Xiang Gui

Transmission‐line‐matrix modeling of grain‐boundary diffusion in thin films

The use of the transmission‐line‐matrix (TLM) method for analyzing the grain boundary and interfacial diffusion problems in thin films is demonstrated. The method employed has a variable mesh and automatic time‐stepping capability, and is highly versatile in treating complex structures and incorporating various boundary conditions. The present model takes account of separate diffusion coefficients in grain boundaries, grains, interfaces, and the substrate. The combined diffusion problems are solved as a function of position and time, and the concentration distributions are presented as clearly visible isometric projections and contour plots. The results are compared with those of semi‐infinite samples (Whipple’s analysis [Philos. Mag. 45, 1225 (1954)]) and idealized thin‐film systems (Gilmer and Farrell’s analysis [J. Appl. Phys. 47, 3792 (1976)]), with the emphasis being placed on the differences due to the treatment of concentration flux along the interface between the film and the substrate and into th...

Three‐dimensional thermal analysis of high density triple‐level interconnection structures in very large scale integrated circuits

A three‐dimensional thermal model of generic multilevel interconnection systems in very large scale integrated (VLSI) circuits is presented. The temperature distributions are quantitatively studied using the transmission‐line matrix modeling method. The temperature increase of a triple‐level parallel and crossing interconnection‐line scheme is found to be several times higher than that of a single‐level parallel line structure if the same magnitude of current density in the 106 A/cm2 range is maintained. More than 50% of the temperature rise occurs across the Si substrate; the treatment of which as a perfect heat sink in many previous thermal analyses of metallization structures is, therefore, inadequate. The large thermal gradients within the SiO2 insulators between different metallization levels can be eliminated and the temperature rise can be significantly reduced if the SiO2 interlevel and passivation dielectrics are replaced by a material with much higher thermal conductivity. Lower temperatures wou...

Numerical solution of the electromigration boundary value problem under pulsed dc conditions

The one‐dimensional electromigration boundary value problem under pulsed dc conditions is numerically investigated by utilizing the transmission‐line matrix modeling method. A perfectly blocking boundary, where void formation and failure occur, is assumed at one end of an interconnection line. At the other end, two physically plausible boundary conditions are considered. From the design‐rule point of view, an approach is proposed to convert conveniently the pulsed stress into an equivalent dc stress that would produce electromigration damage at a similar rate. Based on the fundamental diffusion‐drift model, we show that the vacancy buildup behavior under a pulsed dc stress γp can be described accurately by the dc stress γdc scaled according to the duty factor r of the current pulse, namely, γdc=rγp. This study also represents a theoretical confirmation for the (jr)−2 dependence of the pulsed electromigration failure (where j is the current density), which has been observed in a number of experimental studies.

GRAIN-BOUNDARY DIFFUSION MODELING AND EFFICIENCY EVALUATION OF THIN-FILM DIFFUSION BARRIERS CONSIDERING MICROSTRUCTURE EFFECTS

We have developed a novel grain‐boundary diffusion model using the transmission‐line matrix method. In conjunction with a two‐dimensional Monte Carlo thin‐film growth simulator, this model can be employed for the analysis of impurity diffusion in thin‐film diffusion barriers with realistic microstructures. In the model, the impurity at the upper surface of the barrier layer may diffuse through rapid and irregularly shaped grain‐boundary diffusion paths to reach the bottom surface. Calculations of the impurity concentration and out‐diffusion flux as a function of elapsed diffusion time and position enable the evaluation of the effectiveness of the barrier layer at a microstructure level. Consequently, the diffusion process is depicted with less assumptions and more precisely than previously available approaches. This paper details the grain‐boundary diffusion modeling method outlined above, with the emphasis on the treatment of various boundary conditions. A representative application to titanium nitride (...

Simulation of electromigration in thin‐film diffusion barriers by the transmission line matrix method

A phenomenological model of grain‐boundary diffusion and electromigration in thin‐film diffusion barriers for microelectronic device metallizations is developed by using the transmission line matrix method. Both diffusion and drift effects are included in the numerical analysis with a multidimensional variable mesh structure. Special attention is paid to the ‘‘vertical’’ electromigration effect and a comparison of the two‐dimensional (2D) and three‐dimensional (3D) simulation results. Two fundamental driving forces for impurity grain‐boundary diffusion, the concentration gradient across a diffusion barrier, and the current flow perpendicular to the deposited metal films can reinforce each other, leading to an enhanced impurity diffusion and a reduced barrier efficiency. Such material transport through the diffusion barrier is quantified with a 2D model of parallel planar grain boundaries and a 3D model of rectangular columnar microstructures. Concentration profiles along all directions are visualized in graphs for the cases with and without the electromigration driving force. Average atom penetration as a function of time and the underestimation by the 2D model are also illustrated.

Three-dimensional simulation of impurity diffusion in thin-film diffusion barriers

Three-dimensional (3D) simulation of combined lattice and grain-boundary diffusion of impurities in thin-film diffusion barriers for eemiconductor device metallizations is performed. Calculated results of impurity concentration profiles demonstrate quantitatively an obvious underestimation of the frequently used two-dimensional (2D) analysis with respect to the influence of film geometry and grain-boundary diffusion coefficient. As for the average concentration at the backside of diffusion barriers, approximately a factor of two difference between the 2D and 3D simulation results is found over an interesting range of times and grain size structures. Graphs for predicting the effectiveness of diffusion barriers are presented with several normalized parameters associated with position and time. Particular application examples of aluminum diffusion in titanium nitride films justify the use of this material as an effective diffusion barrier in silicon microelectronic devices.