Elucidating how photoacid diffusion leads to resist contrast and resolution loss

1 Elucidating how photoacid diffusion leads to resist contrast and resolution loss 

During PEB, the resist polymer experiences the time-averaged acid concentration c, which deprotects the polymer or transforms it in a way that alters its solubility properties. For line and space structures, the Gaussian function can be used to approximate the response to the initial acid concentration c(x, y, 0) 8(x) 

Applying the superposition principle, the response to an initially sinusoidal modulation of the photoacid concentration, also called the modulation transfer function (MTF), can be calculated with Eq. (17.3)  

For example, suppose that one wants to know which diffusion length is allowed if one accepts a relative 20% reduction of the resist image MTF due to diffusion. Then the diffusion length Ld = /2Dt may be as large as 0.16 times the pitch (see Fig. 17.26). 

An important result from the application of the continuum theory to this diffusion problem is the fact that shrinking the feature pitch can only be accommodated as long as the photoacid diffusion length is also comparably shrunk. For a pitch of 45 nm, one requires a diffusion length of about 7 run or less. The diffusion 

---