Electron scattering and line profiles in negative electron resists

Abstract
Starting with a depth-dose theory of electron energy dissipation in negative electron resists and a quasimonoenergetic Gaussian scattering theory, we derive theoretical expressions for single-line profiles using the exposure parameters of the Bell Laboratories electron-beam exposure system (EBES). These profiles are calculated by convoluting the Gaussian scattering distribution with the experimentally determined relationship between resist thickness remaining after development and input electron dose. Calculated profiles for the negative electron resist P(GMA-co-EA) agree well with experimental results for the range of feature sizes exposed on EBES. Since features on EBES are built up by multiple passes, the theory is extended to line profiles separated by the address structure of EBES. The calculated resist profiles are in reasonably good agreement with experimental results. The observed profile heights are somewhat greater than predicted by theory since the developed gel is not perfectly rigid and gel interaction takes place between neighboring profiles. The results show the importance of good gel rigidity and high contrast for negative electron resists used in high resolution applications. The range of validity of the trends predicted by the quasimonoenergetic theory for increasing film thickness and operating voltage are extended using a Monte Carlo approach which includes the effects of energy loss. The calculated trends have led to the choice of optimum exposure conditions for EBES.