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Electromigration (EM) has become one major reliability concern in modern integrated circuit (IC) packages. EM is caused by large currents flowing in metals and the resulting mean time to failure (MTTF) is highly dependent on the maximum current value. We here propose a scheme for fast and accurate prediction of the maximum current on the ball grid arrays (BGAs) in a package given the pin current information of the die. The proposed scheme uses neural networks to learn the resistance network of the package and achieve the non-linear current mapping. The fast prediction tool can be used for analysis and design exploration of the pin assignment on the die level.

With the rapid development of electronic devices. There are more and more high performance, multi-functional electronic components, at the same time, their size is getting smaller and smaller. This demand has a greatly promoted the development of electronic packaging. Due to the precision of electronic devices, leading to a sharp increase in the current density through the lead wire, can reach the order of magnitude of 104A/cm2[1], which is easy to cause electromigration failure. In this paper, the problem of electromigration is studied, and the coupling model of multi physical field is put forward, which is based on the combination of electron wind force, temperature gradient, stress gradient and atomic concentration. Firstly, according to the basic EM theory[2], the driving mechanisms of EM are summarized. Secondly, the driving mechanism, such as electronic wind force, temperature gradient, stress gradient and atomic concentration gradient should be overall consideration. In this paper, COMSOL is used to simulate the electromigration of sweat mechanism.

Simulation flow for the die-scale assessment of interconnect stress-migration (SM) and electromigration (EM) with an accounted variation of residual stress was developed. Two complimentary methodologies based on finite-element sub-modeling and compact modeling were proposed. A novel EM and SM model which takes into account a vacancy exchange between grain boundaries and grain interior has demonstrated a capability of predicting times for void nucleation at different test conditions while avoiding unreliable assumptions used in the Black’s equation-based assessment.

As temperature increases, it is suggested that atoms on lattice sites serve as dynamic defects and cause a much more homogeneous distribution of the Maxwell stress throughout the crystal lattice compared with that caused by static defects. Though this stressing effect mostly leads to Joule heating, it also results in distortion of the crystal lattice, which leads to a decrease in the activation energy for atomic diffusion and causes enhancements in the phase growth rates at both interfaces of diffusion couples. Due to this stressing effect, the decrease in the activation energy is proportional to a square term of the current density J. A mean-time-to-failure analysis is performed for failure caused by excessive growth of intermediate phases, and a mean-time-to-failure (MTTF) equation is found. This equation appears similar to Black’s equation but with an extra exponential term arising from the stressing effect of the crystal lattice.

A theoretical model is proposed to investigate the electromigration (EM) behavior in giant magnetoresistance spin valve (GMR SV) read sensors under pulsed direct current (dc) magnetic field during sensor operation. It was found that the externally applied magnetic field gives rise to a more severe Joule heating and consequently raises the device temperature leading to EM acceleration. Black's equation was modified based on Green's function method and the Boltzmann equation to more precisely interpret the EM mean time to failure (MTTF) of GMR SV read sensors under pulsed dc magnetic field. The physical validity of this proposed model was confirmed by the comparisons with experimental results.

Electromigration failure is a major reliability concern for integrated circuits. The continuous shrinking of metal line dimensions together with the interconnect structure arranged in many levels of wiring with thousands of interlevel connections, such as vias, make the metallization structure more susceptible to failure. Mathematical modeling of electromigration has become an important tool for understanding the electromigration failure mechanisms. Therefore, in this work we review several electromigration models which have been proposed over the years. Starting from the early derivation of Black's equation, we present the development of the models in a somewhat chronological order, until the recent develop- ments for fully three-dimensional simulation models. We focus on the most well known, continuum physically based models which have been suitable for comprehensive TCAD analysis.

A non-equilibrium statistical theory for aging dissipative systems formed by atoms is developed and applied to electromigration damage in conductors. A modification of Black’s mean failure time is presented. We describe the experimental relationship between the initial rate of increase in the functional damage and the electric conductor lifetime. Also, for situations where electromigration damage is mainly due to heat dissipation caused by conduction inside the conductor, it was possible to obtain a mean-field theory which yields expressions (that agree with the experimental data) for the increase of resistance with the current stressing time, in test probes of different materials, and for the total volume of hillocks as a function of the current stressing time.

Recently, the size of solder bump interconnects have been significantly reduced with the advent of high-density packaging, and thus the evaluation of electromigration in solder bumps has become necessary. The present paper proposes a simple method to test the electromigration resistance of Pb-free solders. One of the key points of the present method is the fabrication of a simple solder sample that can produce sufficient current density to cause electromigration. Moreover, the actual local temperature of a small area subjected to electromigration in the sample was measured by a direct method. A right-angled diamond-shaped hole was introduced in a thin film of solder using a focused-ion-beam system. A direct current was supplied to the film far from the hole, perpendicular to the diagonal of the hole. In this way, the current density was concentrated near to the corner of the hole, and the value of this was obtained through a theoretical analysis. It was noted that the steady temperature in the film along a line extending from the diagonal, remained constant, although the current density decreased gradually far from the corner. Therefore, the temperature at a position near the corner, where electromigration takes place, can easily be found by measuring the temperature far from the corner. The temperature was measured directly under current flow conditions by utilizing the chemical reagents with known melting points. Finally, by measuring the ratio of hillock volume to the time for the current supply as a measure of the atomic flux divergence due to electromigration, the corresponding resistances of some Pb-free solders to electromigration were evaluated.

The electromigration of Cu interconnection was investigated to solve the Huntigton's equation by numerical analysis. The Cu atoms moved toward anode from cathode and accumulated at the anode end. This result was in good agreement with the result previously derived by our theoretical analysis. The accumulation rate of Cu atoms increased with increasing in current density, but it was not so influenced by temperature. The characteristic of the rate of electromigration showed a liner relationship with current density and exponential relationship with temperature. This result agreed with the equation experimentally derived by Black. This result proved that numerical analysis of atom transport equation enables to predict of electromigration failure time.

Electromigration reliability of solder interconnects is dominated by current density and temperature inside the interconnects. For flip-chip packages, current densities around the regions where the traces connect a solder bump increase significantly due to the differences in feature sizes and electric resistivities between the solder bump and its adjacent traces. This current-crowding effect along with induced Joule heating accelerates electromigration failures. In this paper, the effects of current crowding and Joule heating in a flip-chip package are examined and quantified by three-dimensional electrothermal coupling analysis. We apply a volumetric averaging technique to cope with the current-crowding singularity. The volumetrically averaged current density and the maximum temperature in a solder bump are integrated into Black’s equation to calibrate the experimental electromigration fatigue lives.

Electromigration is a major road block in the pursuit of further miniaturized electronics. In the next generation micro and sub micro electronics current density is expected to exceed 10 7 A/cm 2 . In this paper an electromigration induced strain-current density model is proposed and implemented in finite element procedure for solution of boundary/initial value electromigration problems. Numerical simulations are compared with experimental data. Comparisons validate the model.

Electromigration (EM) is projected to be the major reliability issue for current and future VLSI technologies. However, existing EM models and assessment techniques are mainly based on the constant current density and temperature. Such models will not work well at the system level as the current density (power) and temperature are changing with time due to different tasks (their loans) applied at run time. Existing EM approaches using average current density or temperature, however, will lead to significant errors as shown in this work. In this paper, we propose a new physics-based EM model considering time-varying temperature and current density, which reflects a more practical chip working conditions especially for multi-core and emerging 3D ICs. We study the impacts of the time-varying current densities and temperature profiles on EM-induced lifetime of a wire for both nucleation phase and growth phase. We propose a fast stress calculation method for given time-varying temperature and current densities for the nucleation phase. We further develop new formulae to compute the resistance changes in growth phase due to changing temperature and current densities. Experimental results show that the proposed method shows an excellent agreement with the detailed numerical analysis but with much improved efficiency.

We perform the first systematic study of the nonlinear electromagnetic currents induced by external electromagnetic field in quark-gluon plasma, both in the two cases that the inhomogeneity of electromagnetic field is small (large) so that the collision effect is important (negligible). In the former case, we list and classify possible components of the currents in a systematic way, and make an order estimate of each component by using the Boltzmann equation in the relaxation time approximation. In the latter case, we explicitly calculate the quadratic current by using the Vlasov equation, and find that the current generated by the chiral magnetic effect and the quadratic current can have the same order of magnitude by using the Kadanoff-Baym equation. We also demonstrate this property by using a possible configuration of electromagnetic field realized in heavy ion collision., 12 pages, 4 figures

Void growth and coalescence usually cause reliability concerns to solder joints in integrated circuits. In this paper, a diffuse interface model is developed to simulate the coalescence of micro-voids under the influence of elastic stresses and electromigration. A variable c stands for the composition of vacancies, with c=1.0 indicating the void phase and c=1.0×104 indicating the bulk phase. A double well potential is used to describe the chemical free energy density of the thermodynamic system. In this model, a modified Cahn-Hilliard type equation was solved with a nonlinear multi-grid method to determine the composition field c; the Cauchy-Navier equations for the elastic displacements u and v were solved with a linear multi-grid method to determine the elastic energy density; a steady state equation of electric potential was solved to determine the effective driving force for electromigration. Simulation results show that the applied stresses have significant effects on the coalescence of micro-voids. For the given initial configuration, the tensile stresses accelerate the coalescence of micro-voids; on contrast, the shear and the combined stresses interrupt the coalescence of micro-voids and steady states are eventually achieved under the influence of these stresses. Under the influence of tensile stresses, a simulated “failure” which leads to an opening is also shown.

The long-standing speculation regarding an additional temperature dependence in Black’s equation is addressed. Under the premise that the activation energy measured using Black’s equation, Ea, should be equal to the energy barrier for atomic hopping, we provide evidence for an additional T2 dependence of the failure time. Microscopic modeling provides an explicit connection between the macroscopic model behavior and the microscopic parameters of the model. These results may provide a reliable method for measuring activation energies for self-diffusion in pure metals.

A phase field model is developed for numerically studying the time evolution of insulating voids in a current-carrying single crystal metal thin film. In our model, we include the effects of surface electromigration, surface self-diffusion and current crowding in the fully nonlinear regime. A continuously varying scalar order parameter is used to describe the metal and void “phases” within the wire in this phase field formulation. The time evolution of the metal–void interface is given by two partial differential equations: one embodying the conserved dynamics of the order parameter and the other a modified Laplace’s equation for the electrical potential. We also carry out detailed asymptotic analysis to verify that our phase field formulation faithfully represents the surface electromigration problem.

In this paper, we have studied electromigration (EM) behavior under different current densities experimentally and theoretically. Our experimental results have shown that the dependence of median-time-to-failure on current density is not the same in different regimes of current densities. Both the theoretical analysis and observation of SEM showed that mechanisms causing EM failure in different regimes are different. In the low current density regime EM failure is caused by microstructural changes, while in the high current density regime it is microstructural changes caused by a temperature gradient. We have developed a model to describe the dependence. The calculated results are consistent with experiments.

Intermediate phase growth with electromigration present is important to the performance of solder joints in integrated circuits. Rather than treating the total effective charge number Zt of electromigration as constant, in this paper Zt is treated as a field-dependent function whose contributions arising from both the crystal impurities and imperfections within the bulk and the compositional and phase-field variations across the interface. A diffuse interface model is used to investigate the interfacial migration and phase growth behavior in a binary diffusion couple with a diffusion-controlled mechanism for interfacial reactions. Simulation results show that, compared with the interfacial contribution to Zt, the difference in the bulk contributions to Zt across an interface, which separates two phases at equilibriums, is dominant to the migration rate of this interface; while during the growth of an intermediate phase, the value of Zt within the bulk of the intermediate phase is dominant to the growth rate of this phase, because a larger Zt leads to a larger effective driving force for electromigration and thus a faster migration rate of atoms across the intermediate phase. In both cases when the interfacial reactions are diffusion controlled, the influence from the interfacial contribution to Zt was shown to be almost negligible, because a large increase of Zt within the interfaces will not affect the overall migration rate of atoms significantly.

A simple one-dimensional thermal model of the electromigration phenomenon shows that the usual measurement methods of the temperature during lifetime tests usually lead to an erroneous determination of Black's relation parameters n and Q. The effects of the current density and the temperature estimation method on the errors on n and Q are analysed. An estimation of the temperature of the site where the flux divergence is maximum allows us to understand the behaviour of n and Q. The difference between real and apparent activation energy, at low current densities, is also calculated.

Electromigration (EM) is an important failure mechanism in Ultra-Large-Scale Integration (ULSI) interconnections. The Black's equation is a simple empirical EM model, which is widely accepted in the industry as the most common method to extrapolate the median time to failure (MTF) from the accelerated test condition to the normal operating condition. Although the empirical model of the Black's equation is simple in implementation, its validity has been a great controversy in the literature and will be described later. In this work, we revisit the Black's equation for its success in the industry and its validity. In the presence of the additional driving forces and other important Electromigration physics which are not considered in the Black's equation for today ULSI interconnects, the application of the Black's equation for today's ULSI interconnects become inaccurate as shown experimentally. An alternative model based on the physics-based Electromigration simulation and Eyring model in extrapolation is proposed in this work.

The electromigration threshold in copper interconnects is reported in this study. The length-dependent electromigration degradation rate is observed and quantified in the temperature range of 295–400 °C. Based on the Blech electromigration model [I. A. Blech, J. Appl. Phys. 47, 1203 (1976)], a simplified equation is proposed to analyze the experimental data from various combinations of current density and interconnect length, as well as to estimate the electromigration threshold product of current density and line length, (jL)th, at a certain temperature. The resulting (jL)th value appears to be temperature dependent, decreasing with increasing temperature in the tested range between 295 and 400 °C.

Steps on macroscopic surfaces provide a useful model system for quantifying electron scattering at defects in nanostructures, where the large surface/volume ratio will cause surface effects to dominate. Here, the effects of electron scattering at surface steps are quantified using thin silver films with (111) surface orientation. Using real-time scanning tunneling microscopy (STM) measurements while large current densities are applied to the films, changes in step fluctuations and island motion are observed and quantified. Applying the tools of the continuum step model, the observations are analyzed in terms of step free energies and kinetics, yielding quantitative values of the electromigration force driving the observed mass displacements. The derived magnitudes are surprisingly large in comparison with classical calculations of the force due to electron scattering at the internal surface of a conductor. This result indicates that the specific atomistic characteristics of the scattering sites, in this case kinks at the step edge, may greatly enhance the electromigration force. Within the classical ballistic picture of ballistic momentum transfer, specific mechanisms for such enhancement include enhanced geometric “blocking” at the kinked step edges, changes in carrier density near kinks, and current crowding. Quantum transmission effects at atomic-scale defect sites may also be responsible for the observed enhancement. The nature of classical current crowding as a function of the shape and size of defect was characterized using magnetic force microscopy (MFM) of fabricated micron-scale model structures. Techniques were developed to remove the effects of instrumental broadening using deconvolution, so that full three-dimensional maps of the magnetic fields above the current line are determined. A Green function inversion technique is then used to invert the field distribution to determine the spatial variations in the current density in the sample. Current enhancement is highly localized near defects and is maximized by sharp variations in geometry that require strong deflections of the current path. Current enhancements up to a factor of 4 are found at the most strongly deflecting defects, while small notches of various shapes typically cause local enhancements of tens of percent to a factor of 2. The perpendicular component of the current flow around defects forms a dipole pattern with length scale determined by the length of the defect along the direction of the current flow. The shape and localization of the dipole pattern vary with the sharpness and symmetry of the defect. The current crowding affect alone is not sufficient to explain the greatly enhanced electromigration force observed for scattering at kink sites at steps.

As the electronics industry continues to push for high performance and miniaturization, the demand for higher current densities, which may cause electromigration failures in an IC, interconnects. Electromigration is a phenomenon that metallic atoms constructing the line are transported by electron wind. The damage induced by electromigration appears as the formation of voids and hillocks. A numerical simulation method for electromigration void incubation, and afterwards, void propagation, based on commercial software ANSYS Multiphysics and FORTRAN code, is presented in this paper. The electronic migration formulation considering the effects of the electron wind force, stress gradients, temperature gradients, and the atomic concentration gradient has been developed for the electromigration failure mechanisms. Due to introducing the atomic concentration gradient driving force in atomic flux formulations, the conventional atomic flux divergence method is no longer valid in electromigration (EM) simulation. Therefore, the corresponding EM atomic concentration redistribution algorithm is proposed using FORTRAN code. Finally, the comparison of voids generation through the numerical example of a standard wafer electromigration accelerated test (SWEAT) structure with the measurement result is discussed.

Electromigration of a single atom along a chain of gold atoms was investigated by first-principles calculations based on the nonequilibrium Green's-function technique combined with density-functional theory. In the case of electromigration of a gold atom, we found that the potential barrier along the migration pathway decreases as the applied bias voltage is increased and the migration direction is the same as that of electron flow. By considering the case of electromigration of a sulfur atom along the gold chain, we determined that the electron flow around the migrating atom is responsible for single-atom electromigration. The calculated electromigration rate for the gold atom indicated that the electromigration takes place at temperatures above room temperature.

It is theoretically shown that electromigration can lead to the formation of high electrodiffusional mechanical stresses in a thin-film conductor and a stress gradient along it. The integrodifferential equation with partial derivative determined at one point is obtained and solved. The equation describes the process of mechanical stress gradient build-up (relaxation). It is shown that this equation can be reduced to the equation of diffusion by proper choice of the boundary conditions, the relaxation time constant te is independent of the electric current density and determined by the mechanical and diffusional properties of the conductor material, its structural and geometric parameters, and temperature. For pulsating current, the mass flow increases with decreasing pulse duration and reaches a maximum when the pulse duration becomes less that the critical value τmax = (10−3 to 10−2)te. The projections'growth on a conductor during electromigration is caused by relaxation of electrodiffusional stress exceeding the yield limit of thin films. [Russian Text Ignored].

The characterization and monitoring of electromigration performance is usually performed using wafer level or package level tests. These two types of test involve very different temperature gradient and current density conditions. These differences of stress condition may affect the determination of electromigration parameters, namely the activation energy, Ea, and the current exponent, n, as described in the empirical Black's law: MTF = A.j/sup -n/exp(Ea/kT). The apparent evolution of n and Ea is critical because it complicates the calculation of extrapolated lifetime. To elucidate this apparent inconsistency, we built a numerical model of the flux of matter in a copper line to simulate lifetime and acceleration factor corresponding to wafer and package level electromigration tests. Our numerical model is able to simulate TTF corresponding to electromigration tests on a wide range of current density (two orders of magnitude). The analysis of simulated TTF predicts that the error in Black's law parameters Ea and n may occur both from wafer level (high current density and Joule heating) and package level (low current density). As a consequence, we recommend taking into consideration temperature gradients as well as the Blech effect to extrapolate lifetime correctly.

The electromigration of a flip chip solder bump (eutectic SnPb) has been studied at temperatures of 100, 125 and 140/spl deg/C and current densities of 1.9 to 2.75/spl times/10/sup 4/ A/cm/sup 2/. The under-bump-metallization on the chip side is thin film Al/Ni(V)/Cu and on the board side the bond-pad is thick electroless Ni coated with 30 nm of Au. When stressed at the higher current density, the mean-time-to-failure (MTTF) was found to decrease much faster than was expected from the published Black's equation. The sequence of void propagation is observed at the cathode side. This is due to the current crowding at the contact between the solder bump and the thin UBM. This is confirmed by simulation of current distribution in the solder bump. The Cu-Sn intermetallic compounds formed during reflow are known to adhere well to the thin film UBM, but they were dissolved to the solder bump after current stressing. Therefore, the UBM itself, besides the solder bump, could be part of the reliability problem of the flip chip solder joint under electromigration.

The equation for resistance R(T) at temperature T can be expressed in the form R(T)=(dR/dT).(T-T/sub EO/. When dR/dT is constant over the range of your experiment, T/sub EO/ is then a constant, the temperature at which R(T) extrapolates to zero. If we wish to express the corresponding relationship with /spl beta/(T/sub r/), the temperature coefficient of resistivity (TCR) at temperature T/sub r/, /spl beta/(T/sub r/) is defined in the form /spl beta/(T/sub r/)=(dR/dT/sub r/).(1/R(T/sub r/))=1/(T/sub r/-T/sub EO/). For both these equations it is desirable to use the Kelvin scale for T, especially when activation energy terms occur in the test under consideration. Our experimental measurements of temperature calibration have yielded T/sub EO/ values less than 40 degrees Kelvin, and with sufficient accuracy such that materials properties can be usefully determined provided that the test temperature is not too high. When /spl beta/(T/sub r/) is specified by an independent source, it is necessary that T/sub r/ be included in both theoretical and experimental cases.

Electromigration failure data for integrated circuit metallizations may only be collected in experimentally convenient intervals by the use of highly accelerated conditions of temperature and current density. Large extrapolations are required to apply these data to circuit operating conditions. A common assumption made with these extrapolations is that the dispersion of the log‐normal failure distribution, σ, does not vary with temperature. In this letter we investigate the temperature dependence of the dispersion of failure times due to electromigration of the Al allow layer in contacts to silicon. We show that the dispersion is temperature dependent for these structures and exhibits increasing values with decreasing temperature. The magnitude of the dispersion is consistent with that calculated on the basis of a dominant contribution from fluctuations in the temperature between test structures. It is implied that the intrinsic, temperature‐ independent contribution to the dispersion is small for contact...

A 16.6 cm/sup 2/ monolithic large area integrated multiprocessor system comprising 9 identical programmable video signal processing elements was reconfigured by excimer laser formed connections and discontinuities of conductor lines in a redundant bus system. The yield enhancement of functional processors amounts to 13.3%. On two prototypes, the laser reconfiguration of the bus system led to 4 functional processors per chip at 66 MHz, providing a peak arithmetic performance of 4 GOPS per multiprocessor system. The power supply to defective processors with a high stand-by power consumption was terminated by laser, leading to a halving of power consumption. Furthermore, for the improvement of the laser process, vertical links between two metallization levels were formed on two chips with different standard CMOS layer sequences on special test structures. For the yield statistics of the formed vertical links, a contact resistance R/sub K/>3 /spl Omega/ was treated as a failure. With the laser processing of vertical links with an area of 14/spl times/14 /spl mu/m/sup 2/, a yield of 100% has been achieved. Beyond those, conventional accelerated life time tests were performed to examine the reliability of laser formed vertical links. An extrapolation of Black's equation to operating conditions (100/spl deg/C, 2.5 mA) resulted in a failure rate of 0.1% in 39 years.

Contact chains containing 30 to 37 links, alternated by probe pads, were investigated. Test structures were fabricated with two different layer sequences. Laser antifuses are simple expanded interconnections. Current densities, scaled by first level interconnections (3 mu m/sup 2/, resp. 3.6 mu m/sup 2/), were varied from 0.66*10/sup 6/ A/cm/sup 2/ to 1*10/sup 6/ A/cm/sup 2/, and substrate temperatures from 180 degrees C to 270 degrees C. The test procedure results in multiple censored data, which can be treated by application of hazard plots. Best results were obtained from 14*14 mu m/sup 2/ expansions of sequence 1, connected by two Nd:YAG pulses. A conservative extrapolation of Black's equation to 80 degrees C/1 mA with E/sub A/=0.4 eV, T=T/sub SUB/, and n=-2 showed, that only for two sets of test parameters, a 10 FIT/layer was slightly below 10 years. >

A model for the mechanism of AC electromigration based on the thermal response of Al stripes is proposed. The model is based on the temperature difference between the positive period and the negative period. The thermal time constant of the Al stripe, underlying SiO/sub 2/, and Si substrate is on the order of microseconds and that of the package and ambient is a few seconds. When the cycle time of the current is longer than thermal time constant, the temperature of the Al stripes obeys the current waveform. When the cycle time is shorter than the thermal time constant, the temperature keeps constant. Mean time to failure (MTF) depends on the temperature according to Arrhenius's equation. The temperature difference between positive and negative periods causes an unbalance of atomic flux between the periods. Thus, open-circuit failure can take place under AC conditions. >

Although current density exponents and activation energies are well-known for the elemental processes (like void nucleation due to electromigration generated stress) there is no consensus on which apparent activation energy or current density exponent values should be used in reliability estimates for realistic line structures comprising regimes of both bamboo and polycrystalline sections. In this contribution a Monte-Carlo approach was used to generate realistic-like line structures, and their electromigration lifetimes were simulated. For a given grain structure distribution, the stress evolution along the line was simulated, letting voids nucleate and grow until the largest one reached the specified critical size, resulting in a "failure". By repeating this process for various current densities and temperatures, it was possible to extract the apparent activation energies and current density exponents from the simulation data.

We present data from three wafer level electromigration test techniques, isothermal (ISOT), constant current (CI), and standard wafer level electromigration accelerated test (SWEAT) and compare various aspects of the data. ISOT keeps the test line at a constant temperature. CI applies a constant current of the same magnitude to all lines, without making any adjustments for individual geometric differences. SWEAT holds the time to failure constant by using Black's equation to determine the applied current needed to bring about the chosen failure time. Six different line widths ranging from 0.15 to 4.29 /spl mu/m of AlCu metal were stressed by all three methods, at temperatures from 300 to 380/spl deg/C in 10/spl deg/C steps. Nine wafers were used; one for each temperature, and 17 chips per wafer were tested for each algorithm. The structures were 857 /spl mu/m long, single-level stripes (to avoid thermal anomalies introduced by W studs and vias). Mean initial current values from ISOT were used as the input for the CI tests. Similarly, mean times to failure from ISOT were used as the target median times to failure (/spl tau//sub 50/) for the SWEAT tests. Values for activation energy /spl Delta/H and Black constant (A) were calculated from the ISOT results using current density exponent n=1.7 from package level. /spl tau//sub 50/'s are therefore comparable for all three methods.

The process of the drift of atoms due to an applied voltage, called electromigration, is studied both in materials science and in fundamental physics. The development of voids at the cathode side of an aluminum film and the growth of hillocks at the anode, 1 which is due to self-electromigration, shorten the lifetime of an integrated circuit. This process is commonly attributed to migration along grain boundaries. In the electronic industry a great deal of effort is made in slowing down this process. 2 In the present paper we report about a microscopic study of electromigration in polyvacancy clusters. For a certain cluster shape the results obtained can be considered as a first step in the direction of a microscopic description of electromigration along a grain boundary. In the theory of electromigration one concentrates on the calculation of the driving force, 3‐7 which is commonly written as a sum of two components, a direct force Fdirect and a wind force Fwind . The direct force is due to a net charge of the migrating atom, while the wind force is due to scattering of the current-carrying electrons off the atom. Both forces are proportional to the electric field and can be characterized by a valence

An analysis of polycrystalline Au thin-film interconnects of widths ranging from 850 to 25 nm, and lengths ranging from 1 μm to 20 nm which have been electrically stressed to the point of failure is presented. A new method for testing failure of interconnects is proposed, based on a quantity we call the failure current density. The mean time to failure for fixed current density and also the failure current density are seen to decrease with decreasing wire width contrary to expectations. The failure current density for a given wire width increases as the length decreases. An analysis of the temperature and stress profiles based on calculations of a simple model is presented which shows that the length dependence is due to thermal stresses rather than electromigration, and the width dependence is due to enhanced electromigration due to surface diffusion.

This chapter discusses the concepts of electromigration. Electromigration is defined as the movement of atoms in a solid subject to an electric field. It is a complex phenomenon in which the locally inhomogeneous electric field accompanying the electron transport process acts as the driving force for atom migration. A general description of the response of electrons and atoms to an applied electric field is contained in the phenomenological equations of irreversible thermodynamics. Theoretical and experimental work has established that the driving force for electromigration can conveniently be separated into contributions arising from the electron-wind force and the direct force. In particular, for electromigration the linear phenomenological equations of transport theory provide the necessary connection between particle currents and applied fields. A quantitative description of electromigration thus requires realistic models of the migrating atom and its local environment, of electron transport in the vicinity of the atom and of the diffusion jump itself.

A molecular dynamics simulation has been made for a nano-sized metal line on a refractory metal film by taking a local dynamic electric field into consideration. In order to consider the electric field, the local electrical conductivity in the metal line was calculated by the Cloud in Cell method. Current direction and local current density were determined from the electric field by solving Laplace equations. The forces originated from the electric field and the atomic interaction potential were applied to atoms in the simulation. The simulation showed a generation of void from the cathode and a movement of atoms to the anode followed by the formation of extrusion. This simulation method was found to be a promising one to make clear the mechanism of generation and growth of voids and the extrusion and hillock formations due to electromigration.

The atomic flux divergence obtained from current density and temperature in metal lines undamaged by electromigration is useful to predict the formation of initial void. In this study, a new method to calculate the atomic flux divergence used for predicting the formation of initial void is proposed considering two-dimensional distributions of current density and temperature and also simply considering the line structure not only of polycrystalline line but also of bamboo line. The flux divergence is formulated based on the Huntington-Grone’s equation and modeling of line structure. For the verification, electromigration phenomenon near the corner of an angled polycrystalline line, which results in two-dimensional distributions of current density and temperature, is treated as an example. The usefulness of the proposed method is discussed by comparison of the prediction of void formation near the corner with the experimental result.

The effect of line length on the electromigration behavior of a two-level structure with Ti-AlCu-Ti stripes and interlevel tungsten (W) stud-vias has been investigated. This investigation also represents a complete study of the short-length effect using a technologically-realistic test structure. Lifetime measurements and resistance changes as a function of time were used to characterize this phenomenon, where the latter approach provides new insights into the electromigration behavior of multi-layered metallizations. A linear increase in resistance was followed by a resistance change with time that approached zero. For the same product of current density and stripe length, longer stripes increased in resistance to higher values than shorter stripes. The sigma of the lognormal distribution increased as the current density decreased and/or as the maximum allowed resistance change increased. The lifetime, or t50, at relatively small current densities did not obey Black’s empirical equation. Rather, the life...

The temperature of 1 micrometer dia spot on a conductor was measured for the first time and compared with the predictions of the simulation model and with the data obtained by the line resistance method. Experiments were carried out to determine the dependence of electromigration lifetime on current density and temperature with an accurate measurement of temperature. These data support that the parameters of Black's model are constant at low as well as high current density range.

We introduce a dynamic fuse model for the damage done to a current-carrying polycrystalline metal thin film by electromigration. We determine the exact scaling behavior of the crack tip velocity for a single crack oriented perpendicularly to the direction of the ambient current. A Lifshitz-type theory works well only when the initial density of defects (p) is small. For all p, the mean failure time is to an excellent approximation proportional to the average length of the shortest path across the film in a certain metric. This conclusion is supported by our simulations and by analytical work based on a variational formulation of our problem. Using the shortest-path approximation, we show that the mean failure time tends to zero as (${\mathit{p}}_{\mathit{c}}$-p${)}^{4/3}$ as the percolation threshold p=${\mathit{p}}_{\mathit{c}}$ is approached. We also use the shortest-path approximation to account for experimental results on the lifetime of long polycrystalline metal wires of varying lengths and widths.

Electromigration was analyzed mathematically by solving Huntington's equation. A general solution assuming steady-state conditions was derived by Fourier transformation and complex integration. The analysis revealed that a significant accumulation of atoms at the anode induced hillock formation, and that atomic depletion at the cathode induced void formation. An electromigration acceleration test was performed to observe void formation using Al–0.5%Cu–1.0%Si on a SiO2/Si substrate. Experimental results of in situ observation were in good agreement with the theoretical result. The effect of a local stress field on void formation is discussed.

In this paper we report a systematic study of low-frequency 1/fα resistance fluctuation in a metal film at different stages of electromigration. The resistance fluctuation (noise) measurement was carried out in presence of a dc electromigration stressing current. We observe that in addition to the increase in the spectral power SV(f), the frequency dependence of the spectral power changes as the electromigration process progresses and the exponent α starts to change from 1 to higher value closer to 1.5. We interpret this change in α as arising due to an additional contribution to the spectral power with a 1/f3/2 component, which starts to contribute as the electromigration process progresses. This additional component SV(f) ∼ 1/f3/2 has been suggested to originate from long range diffusion that would accompany any electromigration process. The experimental observation finds support in a model simulation, where we also find that the enhancement of noise during electromigration stressing is accompanied by a change in spectral power frequency dependence.