Dissemination of IT for the Promotion of Materials Science (DoITPoMS)

# Questions

### Quick questions

You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

1. Which force/forces act on metal ions within a conductor, during electromigration – under the application of an electric field? (You may pick more than one answer)

(a) Wind force, F = aneλdσi

(b) Direct force, F = aZejρ

(c) Mechanical back force, F = ΩΔσ/Δx

(d) Moment force, F = Moment/distance from pivot

(e) None of the above

2. The median life of pure Al stripes of width, w (in cm) and thickness, d (in cm) at 50 °C is given by:

t
50 = 4.4×1012wdjn exp(Ee/kT)

where n = 2, Ee = 0.49 eV, j = 1 x 105 A cm-2, w = 0.4 μm and d = 0.5 μm.

What is  the median life of the interconnect?

(a) 0.38 hrs

(b) 3.83 hrs

(c) 38.3 hrs

(d) 380 hrs

3. How does the median life of pure Al stripes compare with that of Al-Si interconnects of the same dimensions as above, for which:

t
50 = 2.2×1015 wdj–n exp(0.54 eV/kT)

 a the same b less by 10% c more by 10% d more by 100,000%

4. Which material properties are desirable for use as interconnects?

 a low availability b low resistivity c low melting point d low electromigration resistance

5. Which material is the mostly used in vias?

 a Aluminium-based alloys b Tungsten c Titanium Nitride d Silver

### Deeper questions

The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

1. In a solid conductor, the mechano diffusion force, Fm, acting on an atom, in a gradient of hydrostatic stress, H / dx, is given by:

where C0 = no. of atoms per unit volume.

A conductor has along it, a segment of length, L, which has a raised atomic diffusivity. The material of the conductor develops damage when the difference in hydrostatic stress between the ends of such a segment reaches the value (ΔσH)crit. Derive the critical condition for the damage to develop in terms of L and current density, j, in the conductor.

2. An IC has several levels of Al-based metallization linked by W vias. In a test, electromigration damage, develops in an Al-based conductor linking two vias when the current density flowing through it from one via to the other 10 μm away exceeds 9×109 A m-2. It is planned to use the same materials with a current density of 1.2×1010 A m-2. What condition must be met by the length of links between vias for damage to be avoided? How will the temperature of the operation affect the development of electromigration damage?

3. In the schematic diagram of a microelectronic device (below), where would electromigration-induced damage be observed? Give your reasons. What type of material would you use for the vias and interconnects, and why?