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MICROLITHOGRAPHY

MICROLITHOGRAPHY 9.21

compound M, which converts to product P on exposure to UV light. The resin is somewhat soluble
in the developer solution, but the presence of the PAC acts as an inhibitor to dissolution, making the
development rate very slow. The product P, however, is highly soluble in the developer, enhancing
the dissolution rate of the resin. Let us assume that n molecules of product P react with the devel-
oper to dissolve a resin molecule. The rate of the reaction is
r = k D P n (9.20)
R R S
where r is the rate of reaction of the developer with the resist and k is the rate constant. From the
R R
stoichiometry of the exposure reaction:
P = M − M (9.21)
o
where M is the initial PAC concentration (i.e., before exposure).
o
The two steps outlined earlier are in series, that is, one reaction follows the other. Thus, the two
steps will come to a steady state such that their rates are equal. Equating the rate equations (Eqs.
(9.19) and (9.20)), one can solve for D and eliminate it from the overall rate equation. After some
S
algebra and letting m = M/M
o
r = R ( a + )(11 − m) n + R (9.22)
a +− m) n min
max
(1
where
D
R max = kD
n
/
kk M +1
R
o
D
a = k k M = n ( +1 ) ( − m ) n
n
/
1
D R o TH
n ( −1 )
where m is the value of m at the inflection point of the development rate function, called the thresh-
TH
old inhibitor concentration. Note that the simplifying constant a describes the rate constant of diffu-
sion relative to the surface reaction rate constant. A large value of a will mean that diffusion is very
fast, and thus less important, compared to the fastest surface reaction (for the completely exposed
resist). The addition of R to equation (9.22) assumes that the mechanism of development of the
min
unexposed resist is independent of the above-proposed development mechanism. In other words,
there is a finite dissolution of resist that occurs by a mechanism that is independent of the presence
of exposed PAC. Note that the addition of the R term means that the true maximum development
min
rate is actually R + R . In most cases R >> R and the difference is negligible.
max min max min
Figure 9.13 shows some plots of this model for different values of n. The behavior of the disso-
lution rate with increasing n values is to make the rate function more “selective” between resist
exposed above m and resist exposed below m . For this reason, n is called the dissolution selec-
TH TH
tivity parameter. Also from this behavior, the interpretation of m as a “threshold” concentration
TH
becomes quite evident. Note that as the developer selectivity parameter n goes to infinity, the resist
approaches the ideal step function response that is desired. Thus, the goal of resist design is to cre-
ate higher values of n, which is directly related to the number of blocked polymer sites in the resist.
9.4 LINEWIDTH CONTROL
Historically, lithography engineering has focused on two key, complimentary aspects of lithograph-
ic quality—overlay performance and linewidth control. Linewidth (or critical dimension (CD)) con-
trol generally means ensuring that the widths of certain critical features, measured at specific points
on those features, fall within acceptable bounds. Overlay describes the positional errors in placing
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