electromigration under high current density. In addition, for thin films, Blech (1976)
proposed a length scale called “Blech’s critical length” below which mass diffusion
due to electron wind force will be totally counterbalanced by stress gradient driving
force in the opposite direction.
In order to solve an arbitrary boundary value problem with irregular boundaries or
initial value problem with arbitrary conditions and composite material properties
involving electromigration, there must be a rational mechanics-based current density- strain constitutive relation and a thermodynamics-based fundamental equation.
Then this formulation can be implemented in a finite element method (or any other
computational mechanics procedure) to solve any problem.
The classical definition of electromigration refers to the structural damage caused
by ion transport in metal because of high current density. Electromigration is usually
insignificant at low current density levels. Quantification of what is “high current
density” is studied extensively by Ye et al. (2003a, b, c, d, e, f), Ye et al.
(2004a, b, c, d), Ye et al. (2006) and Basaran et al. (2003). Electromigration is a
mass transport in a diffusion-controlled process under certain driving forces. The
driving force here is more complicated than what is involved in a pure diffusion
process, in which the concentration gradient of the moving species is the only
component. The electrical driving forces for electromigration consist of the electron
wind force and the direct field force. The electron wind force refers to the effect of
momentum exchange between the moving electrons and the ionic atoms when an
electrical charge—a direct field force—is applied to a conductor with metallic bonds.
When current density, which is proportional to the electron flux density, is high,
enough, this momentum exchange effect becomes significant, resulting in a noticeable mass transport referred to as electromigration. Low melting point alloys when
used at elevated homologous temperature (>0.5T melt Kelvin) are prone to have
considerable atomic diffusivity. For example, solder joints in microelectronics
packaging are prime examples of this category.
8.2.1 Driving Forces of Electromigration Process
8.2.1.1 The Electric Field
Electrical current forces include two driving mechanisms: one is attributed to the
electron wind forces, as originally suggested by Skaupy (1914), which refers to the
effect of the momentum exchange between the moving electrons and the ionic
atoms. This momentum exchange happens because of the scattering of free valence
electrons. Scattered electrons collide with metal atoms and push them in the direction of electron flow (Seith 1955; Seith and Wever 1953; Wever and Seith 1955). On
the other hand, the atoms move in the opposite direction of the applied electric field
when they are ionized; the latter mechanism, the static force of the electric field, is
considered the direct field force. The net effect of these two forces is the so-called
electrical field driving force of the electromigration.
396
8 Unified Mechanics of Metals under High Electrical Current Density:. . .
proposed a length scale called “Blech’s critical length” below which mass diffusion
due to electron wind force will be totally counterbalanced by stress gradient driving
force in the opposite direction.
In order to solve an arbitrary boundary value problem with irregular boundaries or
initial value problem with arbitrary conditions and composite material properties
involving electromigration, there must be a rational mechanics-based current density- strain constitutive relation and a thermodynamics-based fundamental equation.
Then this formulation can be implemented in a finite element method (or any other
computational mechanics procedure) to solve any problem.
The classical definition of electromigration refers to the structural damage caused
by ion transport in metal because of high current density. Electromigration is usually
insignificant at low current density levels. Quantification of what is “high current
density” is studied extensively by Ye et al. (2003a, b, c, d, e, f), Ye et al.
(2004a, b, c, d), Ye et al. (2006) and Basaran et al. (2003). Electromigration is a
mass transport in a diffusion-controlled process under certain driving forces. The
driving force here is more complicated than what is involved in a pure diffusion
process, in which the concentration gradient of the moving species is the only
component. The electrical driving forces for electromigration consist of the electron
wind force and the direct field force. The electron wind force refers to the effect of
momentum exchange between the moving electrons and the ionic atoms when an
electrical charge—a direct field force—is applied to a conductor with metallic bonds.
When current density, which is proportional to the electron flux density, is high,
enough, this momentum exchange effect becomes significant, resulting in a noticeable mass transport referred to as electromigration. Low melting point alloys when
used at elevated homologous temperature (>0.5T melt Kelvin) are prone to have
considerable atomic diffusivity. For example, solder joints in microelectronics
packaging are prime examples of this category.
8.2.1 Driving Forces of Electromigration Process
8.2.1.1 The Electric Field
Electrical current forces include two driving mechanisms: one is attributed to the
electron wind forces, as originally suggested by Skaupy (1914), which refers to the
effect of the momentum exchange between the moving electrons and the ionic
atoms. This momentum exchange happens because of the scattering of free valence
electrons. Scattered electrons collide with metal atoms and push them in the direction of electron flow (Seith 1955; Seith and Wever 1953; Wever and Seith 1955). On
the other hand, the atoms move in the opposite direction of the applied electric field
when they are ionized; the latter mechanism, the static force of the electric field, is
considered the direct field force. The net effect of these two forces is the so-called
electrical field driving force of the electromigration.
396
8 Unified Mechanics of Metals under High Electrical Current Density:. . .