Electromigration

Electromigration refers to the gradual displacement of the metal atoms of a conductor as a result of the current flowing through that conductor. The process of electromigration is analogous to the movement of small pebbles in a stream from one point to another as a result of the water gushing through the pebbles.

Because of the mass transport of metal atoms from one point to another during electromigration, this mechanism leads to the formation of voids at some points in the metal line and hillocks or extrusions at other points. It can therefore result in either: 1) an open circuit if the void(s) formed in the metal line become big enough to sever it; or 2) a short circuit if the extrusions become long enough to serve as a bridge between the affected metal and another one adjacent to it.

Electromigration is actually not a function of current, but a function of current density. It is also accelerated by elevated temperature. Thus, electromigration is easily observed in Al metal lines that are subjected to high current densities at high temperature over time.

Electromigration is widely believed to be the effect of momentum transfer from the electrons of the metal, which move according to the applied electric field, to the ions that constitute the lattice of the metal.

There are two major driving factors that make electromigration happen: 1) the direct action of the electric field on the charged atoms or ions of the metal; and the 2) frictional force or momentum exchange between the flowing electrons and these ions. The total driving force is the sum of the effects of these two factors.

All metal films have imperfections or microstructural variations that cause the atomic flow rates through them to be non-uniformly distributed. This non-uniform atomic flow rates (or flux divergence) through different sections of the conductor result in mass depletion (which causes voids) and mass accumulation (which causes hillocks) as the mass transport mechanism occurs during electromigration.

In Al films, the dominant mechanism of atomic migration is along grain boundaries and surfaces. Lattice mismatches (such as those between adjacent large and small grains or when three grain boundaries meet) can create grain boundary interconnections that provide shorter paths for the atoms, enabling the latter to move faster through the film.

Another important thing to note regarding how grain structures affect electromigration failure rates is the conclusion from various studies that below a critical value for the metal line width, electromigration is impeded. Electromigration failure rates predictably decrease with decreasing line widths, but up to a certain point only.

At the critical limit, the width of the metal line becomes smaller than the grain size itself, such that all grain boundaries are now perpendicular to the current flow. Such a structure is also known as a 'bamboo structure.' This results in a longer path for mass transport, thereby reducing the atomic flux and electromigration failure rate.

There is also a critical lower limit for the length of the metal line that will allow electromigration to occur. Known as the Blech length, any metal line that has a length below this limit will not fail by electromigration. Thus, the Blech length must be considered when designing test structures for electromigration. Otherwise, no failures may be observed, leading to an incorrect conclusion.

The acceleration effect of high temperature on electromigration becomes emphasized only when a void has started to form in the metal line. Prior to any void formation, the metal can still be under uniform thermal distribution. Once a void forms, however, the current density at the section where the void is present increases as a result of the reduced cross-sectional area of the conductor, leading to current crowding around the void.

The higher current density around the void results in localized heating that further accelerates the growth of the void, which again increases the current density. The cycle continues until the void becomes large enough to cause the metal line to fuse open.

Electromigration may be modeled by the following equation, which is known as Black's Equation:

t₅₀ = CJ^-ne^(Ea/kT)

where:

t50 = the median lifetime of the population of metal lines subjected to electromigration;

C = a constant based on metal line properties;

J = the current density;

n = integer constant from 1 to 7; many experts believe that n = 2;

T = temperature in deg K;

k = the Boltzmann constant; and

Ea = 0.5 - 0.7 eV for pure Al.

Electromigration failures take time to develop, and are therefore very difficult to detect until it happens. Thus, the best solution to electromigration problems is to prevent them from taking place.

Electromigration can be prevented by: 1) proper design of the device such that the current densities in all parts of the circuit are practically limited; 2) increasing of the grain sizes of the metal lines such that these become comparable to their widths (whereby bamboo structure is achieved); and 3) good selection and deposition of the passivation or thin films placed over the metal lines in order to limit extrusions caused by electromigration.

Electromigration must not be confused with EOS-induced metal reflow, which is a different phenomenon. Electromigration occurs gradually whereas EOS-induced metal reflow is gross and abrupt.

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