Discussion on the Mechanism of Electromigration from the Perspective of Electromagnetism

Abstract

The mechanism of electromigration is discussed from the perspective of electromagnetism, rather than from the traditional view of momentum exchange owing to collisions between electrons and diffusing ions. It is suggested that, from the perspective of conservation of momentum, the momentum transferred to the diffusing ions is related to the Maxwell stress, and the effective charge is proportional to the density of the net charge within the volume element. It is also suggested that, from Poynting's theorem, the energy associated with electromigration is related to the work done by the electric field, and the conversion of the nonelectrostatic energy from the electric power source into the chemical energy of the diffusion system. From both perspectives, the effective driving force can be shown to have a square dependence on the current density. Therefore, it is suggested that the effective charge number is linearly related to the current density.

A Sharp Interface Model of Intermediate-Phase Growth Under the Influence of Electromigration

“…Solving the homogeneous Eq. (19) with the two boundary conditions given in Eqs. (20) and (21), we have a quasistationary solution for the composition field c in the c phase,…”

“…18,19 The polarity effect in the growth of an intermediate phase arises from conversion of the work done by the electric field into chemical energy stored in the intermediate phase when the electron flow aids diffusion, but into chemical free energy of the system when the electron flow hinders diffusion. Growth of an intermediate phase leads to consumption of chemical free energy; however the work done by the electric field is continuously converted into chemical free energy of the system when the electron flow hinders diffusion.…”

In-situ electron backscatter diffraction of thermal cycling in a single grain Cu/Sn-3Ag-0.5Cu/Cu solder joint

“…The major failure mode of solder joints in thermal cycling is cracking during heterogeneous microstructure evolution, i.e. polygonization and crack nucleation, in the bulk solder near the solder/substrate interface on the Si chip-side, observed in ref [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] . The crack propagates in the region where the mismatch of CTE is large and the induced thermal strain is high in comparison to the surroundings (larger misfit on the Si chip side than PCB side of joint [2,[20][21][22] ).…”

“…This work provides new understanding on the early stages of microstructural deformation and the accumulation of stored energy associated with these bands as the precursor to the more widely studied phenomena of recrystallization and crack propagation in thermal cycling. 11 TG drafted the initial manuscript and conducted the experimental work. YX supported the development of the Matlab code for Sn slip systems.…”

The influence of a field-dependent total effective charge number on the interfacial migration rate and the phase growth behavior during intermediate phase growth with electromigration present

“…Yet, the effective charge numbers are different for different elements and they also vary from one phase to another. Moreover, it has already been shown the charge numbers are linearly related to the applied current densities [4,5]. Thus, it is more reasonable to introduce the field-dependence of the total effective charge number into the modeling of intermediate phase growth with electromigration present.…”