Analytic study of apparent resist sensitivity in electron-beam lithography

The nominal definition of resist sensitivity, i.e., the dose required to clear the resist, carries an implicit assumption that the sensitivity is measured for a sufficiently large feature in electron-beam lithography. However, when the feature size is comparable to or less than the backscattering range of electrons, the actual sensitivity to clear the resist (apparent sensitivity) may be different from the nominal sensitivity. The difference becomes much larger as the feature size approaches the forward-scattering range. In this study, a closed-form mathematical expression of the apparent sensitivity is derived as a function of lithographic and pattern parameters. With the expression, one can analyze the dependency of the apparent sensitivity on each parameter and estimate the actual sensitivity for a specific case given the nominal sensitivity without time-consuming simulation or an expensive experiment. Hence, the analytic result in this paper must provide a useful tool to understand and deal with the resist sensitivity.