8.2.1.2 Stress Gradient
When atoms diffuse from the cathode side to the anode side, they leave behind
vacancies on the cathode side and mass accumulation on the anode side. As a result
there is tension on the cathode side and compressive stress on the anode side. This
stress differential is responsible for the stress gradient.
Of course, mechanical stress gradient influences the electromigration process.
There is an interaction between the stress gradient and the electromigration driving
forces. Stress gradient can counteract or enhance the electromigration process,
depending upon the interaction of all diffusion driving forces.
Essentially, stress gradient is another driving force of mass transport. There is a
strong interaction between the stress gradient and the other driving forces.
However, in thermomigration in the absence of external stress gradients, the mass
moves from the hot side to the cold side, and compression on the cold side and
tension on the hot side develop, which counter the thermal gradient-induced force.
8.2.1.3 Thermal Gradient
The Joule heat generated under high current density is highly localized. Hence, there
is a thermal gradient in the medium, which leads to thermomigration. Thermal
gradient is one of the strongest driving forces of diffusion. Thermomigration cannot
be ignored especially when the thermal gradient is large, in which case the
thermomigration can be the dominant diffusion driving force.
8.2.1.4 Atomic Vacancy Concentration Gradient
It has been estimated that the mass flux due to vacancy concentration gradient is
small compared to those induced by electrical field forces, stress gradient and
thermal gradient. The atomic vacancy concentration gradient is usually small at
the beginning compared to the former two forces. However, as the mass migration
progresses, vacancy concentration gradient increases significantly. At a certain point
in time, vacancy concentration gradient becomes large enough to slow the diffusion.
8.2.2 Laws Governing Electromigration
and Thermomigration Process
Vacancy diffusion is governed by the vacancy conservation equation; mechanical
deformation is governed by the Newtonian mechanics; heat transfer is governed by
8.2 Physics of Electromigration Process
397
When atoms diffuse from the cathode side to the anode side, they leave behind
vacancies on the cathode side and mass accumulation on the anode side. As a result
there is tension on the cathode side and compressive stress on the anode side. This
stress differential is responsible for the stress gradient.
Of course, mechanical stress gradient influences the electromigration process.
There is an interaction between the stress gradient and the electromigration driving
forces. Stress gradient can counteract or enhance the electromigration process,
depending upon the interaction of all diffusion driving forces.
Essentially, stress gradient is another driving force of mass transport. There is a
strong interaction between the stress gradient and the other driving forces.
However, in thermomigration in the absence of external stress gradients, the mass
moves from the hot side to the cold side, and compression on the cold side and
tension on the hot side develop, which counter the thermal gradient-induced force.
8.2.1.3 Thermal Gradient
The Joule heat generated under high current density is highly localized. Hence, there
is a thermal gradient in the medium, which leads to thermomigration. Thermal
gradient is one of the strongest driving forces of diffusion. Thermomigration cannot
be ignored especially when the thermal gradient is large, in which case the
thermomigration can be the dominant diffusion driving force.
8.2.1.4 Atomic Vacancy Concentration Gradient
It has been estimated that the mass flux due to vacancy concentration gradient is
small compared to those induced by electrical field forces, stress gradient and
thermal gradient. The atomic vacancy concentration gradient is usually small at
the beginning compared to the former two forces. However, as the mass migration
progresses, vacancy concentration gradient increases significantly. At a certain point
in time, vacancy concentration gradient becomes large enough to slow the diffusion.
8.2.2 Laws Governing Electromigration
and Thermomigration Process
Vacancy diffusion is governed by the vacancy conservation equation; mechanical
deformation is governed by the Newtonian mechanics; heat transfer is governed by
8.2 Physics of Electromigration Process
397