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Finite Element Modeling for Interconnect Materials and Structures

Published online by Cambridge University Press:  10 February 2011

Lori Bassman
Affiliation:
Stanford Univ., Dept. of Mechanical Engineering, Stanford, CA;
Peter Pinsky
Affiliation:
Stanford Univ., Dept. of Mechanical Engineering, Stanford, CA;
Michael Deal
Affiliation:
Stanford Univ., Dept. of Electrical Engineering, Stanford, CA
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Abstract

We present a Back-End Simulation Tool (BEST) developed to address important issues for modeling polycrystalline and multi-layered interconnect materials. During the temperature cycles of interconnect fabrication, diffusion and mechanical equilibrium processes are coupled. Accurate simulation of these systems leads to very large problems, and it is therefore necessary to partition the problem using a staggered scheme. We have developed an unconditionally stable algorithm which is crucial to the success of this approach. We are also able to consider the coupled effect of an electromigration driving force in conducting materials. In order to predict effectively the deformations and stresses which occur in structures fabricated from these materials, our work addresses the multiple length scales which characterize the problem. The simulations span from interconnect level structures to detailed descriptions of grain boundaries and material interfaces using continuously spatially varying material properties. The formulation naturally enforces segregation of impurities or vacancies (for metal self-diffusion) to and across interfaces and to surfaces. Our solutions of the coupled physical problems with the explicit inclusion of grain and layer structures make this a tool for efficient evaluation of the properties and reliability of new interconnect materials and layered structures. We will show some applications of our model to technologically relevant examples including hillock formation and interface stresses.

Type
Research Article
Copyright
Copyright © Materials Research Society 1998

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