H. Abé

Electromigration failure of metal lines

Abstract.With the scaling down process of microcircuits in semiconductor devices, the density of electric current in interconnecting metal lines increases, and the temperature of the device itself rises. 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. The growth of voids in the metal lines ultimately results in electrical discontinuity. Our research group has attempted to identify a governing parameter for electromigration damage in metal lines, in order to clarify the electromigration failure and to contribute to circuit design. The governing parameter is formulated based on the divergence of the atomic flux by electromigration, and is denoted by AFD. The prediction method for the electromigration failure has been developed by using AFD. The AFD-based method makes it possible to predict the lifetime and failure site in universal and accurate way. In the actual devices, the metal lines used in the integrated circuit products are covered with a passivation layer, and the ends of the line are connected with large pads or vias for current input and output. Also, the microstructure of metal line distinguishes the so-called bamboo structured line from polycrystalline line depending on the size of metallic grains relative to the line width. Considering the damage mechanisms depending on such line structure, our research group has made a series of studies on the development of the prediction method. This article is dedicated to make a survey of some recent achievements for realizing a reliable circuit design against electromigration failure.

Stress intensity factors for a semi-elliptical crack in the surface of a semi-infinite solid

The stress intensity factors are presented for a vertical semi-elliptical surface crack in an elastic semi-infinite body which is subjected to a constant pressure on the crack surface. The approach utilizes a singular integral equation which is defined over the crack area only, where the weakness of the stress singularity is taken into account near the corner points at which the crack periphery intersects the surface of the semi-infinite body.This pertinent approach provides the proper assessment of the stress intensity factors in the vicinity of the corner points, and reveals that the stress intensity factor reaches a maximum value near the corner point and then decreases to zero as the point is approached.RésuméOn présente les facteurs dintensité de contrainte pour une fissure de surface verticale semi-elliptique dans un corps élastique semi-infini soumis à une pression constante sur la surface de la fissure. Lapproche utilisée recourt à une intégrale singulière définie uniquement sur la superficie de la fissure, où lon prend en considération laffaiblissement de la singularité des contraintes au voisinage des points où la périphérie de la fissure est en intersection avec la surface du corps semi-infini.Cette approche permet dobtenir les facteurs dintensité de contrainte au voisinage des points considérés et révèle que le facteur dintensité des contraintes passe par un maximum en ceux-ci et décroît vers zéro lorsquon sen éloigne.

A Method to Predict Electromigration Failure of Metal Lines

A new calculation method of atomic flux divergence (AFDgen) due to electromigration has recently been proposed by considering all the factors on void formation, and AFDgen has been identified as a parameter governing void formation by observing agreement of the numerical prediction of the void with experiment. In this article, a method to predict the electromigration failure of metal lines was proposed by using AFDgen. Lifetime and failure site in a polycrystalline line were predicted by numerical simulation of the processes of void initiation, its growth to line failure, where the change in distributions of current density and temperature with void growth was taken into account. The usefulness of this prediction method was verified by the experiment where the angled aluminum line was treated. The failure location was determined by the line shape and the operating condition. The present simulation accurately predicted the lifetime as well as the failure location of the metal line.

Experimental verification of prediction method for electromigration failure of polycrystalline lines

A prediction method for electromigration failure in polycrystalline lines has been proposed using the governing parameter of electromigration damage, the atomic flux divergence (AFDgen), and the usefulness has been verified by experiment where various line shapes were treated under various operating conditions. In the prediction method, lifetime and failure site in a metal line have been predicted by numerical simulation of the processes of void initiation, its growth, to line failure. The simulation has predicted accurately the lifetime as well as the failure site of the metal line. In the verification, however, the metal lines treated had the same grain size, that is, the same microstructure. In this article, the prediction method for the electromigration failure of polycrystalline lines was verified in more detail, by comparing the prediction results of lifetime and failure site with the results of experiments using not only various shaped lines but also lines whose microstructures were different.

Fracture strength of chemically vapor deposited diamond on the substrate and its relation to the crystalline structure

Abstract The mechanical strength of chemically vapor deposited diamond is characterized in terms of fracture toughness. The toughness of film and adhesion interface to the substrate were independently measured using techniques recently developed by the authors. In this paper, diamond was deposited by microwave plasma chemical vapor deposition using a variety of deposition conditions. The fracture toughness of the interface initially increased and then decreased with increasing amounts of methane in the source gas mixture. On the contrary, the toughness of the films was simply found to decrease with respect to the increment of methane concentration. This interesting trend of toughness was explained by the crystalline structure of the deposited diamond.

Fracture toughness of the interface between CVD diamond film and silicon substrate in the relation with methane concentration in the source gas mixture

Diamond films produced by chemical vapor deposition (CVD) have been reported to show various excellent properties. However, low toughness of diamond films, especially the interface between the films and substrates, has been a severe problem. In order to find the dominant factors to control the adhesive strength of CVD diamond films, we obtained diamond films with various crystalline structures deposited on silicon (100) substrates under various methane concentrations in the source gas mixture. The toughness of the interface between the diamond film and silicon substrate was evaluated for the first time by a recently developed method. The toughness showed an interesting behavior with respect to the variation of methane concentration. The obtained results were quantitatively compared to the data already obtained for the case of CVD diamond particles deposited on silicon substrates.

Three-dimensional simulation of crack extension in brittle polycrystalline materials

Abstract Crack extension resistance in brittle polycrystals was investigated from the viewpoint of three-dimensional microcrack evolution. Even in the case of macroscopically two-dimensional cracks, inhomogeneous distribution of microscopic stress along the crack front gives rise to three-dimensional structures of extended crack surfaces. Numerical simulations of macroscopic crack extension were carried out, which showed that three-dimensional distribution of grain-by-grain thermal stress leads to a significant increase in the crack extension resistance. It was concluded that three-dimensional interpretation on the microscopic inhomogeneity is necessary for the correct comprehension of macroscopic crack extension behavior in brittle polycrystals.

Atomic flux divergence in bamboo line for predicting initial formation of voids and hillocks

Abstract A calculation method of the atomic flux divergence due to electromigration, AFDgen, has been proposed considering two-dimensional distributions of current density and temperature and also simply considering the line structure of not only polycrystalline line but also bamboo line. The validity of AFDgen for bamboo lines has been verified in comparison of void formation calculated by using AFDgen with experimental results, and it has been shown that void formation in bamboo line is able to be predicted by using AFDgen. In this study, angled bamboo lines are treated for prediction of hillock formation, and hillock formation predicted by using AFDgen is compared with that measured in experiment. In addition to the verification of void prediction, the usefulness of the prediction method for electromigration damage using AFDgen is discussed in more detail.