the Fourier’s law; and the electric field is governed by Maxwell’s equation of
conservation of charge. Degradation is governed by the laws of thermodynamics.
Fig. 8.1 shows a microelectronics solder joint before and after electromigration/
thermomigration failure.
In the following section, all these laws are used to model the unified mechanics of
electromigration and thermomigration processes.
When the only acting load is an electrical potential field, the primary deformation
mechanism is due to atomic diffusion, which is a mass transport by atomic motion
process. Diffusion in solids occurs only at the atomic or molecular level. However,
diffusion in solids may be observed in the macroscopic scale given enough time.
Diffusion that results in the net transport of matter over macroscopic distances is
considered a nonequilibrium process. It does not stop until the phase eventually
achieves fully thermodynamic equilibrium or diffusion driving force is removed.
The laws of diffusion were first developed by Adolf Fick when studying the
diffusion of the saltwater system (Fick 1855). Fick’s diffusion laws establish the
mathematical relationship between the rate of diffusion and the concentration gradients, which is the driving force of the mass transport.
Al
Silicon Die
Ni UBM
Ni UBM
140 μm
40 µm 700×
50 µm 600×
100
μm
Solder
Solder
Cu
Cu Plate
Underfill
Underfill
PCB
Fig. 8.1 Electronics solder joint profile after electromigration and thermomigration failure
398
8 Unified Mechanics of Metals under High Electrical Current Density:. . .