Stress-induced migration model based on atomic migration
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Stress-induced migration is one of the problems related to the reliability of metal interconnections in semiconductor devices. This phenomenon generates voids and disconnections in the metal interconnections. The purposes of this work are to establish the stress-induced model based on atomic migration and theoretically clarify the temperature characteristics of void formation and disconnection using the presented model. First, the stress-induced migration model based on atomic migration in which the driving force is the gradient of elastic potential is presented. Next, to clarify the temperature characteristics of stress-induced migration, the presented model is applied to the formation of voids and disconnections and the results of theoretical analyses are compared with experimental results. It was found that the temperature characteristics of the void formation show various patterns depending on the void interval, and the temperature characteristics of the disconnection show various patterns depending on the void interval and void radius. These theoretical results are in agreement with the experimental results.
I. INTRODUCTION
The stress-induced migration phenomenon is one of the problems related to the reliability of metal interconnections in semiconductor devices. This phenomenon generates voids and disconnections in the metal interconnections during long high-temperature storage. This type of failure was first reported in 1984,1,2 and many studies have since been performed to clarify the mechanism of stress-induced migration. As a result of these studies, the formation process of voids and disconnections due to stress-induced migration is considered to be as follows: vacancies generated thermodynamically in the metal interconnections migrate along the stress gradient, accumulate at vacancy sinks, and lead to the formation of voids and disconnections.3–6 Namely, stress-induced migration has been explained as the migration of vacancies; however, the stress-induced migration model with actual atoms constituting an interconnection is more convenient for considering the stress-induced migration phenomenon. The purposes of this work are to establish the stress-induced model based on atomic migration and to theoretically clarify the temperature characteristics of the void formation and disconnection using the presented model. First, the stress-induced migration model based on atomic migration under a residual thermal stress is a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2004.0288 J. Mater. Res., Vol. 19, No. 8, Aug 2004
http://journals.cambridge.org
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presented in detail. A similar model has already been used by some researchers; however, its physical base is unclear.7–11 This model is probably based on the Nabarro–Herring model.12,13 The Nabarro–Herring model is derived from on enthalpy-free material and explains a creep phenomenon. The presented model is based on elastic potential and composed of three basic computation processes: (i) residual
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