Interconnected Segments Research Articles

Physically based simulation of electromigration-induced degradation mechanisms in dual-inlaid copper interconnects

Physically based simulations are used to predict an electromigration (EM)-induced void nucleation and growth in dual-inlaid copper interconnects. Incorporation of all important atom migration driving forces into the mass balance equation and its solution together with the solution of the coupled electromagnetics, heat transfer, and elasticity problems allows one to simulate EM-induced degradation in a variety of interconnect segments characterized by different dominant channels for mass transport. The existence of the weak interfaces between copper and diffusion barriers results in different EM-induced degradation pictures in aluminum and copper interconnects. The interface bonding strengths, significantly influencing the interface diffusivity and, consequently, the mass transport along interfaces in the case of copper interconnect, result in completely different degradation and failure pictures for the weak and strengthened copper/capping layer interfaces. Strengthening of the top interface of inlaid copper interconnect metal line is a promising way to prolong the EM lifetime. The correspondence between simulation results and experimental data indicates the applicability of the developed model for the optimization of the physical and electrical design rules. By varying the interconnect architecture, segment geometry, material properties, and some of the process parameters, users will be in a position to generate on-chip interconnect systems with high immunity to EM-induced failures.

Direct evidence of electromigration failure mechanism in dual-damascene Cu interconnect tree structures

In situ secondary electron microscope (SEM) characterizations were carried out to study electromigration failure mechanism in dual-damascene Cu interconnect tree structures, which are important for reliability assessment as well as design optimizations of on-chip interconnects. Direct evidence of electromigration-induced degradation in interconnect tree structure consisting of void nucleation and void movement in opposite direction to electron flow along the Cu∕SiNx interface was unraveled. The peculiar electromigration behavior of Cu interconnect tree structures can be clearly understood based on this mechanism. Dependence of electromigration mechanism of a segment in a Cu interconnect tree on current configuration in neighboring interconnect segment is discussed in detail.

Development of an integrated reflow soldering control system using incremental hybrid process knowledge

In this paper, we present an industrial application of intelligent knowledge-based reflow soldering control system to economically determine process parameters and assess the outputs for surface mount assembly. The system performance of surface mounting is significantly affected by three major interconnected process segments (including solder paste application, component placement, and solder reflow) and in combination. Many surface mount manufacturers have suffered both quality and productivity losses due to the lacks of effective line setup procedures, rapid process troubleshooting, and appropriate corrective action. This proposed system develops an integrated process control scheme, the framework of hybrid process knowledge extraction through neuro-fuzzy data training, and a knowledge-based system with a GUI man-machine interface for predicting and controlling the given system performance. The efficiency and effectiveness of the proposed system are illustrated using DPMO measurement and productivity analysis.

A model for electromigration-induced degradation mechanisms in dual-inlaid copper interconnects: Effect of interface bonding strength

A physical model and a simulation algorithm are used to predict an electromigration-(EM-) induced void nucleation and growth in dual-inlaid copper interconnect. Incorporation of all important atom migration driving forces into the mass balance equation and its solution together with solution of the coupled electromagnetics, heat transfer, and elasticity problems allows to simulate EM-induced degradation in a variety of dual-inlaid copper interconnect segments characterized by different dominant channels for mass transport. The interface bonding strengths, significantly influencing the interface diffusivity and consequently the mass transport along interfaces, result in completely different degradation and failure pictures for the weak and strengthened copper∕capping layer interfaces. Strengthening of the top interface of inlaid copper interconnect metal line is a promising way to prolong the EM lifetime. The results of the numerical simulation have been proven experimentally by the EM degradation studies on the fully embedded dual-inlaid copper interconnect test structures. EM-induced void formation, movement, and growth in a copper interconnect were continuously monitored in an in situ scanning electron microscopy experiment. The correspondence between simulation results and experimental data indicates the applicability of the developed model for optimization of the physical and electrical design rules. Simulation-based optimization of the interconnect architecture, segment geometry, material properties, and some of the process parameters can generate on-chip interconnect systems with a high immunity to EM-induced failures.

Quadratic representation for roadway profile that minimizes earthwork cost

Roadway design usually involves choices regarding grade selection and earthwork (transportation) that can be solved using linear programming. Previous work considered the road profile as series of interconnected linear segments. In these models, constraints are included in the linear programming formulation to insure continuity of the road, which cause sharp connectivity points at the intersection of the linear segments. This sharp connectivity needs to be smoothed out after the linear programming solution is found and the earth in the smoothed portion of the roadway has to be moved to the landfill. In previous research, the smoothing issue is dealt with after an optimal solution is found. This increases the work required by the design engineer and consequently increases the construction cost; furthermore, the optimal solution is violated by this smoothing operation. In this paper, the issue of sharp connectivity points is resolved by representing the road profile by a quadratic function. The continuity constraints are dropped (unneeded) and global optimality is guaranteed. Moreover, no violation is incurred to implement the optimum results. Although a quadratic function is used to represent the road profile, the mathematical model is purely linear in nature.

Mortality Dependence of Cu Dual Damascene Interconnects on Adjacent Segment

AbstractThree terminal ‘dotted-I’ interconnect structures, with vias at both ends and an additional via in the middle, were tested under a variety of test conditions. Failures (mortalities) were observed even when segments were tested under conditions that would not have led to failure in two-terminal structures. Mortalities were found in right segments with jL values as low as 1250 A/cm, which is lower when compared to the immortality condition (jL)cr of 3700 A/cm reported for similar via-terminated structures. Moreover, we found that the mortality of a dotted-I segment is dependent on the direction and magnitude of the current in the adjacent segment. These results suggest that there is not a definite value of the jL product that defines true immortality in individual segments that are part of an interconnect tree. More importantly, the critical jL value for a single segment of Cu interconnects may be reduced or increased by an adjacent segment. Therefore independently determined (jL)cr values cannot be directly applied to interconnects with branched segments, but rather the magnitude as well as the direction of the current flow in the adjoining segments must be taken into consideration in evaluating the immortality of interconnect segments in an interconnect network.

Parallel iterative methods for dense linear systems in inductance extraction

Accurate estimation of the inductive coupling between interconnect segments of a VLSI circuit is critical to the design of high-end microprocessors. This paper presents a class of parallel iterative methods for solving the linear systems of equations that arise in the inductance extraction process. The coefficient matrices are made up of dense and sparse submatrices where the dense structure is due to the inductive coupling between current filaments and the sparse structure is due to Kirchoff’s constraints on current. By using a solenoidal basis technique to represent current, the problem is transformed to an unconstrained one that is subsequently solved by an iterative method. A dense preconditioner resembling the inductive coupling matrix is used to increase the rate of convergence of the iterative method. Multipole-based hierarchical approximations are used to compute products with the dense coefficient matrix as well as the preconditioner. A parallel formulation of the preconditoned iterative solver is outlined along with parallelization schemes for the hierarchical approximations. A variety of experiments is presented to show the parallel efficiency of the algorithms on shared-memory multiprocessors.

Electromigration-induced damage in bamboo Al interconnects

Depletion and hillock formation were examined in-situ in a scanning electron microscope (SEM) during electromigration of bamboo Al interconnect segments. Hillocks formed directly at the anode ends of the segments by epitaxial addition of Al at the bottom Al/TiN interface. Depletion occurred nonuniformly from the cathode end and stopped once the distance between the leading void and the hillock reached the critical length for electromigration at the given current density. A modified equation for the drift velocity is proposed, which includes the effect of nonuniform depletion and predicts that interconnects with nonuniform depletion are more reliable than those with uniform depletion.

Carbon foam: Spanning the phase space between graphite and diamond

We study an unusual class of carbon structures, based on rigidly interconnected segments of graphite. The resulting foamlike systems cover the structural phase space extending from hexagonal diamond to graphite. Related to the most stable phases of carbon, these hybrid systems show an unusually high structural stability at low mass densities. Our density-functional calculations indicate that carbon foam is metallic, stable, and structurally rigid.

A conceptual model of preferential flow systems in forested hillslopes: evidence of self‐organization

AbstractPreferential flow paths are known to be important conduits of subsurface stormflow in forest hillslopes. Earlier research on preferential flow paths focused on vertical transport; however, lateral transport is also evident in steep forested slopes underlain by bedrock or till. Macropores consisting of decayed and live roots, subsurface erosion, surface bedrock fractures, and animal burrows form the basis of a ‘backbone’ for lateral preferential flow in such sites. Evidence from field studies in Japan indicates that although individual macropore segments are generally <0·5 m in length, they have a tendency to self‐organize into larger preferential flow systems as sites become wetter. Staining tests show clear evidence of interconnected macropore flow segments, including: flow within decayed root channels and subsurface erosion cavities; flow in small depressions of the bedrock substrate; fracture flow in weathered bedrock; exchange between macropores and mesopores; and flow at the organic horizon–mineral soil interface and in buried pockets of organic material and loose soil. Here we develop a three‐dimensional model for preferential flow systems based on distributed attributes of macropores and potential connecting nodes (e.g. zones of loose soil and buried organic matter). We postulate that the spatially variable and non‐linear preferential flow response observed at our Japan field site, as well as at other sites, is attributed to discrete segments of macropores connecting at various nodes within the regolith. Each node is activated by local soil water conditions and is influenced strongly by soil depth, permeability, pore size, organic matter distribution, surface and substrate topography, and possibly momentum dissipation. This study represents the first attempt to characterize the spatially distributed nature of preferential flow paths at the hillslope scale and presents strong evidence that these networks exhibit complex system behaviour. Copyright © 2001 John Wiley & Sons, Ltd.

Traffic Analysis for Real-Time Communication Networks Onboard Ships

The paper presents a novel method for establishing worst case estimates of queue lengths and transmission delays in networks of interconnected segments each of ring topology as defined by the ATOMOS project for marine automation. A non probabilistic model for describing traffic is introduced as well as theoretical work verifying the correctness of an iterative algorithm estimating worst case queue lengths and in turn transmission delays.

Effect of “bamboo” grain boundaries on the maximum electromigration-induced stress in microelectronic interconnect lines

A model which describes the steady-state mechanical stresses resulting from electromigration in microelectronic interconnect lines is presented. This model is valid when sidewall and grain boundary interface diffusion are the dominant transport paths, and accounts for the two-dimensional microstructure present in such lines. By applying the model to simulated line microstructures, we find that bamboo grain boundaries may substantially increase the maximum electromigration stress. Furthermore, microstructural simulations on bounded interconnect segments show that variations in grain size may lead to a large scatter in the maximum stress, particularly as line length decreases.

Introduction of a hybrid model for the discrete 3D simulation of dislocation dynamics

A hybrid model is suggested to discretely consider self forces and non-conservative effects in 3D dislocation dynamics. The dislocations are idealized as line defects in a homogeneous linear elastic medium. Each dislocation line consists of interconnected straight segments. The displacement and stress fields associated with the segments are formulated for general anisotropy and arbitrary crystal symmetry using Brown's theorem and the integral formalism in the version of Asaro and Barnett. The stress field of each dislocation is then computed through a linear superposition of the stress contributions of all segments. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. The differential equations of the individual segments are coupled through the line tension which is discretely considered by calculating the self interaction force among the segments that belong to the same dislocation according to the concept of Brown. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The influence of temperature is introduced by regarding the crystal as a canonical ensemble and by including a stochastic Langevin force as proposed by Rönnpagel.

On the consideration of climb in discrete dislocation dynamics

Abstract A concept is outlined to incorporate dislocation climb in a discrete three-dimensional model of dislocation dynamics. Each dislocation line consists of a sequence of interconnected piecewise straight segments which are embedded in a homogeneous linear elastic medium. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The osmotic force on each segment depends on the local point defect concentration. The mechanical structure evolution law must thus be complemented with a chemical structure evolution equation. Corresponding formulations are derived using the continuity equation and Fick's first law of diffusion.

On the consideration of climb in discrete dislocation dynamics

Abstract A concept is outlined to incorporate dislocation climb in a discrete three-dimensional model of dislocation dynamics. Each dislocation line consists of a sequence of interconnected piecewise straight segments which are embedded in a homogeneous linear elastic medium. The dynamics are described by solving Newton's equation of motion for each portion of dislocation. Non-conservative dislocation motion is introduced by considering the osmotic force that arises from emitting or adsorbing point defects at the climbing segment. The osmotic force on each segment depends on the local point defect concentration. The mechanical structure evolution law must thus be complemented with a chemical structure evolution equation. Corresponding formulations are derived using the continuity equation and Fick's first law of diffusion.

General entire-domain Galerkin method for analysis of wire antennas in the presence of dielectric bodies

A novel, entire-domain moment-method is proposed for the analysis of wire antennas and scatterers in the presence of lossy inhomogeneous dielectric bodies of finite extent. The wire part of the structure is approximated by arbitrarily positioned and interconnected straight-wire segments of lengths which can exceed one wavelength. The dielectric bodies are approximated by a system of trilinear hexahedrons, which can be electrically large (can also exceed one wavelength inside the dielectric, in any direction). The current along wires and inside dielectric bodies is approximated by one- and three-dimensional polynomials, respectively. The unknown current-distribution coefficients are obtained by a Galerkin-type solution of the system of coupled two-potential integral equations. The method is accurate, efficient and reliable. Its fundamental advantage over the (only existing) subdomain methods for the analysis of the same type of structures is a significantly reduced number of unknowns and, consequently, greatly reduced computing time. The proposed method enables rapid analysis of wire/dielectric structures exceeding moderate electrical size with even standard personal computers.

Language and Reality, One More Time

I shall propose a rationale for a version of the Sapir-Whorf Hypothesis. I say so-called since the ideas of Sapir and Whorf were offered more as a conceptual framework or interpretive perspective than as a scientific hypothesis. Understood in this way, these ideas remain extremely interesting and worthy of exploration. I am proposing a soft version in order to avoid the overly deterministic and rationalistic implications of the rigorous formulation sometimes known as relativity. This version still carries serious ramifications for any understanding of the relationship between language and reality. basic idea of this proposal is that the structure of our native language can and does strongly influence our perceptual and conceptual patterns, and thus contributes significantly to the make up and contour of reality as experienced. scope of this influence includes our experience of both social and physical reality. Thus it is fair to say that to a large degree the world is linguistically constituted. In what follows I shall demonstrate and document this basic theme with examples from both Hopi and other Native American languages, as well as some from the English language. focus point will be the inter-active of the relationship between speech and embodiment, First, consider perceptual patterns. In Hopi language, in addition to personal and demonstrative pronouns, there are what are called remotes, which refer to a person or thing that is not present or that is unknown to the speaker. This linguistic classification introduces and sets in motion a perceptual expectation and/or awareness quite distinct from those common to IndoEuropean languages and experience. Since it is not common to speak about persons, places, and things in Hopi without indicating whether or not they are remote, it would seem that this feature of experienced reality would be something that Hopi speakers would be more likely to notice. It would be part of the grid through which they interact with their environment on a primary level, not just a secondary one. Along the same line, in addition to the usual distinction between singular and plural, in Hopi there is dual number for both subjects and objects that have an animate nature. Interestingly enough, this classification also includes clouds, stars, and vehicles. Such things can be said to come in groups of one, two, or many. Not only would this way of speaking heighten one's awareness of the coupling phenomenon, but it might well make one more cognizant of the differences between animate and inanimate features of reality. In a sense, the language can be said to force, or at least direct, its users to experience the world in this way. In like manner, Hopi verbs not only express tense, but they also designate aspect, thereby indicating if an activity has been completed (perfective) or not (imperfective). In addition, however, according to Whorf, Hopi verbs also formalize different varieties of the contrast between point-locus and extent-locus, such that the verb inflections serve to distinguish the manner of the action rather than simply whether or not it has been completed. The phenomenon denoted by the root, shown in the punctual aspect as manifested about a point, becomes manifested as a series of repeated interconnected segments of one large phenomenon of a stretched-out segmental character (Whorf, p. 52). On the other hand, when the phenomenon focused by the verb stem is of a dynamic nature, the appropriate inflections become those that indicate whether a given line is meandering, zigzagged, serrated, or fringed, or whether a fluid makes one wave or a continuous flow of waves. In the first case, the action might be said to carry a static character, while in the latter it can be said to exhibit a vibrational quality. In both cases, however, it is the verb that designates the nature of the phenomenon, not the noun. …

Changes in catalase and glucose-6-phosphatase distribution patterns within oval cell compartment as possible differentiation markers during viral hepatocarcinogenesis in woodchucks

Cytochemical analysis at the ultrastructural level was performed to characterize expression of catalase and glucose-6-phosphatase (G6Pase) activity as possible differentiation markers in oval cells proliferating during hepatocarcinogenesis induced in woodchucks by chronic infection with the woodchuck hepatitis virus (WHV) and additional treatment with aflatoxin B 1 (AFB 1). Oval cells from WHV-carriers treated with AFB 1 showed two types of catalase-positive organelles: 1) microperoxisomes appearing as small strongly osmiophilic bodies corresponding to those present in biliary cells from control woodchucks, 2) peroxisomes with a hepatic staining pattern resembling those of mature hepatocytes but lacking a nucleoid. While in oval cells penetrating into the parenchyma a catalase-positive reaction product was restricted to rare microperoxisomes, in close vicinity to the portal tract about 30% of the oval cells produced peroxisomes with a hepatic staining pattern, indicating the existence of two different populations within the oval cell compartment. Peroxisomes with a hepatic staining pattern formed clusters and exhibited pleomorphism with marked variation in shape and size, the size sometimes coming up to that of normal hepatocellular peroxisomes. Serial sections revealed the complex organization of these peroxisomes. They consisted of several interconnected segments forming a peroxisomal reticulum. These findings are consistent with the hypothesis that a subpopulation of oval cells represents committed precursor cells capable of differentiating into hepatocytes. Activity of G6Pase was not demonstrable in this subpopulation of oval cells and became positive only in transitional cells. Differential expression of catalase and G6Pase activity in a stepwise fashion within the oval cell compartment appear to mark differentiation of oval cells into hepatocytes. Thus, elevated expression of catalase may be a useful early marker for the distinction of different subpopulations of oval cells committed to hepatic cell lineages before definitely changing their phenotype, whereas expression of G6Pase activity seems to begin later, accompanying morphological changes towards the phenotype of mature hepatocytes.

Changes in catalase and glucose-6-phosphatase distribution patterns within oval cell compartment as possible differentiation markers during viral hepatocarcinogenesis in woodchucks

Cytochemical analysis at the ultrastructural level was performed to characterize expression of catalase and glucose-6-phosphatase (G6Pase) activity as possible differentiation markers in oval cells proliferating during hepatocarcinogenesis induced in woodchucks by chronic infection with the woodchuck hepatitis virus (WHV) and additional treatment with aflatoxin B1 (AFB1). Oval cells from WHV-carriers treated with AFB1 showed two types of catalase-positive organelles: 1) microperoxisomes appearing as small strongly osmiophilic bodies corresponding to those present in biliary cells from control woodchucks, 2) peroxisomes with a hepatic staining pattern resembling those of mature hepatocytes but lacking a nucleoid. While in oval cells penetrating into the parenchyma a catalase-positive reaction product was restricted to rare microperoxisomes, in close vicinity to the portal tract about 30% of the oval cells produced peroxisomes with a hepatic staining pattern, indicating the existence of two different populations within the oval cell compartment. Peroxisomes with a hepatic staining pattern formed clusters and exhibited pleomorphism with marked variation in shape and size, the size sometimes coming up to that of normal hepatocellular peroxisomes. Serial sections revealed the complex organization of these peroxisomes. They consisted of several interconnected segments forming a peroxisomal reticulum. These findings are consistent with the hypothesis that a subpopulation of oval cells represents committed precursor cells capable of differentiating into hepatocytes. Activity of G6Pase was not demonstrable in this subpopulation of oval cells and became positive only in transitional cells. Differential expression of catalase and G6Pase activity in a stepwise fashion within the oval cell compartment appear to mark differentiation of oval cells into hepatocytes. Thus, elevated expression of catalase may be a useful early marker for the distinction of different subpopulations of oval cells committed to hepatic cell lineages before definitely changing their phenotype, whereas expression of G6Pase activity seems to begin later, accompanying morphological changes towards the phenotype of mature hepatocytes.

Performance driven spacing algorithms using attractive and repulsive constraints for submicron LSI's

This paper proposes one-dimensional spacing algorithms that minimize [maximize] the degree of separation [proximity] among the specified elements of a given integrated circuit layout. Number of problems on chip and MCM systems such as poor performance, higher crosstalk, lower yield etc. are related to the degree of separation [proximity]. The proposed algorithms utilize the attractive [repulsive] constraints to shrink [expand] the distances among the specified elements while keeping the layout free of any design rule errors. The spacing problem is reduced to a parametric linear programming problem and a network simplex algorithm is proposed for solving it. The proposed algorithms are implemented into a system called PERFECT for performance enhancement and crosstalk reduction. Given a routed design, PERFECT minimizes delay due to the coupled capacitance, which could contribute as much as 50-75% to the interconnect delay in near future. PERFECT utilizes the repulsive constraints between interconnect segments for the purpose. The experimental results show a significant delay improvement and the crosstalk reduction for submicron technologies. >