Chapter 8
Unified Mechanics of Metals under High
Electrical Current Density:
Electromigration and Thermomigration
8.1 Introduction
Electromigration and thermomigration are in principal irreversible mass diffusion
mechanisms under high current density and high temperature gradient, respectively.
However, thermomigration can take place alone in the absence of electrical current,
while electromigration cannot happen without thermomigration due to Joule heating,
except for special circumstances.
8.2 Physics of Electromigration Process
When a solid conductor (metal) is subjected to an electrical potential gradient, the
current enters from the anode side and travels to the cathode side, and the electrons
travel from the cathode to the anode side. Electromigration is a mass diffusioncontrolled phenomenon. When a conductor is subject to a high current density, the
so-called electron wind transfer part of the momentum to the atoms (or ions) to make
the atoms (or ions) moves in the direction of the current. As a result, the degradation
of the conductor occurs mainly in two forms; in the anode side, the atoms will
accumulate and finally form hillocks, and the vacancy concentration in the cathode
side will form voids. Both hillocks and voids will cause the degradation of the
material and eventual failure. The damage evolution due to electromigration can be
modeled as an irreversible mass transport process. The purpose of this chapter is to
present the formulation of modeling the electromigration- and thermomigrationinduced material degradation process using the unified mechanics theory.
The physical mechanism of electromigration has been extensively investigated.
Black (1969) established the relationship between the mean time to failure and
current density for confined thin films on a substrate. The experiments by Blech
(1976) revealed that the stress gradient could act as a counterforce to
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_8
395
Unified Mechanics of Metals under High
Electrical Current Density:
Electromigration and Thermomigration
8.1 Introduction
Electromigration and thermomigration are in principal irreversible mass diffusion
mechanisms under high current density and high temperature gradient, respectively.
However, thermomigration can take place alone in the absence of electrical current,
while electromigration cannot happen without thermomigration due to Joule heating,
except for special circumstances.
8.2 Physics of Electromigration Process
When a solid conductor (metal) is subjected to an electrical potential gradient, the
current enters from the anode side and travels to the cathode side, and the electrons
travel from the cathode to the anode side. Electromigration is a mass diffusioncontrolled phenomenon. When a conductor is subject to a high current density, the
so-called electron wind transfer part of the momentum to the atoms (or ions) to make
the atoms (or ions) moves in the direction of the current. As a result, the degradation
of the conductor occurs mainly in two forms; in the anode side, the atoms will
accumulate and finally form hillocks, and the vacancy concentration in the cathode
side will form voids. Both hillocks and voids will cause the degradation of the
material and eventual failure. The damage evolution due to electromigration can be
modeled as an irreversible mass transport process. The purpose of this chapter is to
present the formulation of modeling the electromigration- and thermomigrationinduced material degradation process using the unified mechanics theory.
The physical mechanism of electromigration has been extensively investigated.
Black (1969) established the relationship between the mean time to failure and
current density for confined thin films on a substrate. The experiments by Blech
(1976) revealed that the stress gradient could act as a counterforce to
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_8
395