm-thick Au interconnects on a quartz substrate were tested in-situ inside a dual-beam microscope by applying direct current, alternating current and alternating current with a small direct current component. The failure behavior of the Au interconnects under three kinds of electric currents were characterized in-situ by scanning electron microscopy. It is found that the formation of voids and subsequent growth perpendicular to the interconnect direction is the fatal failure mode for all the Au interconnects under three kinds of electric currents. The failure mechanism of the ultrathin metal lines induced by the electric currents was analyzed.     

Modeling of electromechanically-induced failure of passivated metallic thin films used in device interconnections

A theoretical analysis is presented of the failure of metallic thin films used for device interconnections in integrated circuits. Failure is mediated by void dynamics, which is driven by surface electromigration and processing related residual thermal stresses in the films. The analysis is based on surface mass transport modeling coupled strongly with the electrostatic and elastic deformation problems in the metallic films. Special emphasis is placed on the combined effects on void dynamics of anisotropy both in surface diffusivity along a void surface and in the applied stress tensor. A systematic parametric study is carried out based on self-consistent numerical simulations of surface morphological evolution. Void dynamics is analyzed and results are presented for void morphological stability in terms of critical stress levels as a function of stress state and surface mobility anisotropy. Finally, the role of plastic deformation is discussed around crack-like features emanating from void surfaces in ductile metallic films based on results of molecular-dynamics simulations in Cu.     

Estimation of Creep Voids Using a Progressive Damage Model and Neural Networks

In order to develop nondestructive techniques for the quantitative estimation of creep damage, a series of crept copper samples were prepared and their ultrasonic velocities were measured. Velocities measured in three directions with respect to the loading axis decreased nonlinearly and their anisotropy increased as a function of creep-induced porosity. A progressive damage model was described to explain the observed void—velocity relationship, including the anisotropy. The model study showed that the creep voids evolved from sphere toward flat oblate spheroid with its minor axis symmetrically distributed with respect to the stress direction. This model allowed us to determine the average aspect ratio of voids for a given porosity content. The back-propagation neural network (BPNN) was applied for estimating the porosity content. The measured velocities were used to train the BPNNs, and its performance was tested on another set of creep samples containing 0—0.7\percent porosity. When the void aspect ratio was used as input parameter in addition to the velocity data, the neural network algorithm provided a much better estimation of the void content.     

Analysis of damage formation and propagation in metallic thin films under the action of thermal stresses and electric fields

Summary A quantitative analysis is presented of void formation, morphological stability, and evolution in metallic thin films, which are problems that underlie serious reliability issues in interconnections used in integrated circuits. The analysis is based on the coupling of bulk and interfacial mass transport phenomena with elastic deformations and current stressing. The formation and growth of intergranular voids in bamboo-structure conductor lines due to stresses that develop during processing is investigated. The investigation is aided by self-consistent simulation of bulk and grain-boundary diffusional processes using bicrystal models with elastic grains. A systematic analysis is presented of the morphological evolution of transgranular voids in passivated and unpassivated aluminum lines under current densities that are typical of electromigration testing. The effects of the electric field and surface properties on the morphological stability of voids are examined and morphologies that bifurcate from rounded or wedge-like void shapes are predicted. The theoretical results are discussed in the context of experimental data of void propagation under electromigration conditions.     

Transmission of visible light through oxidized copper films: feasibility of using a spectral projected gradient method

Transmittance measurements at normal incidence were carried out over the visible spectral range for metallic thin films deposited by electron beam evaporation on thick glass substrates. The presence of an inhomogeneous thin layer of Cu2O covering the deposited Cu films is required for a satisfactory model of the measurements taken from various samples with increasing thickness. A spectral projected gradient method is used to invert the transmission spectra from which the wavelength dependence of the effective dielectric function of the oxidized coating layer is obtained. Then an effective medium model is used to estimate the volume fraction of internal voids randomly distributed through the surface layer.     

Measurement of electromigration-induced stress in aluminum alloy interconnection

The behavior of electromigration-induced stress in Al-1.0% Si-0.5% Cu alloy interconnections was investigated in situ by synchrotron radiation at the SPring-8. The electromigration tests were performed as a function of applied current density. When the current was applied to the lines, 111 diffraction peak shifted to lower angle for all measurement points. This indicated that compressive stresses were present at all measurement positions in the lines. When the applied current was stopped, 111 diffraction peak reverted to its initial position for all measurement points. At constant current density, the position of 111 diffraction peak didn't change for any of the measurement positions.     

Continuum and atomistic modeling of electromechanically-induced failure of ductile metallic thin films

A multiscale modeling approach is presented for the analysis of electromechanically-induced void morphological evolution and failure in ductile metallic thin films, which are used for device interconnections in integrated circuits. Self-consistent mesoscopic simulations of surface morphological evolution are combined with atomistic calculations of surface properties and molecular-dynamics (MD) simulations of plastic deformation mechanisms in the vicinity of void surfaces. Results are presented that demonstrate a coupled mode of surface instability that leads to formation of electromigration-induced slit-like features and stress-induced crack-like features on void surfaces. In addition, MD results are presented for the dislocation-mediated mechanism and the kinetics of void growth in ductile metallic systems subject to hydrostatic and biaxial tensile strains. The incorporation of MD-derived constitutive information for plastic deformation into the mesoscopic analysis and simulation framework also is discussed.     

On the connection between microstructure and surface roughness of brass sheets and their formability

The aim of this work was the analysis of the relationships between material properties and forming limits of a sheet, caused by the strain localization in the groove. In particular, we aim at the replacement of a nonmeasurable inhomogeneity coefficient of the material, the value of which has to be taken a priori, by measurable coefficients. In the proposed model, it is assumed that the material heterogeneity is a result of surface roughness and presence of internal defects (voids). The value of inhomogeneity coefficients changes with increasing strain. The experiments were carried out for M85 brass sheets, annealed to produce different microstructures. The measured values of some material parameters: strain-hardening constants n and C, normal anisotropy factors, inhomogeneity coefficients (surface roughness and volume fraction of voids) as well as forming limit curve demonstrated their dependence on the grain size. As a result of the experimental work, original equations were proposed, describing the relationship between inhomogeneity coefficients and effective strain and grain size. These equations were used in the theoretical calculation of the forming limit diagram. The theoretical calculations of the strain limits of the tested sheets were based on the associated flow rules, assuming strain-hardening and strain-softening process (Shima–Oyane equation and equations based on the Gurson theory). The analysis of the influence of different material parameters on the forming limit diagram has shown that in the case of the material tested, the value of limit strains depends decisively on the values of the inhomogeneity coefficients and grain size. The postulates showing proportional relationship between the value of a strain-hardening exponent and limit strains were not confirmed.     

A 2-D mesoscopic model coupling mechanical and diffusion for electromigration in thin films

Electromigration is an important mechanism of deformation and failure in miniaturized electronics materials. In this paper, a 2-D mesoscopic simulation method is developed for analyzing electromigration-induced stress in thin films and finite element method is implemented for solution. Numerical simulations are compared with theoretical result and comparisons validate the model. The method has advantage in describing boundary conditions for constrained diffusion when focusing on creep process of thin films.     

Optical anisotropy,molecular orientations,and internal stresses in thin sulfonated poly(ether ether ketone) films

The thickness, the refractive index, and the optical anisotropy of thin sulfonated poly(ether ether ketone) films, prepared by spin-coating or solvent deposition, have been investigated with spectroscopic ellipsometry. For not too high polymer concentrations (≤5 wt%) and not too low spin speeds (≥2000 rpm), the thicknesses of the films agree well with the scaling predicted by the model of Meyerhofer, when methanol or ethanol are used as solvent. The films exhibit uniaxial optical anisotropy with a higher in-plane refractive index, indicating a preferred orientation of the polymer chains in this in-plane direction. The radial shear forces that occur during the spin-coating process do not affect the refractive index and the extent of anisotropy. The anisotropy is due to internal stresses within the thin confined polymer film that are associated with the preferred orientations of the polymer chains. The internal stresses are reduced in the presence of a plasticizer, such as water or an organic solvent, and increase to their original value upon removal of such a plasticizer.     

Si-supported mesoporous and microporous oxide interconnects as electrophoretic gates for application in microfluidic devices

Microfluidic analysis systems are becoming an important technology in the field of analytical chemistry. An expanding area is concerned with the control of fluids and species in microchannels by means of an electric field. This paper discusses a new class of Si-compatible porous oxide interconnects for gateable transport of ions. The integration of such thin oxide films in microfluidics devices has been hampered in the past by the compatibility of oxides with silicon technology. A general fabrication method is given for the manufacture of silicon microsieve support structures by micromachining, on which a thin oxide layer is deposited by the spin-coating method. The deposition method was used for constructing gamma-alumina, MCM-48 silica, and amorphous titania films on the support structures, from both water-based and solvent-based oxide sols. The final structures can be applied as microporous and mesoporous interconnecting walls between two microchannels. It is demonstrated that the oxide interconnects can be operated as ion-selective electrophoretic gates. The interconnects suppress Fick diffusion of both charged and uncharged species, so that they can be utilized as ionic gates with complete external control over the transport rates of anionic and cationic species, thus realizing the possibility for implementation of these Si-compatible oxide interconnects in microchip analyses for use as dosing valves or sensors.     

Estimation of Creep Voids Using a Progressive Damage Model and Neural Networks

Abstract

In order to develop nondestructive techniques for the quantitative estimation of creep damage, a series of crept copper samples were prepared and their ultrasonic velocities were measured. Velocities measured in three directions with respect to the loading axis decreased nonlinearly and their anisotropy increased as a function of creep-induced porosity. A progressive damage model was described to explain the observed void-velocity relationship, including the anisotropy. The model study showed that the creep voids evolved from sphere toward flat oblate spheroid with its minor axis symmetrically distributed with respect to the stress direction. This model allowed us to determine the average aspect ratio of voids for a given porosity content. The back-propagation neural network (BPNN) was applied for estimating the porosity content. The measured velocities were used to train the BPNNs, and its performance was tested on another set of creep samples containing 0–0.7% porosity. When the void aspect ratio was used as input parameter in addition to the velocity data, the neural network algorithm provided a much better estimation of the void content.     

In-situ revealing the degradation mechanisms of Pt film over 1000 ℃

Degradation of a metallic film under harsh thermal-mechanical-electrical coupling field conditions deter-mines its service temperature and lifetime.In this work,the self-heating degradation behaviors of Pt thin films above 1000 ℃ were studied in situ by TEM at the nanoscale.The Pt films degraded mainly through void nucleation and growth on the Pt-SiNx interface.Voids preferentially formed at the grain boundary and triple junction intersections with the interface.At temperatures above 1040 ℃,the voids nucleated at both the grain boundaries and inside the Pt grains.A stress simulation of the suspended membrane suggests the existence of local tensile stress in the Pt film,which promotes the nucleation of voids at the Pt-SiNx interface.The grain-boundary-dominated mass transportation renders the voids grow preferen-tially at GBs and triple junctions in a Pt film.Additionally,under the influence of an applied current,the voids that nucleated inside Pt grains grew to a large size and accelerated the degradation of the Pt film.     

Galerkin boundary integral method for evaluating surface derivatives

A Galerkin boundary integral procedure for evaluating the complete derivative, e.g., potential gradient or stress tensor, is presented. The expressions for these boundary derivatives involve hypersingular kernels, and the advantage of the Galerkin approach is that the integrals exist when a continuous surface interpolation is employed. As a consequence, nodal derivative values, at smooth surface points or at corners, can be obtained directly. This method is applied to the problem of electromigration-driven void dynamics in thin film aluminum interconnects. In this application, the tangential component of the electric field on the boundary is required to compute the flux of atoms at the void surface.     

Structure and magnetic properties of Fe films with pyramid-like nanostructures deposited by oblique target direct current magnetron sputtering

Fe thin films were deposited by oblique target direct current magnetron sputtering on Si (100) and (111) substrates. The structure, surface morphology and magnetic properties of the thin films were characterized using X-ray diffraction, field emission scanning electron microscopy, and superconducting quantum interference device magnetometer, respectively. The results reveal that the structure of the as-deposited Fe thin films is body-centered cubic with the preferential [110] crystalline orientation. A pyramid-like nanostructure with sharp tip was formed on the surfaces of Fe thin films under appropriate sputtering power. Formation of the pyramid-like nanostructure is mainly owed to the enhancement of atomic mobility and the bombardment effect with increasing of sputtering power. Meanwhile, the crystalline orientation of Si substrate and the intrinsic stress in the films are expected to have little contribution to the formation of the pyramid-like nanostructure. The magnetic anisotropy was found in the as-deposited Fe thin films, and varies with the thickness of the Fe thin films. As the film thickness increases from 604 to 1,786 nm, the magnetic anisotropy field and the uniaxial anisotropy constant increase from 3.8 to 5.6 kOe, and from 0.4 × 10⁶ to 1.1 × 10⁶ erg/cm³, respectively, which indicates that besides magnetocrystalline anisotropy, stress induced anisotropy and shape anisotropy also exist in the as-deposited Fe thin films.