Shot noise models for sequential processes and the role of lateral mixing

Shot noise in electron-beam and extreme ultraviolet (EUV) exposure fundamentally limits the useful sensitivity of resists. Here the exposure, amplification, and deprotection of chemically amplified resists are treated as a sequence of statistical events to determine the effect of shot noise. Noise among processes is additive, and a sequential Poisson process is used to illustrate the "acid bottleneck" that occurs when less than one acid electron is generated per input electron. Lateral mixing, due to effects such as electron scattering and acid diffusion, is accounted for in a binomial sorting model that shows that the effect is simply a function of the total number of quanta reaching the voxel irrespective of their path. Electron exposure is estimated to generate on average one acid every 3.8, 21, and 36 nm along the trajectories of 5, 50, and 100 keV electrons respectively. Acid generation appears well correlated with energy deposition, at about 22 eV/acid required for EUV and electron exposure or three times the deep ultraviolet level. The model was validated by observing the fraction of small (24 and 32 nm across) contacts that cleared as a function of exposure dose at 100 keV. Approximately 4500 electrons were required to clear, independent of contact size. However, the slope was indicative of a process with only 50 effective events possibly owing to resist surface effects. Circular dissolution smoothing and mechanical fracture are suggested as speculative sources for the near feature size correlation length of the line-edge roughness. (c) 2006 American Vacuum Society.