Page 185 - Materials Science and Engineering An Introduction

5.6 Diffusion in Semiconducting Materials • 157

Now, from Equation 5.13,
1/2
Q 0
x j = c (4D d t d )ln a b d
C B 1pD d t d
2
= c (4)(1.51 * 10 -17 m /s)(7200 s) *
1/2
18
3.44 * 10 atoms/m 2
lnC S s
20
2
3
(1 * 10 atoms/m )2(p)(1.51 * 10 -17 m /s)(7200 s)
-6
= 2.19 * 10 m = 2.19
m
(c) At x 1
m for the drive-in treatment, we compute the concentration of B atoms using
Equation 5.11 and values for Q 0 and D d determined previously as follows:
Q 0 x 2
C(x, t) = expa - b
1pD d t 4D d t
-6
18
3.44 * 10 atoms/m 2 (1 * 10 m) 2
= expc - -17 2 d
2
2(p)(1.51 * 10 -17 m /s)(7200 s) (4)(1.51 * 10 m /s)(7200 s)
23
= 5.90 * 10 atoms/m 3
M A T E R I A L S O F I M P O R T A N C E

Aluminum for Integrated Circuit Interconnects

ubsequent to the predeposition and drive-in heat Interconnects
Streatments just described, another important step 4 m
in the IC fabrication process is the deposition of very
thin and narrow conducting circuit paths to facilitate
the passage of current from one device to another;
these paths are called interconnects, and several are
shown in Figure 5.11, a scanning electron micrograph
of an IC chip. Of course, the material to be used for
interconnects must have a high electrical conductiv-
ity—a metal, because, of all materials, metals have
the highest conductivities. Table 5.3 gives values for
silver, copper, gold, and aluminum, the most conduc-
tive metals. On the basis of these conductivities, and
discounting material cost, Ag is the metal of choice,
followed by Cu, Au, and Al.
Once these interconnects have been deposited,
it is still necessary to subject the IC chip to other Figure 5.11 Scanning electron micrograph of an
heat treatments, which may run as high as 500 C. If, integrated circuit chip, on which is noted aluminum
during these treatments, there is significant diffusion interconnect regions. Approximately 2000 .
of the interconnect metal into the silicon, the elec- (Photograph courtesy of National Semiconductor Corporation.)
trical functionality of the IC will be destroyed. Thus,
because the extent of diffusion is dependent on the of D in silicon. Figure 5.12 plots the logarithm of D
magnitude of the diffusion coefficient, it is necessary versus 1/T for the diffusion, into silicon, of copper,
to select an interconnect metal that has a small value gold, silver, and aluminum. Also, a dashed vertical line

(continued)