Page 186 - Materials Science and Engineering An Introduction

158 • Chapter 5 / Diffusion

Table 5.3 Room-Temperature Electrical Conductivity Temperature (°C)
Values for Silver, Copper, Gold, and 1200 1000 800 700 600 500 400
Aluminum (the Four Most Conductive 10 –8 Cu in Si 7.1 × 10 –10
Metals)
Au in Si
Electrical Conductivity 10 –12 2.8 × 10 –14
1
Metal [(ohm-m) ] Ag in Si
Silver 6.8 10 7 10 –16 6.9 × 10 –18
Copper 6.0 10 7 Al in Si
Gold 4.3 10 7 Diffusion coefficient (m 2 /s) 10 –20
Aluminum 3.8 10 7

has been constructed at 500 C, from which values of 10 –24 3.6 × 10 –26
D for the four metals are noted at this temperature. –28
Here it may be seen that the diffusion coefficient for 10
2
aluminum in silicon (3.6 10 26 m /s) is at least eight 0.6 0.8 1.0 1.2 1.4
8
orders of magnitude (i.e., a factor of 10 ) lower than Reciprocal temperature (1000/K)
the values for the other three metals.
Aluminum is indeed used for interconnects in some Figure 5.12 Logarithm of D-versus-1/T (K) curves
integrated circuits; even though its electrical conductiv- (lines) for the diffusion of copper, gold, silver, and alu-
ity is slightly lower than the values for silver, copper, minum in silicon. Also noted are D values at 500 C.
and gold, its extremely low diffusion coefficient makes
it the material of choice for this application. An alumi- More recently, copper interconnects have also
num–copper–silicon alloy (94.5 wt% Al-4 wt% Cu-1.5 been used. However, it is first necessary to deposit
wt% Si) is sometimes also used for interconnects; it not a very thin layer of tantalum or tantalum nitride be-
only bonds easily to the surface of the chip, but is also neath the copper, which acts as a barrier to deter dif-
more corrosion resistant than pure aluminum. fusion of copper into the silicon.

5.7 OTHER DIFFUSION PATHS

Atomic migration may also occur along dislocations, grain boundaries, and external
surfaces. These are sometimes called short-circuit diffusion paths inasmuch as rates are
much faster than for bulk diffusion. However, in most situations, short-circuit contribu-
tions to the overall diffusion flux are insignificant because the cross-sectional areas of
these paths are extremely small.

SUMMARY

Introduction • Solid-state diffusion is a means of mass transport within solid materials by stepwise
atomic motion.
• The term interdiffusion refers to the migration of impurity atoms; for host atoms, the
term self-diffusion is used.

Diffusion • Two mechanisms for diffusion are possible: vacancy and interstitial.
Mechanisms Vacancy diffusion occurs via the exchange of an atom residing on a normal lattice
site with an adjacent vacancy.
For interstitial diffusion, an atom migrates from one interstitial position to an
empty adjacent one.
• For a given host metal, interstitial atomic species generally diffuse more rapidly.