3.3.3 Total Electromigration Strain

The total strain induced by electromigration is given by the sum of the vacancy migration and vacancy generation/annihilation components,

$$\symStrain^{v}_{ij} = \symVacMigStrain + \symVacGenStrain.$$ (3.40)

Taking the time derivative of (3.40), and using (3.35) and (3.39), the total strain rate produced by electromigration is given by

$$\ensuremath{\ensuremath{\frac{\partial \symStrain^{v}_{ij}}{\part... ...tor)\ensuremath{\nabla\cdot{\vec\JV}} + \symVacRelFactor\G\right]\symKronecker.$$ (3.41)

Since $\symStrain^{v}_{ij}$ is a diagonal tensor with equal entries, one can write (3.41) in terms of the trace of the strain tensor

$$\ensuremath{\ensuremath{\frac{\partial \symStrain^{v}}{\partial t... ...\symVacRelFactor)\ensuremath{\nabla\cdot{\vec\JV}} + \symVacRelFactor\G\right].$$ (3.42)

Given the dependence of the electromigration induced strain on the source function $\G$, the modeling approach for mechanisms of generation and annihilation of vacancies becomes of crucial importance.