Electromigration, or electrotransport, describes the phenomenon of atomic diffusion in metal driven by an electric current. Its study can be traced back more than a century, starting with the first observation reported by Geradin [Reference Gerardin1] in molten alloys of lead-tin and mercury-sodium. Systematic studies did not start until the early 1950s with the work of Seith and Wever at the University of Muenster, Germany [Reference Seith and Wever2]. By measuring the mass transport across the phase diagram of some Hume–Rothery alloys, they observed that the direction of mass transport can be reversed and is correlated with the type of the majority charge carriers, i.e., electrons or holes, in the specific alloy phase. This observation provided the first evidence concerning the nature of the driving force for electromigration. It showed that the atomic motion is not determined solely by the electrostatic force imposed by the applied electric field; instead, it depends on the direction of motion of the charge carriers. This prompted Seith to introduce the idea originated by Skaupy [Reference Skaupy3] of “electron wind” to account for the induced mass transport, an idea that laid the foundation for the basic understanding of electromigration. Seith and Wever [Reference Seith and Wever4] also introduced the method of using the displacement of an indentation on a metal wire to measure the induced mass transport. This “marker motion” technique, now called the vacancy flux method, has become one of the standard measurements of electromigration in bulk metals.
The concept of the “electron wind” driving force was first formulated by Fiks [Reference Fiks5] and Huntington and Grone [Reference Huntington and Grone6]. Working independently, these authors employed a semiclassical “ballistic” approach to treat the collision of the moving atom by the charge carriers. In a more rigorous treatment, Huntington and Grone considered the initial and final quantum states of the charge carriers involved in the collision process, where the “wind” force experienced by the moving atom is derived by integrating the spatial variation of the interaction with the charge carriers. These ideas yielded a driving force depending on the type of defect, the interaction with the charge carriers, and the atomic configuration of the jumping path.
The formulation of the driving force was a major contribution to the study of electromigration, as it demonstrated the possibility of using electromigration to probe the interaction of mobile defects with charge carriers in metals. This has stimulated considerable interest starting in the 1960s in theoretical and experimental studies on electromigration in metals. In theoretical studies, Bosvieux and Friedel [Reference Bosvieux and Friedel7] developed the first quantum mechanical formulation of the driving force in terms of electron–ion interactions for a simple case of impurity atoms in a “jellium.” With some simple model assumptions, these authors have formulated an approach that can be extended to metals with more complex electronic structures. This has stimulated a series of subsequent theoretical studies with focus on the physical basis of the driving force, particularly regarding the dynamic screening of the moving ion and the effect of the band structure on the electron–ion scattering. (See reviews by Verbruggen [Reference Verbruggen8] and Sorbello [Reference Sorbello9].) While the theory continued to develop, experimental data have accumulated to show systematic trends to collaborate the theoretical results. In the experimental studies, the interest was initially concentrated on self-electromigration in pure metals using primarily the vacancy flux method and with a few using radioactive isotopes. These studies were first focused on metals with electron charge carriers and then extended to metals with hole carriers (see the reviews by Huntington [Reference Huntington, Nowick and Burton10]). The experimental study was later extended to alloys and liquid metals by Rigney [Reference Rigney, Nowick and Burton11].
Until that time, the application of electromigration (EM) was rather limited, with efforts largely directed toward the purification of interstitial, particularly gaseous, impurities in refractory metals [Reference Peterson, Hummel and Huntington12]. The interest and the direction of electromigration study took a drastic turn in 1966 when Blech and Sello [Reference Blech and Sello13] reported that the crack formation in aluminum conductor lines on silicon chips was induced by electromigration. This was a serious reliability problem for the microelectronics industry, coming at a time when the microelectronics industry was starting the development of very-large-scale integration (VLSI) of integrated circuits [Reference Ho14]. This has generated significant interest to study electromigration, not only for its basic physics, but as an important reliability problem for the integrated circuits. Most of the studies were aimed at electromigration in thin film conductors used for multilevel on-chip interconnects with linewidths of submillimeters and operated at moderate temperatures of about half the absolute melting point. Under these conditions, the current density driving the mass transport increases by more than two orders of magnitude, while electromigration occurs primarily along structural defects, such as surfaces, interfaces, and grain boundaries. Particularly relevant to damage formation is the flux divergence site where damages in the form of voids or hillocks can form because of the local imbalance of atomic flux induced by material and microstructure inhomogeneity. Such characteristics of EM damage have shifted the focus of the investigations from bulk materials to thin films and conductor lines [Reference d’Heurle and Rosenberg15–Reference Ho, d’Heurle, Gangulee, Hummel and Huntington17].
Until the early 1990s, interest in EM was primarily focused on aluminum lines, the dominant material used for on-chip interconnects at that time. As the technology evolved, the Al on-chip interconnects became more complex with multiple metal levels integrated with SiO2 interlayered dielectrics. Following Moore’s law [Reference Moore18], device scaling continues to reduce the size of the conductor lines by a factor of ~0.7 every technology generation, with corresponding increase in its number to sustain the improvement of device density and chip performance. This cumulated to the development of Al/SiO2 interconnects with 5–6 metal levels and a minimum linewidth of ~0.4 µm for high-performance microprocessors of the 0.25 µm technology node. At this time, the study of electromigration has advanced well into the microscale domain with materials and microstructure characteristics distinctly different from bulk metals or thin films.
One distinct aspect of EM in conductor lines arises from the thermal stresses generated in the line due to the confinement by the Si substrate and the interlevel dielectrics and barriers to contain the metal line. The thermal stress provides an additional driving force to counter the electrical current for mass transport and can substantially affect the kinetics and mechanism for damage formation. The stress effect on EM was first observed by Blech in 1976 in a study of EM in Al conductor lines [Reference Blech and Kinsbron19] and established the concept of a critical current density-length (jLc) product with a “critical length” Lc where the stress gradient can completely counteract the current j driving force to stop EM [Reference Blech20, Reference Blech and Tai21]. The stress effect took a drastic turn in the 1980s to become an important reliability problem with the finding of stress-induced void formation in passivated Al lines that can cause line failure without EM [Reference Klema, Pyle and Domangue22, Reference Curry, Fitzgibbon, Guan, Muollo, Nelson and Thomas23]. This phenomenon has generated great interest at that time to investigate the thermal stress characteristics and the stress voiding phenomenon. It soon became clear that stress voiding is synergetic to electromigration, and together they form a framework for analyzing the kinetics of damage formation under EM. This has led to the formulation of the Korhonen equation [Reference Korhonen, Borgesen and Li24, Reference Korhonen, Black and Li25] and subsequently more general 3D analyses.
This can be considered the first major period of EM studies on conductor lines driven by technological needs to develop Al-based on-chip interconnects for large-scale integration. Significant interest has been generated from the industry and university laboratories with research topics focusing on effects of materials, microstructure, and line dimensions on mass transport and the development of reliable EM structures. These included the solute effect [Reference d’Heurle and Rosenberg15], the intermetallic layer effect [Reference Howard, White and Ho26], and the development of statistical studies [Reference Gall, Gall and Capasso27], among others.
Since then, the study of electromigration has been sustained by unprecedented advances of the IC miniaturization from the micro- to the nanoscale, with continuing improvement of the device density, chip performance, and manufacturing cost as predicted by Moore’s law. This has prompted the development of Cu interconnects to replace Al interconnects in 1997 [Reference Edelstein, Heidenreich and Goldblatt28]. and subsequently the implementation of low k dielectrics as interlevel dielectrics [Reference Lee, Leu and Ho29]. The development of Cu damascene structures brought new focus into the study of EM and thermal stresses in Cu interconnects. This began the second major period of electromigration studies where not only the basic material set has changed but also the interconnect structure with the development of the dual damascene process for Cu interconnects [Reference Rosenberg, Edelstein, Hu and Rodbell30]. While Cu has better intrinsic reliability than Al, electromigration continued to be a major reliability concern with distinct characteristics and damage mechanisms. The degradation of EM reliability for Cu damascene lines depends on materials and processing, particularly relating to defects induced by chemical-mechanical polishing (CMP) at the interface and the plasma processing of the weak low k dielectrics. Several important studies have been reported, including the analysis by Lane et al. showing that the activation energy for void growth under EM can be directly correlated to the bond energy of the Cu interface [Reference Lane, Liniger and Lloyd31]. Also important was the prediction by Hu et al. that the EM lifetime would degrade by half for every technology node due to dimensional scaling even with a constant current density [Reference Hu, Rosenberg and Lee32]. Results of these studies clearly showed that interfacial engineering is an effective approach for improving the EM reliability for Cu damascene interconnects. This has led to several approaches to improve EM reliability for Cu metallization, including metal cap layers [Reference Hu, Gignac and Rosenberg33] and solute alloying [Reference Hu, Ohm and Gignac34], among others.
With continued scaling, the dimensions of the Cu lines reach to the nanoscale, which significantly increases the number and complexity of the interconnects together with changes in the Cu microstructure and increases in the line resistivity. Responding to the technological needs, the EM studies of Cu damascene structures were extended to the nanoscale and the development of alternate metallization. These included the formulation of general 3D kinetic analyses [Reference Sukharev, Zschech and Nix35, Reference Gleixner and Nix36], the development of statistical tests at a massive scale [Reference Volinsky, Hauschildt and Vella37, Reference Oates38], the scaling effect on microstructure [Reference Ganesh, Darbal and Rajasekhara39, Reference Cao, Zhang, Ho, Justison and Hauschildt40], and electrical resistivity [Reference Croes, Adelmann and Wilson41, Reference Gall42].
This book aims to provide a comprehensive review of the current understanding of electromigration and interconnect reliability from fundamentals to nanointerconnects. It is organized into nine chapters and largely follows the chronological order of electromigration studies, starting from the basic studies in metals and extending to interconnects from the microscale to the nanoscale. First, the fundamentals of electromigration and the studies of bulk metals are reviewed in Chapter 2, including a formulation of electromigration based on irreversible thermodynamics, a kinetic analysis of the solute effect and a review of the theory and bulk materials studies. In Chapter 3, the discussion on EM in metal lines starts with thermal stresses induced by dielectric and substrate confinement with distinctive characteristics to interact with EM to control the mass transport and void formation. Here we describe the X-ray diffraction technique used to determine the triaxial stress state in Al and Cu lines and show how the structural confinement can give rise to substantial hydrostatic stresses to induce void formation leading to line failure. This is followed by Chapter 4 analyzing the kinetics of mass transport under EM and thermal stresses leading to the Korhonen equation and the Blech “short-length” effect. Here analytical solutions and simulations are presented in 1D to analyze the microstructure and stress effects on damage formation and early failures under EM.
Starting from Chapter 5, the discussion is focused on EM in Cu interconnects and topics related to the scaling effects at nanoscale, including microstructure evolution, electrical resistivity, massive-scale statistical tests, and power grid applications. The discussion proceeds first in Chapter 5 on EM characteristics and reliability studies of Cu conductor lines as scaling continues to the nanoscale for ultra large-scale integration (ULSI). The Cu interconnects fabricated by the dual damascene process have structural features leading to mass transport and failure mechanisms distinctly different from the Al interconnects. Several innovative approaches have been developed to improve EM reliability for Cu interconnects, including the use of cap layers and alloying effects, which will be discussed. In Chapter 6, we investigate the scaling effect on microstructure evolution and the implication on EM reliability of Cu and Co interconnects. The scaling effect on microstructure was measured using a high-resolution transmission electron microscopy (TEM)-based precession electron diffraction (PED) technique. With this technique, microstructure evolution was measured to 22 nm linewidth for Cu interconnects and to 26 nm linewidth for Co interconnects. Based on the PED results, Monte Carlo simulation was developed based on total energy minimization to project the scaling effect on grain growth and EM reliability for future technology nodes.
In Chapter 7, the analysis of EM and stress evolution is generalized from 1D to 3D damascene interconnects. This chapter starts with a general 3D analysis of stress evolution by treating the vacancies and displaced atoms generated under EM as local volumetric strains in the grain interior and at grain boundaries (GBs). Then a physics-based simulation is set up to analyze the microstructure effects on stress evolution and void formation, considering the variations of the GB diffusivities and elastic properties of individual grains in the interconnect. Results from the simulation are combined with scanning and transmission electron microscopies to study void nucleation, migration, growth, and shape evolution, leading to interconnect degradation.
With continued scaling to the nanoscale, the statistical nature of damage formation becomes important to assess EM reliability, which is dominated by the early failures of the weakest links. This topic is discussed in Chapter 8, presenting a novel approach based on the Wheatstone Bridge technique to perform statistical EM tests at a massive scale to detect early failures in very large systems. In contrast, we show in Chapter 9 that recent measurements showed that the weak link approach cannot accurately predict the lifetime for power grid–like structures. A novel approach is presented for power grid EM assessment using a physics-based approach combined with a mesh model to account for redundancy while still fast enough to be practically useful. Existing physical models for EM in metal branches are extended to track EM degradation in multibranch interconnect trees across the die. These problems are important for future development of reliable Cu interconnects as scaling continues to expand the wiring structure to the material limit at the nanoscale.
