In chemically amplified resists, acids are generated upon DUV illumination. What DUV illumination really creates is an electrolyte solution with non-uniform acid distribution. Since H+ carries a charge, its diffusion behavior is quite different from that of a neutral particle. The long range Coulomb interaction between charged particles can be very important in a medium with low dielectric constant such as resist. The diffusion of acid and its counter ion are strongly correlated, leading to a decrease of the effective diffussivity of acid. Detailed theoretical analysis shows that the diffusion coefficient that determines the critical dimensional change caused by acid diffusion is the effective acid diffusion coefficient Da equals 2Dx, which is determined by the diffusivity of the counter ion. The diffusion coefficient that is related to chemical amplification is the acid intrinsic diffusion coefficient DH+. The charge carried by H+ also makes its evaporation difficult due to large energy barrier created by electric potential difference between two phases and the 'image force' when H+ crosses over the resist/air rate depends on the acid diffusivity, acid strength and acid equilibrium vapor pressure at the post exposure bake temperature from the kinetic theory.
Xuelong Shi, Xuelong Shi,
"Role of acid charge in chemically amplified resists", Proc. SPIE 3678, Advances in Resist Technology and Processing XVI, (11 June 1999); doi: 10.1117/12.350267; https://doi.org/10.1117/12.350267