Proximity correction for electron beam lithography using a three-Gaussian model of the electron energy distribution

Abstract

Accurate proximity correction has proven essential for the patterning of submicron features using electron beam lithography. The use of a two-Gaussian model, which accounts for the finite beam size and forward scattering in the resist as well as backscattering, has demonstrated widespread success. It has been shown, however, that in certain instances, such as for features of order 100 nm or less or for exposure on high atomic number substrates, the two-Gaussian expression is unable to adequately fit the absorbed energy distribution in the resist. Suggested modifications, such as the addition of a third Gaussian term to account for large angle electron scattering, or the inclusion of an exponential term which may account for an increased absorption rate in high Z materials, have resulted in improved fits. This paper describes a study to determine the improvement gained in exposed features by including additional Gaussian terms in the expression for the absorbed energy distribution in the resist. A very high resolution probe (beam diameter ∼20 nm FWHM) is used so that forward scattering effects in the resist may be separated from the primary beam distribution. PMMA is exposed on Si and GaAs substrates at 25 keV using proximity correction parameters generated by curvefitting the three-Gaussian model and the two-Gaussian model to the absorbed energy distributions. The three-Gaussian model is seen to provide improved proximity correction particularly in the 100 nm size scale.