Apparent resist sensitivity of a pattern of multiple features in electron beam lithography

In electron-beam (e-beam) lithography, it is essential to use a proper dose such that features are clearly resolved. One of the important metrics in the e-beam lithographic process is resist sensitivity, which is defined as the dose required for the resist to be fully developed. This nominal (resist) sensitivity assumes that a sufficiently large area of resist is exposed. However, the apparent (resist) sensitivity may deviate significantly from the nominal sensitivity in practice. Previously, the apparent sensitivity was analytically studied with the double-Gaussian model of point spread function. A closed-form mathematical expression of the apparent sensitivity was derived for a single feature as a function of lithographic and pattern parameters. In this work, the analytic study of the apparent sensitivity has been extended to a pattern of multiple features by taking into account the exposure contributions from other features in the pattern. Closed-form expressions of the apparent sensitivity are derived for both uniform and nonuniform line/space patterns as in a single feature. In the case of non-uniform line/space pattern, practical approximation methods for evaluating the apparent sensitivity are also developed for simpler expressions. The usefulness of the closed-form expressions is demonstrated for typical cases, and the accuracy of the approximation methods is examined in a comprehensive manner. As a result, this work has widened the applicability of an analytic study of the apparent sensitivity in e-beam lithography.