Line-edge roughness, Part 3.(The Lithography Expert)

In the last two editions of this column [1, 2], a stochastic modeling approach to the fundamental mechanisms behind the formation of line-edge roughness (LER) was given. The model begins with photon shot noise, which follows Poisson statistics, then looks at the initial distribution of photoacid generator (PAG) in the resist, which also follows Poisson statistics. The exposure reaction itself is probabilistic, with the probability that any particular PAG will be exposed given by the solution to the continuum kinetic equation of exposure. Reaction-diffusion of chemically amplified resists is reasonably complicated, but still amenable to this type of treatment. The time-averaged concentration of acid controls the amount of deprotection (deblocking) at any location, and it is the ratio of the diffusion length of the acid to the capture range of the deprotection reaction that determines how much statistical smoothing this time-averaging will cause.

As a review, for a given volume of resist under consideration, the statistical variance in the final blocked …