Passivated Interconnects Research Articles

Prediction of Electromigration Critical Current Density in Passivated Arbitrary-Configuration Interconnect

A critical current density, a criterion of electromigration (EM) resistance in interconnects, above which EM damages initiate has been studied to minimize EM damages of interconnects. In general, the assessment of a critical current density is confined to straight interconnect called as Blech specimen, although the critical current density is sensitive to structural characteristic. This work proposes a procedure of predicting a critical current density for any arbitrary-configuration interconnect by using the analogy between atomic density and electrical potential. In the models of straight and barrel interconnects as the typical solder bumps in modern flip-chip technology, the critical current density is predicted through calculating electrical potential by proposed formulation and simulation based on the finite element analysis (FEA). The critical current density for straight interconnect obtained by experiment leads to numerically calculate the critical electrical potential, which is independent of interconnect configuration. The critical potential corresponds to the critical atomic density, below which the accumulation of atoms allows. The calculated critical electrical potential determines a critical current density for arbitrary-configuration interconnect including current crowding effect. This finding can predict a critical current density for actual arbitrary-configuration model and provide an insight for the applying to the packaging design such as ball grid array and C4 flip-chip solder bumps.

Competition between dislocation nucleation and void formation as the stress relaxation mechanism in passivated Cu interconnects

We perform systematic calculations to study the competition between the dislocation nucleation and void formation as stress relaxation mechanism in Cu interconnects under thermal stress, which is related to the aspect ratio (ratio of the film thickness to width) of the Cu lines. It is quantitatively found from both elastic-perfectly plastic model and kinematic strain hardening model that there exists a critical aspect ratio, below and above which the stress relaxation is dominated by the dislocation nucleation and void formation, respectively. The critical aspect ratio is revealed to modulate by both the length scale of the interconnects and the interfacial strength between the Cu lines and surroundings, suggesting potential application to achieve artificial controlling on stress relaxation mechanism in Cu lines. Calculations are in good agreement with available experiments.

The Thermal Residual Stress Redistribution in a Bamboo Interconnect

An analytical expression is developed to predict the thermal residual stress redistribution in a passivated bamboo interconnect based on the coupling of the grain boundary diffusion with the interconnect-passivation interface diffusion. Quantitative results show that the thermal stress redistribution in the interconnect depends strongly on the microstructure of the interconnect, the initial state of the thermal residual stress and the diffusivity ratio of the grain boundary to the interface.

Effects of microstructure on the formation, shape, and motion of voids during electromigration in passivated copper interconnects

In situ scanning electron microscope observations have been performed on passivated damascene Cu interconnect segments of different widths during accelerated electromigration tests. In some cases, voids form and grow at the cathode. However, an alternative failure mode is also observed, during which voids form distant from the cathode end of the interconnect segment and drift toward the cathode, where they eventually lead to failure. The number of observations of this failure mode increased with increasing linewidth. During void motion, the shape and the velocity of the drifting voids varied significantly. Postmortem electron backscattered diffraction (EBSD) analysis was performed after in situ testing, and a correlation of EBSD data with the in situ observations reveals that locations at which voids form, their shape evolution, and their motion all strongly depend on the locations of grain boundaries and the crystallographic orientations of neighboring grains.

Hydrostatic stress and hydrostatic stress gradients in passivated copper interconnects

A numerical evaluation of the effects of geometrical factors on the hydrostatic stress and hydrostatic stress gradients in passivated copper interconnects was performed. These values were correlated with experimental values in the literature on the location of voids in the interconnect. Copper interconnects of aspect ratios between 0.1 and 10 were studied. Numerical work using the commercial ANSYS software and analytical work based on the Eshelby and Wikström models were performed. Comparison is made between the analytical, numerical and experimental results (obtained from the literature). It was found that for an interconnect with no pre-existing voids, maximum hydrostatic stress gradients occurred at the corners of the interconnects suggesting that void growth is most probable at the corners of the interconnect. The stress gradient within the interconnect with aspect ratio of 10 is about 10 times larger than that in interconnects of aspect ratios 0.1 and 1. This suggests that the narrowest interconnects are most likely to undergo voiding. This study found that it is insufficient to look only at the hydrostatic stress at the centre of the interconnect and that stress gradient also needs to be taken into consideration to assess reliability.

The effect of aspect ratio scaling on hydrostatic stress in passivated interconnects

In this study, numerical work using ANSYS and analytical work based on Eshelby models were performed to examine the effect of aspect ratio scaling on the hydrostatic stress in passivated metal interconnects. Aluminium and copper interconnects passivated with phosphosilicate glass (PSG) with aspect ratios ranging from 1 × 10 − 4 to 100 were studied. Copper interconnects in damascene structure were also studied. The results from analytical models agreed well with numerical results and relevant experimental results. The results showed a decreasing trend of hydrostatic stress with aspect ratio for narrow interconnects, and increasing trend of hydrostatic stress for wide interconnects, with a maximum hydrostatic stress at an aspect ratio of 1. It was observed that there is a large scaling effect. For example, in the case of aluminium interconnect, stress values vary between 50 MPa and 463 MPa. It was also observed from the hydrostatic stress contours that the regions of highest stress do not correspond to the void locations seen experimentally. This implies that it is insufficient to look only at hydrostatic stress for determination of failure sites. Another factor that should be examined is the stress gradient.

Electromigration in passivated Cu interconnects studied by transmission x-ray microscopy

Time-resolved x-ray microscopy studies of the electromigration in inlaid Cu line/via structures were performed on focused-ion-beam-prepared cross sections of an advanced interconnect layer system. Multiple x-ray images were recorded at 1.8 keV photon energy while stressing the passivated Cu structures with an applied current. The image sequences show that void formation is a dynamic process, with voids being observed to nucleate and grow within the Cu via and migrate towards the via sidewall. Correlation of the real time x-ray microscopy images with postmortem high voltage transmission electron and scanning electron micrographs indicates that the void nucleation occurs at grain boundaries in the copper, and that the voids migrate along these grain boundaries during electromigration. By taking multiple images at different viewing angles, the three-dimensional arrangement of an interconnect stack with Cu line / via structures was reconstructed. In future studies time-resolved tomography will be used to visualize void dynamics within the volume, thereby identifying pathways for Cu diffusion.

Electromigration in integrated circuit interconnects studied by X-ray microscopy

To study mass transport phenomena in advanced microelectronic devices with X-rays requires penetration of dielectric and Si layers up to 30 μm thick. X-ray imaging at 1.8 keV photon energy provides a high amplitude contrast between Cu or Al interconnects and dielectric layers and can penetrate through the required thickness. To perform X-ray microscopy at 1.8 keV, a new Ru/Si multilayer was designed for the transmission X-ray microscope XM-1 installed at the Advanced Light Source in Berkeley. The mass flow in a passivated Cu interconnect was studied at current densities up to 10 7 A/cm 2. In addition, we demonstrated the high material contrast from different elements in integrated circuits with a resolution of about 40 nm.

Dynamical x-ray microscopy investigation of electromigration in passivated inlaid Cu interconnect structures

Quantitative time-resolved x-ray microscopy mass transport studies of the early stages of electromigration in an inlaid Cu line/via structure were performed with about 40 nm lateral resolution. The image sequences show that void formation is a highly dynamic process, with voids being observed to nucleate and grow within the Cu via and migrate towards the via sidewall. Correlation of the real time x-ray microscopy images with postmortem high voltage electron micrographs of the sample indicates that the void nucleation occurs at the site of grain boundaries in Cu, and that the voids migrate along these grain boundaries during electromigration.

Modeling of thermal stresses in passivated interconnects

Analytical modeling is performed to obtain closed-form solutions for the thermal stresses in passivated interconnects in microelectronic devices. A periodic unit cell of a planar passivated interconnect on a substrate is considered. When the aspect ratio of the cross section of the interconnect line has a limiting value, zero or infinity, closed-form solutions for the volume-averaged thermal stresses in the interconnect can be readily derived. These analytical solutions agree with existing finite element calculations. Using the modified shear lag model, the general closed-formed solutions for the thermal stress distributions in the cross section of the unit cell normal to the interconnect line are derived. Specific results are calculated for the system of Al interconnect lines on Si substrate with SiO2 passivation. The effects of the geometrical parameters in the system (e.g., interconnect aspect ratio, distance between interconnect lines, and passivation thickness) on the thermal stress distributions are examined.

Note on the thermal stresses in passivated metal interconnects

An analytical model to compute thermal stresses in passivated metal interconnects is proposed in this article. Typical aspect ratio of passivated metal interconnects is 1 or less (frequently between 0.5 and 1). Previous Eshelby-based analytical model by Niwa et al. [J. Appl. Phys. 68, 328 (1990)] is not very accurate as it fails to take into account the proximity of the interconnect to the free surface of the passivation. A recently proposed model by Wikström et al. [J. Appl. Phys. 86, 6088 (1999)] precisely does not work when the aspect ratio < 1. The analytical model proposed in this letter can predict stresses (average and spatial variations) in passivated metal interconnects with superior accuracy. The effect of free surface of passivation is fully taken into account and comparisons with previous works are presented.

In situ x-ray microscopic observation of the electromigration in passivated Cu interconnects

X-ray imaging of electromigration in a passivated Cu interconnect was performed with 100-nm spatial resolution. A time sequence of 200 images, recorded with the European Synchrotron Radiation Facility x-ray microscope in 2.2 h at 4 keV photon energy, visualizes the mass flow of Cu at current densities up to 2×107 A/cm2. Due to the high penetration power through matter and the element specific image contrast, x-ray microscopy is a unique tool for time-resolved, quantitative mass transport measurements in interconnects. Model calculations predict that failures in operating microprocessors are detectable with 30 nm resolution by nanotomography.

Modeling electromigration and the void nucleation in thin-film interconnects of integrated circuits

The modern tendency for increasing the productivity of microelectronic devices at the expense of the size shrinkage and the development of densely packed multilevel microelectronic structures stipulates the rising concern for the reliability of integrated circuits. The damage of integrated circuits is mainly caused by electromigration in thin-film interconnects. The current-induced redistribution of vacancies and the action of vacancy sinks/sources lead to heterogeneous volume deformations, which, in turn, cause the rise of mechanical stresses. The interconnect failure is initiated by the nucleation of voids taking place on the crystalline structure heterogeneities like triple points, inclusions, etc. or in the plug region of multilevel metallizations. In the latter case the interconnect damage is also caused by the edge depletion. Mechanical stresses induced by electromigration strongly influence the nucleation process. In the present work we propose a general 3D model for electromigration and the rise of mechanical stresses in a passivated aluminum interconnect. A system of differential equations describing electromigration and induced deformation of an interconnect is derived. We also propose a kinetic model for the void nucleation, elaborated on the basis of the classical theory of the new phase nucleation. Integral equations for the time to the void nucleation are deduced. Based on these models numerical calculations for the void formation in a triple point of the interconnect crystalline structure and for both failure mechanisms in the plug region have been carried out. The times to nucleation and characteristic sizes of voids are calculated as functions of temperature and electric current density. The results obtained agree well with experimental data.

Effects of line and passivation geometry on curvature evolution during processing and thermal cycling in copper interconnect lines

A simple theoretical analysis for curvature evolution in unpassivated and passivated copper interconnect lines on a silicon substrate is proposed. A layer consisting of copper and oxide lines is modeled as a homogenized composite that has different elastic moduli and thermal expansion coefficients in two different directions, i.e. along and across the lines, due to the anisotropic line geometry. These effective thermoelastic properties of the composite layer are approximated in terms of volume fractions and thermoelastic properties of each line using standard composite theory. This analogy facilitates the calculation of curvature changes in Damascene-processed copper lines subjected to chemical–mechanical polishing and/or thermal cycling. The effects of line height, width and spacing on curvature evolution along and across the lines are readily extracted from the analysis. In addition, this theory is easily extended to passivated copper lines irrespective of passivation materials by superimposing the curvature change resulting from an additional layer. Finite element analysis has been used to assess the validity of the theoretical predictions; such comparisons show that the simple theory provides a reasonable match with numerical simulations of curvature evolution during the Damascene process in copper interconnects for a wide range of line and passivation geometry of practical interest.

Analysis of average thermal stresses in passivated metal interconnects

Volume-averaged thermal stresses in passivated metal interconnects on Si substrates are derived for situations where the thickness to width ratio of the interconnect lines is “small” or “large.” The analysis provides different components of volume-averaged stresses for the most general case of thermal and elastic anisotropy in the passivation layer, the interconnect line, and the substrate. It is shown that the theoretical predictions, particularly those for the hydrostatic stresses, are in agreement with detailed finite element calculations for a wide range of line and passivation geometries of practical interest. The theoretical predictions of average hydrostatic stresses are also found to be in reasonable agreement with available experimental results for thermal stresses derived from x-ray diffraction measurements on passivated Cu lines. The present theoretical results are shown to be far more accurate than prior stress analyses for periodic passivated lines based on Eshelby’s theory of inclusions.

Void nucleation on intentionally added defects in Al interconnects

Void nucleation in passivated aluminum interconnects was studied using high voltage scanning electron microscopy. To test theories about stress-induced and electromigration void nucleation, Ar ions were implanted into Al specimens. The Ar atoms precipitated and formed bubbles that served as nucleation sites with high surface energy. In the implanted samples, voids formed away from the interconnect sidewalls, in contrast to voids in ordinary passivated Al interconnects. The evolution of the void volume was also affected by the reduction in the nucleation barrier. These results strongly support the theory of void nucleation on interface flaws in Al interconnects.

The piezoresistance of aluminum alloy interconnect structures

The effects of applied strain on the resistivity of Al thin film metallization interconnects have been measured with a novel methodology that uses thermal expansion mismatch to produce the strain. The interconnect volumetric strain is induced by thermal cycling of passivated and unpassivated interconnects between ≈70 and 373 K. The coefficient of piezoresistivity, defined as dρ/dεv, where ρ=resistivity and εv=volumetric strain, is determined by properly accounting for the degree of interconnect constraint and thermal expansion mismatch strain induced during temperature changes. The volumetric strains are calculated for unpassivated and passivated lines of varying thickness and width. A model which incorporates the geometrical and piezoresistance effects on the measured interconnect resistance during temperature changes is described. The coefficient of piezoresistivity is calculated by a fitting procedure which provides an accurate and consistent fit for both unpassivated and passivated interconnects of different geometries and different strain states. The measured coefficient dρ/dεv is 2.0×10−5 Ω cm in tension, similar to earlier results in bulk Al samples measured in compression but significantly higher than values recently measured in Al interconnects. The application of the calibrated coefficient of piezoresistivity for the measurement of electromigration-induced stresses in novel interconnect test structures will be described.

Diffusion and electromigration of copper in SiO2-passivated single-crystal aluminum interconnects

We have experimentally studied the diffusion and electromigration of Cu in passivated single-crystal Al interconnects, fabricated on oxidized Si wafers. The test structure consisted of parallel lines (0.4 μm thick and 5 μm wide), with alternating lines terminating in shared contact pads. Cu was locally added to the same regions in all the lines, and the effects of temperature and electric fields on diffusion along the lines were characterized by analyzing the Cu concentration profile measured by electron-probe microanalysis. The activation energy for diffusion was found to be 0.8±0.2 eV in the temperature range 320–400 °C, which suggests that the path for diffusion of Cu is along the Al/AlOx/SiOy interface for these single crystals. The apparent effective valence (Z*) characterizing electromigration was measured to be −5.4±1.2 at 350 °C.

A Detailed Study of Void Motion In Passivated Aluminum Interconnects

AbstractVoid motion can be an important part of electromigration failure in interconnects. Investigating this process is difficult due to the large variation in behavior in identical samples tested under identical conditions. To deal with the large variability, we have tested 50 samples to failure at four different accelerated test conditions. Because our automated, in-situ technique images an entire test structure, the complete history of a test line is recorded. By testing many samples under direct observation, the complex motion of electromigration voids was comprehensively studied.

In Situ Stem Technique for Characterization of Nanoscale Interconnects During Electromigration Testing

AbstractA technique for observing microstructure and morphology changes during annealing or electromigration of 100 nm-scale and smaller interconnects is presented. The technique is based on dynamic in situ characterization using a UHV field-emission scanning transmission electron microscope (STEM) and can enable full microstructural characterization (images, diffraction patterns and compositions) during electromigration testing. Initial steps in the validation of the approach include in situ electron-beam OMCVD of Al-containing wires and observation of these wires. Although the deposition conditions were not optimized, Al-containing wires, with high edge acuity, thickness uniformity, and with minimum interconnect widths as small as 15 nm have successfully been deposited. In situ imaging of the annealing of 100 nm Al films on 25 nm Si3N4 substrates at 350°C demonstrates that an image resolution of 10 nm should readily be attainable in passivated nanoscale interconnects during electromigration.