Electromigration-induced Resistance Research Articles

Atomic drift-less electromigration model for submicron copper interconnects

Electromigration in chip level interconnect is commonly described by atomic drift due to electron-wind force that arises from electron-ion momentum transfer. As an alternative to this model, in early 1980’s, Sah proposed a two dimensional analytical ‘void-surface bond-breaking’ model by dropping the atomic drift term that resulted from electron-wind force (in his book ‘Fundamentals of Solid-State Electronics’) and the rate of change of area of void is computed. Due to the continuous down scaling and evolution of interconnect patterning technologies, the void growth process in modern interconnect becomes more complex and electromigration failures are found to be catastrophic in nature instead of gradual type failures observed in early days. In this work, Sah’s model is revisited from the perspective of its applicability to modern submicron copper interconnects. The electromigration-induced resistance change behavior is analytically derived considering a three-dimensional atomic drift-less model. A good correlation between the findings of our model with experimental observations is presented. Keywords: Analytical model, Copper, Drift-less, Electromigration, Resistance change, Time to failure

Electromigration-induced resistance switching in indented Al microstrips

Non-volatile resistive memory cells are promising candidates to tremendously impact the further development of Boolean and neuromorphic computing. In particular, nanoscale memory-bit cells based on electromigration (EM)-induced resistive switching in monolithic metallic structures have been identified as an appealing and competitive alternative to achieve ultrahigh density while keeping straightforward manufacturing processes. In this work, we investigate the EM-induced resistance switching in indented Al microstrips. In order to guarantee a large switching endurance, we limited the on-to-off ratio to a minimum readable value. Two switching protocols were tested, (i) a variable current pulse amplitude adjusted to ensure a precise change of resistance, and (ii) a fixed current pulse amplitude. Both approaches exhibit an initial training period where the mean value of the device’s resistance drifts in time, followed by a more stable behavior. Electron microscopy imaging of the devices show irreversible changes of the material properties from the early stages of the switching process. High and low resistance states show retention times of days and endurances of ∼103 switching cycles.

Experimenting and modeling of catastrophic failure in electromigration-induced resistance degradation for deep submicron dual-damascene copper interconnects

The features of electromigration-induced resistance change profile are important aspects of reliability, especially for ULSI interconnect. By experimenting on 0.28 µm wide Cu dual-damascene interconnects, clear evidence of catastrophic failure is observed even when the failure criterion of only 2% resistance change is imposed. Applying theoretical constitutive law of degradation and using basic principles of generic model, constitutive equation for resistance degradation in electromigration is derived and simulated for catastrophic failure. Then real-time resistance change profile is obtained by a simple analytical model which incorporates the Nernst-Einstein relation of mass transport. The convergence of the analytical model to the generic one is also shown. The various aspects of catastrophic failure are discussed. A good correlation between the results obtained from the model and experiment are shown.

Direct observation of void morphology in step-like electromigration resistance behavior and its correlation with critical current density

Electromigration-induced resistance behavior of via-terminated metal lines was studied. We found a strong correlation between void morphology and step-like resistance behavior. For the lines which exhibit pronounced resistance steps, voids are formed at the top or bottom Al/TiN interface. For the lines which exhibit gradual resistance increases, only complete void formation severing the whole line occurs. The step-like resistance behavior is more pronounced when the current density is close to the critical current density. Possible mechanisms for the resistance steps are discussed.

A three-dimensional nonlinear analysis of electromigration-induced resistance change and Joule heating in microelectronic interconnects

This paper reports a three-dimensional nonlinear numerical model developed for the deep submicron interconnects that carry high current densities in integrated circuits. This model can solve a thermoelectrically coupled field to analyze resistance variation and Joule heating as a function of electromigration-induced voiding in various interconnect structures. As a result, the model can identify the critical void volume that is directly related to the time to electromigration failure. The model is particularly useful as an analytical tool that can quantitatively evaluate the effects of the architecture and physical properties of various refractory films and diffusion barriers on the electromigration reliability.

Stochastic simulation of electromigration failure of flip chip solder bumps

Stochastic simulations are performed for the first time to explore the nature of electromigration failure of SnPb flip chip solder bumps at room temperature. Treating the SnPb flip chip solder bump as a random resistor network and electromigration as a diffusion-controlled depletion–accumulation process, the main features of limited experimental observations are well reproduced. The microstructure and current density dependence of the time to failure, the median time to failure and the dynamics of void/hillock growth, as well as the electromigration-induced resistance fluctuations are obtained to provide a comprehensive interpretation of electromigration process and failure in terms of physical parameters in SnPb solder bumps. The approach introduced in the present work can be used for elucidating the most important factors in controlling the electromigration and its rate of flip chip solder bumps, and thus contribute to their optimal design.

Electromigration saturation in a simple interconnect tree

Electromigration-saturation experiments have been carried out on passivated “L”-shaped interconnects which had three contacts through W-filled vias at the ends and at the corners of the L’s. Currents of different magnitudes and directions were independently applied in the two limbs of the L’s. Variations in the steady-state electrical resistances were observed, and attributed to a variation in the location of the voids along the lines. Variations in the rate of approach to the steady state were also observed, and are attributed to variations in void shapes. The effects of electromigration in L-shaped interconnects were simulated using an electromigration simulator based on the one-dimensional Korhonen et al. [J. Appl. Phys. 73, 3790 (1993)] model for electromigration, modified to include the effects of junctions. It is shown that, using a single set of input parameters and information about void shapes, the simulation can be used to make accurate worst-case predictions of the evolving and the steady state values of electromigration-induced resistance changes in these simple L-shaped interconnect trees.

Determination of the Effects of Strain on Electrical Resistivity in Patterned Interconnects

AbstractSensitive measurements of electromigration-induced resistance changes in metallization interconnects have been previously interpreted as due to precipitation effects, vacancy concentration changes and local stress changes (due to the piezoresistance effect). The latter have the potential for characterizing the early stages of electromigration-induced diffusive phenomena prior to larger scale effects such as voiding and subsequent localized joule heating which seriously complicate the interpretation of small resistance changes. However the utility of such “early" measurements is also hindered by lack of an accurate knowledge of the stress coefficient of resistivity as a proper characterization of the change in strain state of the Al. We present measurements of the effects of volumetric strain on the resistivity of Al interconnects where the strain is induced by thermal expansion mismatch between the Al and surrounding passivations. The piezoresistance effect is characterized by properly accounting for the degree of interconnect constraint (and volumetric strain) induced by thermal expansion mismatch as a function of temperature for both passivated and unpassivated lines. Sensitive interconnect resistance versus temperature measurements for differently constrained interconnects (with different volumetric strains) thus allows for the measurement of the piezoresistance effect. Other effects such as solute or vacancy concentration changes with temperature are minimized since the measurements are performed by cooling the passivated and unpassivated lines from room temperature to approximately 70K, rather than by significant heating above room temperature. We determine the piezoresistance coefficient, defined as dρ/dɛv, where ρ = resistivity and ɛv = volumetric strain, to be approximately 1.5−5 Ω-cm, in rough agreement with previous work. The interpretation of sensitive resistance measurements as volumetric strains in isolated sections of interconnects undergoing electromigration-induced diffusion processes is described for specialized test structures.

A new technique to characterize the early stages of electromigration-induced resistance changes at low current densities

One of the promising tools to study electromigration (EM) in metal lines is the high resolution resistance measuring (HRRM) technique. Since the resistance is sensitive both to structural and geometrical changes in a metal line, this technique is very useful to study the early stages of EM-induced damage. However, with a conventional HRRM-technique it is impossible to separate resistivity from geometrical variations. Here, a new analyzing technique is presented which is able to separate these two contributions during EM-experiments at low current densities. It is found that only during the very first stage of EM resistance variations are due to resistivity variations. On the contrary, resistance variations ΔRR>2000ppm are mainly caused by a decrease in the cross section of the metal line.

Line Length Dependence of Small, Electromigration Induced Resistance Changes in Aluminum

AbstractTwo series of experiments were carried out to investigate the line length dependence of changes in the electrical resistance caused by passing a DC current through thin film Al conductors. First, the effect of adding side branches with a spacing of 5 μ m to 150 μ m long lines was studied. Experiments performed at T = 148 °C and at a DC current density of 0.5 MA/cm2 showed three effects due to adding the side branches: i) the magnitude of the resistance changes is reduced, ii) the resistance changes saturate on a time scale of one hour, and iii) the resistance changes fully recover after switching off the current. In the second series of experiments the current, temperature and line length dependence of resistance changes induced in short (3-100 μ m) lines between bonding pads were studied. For current densities smaller than a certain length dependent critical value the resistance saturates after applying the current and relaxes back to the original value after removing the current. The time to relax back, which is comparable to the time to reach saturation, is proportional to the sample length squared. This and the activation energy derived from the temperature dependence of the relaxation process suggest strongly that the observed time dependence of the resistance changes is determined by grain boundary diffusion (electromigration) along the whole length of the line.

Critical Review of 1-Particle Models in Electromigration Resistance Change Modeling

ABSTRACTAn investigation is made into the capability of one-particle models in modeling electromigration-induced resistance changes. Analytically obtained solutions to the model equations are used to gain more insight into the vacancy distribution as a result of the applied boundary conditions. These solutions are then used to determine the resistance change modeling capabilities of three types of one-particle models.

The 1/f2 Noise Spectrum Derived from Electromigration–Induced Resistance Change

A model based on the electromigration-induced resistance change was used to analyze the noise characteristics of aluminum thin-film resistors, and the 1/f2 noise power spectrum was derived theoretically from the rate equation of the resistance change. Experiments were performed on samples stressed with a current density of 1 × 106 A/cm2 at 125°C for 50 hours. The measured noise indeed showed 1/f2 noise and the results were analyzed quantitatively with the derived model.

Study of electromigration-induced resistance and resistance decay in Al thin-film conductors

Using an ac Bridge technique, the resistance of thin-film (500 nm thick) Al and AlCu(5%) conductor stripes was monitored during high direct current density (1×106 A cm−2) stressing. The resistance was found to increase approximately linearly with time during stressing with a rate that was thermally activated. Surprisingly the activation energy varied considerably between nominally identical samples. After 3 h of stressing, the current was turned off and an exponential decay in the resistance was observed with a time constant of several hours. The decay was also thermally activated with an energy that varied from film to film. Both results suggest that the activation energy for resistance change during electrical stress can be significantly different in nominally identical films.