text: A governing equation which describes the atom concentration evolution throughout some interconnect segment, is the conventional mass balance (continuity) equation
  where  is the atom concentration at the point with a coordinates  at the moment of time , and  is the total atomic flux at this location. The total atomic flux  is a combination of the fluxes caused by the different atom migration forces. The major forces are induced by the electric current, and by the gradients of temperature, mechanical stress and concentration. .
  To define the fluxes mentioned above:
  Here  is the electron charge,  is the effective charge of the migrating atom,  the resistivity of the conductor where atom migration takes place,  is the local current density,  is the Boltzmann constant,  is the absolute temperature.  is the time and position dependent atom diffusivity.
  : . &emsp;We use  the heat of thermal diffusion.
  here  is the atomic volume and  is initial atomic concentration,  is the hydrostatic stress and  are the components of principal stress.
  Assuming a vacancy mechanism for atom diffusion we can express <math>
  D where  is the effective activation energy of the thermal diffusion of metal atoms. The vacancy concentration represents availability of empty lattice sites, which might be occupied by a migrating atom.