Atom transport during electromigration

The electromigration force Q acting on each metal ion is usually ex- 

The flux of metal ions in response to the force Q induced on each is customarily written as 

As was noted in the study of evolution of compositional variations in Section 9.6.4, the local rate of mass accumulation due to a mass flux vector is the negative of the flux divergence. The local addition of material is represented in continuum modeling as a stress-free volumetric strain. At fixed overall strain, the rate of material addition induces a proportional rate of increase in mean normal compressive stress. In the present onedimensional configuration, this connection is expressed as 

If the self-diffusion mobility is assumed to be constant, then the equation reduces to the standard form of the diffusion equation in one dimension for stress, that is, 

In spite of the fact that they do not appear in this partial differential equation, the electrical parameters are still central to the description of the process because the boundary conditions commonly are expressed in terms of mass flux. 

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