Models of void electromigration
Models of void electromigration
We study the motion of voids in conductors subject to intense electrical current densities. We use a free-boundary model in which the flow of current around the insulating void is coupled to a law of motion (kinematic condition) for the void boundary. In the first part of the paper, we apply a new complex variable formulation of the model to an infinite domain and use this to (i) consider the stability of circular and flat front travelling waves, (ii) show that, in the unbounded metal domain, the only travelling waves of finite void area are circular, and (iii) consider possible static solutions. In the second part of the paper, we look at a conducting strip (which can be used to model interconnects in electronic devices) and use asymptotic methods to investigate the motion of long wavelength voids on the conductor boundary. In this case we derive a nonlinear parabolic PDE describing the evolution of the free boundary and, using this simpler model, are able to make some predictions about the evolution of the void over long times.
97-134
Cummings, Linda
70a32c64-8b0a-4740-a3bd-598866668be5
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Ben Amar, Martine
642b3f67-e9e6-4fe2-a385-30ca2ca50260
April 2001
Cummings, Linda
70a32c64-8b0a-4740-a3bd-598866668be5
Richardson, Giles
3fd8e08f-e615-42bb-a1ff-3346c5847b91
Ben Amar, Martine
642b3f67-e9e6-4fe2-a385-30ca2ca50260
Cummings, Linda, Richardson, Giles and Ben Amar, Martine
(2001)
Models of void electromigration.
European Journal of Applied Mathematics, 12 (2), .
(doi:10.1017/S0956792501004326).
Abstract
We study the motion of voids in conductors subject to intense electrical current densities. We use a free-boundary model in which the flow of current around the insulating void is coupled to a law of motion (kinematic condition) for the void boundary. In the first part of the paper, we apply a new complex variable formulation of the model to an infinite domain and use this to (i) consider the stability of circular and flat front travelling waves, (ii) show that, in the unbounded metal domain, the only travelling waves of finite void area are circular, and (iii) consider possible static solutions. In the second part of the paper, we look at a conducting strip (which can be used to model interconnects in electronic devices) and use asymptotic methods to investigate the motion of long wavelength voids on the conductor boundary. In this case we derive a nonlinear parabolic PDE describing the evolution of the free boundary and, using this simpler model, are able to make some predictions about the evolution of the void over long times.
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European Journal of Applied Mathematics 2001 Cummings.pdf
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Accepted/In Press date: 7 August 2000
Published date: April 2001
Organisations:
Applied Mathematics
Identifiers
Local EPrints ID: 404021
URI: http://eprints.soton.ac.uk/id/eprint/404021
ISSN: 0956-7925
PURE UUID: 6f18639d-6b4c-442b-bc7c-2d57a077be69
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Date deposited: 19 Dec 2016 16:53
Last modified: 16 Mar 2024 04:00
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Author:
Linda Cummings
Author:
Martine Ben Amar
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