Anisotropic phase field solution for morphological evolution and migration of inclusions in piezoelectric films

Li, H.B.; Wang, X.; Fang, Caiwen

doi:10.1016/j.apm.2014.12.005

Cited by 2 publications

(2 citation statements)

References 40 publications

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“…Li et al (2012) analyzed the effects of electrical conductivity and anisotropic surface energy on the migration and evolution of inclusions under the electric field. Li et al (2015) simulated the morphological evolution of inclusions in piezoelectric films under mechanical and electric loads. Santoki et al (2018Santoki et al ( ), (2019 analyzed the evolution of circular voids into finger-like cracks and the effect of anisotropic surface energy on the evolution of circular inclusions, respectively.…”

Section: Introductionmentioning

confidence: 99%

Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

Zhang¹,

Huang²

2021

Modelling Simul. Mater. Sci. Eng.

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Interconnect lines of integrated circuits inevitably exist micro-damage, such as voids, inclusions or cracks. Under the effect of different intrinsic physical mechanisms as well as external driving forces, the micro-damage will have different morphological evolution and even destabilize and split, which can affect the various properties of the interconnects. Based on the theory of diffusion interface of microstructure evolution in solid materials, a phase field model is established to simulate the morphological evolution of micro-damage in the interconnect line under electromigration-induced surface diffusion. Unlike the previously published work, the bulk free energy density and the degenerate mobility used in the model are both constructed by quartic double-well potential function. The applicability of the model for the morphological evolution of intracrystalline voids is proved by asymptotic analysis. The governing equation of the phase field method is solved by finite element method. And, the validity of the method is confirmed by the agreement of the numerical solutions with the theoretical solutions of a small circular void. The effects of the relative electric field intensity Χ, the linewidth h ∽ and the initial aspect ratio β on void evolution are discussed in detail. The results indicate that the intracrystalline voids drift in the direction of the electric field, and there is a destabilization critical value Χ cr . When Χ ≧Χ cr , there exist two splitting forms after destabilization for circular void, type I and type II, respectively. The value of Χ cr decreases as h ∽ decreases or β increases. The smaller h ∽ or the larger β is more prone to cause void destabilization. The effect of h ∽ or β on Χ cr is more significant as h ∽ or β is relatively small. In particular, when h ∽ or β is sufficiently large, there exists upper or lower limit for Χ cr , respectively.

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Section: Introductionmentioning

confidence: 99%

Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

Zhang¹,

Huang²

2021

Modelling Simul. Mater. Sci. Eng.

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“…Even so, many researches have been done for piezoelectric structures. Li, Wang and Fang investigated the migration of inclusions and morphological evolution in piezoelectric films with electric and mechanical loads, and the result reveals that tangential stress gradient in the phase interface layer can significantly influence the migration of inclusions and morphological evolution. By controlling the drop height of the wedge from the water surface, Panciroli and Porfiri investigated the hydroelastic impact of an active flexible wedge and found that piezohydroelastic response of the structure is mainly influenced by the corresponding impact velocity.…”

Section: Introductionmentioning

confidence: 99%

Two‐dimensional Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure

et al. 2019

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Piezoelectric materials, as functional material, are widely used in electronic devices, such as piezoelectric sensors, piezoelectric energy harvester and piezoelectric actuators. In some electronic devices, piezoelectric materials are placed between two substrates in the form of thin sheet. Therefore, this kind of piezoelectric structure is simplified into a three‐phase orthotropic piezoelectric structure which consists of an infinite piezoelectric plate and two semi‐infinite bodies in this paper. In this case, the Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure is deduced. Based on this solution, the accurate electro‐elastic fields of the three‐phase orthotropic piezoelectric structure are given. And some numerical examples are designed to investigate the effects of various material properties of the piezoelectric plate or the substrates on the stresses at interfaces and the electric potential difference between interfaces of piezoelectric plate.

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Anisotropic phase field solution for morphological evolution and migration of inclusions in piezoelectric films

Cited by 2 publications

References 40 publications

Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

Two‐dimensional Green's function solution for a tangential line force buried in the three‐phase orthotropic piezoelectric structure

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